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Full text of "A practical arithmetic"

A PRACTICAL 
ARITHMETIC 



STEVENS 

M 

BUTLER 



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GAYLORD 






PRINTEDINU.S.A. 



Cornell University Library 
QA 106.S84 



A practical arithmetic, 




3 1924 000 431 621 



A PRACTICAL ARITHMETIC 




The original of tliis book is in 
tine Cornell University Library. 

There are no known copyright restrictions in 
the United States on the use of the text. 



http://www.archive.org/details/cu31924000431621 



PEACTICAL ARITHMETIC 



BY 

F. L. STEVENS 

PROFESSOR IN THE NORTH CAROLINA COLLEGE OF AGRICULTURE 

AND MECHANIC ARTS, AUTHOR OP " AGRICULTURE 

FOR beginners" 

TAIT BUTLER 

president AMERICAN ASSOCIATION OF FARMERS' 
INSTITUTE WORKERS 

MRS. F. L. STEVENS 

FORMERLY TRAINING TEACHER, COLUMBUS, OHIO 
NORMAL SCHOOL , 



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NEW YORK 

CHARLES SCRIBNER'S SONS 

1910 



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COPYRIGHT, 1909, BY 
CHARLES SCRIBNER's SONS 



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PEEFACE 

The primary object of arithmetic is to enable tlie 
student to acquire skill in computation. In addition to 
the attainment of this essential end, great benefit is de- 
rived from the exercise of the reasoning powers and 
their consequent development. While the first of these 
must ever remain the fundamental reason for the study 
of arithmetic, and the second will always be held in 
high esteem, there is a third major object which the 
teaching of arithmetic may accomplish, one which is usu- 
ally almost entirely ignored in the preparation of an 
arithmetic ; namely, the incidental teaching of valuable 
facts by basing the problems of the book upon the prob- 
lems of real life. 

In the preparation of this book, it has been the aim 
of the authors to secure the maximum results in these 
three functions of arithmetic teaching. 

It is chiefly in the careful consideration which has been 
given to the subject-matter of the problems, and to the 
inferences that will unconsciously and unavoidably remain 
in the mind of the pupil, that this book differs from other 
arithmetics. 

Skill in computation comes from learning a few methods, 
followed by extensive drill or practice. Methods have 
been carefully and clearly presented in this book, and 
an abundance of drill problems provided. 

The development of the reasoning powers comes from 
work with problems requiring careful analysis before pro- 
ceeding to the more mechanical solution. A large number 



VI PREFACE 

of carefully graded thought problems, necessitating accu- 
rate analysis, serves this end. 

The special value of this book, however, depends upon 
the fact that a large proportion of its problems bring out 
clearly in their statement or in their solution important 
facts bearing upon the practical activities of life. Since 
agriculture is the one fundamental industry of America, 
especial attention has been given to this subject, and a 
large proportion of the thought problems are based upon 
agriculture, without, however, in any way leading to 
neglect of other industries. 

The problems relating to agriculture are based upon 
wholly reliable information, uf)on the most recent find- 
ings of the State Experiment Stations and of the National 
Department of Agriculture. The facts used in these 
problems and the legitimate inferences which may be 
djiawn from them are trustworthy. In solving these 
problems, the pupil will unconsciously absorb and retain 
many valuable facts and principles relating to agricul- 
tural practice, such, for example, as the value of seed 
selection, purity and vitality, judicious use of fertilizers, 
balancing of animal rations, crop rotation, prevention or 
treatment for plant diseases, conservation of soil moisture, 
preservation of soil fertility, prevention of insect injury, 
economy in methods of harvesting, proper dairy methods, 
the improvement of the herd by selection, poultry culture, 
value of good roads, etc. 

A feature of value is the outline problems to be com- 
pleted by the pupils with data from their homes. 

Teachers, parents and pupils are invited to write to the 

authors of this book for information upon any agricultural 

points involved. 

THE AUTHORS. 
Raleigh, N.C, November, 1908. 



CONTENTS 

FAQS 

Notation and Numeration 1 

The Arabic System 1 

The Roman System 9 

United States Money 11 

Addition 13 

Addition of United States Money 19 

Subtraction . 29 

Subtraction of United States Money 36 

Multiplication 41 

Multiplication of United States Money .... 52 

Division . . r ^ 57 

Short Division 61 

Long Division 64 

Division of United States Money 68 

Cancellation 72 

Review Problems 74 

Divisors and Multiples 86 

Tests of Divisibility, Greatest Common Divisor, Least Com- 
mon Multiple. 

Decimal Fractions 92 

Notation and Numeration 92 

Addition 95 

Subtraction 97 

Multiplication 99 

Division 103 

Review Problems 106 

Common Fractions 113 

Addition 120 

vii 



viii CONTENTS 

PAGE 

Subtraction 122 

Multiplication 125 

Division 129 

Review Problems 138 

Accounts and Bills 147 

Denominate Numbers 150 

Units of Length, Reduction, Metric Units of Measure, 
Representation of Magnitudes, Surface Measure (English 
and Metric), Surveyor's Measures, Measures of Volume 
(English and Metric), Measures of Weight (English and 
Metric), Measures of Time, Angle Measure, Counting, 
Addition and Subtraction, Multiplication, Division. 

Review Problems 179 

Measurements 186 

Practical Measurements 198 

Plastering, Painting, Paving, Carpeting, Papering, Masonry 
and Brickwork, Wood Measure, Board Measure, Round 
Logs, Temperature, Longitude and Time, Standard Time. 

Review Problems 216 

Percentage 227 

Profit and Loss 256 

Commission 260 

Commercial Discount 263 

Insurance .......... 265 

Taxes 268 

Interest 275 

Stocks and Bonds ......... 285 

Bank Discount 293 

Partial Payments 296 

Ratio 302 

The Nutritive Ratio, Specific Gravity. 

Proportion 308 

Levers, Compound Proportion. 



CONTENTS ix 

PAGE 

Powers 318 

Roots 321 

Miscellaneous Review Problems 326 

Appendix 367 

Surfaces of Solids, Volumes of Solids, Extraction of Cube 
Root, Proof of Fundamental Processes by casting out 
Nines, Arithmetical Progression, Geometrical Progression, 
Tables of Measures, Weights of Produce, Interest Tables, 
Cattlemen's Notation, Lumbermen's Notation. 



PKACTICAL ARITHMETIC 



oiOic^ 



NOTATION AND NUMERATION 

EXERCISE 1. — ORAL 

1. How many ones in 2, 8, 9? 

2. How many tens in 20, 30, 50? 

3. How many tens and ones in 18, 36, 45, 47, 98 ? 

4. How many one hundreds in 200, 400, 600, 900? 

5. How many one hundreds, tens, and ones in : 

876 425 743 437 982 

123 896 456 847 225 

378 549 874 953 629 

6. How many one hundreds in this number, 1000? 

7. What name is given to this number? 

8. How many thousands, hundreds, tens, and ones in : 

6387 4702 6512 5068 6728 

7080 1400 8150 6740 4963 

8824 1814 3096 2263 9184 

9. How many thousands in this number, 10000? 

10. How many ten-thousands, thousands, hundreds, 
tens, and ones in : 

50207 34291 23845 10205 23814 

35842 78354 91846 35841 87961 

26459 52796 87964 88249 18462 

1 



PRACTICAL ARITHMETIC 



11. How many thousands in this number, 100000? 

12. How many hundred-thousands, ten-thousands, thou- 
sands, hundreds, tens, and ones in: 



259132 


271186 


350006 


495271 


468796 


660878 


504001 


116006 


203841 


398178 


802136 


275360 


275253 


134410 


884192 



1. Hundreds, tens, and ones written together form a 
group or period, called Units' Period. 

2. Hundred-thousands, ten-thousands, and thousands 
written together form a period, called Thousands' Period. 

3. The next period higher than thousands' period is 
called Millions' Period ; the next higher, Billions' Period, 
and the next Trillions' Period ; but rarely is there use for 
these larger numbers. 

4. The following diagram will aid in reading large 
numbers. Read the numbers given : 



Names of 


Trill- 


Bill- 


Mill- 


Thou- 


Units 


Periods : 


ions 


ions 


ions 


sands 




Periods : 


1 
11 


■* P-i 


^1 


o 




Orders : 


hundreds 

tens 

units 


hundreds 

tens 

units 


hundreds 

tens 
units 


liundreds 

tens 

units 


hundreds 

tens 

units 










000 


12 9 


654 




00 


00 


004 


20 1 


250 




000 


00 


020 


045 


600 




020 


006 


302 


4 63 


001 



204 875 001 609 451 



NOTATION AND NUMERATION 3 

5. Numbers of more than four figures are usually 
written with a comma between the periods, thus: 

1,642,001 63,105,005 78,121 

6. To read a number. Begin at the right and point 
off into periods of three figures each ; then begin at the 
left and read each period as if it stood alone, adding the 
name of the period. 

7. The place value of a figure. What effect does it 
have upon the value of a figure to move it one place to 
the left in its period? To move it one place to the right? 

jNIoving a figure one place to the left increases its 
value tenfold. iNIoving a figure one place to the right 
decreases its value tenfold. 

exercise 2. — oral 
The Meaning of Numbers 

There are 5 people in my neighbor's home : father, 
mother, daughter, and 2 sons. In 20 such homes there 
would be 100 people. In a small village of 100 homes 
there are about 500 inhabitants. Ten times as many peo- 
ple as this in one community would be 5000, and in 100 
such towns together there would be 500,000 people. 

The following numbers show the population of some 
capital cities in 1900. Read the numbers and try to 
realize their meaning : 



1. Albany, 


94,151 


3. Richmond, 


85,050 


2. Harrisburg, 


50,167 


4. Trenton, 


73,307 



PRACTICAL ARITHMETIC 



5. 


Dover, 


3,329 


15. 


Jefferson Cit 


y, 9,664 


6. 


Baltimore, 


508,957 


16. 


Madison, 


19,164 


7. 


Augusta, 


39,441 


17. 


Lansing, 


16,485 


8. 


Boston, 


560,892 


18. 


Columbus, 


125,560 


9. 


Concord, 


19,632 


19. 


Springfield, 


34,157 


10. 


Providence, 


175,597 


20. 


Raleigh, 


13,643 


11. 


Bismarck, 


3,319 


21. 


Jackson, 


7,816 


12. 


Pierre, 


2,305 


22. 


Tallahassee, 


2,981 


13. 


Lincoln, 


40,167 


23. 


Phoenix, 


5,544 


14. 


St. Paul, 


163,065 


24. 


Atlanta, 


89,872 



Read the following numbers, which express the corn 
and wheat produced and the number of milk cows of cer- 
tain states in 1906 : 







COEN, Bushels 


Wheat, Bushels 


Milk Cows 


25. 


North Carolina, 


41,796,846 


6,297,028 


282,600 


26. 


New York, 


22,685,000 


9,350,180 


1,826,211 


27. 


Georgia, 


52,066,596 


3,161,070 


305,469 


28. 


Ohio, 


141,645,000 


43,202,100 


919,100 


29. 


[Mississippi, 


40,789,207 


17,610 


329,664 


30. 


Iowa, 


373,275,000 


9,212,218 


1,555,300 


31. 


Texas, 


155,804,782 


14,126,186 


993,122 


32. 


Kansas, 


195,075,000 


81,830,611 


729,274 



8. Any one thing is called a Unit. 

9. A unit or collection of units is called a Number. 

10. Numbers representing whole units are called Whole 
Numbers, Integral Numbers, or Integers. 



NOTATION AND NUMERATION 5 

11. Figures or Digits are symbols used to express 
numbers. 

12. The process of reading numbers is called Numeration. 

13. Numbers may be expressed by Figures, Letters, or 
Words. 



EXERCISE 3. — WRITTEN 

Write these numbers in figures, using the comma to 
separate periods : 

1. Six hundred seventy-five. 

2. Two hundred thirteen. 

3. Four hundred ninety-six. 

4. Two hundred twenty-nine. 

5. Fouj hundred eight. 

6. One thousand, three hundred fifty-two. 

7. Six thousand, forty. 

8. Eighty thousand, eighty. 

9. Seven thousand, three hundred. 

10. Thirteen thousand, four hundred fifty. 

11. Ninety-nine thousand, nine. 

12. Forty-four thousand, sixteen. 

13. Four hundred six thousand, one hundred fifty. 

14. Three thousand, fourteen. 

15. Nine thousand, seventy-seven. 

16. Fifty thousand, sixty-eight. 

17. Eleven thousand, nine hundred seventy -three. 

18. Seven hundred eighty-five thousand, two, 



6 PRACTICAL ARITHMETIC 

19. Ninety-two thousand, one hundred six. 

20. One million, three hundred ninety-seven thousand. 

21. Eight thousand, four hundred eighty-two. 

22. Nineteen million, one hundred fifty-six thousand. 

23. Eight million, six. 

24. Five thousand, one hundred thirty-one. 

25. Sixty-three million, sixty-eight thousand, seven. 

14. The art of writing numbers is called Notation. 

BXBECISE 4.— WRITTEN 

Write in figures the following numbers, which express 
the wool production and the number of hogs in several 
states, arranging in columns and using the comma between 
the periods, as in Exercise 2. 

POUNDS OF WOOL, PRODUCED IN 1906 

1. North Carolina, eight hundred seventy-one thou- 
sand, two hundred fifty. 

2. Alabama, five hundred sixty-eight thousand, seven 
hundred fifty. 

3. Montana, thirty-five million, eight hundred fifteen 
thousand. 

4. Florida, three hundred sixteen thousand, six hun- 
dred two. 

5. Wyoming, thirty-two million, eight hundred forty- 
nine thousand, seven hundred fifty. 

6. Texas, nine million, three hundred sixty thousand. 

7. Missouri, four million, six hundred seven thousand, 
three. 



NOTATION AND NUMERATION 7 

NUMBER OF HOGS IN 1907 

8. New York, six hundred seventy-five thousand, five 
hundred forty-five. 

9. Iowa, eight million, five hundred eighty-four thou- 
sand, five hundred. 

10. Pennsylvania, nine hundred eighty-nine thousand, 
six hundred eighty-five. , 

11. Kentucky, one million, two hundred thirteen thou- 
sand, three hundred eighty. 

12. Illinois, four million, four hundred forty-nine thou- 
sand, seven hundred five. 

13. Texas, two million, eight hundred sixty thousand, 
eight hundred seventy-nine. 

14. Ohio, two million, four hundred thirty-six thousand, 
seven hundred ninety-seven. 

15. Alabama, one million, two hundred fifty-one thou- 
sand, two hundred fifty-one. 

16. Nebraska, four million, eighty thousand. 

The following are the distances between several impor- 
tant cities. Write the numbers in figures and try to real- 
ize what they mean. 

17. By rail from Albany, N.Y., to Troy, N.Y., six 
miles; from Utica, N.Y., to Rome, N.Y., fifteen miles ; 
from Syracuse, N.Y., to Rochester, N.Y., eighty-one 
miles. 

18. From St. Paul, Minn., to Portland, Ore., two 
thousand fifty-three miles; from Cleveland, O., to Cin- 
cinnati, O., two hundred sixty-three miles. 



8 



PRACTICAL ARITHMETIC 



19. From Chattanooga, Teiin., to New Orleans, La., 
xour hundred ninety-two miles ; from Nashville, Tenn., to 

New Orleans, La., 
six hundred twenty- 
four miles ; from 
New Orleans, La., 
to Atlanta, Ga., four 
hundred ninety-six 
miles. 

20. By water from 
New York to Liver- 
pool, three thousand 
fifty-eight miles ; 
from San Francisco 
to Yokohama, four 




Street Scene in Atlanta, Ga. 

From a photog:raph. 
Copyright, 1907, by Underwood & Dnderwood. 



thousand, seven hundred ninety-one miles. 

21. From New York to Manila, sixteen thousand, five 
hundred miles; from New York to Havana, one thou- 
sand, four hundred twenty miles. 

22. From New York to Strait of Magellan, six thousand 
eight hundred ninety miles ; from Strait of Magellan to 
San Francisco, six thousand one hundred ninety -nine miles. 

23. By rail from New York to Omaha, one thousand 
three hundred eighty-five miles ; to San Francisco, three 
thousand two hundred fifty miles. 

24. The railroads of the United States aggregate one 
hundred ninety-three thousand miles, bearing thirty-eight 
thousand locomotives, fourteen thousand coaches, carry- 
ing yearly six hundred million passengers, and one bill- 
ion tons of freight. They cost about five billion dollars. 



ROMAN NOTATION 

15. The system of notation and numeration already- 
explained is commonly called the Arabic System. There 
is still another system known as the Roman System. 

16. In the Roman system of notation seven capital 
letters of the alphabet and combinations of these letters 
are used to express numbers. The letters and their 
values are as follovsrs :, 

I V X L C D M 

1 5 10 50 100 500 1000 

17. A bar placed over a letter increases its value a 
thousand fold, e.g., V denotes 5000; X denotes 10,000. 

18. When these symbols are used in combination their 
values are governed by the following laws : 

I. Each repetition of a letter repeats its value, e.g., 
XX denotes 20, XXX denotes 30, CC denotes 200, MMM 
denotes 3000. 

II. When a letter is placed after one of greater value, 
its value is to be added to that of the preceding letter, 
e.g., XI represents 10 and 1, or 11 ; VII represents 5 and 
2, or 7 ; XVI represents 10 and 5 and 1, or 16 ; CXXI 
represents 100 and 10 and 10 and 1, or 121. 

III. When a letter is placed before another of greater 
value, its value is taken from that of the letter of greater 
value, e.g., IX represents 10 less 1, or 9; XL represents 
50 less 10, or 40 ; XC represents 100 less 10, or 90. 

IV. When a letter is placed between two letters of 

9 



10 PRACTICAL. ARITHMETIC 

greater value, its value is taken from that of the letter 
which follows it, e.^., XIX represents 10 and 9, or 19; 
CXC represents 100 and 90, or 190. 

BXEECISE 5. — WRITTEN 

Express in Arabic notation : 

1. XI 11. XXVII 21. MDLX 

2. XX 12. XCV 22. MDXLVI 

3. XIV 13. XLIV 23. MDCCXLIV 

4. XXX 14. LXXIV 24. MMDCCXCIII 

5. XL 15. CCLIV 25. VCCCLXXVI 

6. XVI 16. CDLVI 26. XDCCXCIX 

7. LV 17. DCIX 27. DXLIV 

8. LIX 18. MCXL 28. MDCCLXXXIII 



9. LXXVIII 19. MCXLV 29. MMCCCCLXIV 
10. XLIX 20. MDLIV 30. MMMDCCXIX 

EXERCISE 6.— WRITTEN 

Express in Roman notation : 



1. 


11 


11. 


98 


21. 


421 


2. 


17 


12. 


73 


22. 


943 


3. 


19 


13. 


116 


23. 


719 


4. 


42 


14. 


240 


24. 


1425 


5. 


33 


15. 


375 


25. 


1764 


6. 


12 


16. 


480 


26. 


5861 


7. 


26 


17. 


510 


27. 


24,854 


8. 


54 


18. 


450 


28. 


256,845 


9. 


88 


19. 


375 


29. 


1,450,819 


10. 


75 


20. 


741 


30. 


3,840,006 



UNITED STATES MONEY 

19. In the money of the United States the unit is the 
Dollar. In writing it is expressed by the sign |, e.g., 
!? 25 is read twenty -five dollars. 

20. Our monej' system is based upon the same system of 
tens and groups of tens which we studied in Arabic nota- 
tion. That is, ten units of one order make a unit of the 
next higher order. 

21. Ten ten-cent pieces equal one dollar. Ten one- 
cent pieces equal a ten-cent piece. A still smaller divi- 
sion of our money which we do not commonly use is 
called Mills. Ten mills equal one cent. 

Ten cents is one-tenth of a dollar. One cent is one 
one-hundredth of a dollar. One mill is one one-thou- 
sandth of a dollar. 

22. The period used to separate dollars and cents is 
called the Decimal Point. 

23. The following diagrams serve to show the arrange- 
ment of dollars, cents, and iiaills as they are written: 



F3 CO 



a 



a> 



m — . -7. 



1245 . 245 



.a +-> 3 T3 +3 J5 +J 

•t 2 4 5 . 2 4 5 



11 



12 



PRACTICAL ARITHMETIC 



EXERCISE 7. — ORAL 

Read as dollars and cents : 

1. I 8.24 5. I 25.06 9. 1349.99 13. $ 542.89 

2. $ 8.72 6. I 91.07 10. ^698.42 14. I 560.90 

3. I 9.87 7. f 92.09 11. 1100.10 15. $1845.24 

4. $10.25 8. $900.09 12. I 99.99 16. $6291.98 

Read as dollars, cents, and mills : 

17. $5,842 20. $ 17.001 23. $981,701 26. $699,764 

18. $3,205 21. $ 70.070 24. $909,701 27. $263,809 

19. $4,998 22. $191,672 25. $340,034 28. $ 89.617 



EXERCISE 8. — WRITTEN 

Express the following in figures, using the dollar sign 
and decimal point : 

1. Twenty dollars and fifty cents; thirty-four dollars 
and five cents. 

2. Eighteen dollars and thirty-five cents; ninety -five 
dollars and twenty cents; thirty-one dollars and sixty 
cents ; one hundred twenty dollars and four cents. 

3. One hundred dollars and ten cents ; fifty-four dol- 
lars and nineteen cents ; fifty-three dollars and fifty-five 
cents; nineteen dollars and ninety cents. 

4. Eighty dollars and one cent, five mills ; fifty dollars and 
fifty cents ; three hundred dollars and six cents, one mill ; 
four hundred thirty-three dollars and thirty-three cents. 

5. Five hundred dollars and three-tenths ; two hundred 
dollars and thirty-three hundredths ; one hundred dollars 
and three hundred thirty-three thousandths. 



ADDITION 

24. The growth of an apple twig in 1905 was 4 inches 
and in 1906 it was 6 inches. How many inches did it 
grow in the two years? 

Addition is the process of finding the number that 
is equal to two or more numbers taken together. 

25. The result obtained by adding numbers is called 
the Sum. 

26. The sign of addition, +, is called Plus. When 
placed between numbers it means that they are to be 
added. 

27. The sign of equality, =, when placed between 
numbers shows that they are equal. Thus 7 + 3 = 10 is 
read seven plus three equals ten. 

28. Find the sums of the following, which include all 
the combinations of two numbers from one to nine : 



2 + 7 = 


2 + 1 = 


3 + 1 = 


1 + 9 


4 + 2 = 


8 + 7 = 


1 + 6 = 


3 + 5 


3 + 4 = 


1 + 1 = 


2 + 4 = 


1 + 7 


2 + 3 = 


7 + 2 = 


3 + 7 = 


4 + 3 


7 + 1 = 


3 + 3 = 


5 + 4 = 


6 + 1 


8 + 2 = 


4 + 5 = 


1 + 4 = 


3 + 2 


1 + 9 = 


6 + 4 = 


2 + 2 = 


1 + 2 


5 + 2 = 


1 + 8 = 


5 + 5 = 


4 + 6 


3 + 6 = 


2 + 5 = 


8 + 1 = 


6 + 2 



13 



14 PRACTICAL ARITHMETIC 



6 + 3 = 


4 + 4 = 


2 + 8 = 


1 + 8 = 


5 + 3 = 


2 + 6 = 


3 + 4 = 


4 + 1 = 


1 + 5 = 









Practise adding these numbers daily until the sum of 
any of these combinations can be told at a glance. 

EXERCISE 9. — OEAL 

1. A man fed a colt 2 quarts of oats, a driving horse 
4 quarts, and a draught horse 6 quarts. How many quarts 
of oats did he use at a feeding? 

2. If the morning and the afternoon each becomes 5 
minutes longer during the second week in March, how 
much longer are the days of the second week than the 
days of the first week ? 

3. If the cost of hauling Kansas wheat to the railroad 
station is 3 cts. a bushel, and the freight to New York is 
11 cts. a bushel, what is the total cost of transportation ? 

4. A dairyman had 4 cows. One gave 5 quarts, one 
7 quarts, one 8 quarts, and another 9 quarts of milk at a 
milking. How many quarts did all give at a milking ? 

5. A morning from sunrise to noon in September is 
6 hours, and from noon to sunset is 6 hours. What is 
the total length of the day ? 

6. A ration for a cow is : corn and cob meal, 5 lbs. ; 
cotton-seed meal, 4 lbs. ; hay, 20 lbs. What is the weight 
of the entire ration? 

7. The number of cloudy days in January was 9, the 
rainy days were 4. How many days were rainy and 
cloudy ? 



ADDITION 15 

8. If a fruit cake requires 3 lbs. of currants, 2 lbs. of 
raisins, and 1 lb. of citron, how many pounds of fruit are 
used in the cake ? 

9. If the increase in temperature at Raleigh, N. C, in 
1907 was 26 degrees from February to May and 14 degrees 
from May to August, what was the total increase in tem- 
perature during the six months ? 

10. If the temperature decreases 8 degrees from July 
to September and 33 degrees from September to March, 
what is the total decrease in temperature ? 

11. The number of senators from each of several sec- 
tions of our country in 1890 was as follows : from the 
New England States, 12; the Middle States, 8; the 
Pacific States, 10. How many senators were there from 
all these sections ? 

12. The number of senators from the two largest sec- 
tions of our country in 1890 was as follows : the South, 28 ; 
the Northwest, 24. How many senators were there from 
these sections? 

13. A ration for a cow is 15 lbs. of hay, 30 lbs. of 
silage, 4 lbs. of cotton-seed meal, 3 lbs. of wheat bran, 
and 3 lbs. of corn meal. What is the weight of the 
entire ration ? 

14. Count from 3 to 99 by threes. 

15. Count from 4 to 100 by fours. 

16. Count from 6 to 96 by sixes. 

17. Count from 9 to 99 by nines. 

18. At Raleigh, N.C., in 1907 the lowest temperature 
for the month of October was 36 degrees, the highest 



16 PRACTICAL ARITHMETIC 

temperature was 45 degrees higher. What was the high- 
est temperature ? 

19. Two skilled laborers earned 13 and $5 respectively 
a day. How much did the two earn together ? 

20. Two unskilled laborers earned respectively il.25 
and f 1.50 a day. How much did the two earn ? 

21. The cultivation of an acre of corn costs $6, the fer- 
tilizers $ 3, harvesting and other expenses f 3. What is 
the cost of the crop per acre ? 

22. A ration for a horse vreighing 1000 lbs. when doing 
moderately hard work is 6 lbs. of corn,- 8 lbs. of oats, and 
15 lbs. of hay. What is the weight of the ration? 

23. A ration for a fattening beef animal weighing 
1000 lbs. is 30 lbs. of corn silage, 12 lbs. of corn stover, 
5 lbs. of cotton-seed meal, and 4 lbs. of cotton seed. 
What is the weight of the ration? 

24. If a man vs^ishes to seed an acre for a meadow and 
iises 11 lbs. of timothj', 6 lbs. of red top, and 5 lbs. of 
clover seed, how many pounds of seed does he sow on the 
acre ? 

25. If 1000 lbs. of an average mixed stable manure 
contain 5 lbs. of nitrogen, 6 lbs. of potash, and 3 lbs. of 
phosphoric acid, how many pounds of these plant foods 
does it contain ? 

26. If the plants in a ton of dry clover hay used 39 
lbs. of nitrogen, 37 lbs. of potash, and 11 lbs. of phos- 
phoric acid in growth, how many pounds of these mate- 
rials were used by the plants ? 

27. If a ton of wheat straw iased in growing 11 lbs. 



ADDITION 17 

of nitrogen, 23 lbs. of potash, and 4 lbs. of phosphoric 
acid, how many pounds of these materials were taken 
from the soil ? 

28. If a ton of oat grain used in growing 35 lbs. of 
nitrogen, 9 lbs. of potash, and 13 lbs. of phosphoric acid, 
how many pounds of these materials were used ? 





EXERCISE ID. 


— WRITTEN 






Find the sum 


of: 












1. 2. 


3. 


4. 


5. 


6. 


7. 


8. 


9 4 


5 


8 


7 


2 


5 


6 


2 4 


2 


7 


5 


3 


4 


4 


3 5 


1 


2 


4 


5 


2 


4 


4 8 


5 


4 


2 


4 


3 


y 


5 7 


7 


_5_ 


1 


6_ 


2 





9. 10. 11. 12. 13. 14. 15. 16. 

76954862 
63887888 
95796964 
88654979 
56873294 

4 _8_711-i-- 
29. Add 259, 634, and 872. 

259 The sum of the units' column is 15, or 5 units and 

g34 1 ten ; the 6 representing units is written under the 
units' column. The sum of the tens' column + 1 ten 
carried from the first column is 16. The figure repre- 
senting the 6 tens is placed under the tens' column, 



872 



1765 

and the 1 representing hundreds is added with the hundreds' 



18 PRACTICAL ARITHMETIC 

column. The sum of the hiiudreds' column + 1 from the tens' 
column is 17. The last sum is placed under the column 
added. 

30. Rule for Addition. Write the immbers to be added 
so that the figures representing units stand under units, 
tens under tens, hundreds under hundreds, etc. Begin 
at the riglit and add each column separately, placing the 
sum underneath if it is less than ten. If the sum of any 
column exceeds nine, set down the right-hand figure and 
add the other figure or figures to the next column at the 
left. 

EXERCISE 11. — WRITTEN 



Add: 












1. 


2. 


3. 


4. 


5. 


6. 


56 


78 


14 


4 


126 


696 


76 


43 


18 


25 


205 


348 


99 


21 


7 


79 


811 


319 


4 


7 


39 


64 


79 


871 


18 


51 


88 


23 


236 


296 


15 


75 


78 


49 


815 


64 


37 


64 


99 


86 


429 


337 


7. 


8. 


9. 


10. 


11. 


12. 


526 


237 


124 


58 


321 


379 


448 


213 


87 


222 


118 


672 


973 


716 


116 


972 


961 


789 


87 


89 


615 


736 


69 


709 


988 


825 


793 


845 


296 


69 


147 


298 


611 


47 


348 


879 


268 


794 


989 


623 


799 


27 



ADDITION OF UNITED STATES MONEY 



31. Add 14.25, $16.50, f .45, 1150, 13.455. 

S4 '"'5 

'^ ■^' Write the numbers to be added so ihat units 

of the same order shall stand in the same col- 
umn, with the decimal points in a vertical line. 
Add as in integral numbers. The decimal point 
in the sum should stand directly in line with 
the decimal points of the numbers added. 



:;3 

16.50 

.45 

150.00 

3.455 

1174.655 



EXERCISE 12. — "WRITTEN 



Add: 

1. 

12.50 

3.05 

.90 

.06 

7.25 



2. 

11.006 
21.05 
3.425 
42.14 
75.141 



3. 

1340.006 

10.01 

62.62 

324.05 

231.005 



4. 

$30,006 

300.10 

106.001 

10.50 

3.75 



1. Add 

2. Add 

Add 
Add 
Add 
Add 

$6798.98. 



3. 
4. 
5. 
6. 



EXERCISE 13. — WRITTEN 

$3.05, $20,006, $45.2.5, $6.25, $3,755. 
$63.43, $25,002, $23,025, $300.45, $62,725. 
$90.,93, $84,005, $2,005, $16.85, $4.35, $1.98. 
$63.05, $400.62, $50.50, $200.20, $3.75, $4.25. 
$50,005, $560.35, $428.72, $34.91, $863,100. 
$678.78, $67249.16, $9381.62, $862.98, 

19 



20 PRACTICAL ARITHMETIC 

EXBHCISB 14. — WBITTEN 

Find the sum of : 



1. 


2. 


3. 


4. 


5. 


6314 


6798 


8569 


7873 


2361 


7581 


8347 


7863 


2578 


5671 


6384 


6437 


9088 


5447 


1983 


2678 


8089 


8637 


9138 


3612 


7896 


1463 


4475 


7819 


9278 


6. 




7. 


8. 


9. 


$4798.75 


19862.79 $ 


428.69 


17963.07 


267.98 




299.89 


1796.99 


629.67 


495.12 




4621.00 


289.78 


1198.79 


490.07 




7978.91 


964.68 


682.87 


989.75 




7842.29 


629.29 


298. 


862.93 




7096.07 


729.62 


391.09 



Find the sum of : 

10. 213, 14, 594, 672, 10, 756, 1875, 67. 

11. 310, 64, 236, 79, 118, 296, 51, 9. 

12. 716, 615, 1857, 9241, 19, 65, 452. 

13. 463, 7, 8700, 1207, 1439, 4245, 5402. 

14. $7.42, $28.75, $30,015, $500.00, $89,675, $620,908. 

15. $62.50, $934.25, $245.63, $72.00, $786.21, $5.04. 

16. $650.30, $12,645.32, $100.84, $100,084, $256.25. 

17. 7,682,963, 842,981, 428,792, 6879, 84,289, 831. 

18. 6,687,328, 64,298, 179,632, 281, 7, 698, 768,342, 

19. 1,786,984, 6,827,341, 92,712, 863,298, 347,829. 

20. $862.79, $9341.05, $67,294,73, $76,932.06. 

21. 1,796,328, 6,297,348, 291, 7,283,409, 8624. 



ADDITION 



21 



EXERCISE 15. — WRITTEN 

The exports of cheese for 1901-1905 were 



Country 


1901 


1902 


1903 


1904 


1905 




Pounds 


Pounds 


Pounds 


Pounds 


Pan ml a 


Bulgaria . . . 


6,449,020 


5,651,335 


7,064,385 


6,624,517 


7,227,816 


Canada . . . 


200,946,401 


229,099,925 


233,980,716 


215,733,259 


215,834,543 


France .... 


17,795,274 


20,545,803 


23,119,970 


20,711,480 


22,125,152 


Germany . . . 


3,211,693 


3,119,981 


2,813,539 


2,5117,927 


2,650,397 


Italy . . . . 


24,104,455 


28,841,967 


33,158,617 


30,299,443 


37,694,647 


Netherlands 


104,2i;S),090 


104,785,152 


109,025,968 


103,069,081 


98,438,575 


New Zealand . 


11 ,680,928 


8,371,552 


8,375,360 


9,466,912 


9,918,944 


Russia . . . . 


1,610,414 


1,655,230 


1,406,557 


1,396,951 


1,119,497 


Switzerland . . 


60,075,729 


54,491,422 


53,642,.S6:! 


56,688,989 


61,383,731 


United States . 


27,203,184 


18,987,178 


23,335,172 


10,134,424 


16,562,451 


Other countries 


7,924,000 


9,469,000 


8,833,000 


7,050,000 


5,092,000 



1-5. Find the total exports for each year. 
6-16. Find the total exports from each country. 

The pupil should add as many of the following problems 
as need be to attain speed and accuracy. 





U 


h 


c 


d 


e 


1 


86793 


84928 


76321 


42894 


78621 


2 


84697 


68296 


98988 


86796 


78629 


3 


17986 


79826 


42391 


76842 


68792 


4 


28649 


78421 


97632 


49988 


68499 


5 


99763 


89792 


88767 


84921 


69837 


6 


89798 


66787 


62849 


76639 


62897 


7 


56845 


86283 


32918 


74289 


88997 


8 


67632 


97987 


98999 


77877 


68298 


9 


74911 


83172 


64829 


79638 


28429 


10 


64523 


68791 


48796 


42981 


78429 


11 


69354 


81786 


86429 


36827 


64287 


12 


98782 


88793 


34287 


42963 


96832 



22 PEACTICAL ARITHMETIC 

17-21. Find the sum of columns a, h, c, d, e. 

22-33. Find the sum of each line of numbers from 1 to 
12 without copying. 

34-47. Find the sums of the numbers in diagonal rows, 
thus : b 1, a 2, also c 1, J 2, a 3, and all other possible rows 
having the same direction, as d 1 to a 4, etc. 

48-61. Similarly, find the sums of the numbers in diag- 
onal rows dl, e 2, also c 1, d 2, e S, and by all other pos- 
sible rows having the same direction. 

EXERCISE 16. — WRITTEN 

1. A dairyman has 6 cows. The first gives 18 lbs. of 
milk, the second 11 lbs., the third 23 lbs., the fourth 
26 lbs., the fifth 32 lbs., the sixth 40 lbs. How much do 
they all give? 

2. If a 200-lb. sack of fertilizer contains 8 lbs. of 
nitrogen, 10 lbs. of potash, and 16 lbs. of phosphoric 
acid, how many pounds of these plant foods are there in 
a sack ? 

3. If a reader costs 43 cts., a history 86 cts., an arith- 
metic 49 cts., a geography $1.08, a tablet 8 cts., pens and 
pencils 7 cts., what is the cost of the equipment? 

4. In the stomach and crop of a bob-white there were 
found 400 pigweed seeds, in another 500 ragweed seeds, 
in another 550 sheep-sorrel seeds, in another 640 seeds of 
pigeon grass. How many of these weed seeds were con- 
sumed by these four bob-whites ? 

5. When thoroughly dry, the weight of the different 
parts of the cotton plants grown on an acre of land was 
as follows: lint 300 lbs., seed 507 lbs., bolls 363 lbs.. 



ADDITION ■ 23 

leaves 566 lbs., roots 130 lbs., stems 604 lbs. What was 
the total weight of plants produced to yield 300 lbs. of 
lint cotton ? 

6. If the material grown on an acre in corn weighs as 
follows : ears 4325 lbs., stover, which consists of stalks, 
2379 lbs., leaves 1190 lbs., and shucks 397 lbs., how 
much did the ears and stover together weigh? How 
much did the stover weigh ? 

7. A farmer sold the following products during the 
year: 1 horse |145, 9 beef animals |468, 18 hogs $234, 
13 lambs 152, 309 bus. potatoes $12Q, 10 bales cotton 
1528, 150 bus. seed oats |75, 100 bus. seed corn |100, 50 
chickens $22, 200 doz. eggs $38, 12 turkeys $21, 220 
bus. wheat $191. To what did his total sales amount? 

8. The different parts of the dressed carcass of a beef 
animal that, when alive, weighed 1550 lbs. weigh as fol- 
lows : neck 40 lbs., chuck 237 lbs., prime ribs 117 lbs., 
porter-house steak 103 lbs., sirloin steak 87 lbs., rump 
36 lbs., round steak 183 lbs., shank 30 lbs., flank, 52 lbs., 
ribs plate 138 lbs. What is the weight of the dressed 
carcass ? 

9. A New England cottage was built at a cost as 
follows: masonry $250, lumber and mill work $700, car- 
pentering $400, plumbing $170, painting $90, hardware 
$20, heater, $200. What did the house cost when com- 
pleted ? 

10. A cottage planned to cost $1000 was built for the 
following cost: foundation and brickwork $428.80, lum- 
ber $370.15, carpentering $264.87, painting and plaster- 



24 PRACTICAL ARITHMETIC 

ing 8253.25, hardware 138.90, tin work, |13.78. What 
did the house actually cost ? 

11. A farm costing $5250 is equipped as follows: 
house 11579.42, farm mules 1850.00, 1 horse 1175.00, 
cattle $275.00, hogs 1112.00, implements and tools 
1672.00. What is the total value of the farm and its 
equipment ? 

COST OF FURNISHING A HOUSE 

Two young people equip their home with the following 
articles. Find the cost of each room separately. 

12. Kitchen: Linoleum, 120.00; range, 145.00; table, 
11.50; chair, $1.00; utensils, $13.00; laundry outfit, 
$8.25; refrigerator, $21.00; lamp, 45 cts.; clock, $1.00; 
cutlery, 75 cts. 

13. Dining Room : Table, $20.00 ; six chairs, $24.00; 
sideboard, $30.00; rug,$12.00; clock,$4.98; silence cloth, 
$1.25 ; lamp, $2.97 ; 3 dozen napkins, $9.48 ; 2 dozen nap- 
kins, $4.30; six table-cloths, $15.00; six plated knives, 
$4.50 ; six solid silver forks, $12.00 ; 12 solid silver spoons, 
$10.00; three tablespoons, $6.00; dishes, $15; glass- 
ware, $7.45. 

14. Living Room: Lamp, $3.50; table, $15.00; Mor- 
ris chair, $14.60; chair, $5.45; rattan chair, $9.25; 
arm-chair, $7.50 ; bookcase, $9.45; magazine stand, $6.25; 
rug, $34.50. 

15. Hall: Lamp, $3.25; hall rack, $16.35; chair, 
$3.45; rug, $6.00. 

16. Bedroom: Bureau, $22.35; chiffonier, $11.25; 
washstand, $4.00; toilet set, $6.25; chair, $2.75; lamp. 



ADDITION 25 

11.50; bed, $13.00; springs, 15.00 ; mattress, 115.00; 12 
sheets, 19.60; 12 pillow cases, 15.00; 2 pairs blankets, 
f 10.00; 1 comfortable, 11.00; 2 counterpanes, 13.45; 
2 dozen towels, 16.00; 1 dozen yards toweling, $1.80; 
rug or matting, $5.80. 

17. Find the total amount spent in furnishing the house. 



18. If a family of two persons spends for rent $130, 
food $210, clothing $80, fuel $30, light $6, insurance 
$24, replenishing $ 10, carfare $5, literature $5, charity 
$10, and saves $20, what is the income? 

19. A second family of five persons spends for house 
rent $240, table expense $364, clothing $175, fuel $52, 
light $3, hired help $50, renewals $50, dentist $25, boys 
spending money $13, spending money of other children 
$5. What is the income? 

20. What is the cost of raising an acre of corn, estimat- 
ing rent at $3.03, fertilizer $1.86, preparation of the 
soil $1.62, planting $.42, cultivating $1.80, harvesting 
$3.00, and other expenses $1.76? 

21. What is the total cost of raising an acre of upland 
cotton, allowing for the rent of land $3.25, fertilizer 
$2.46, preparing the soil $3.00, seed $.21, planting $.28, 
cultivating $2.31, picking $3.37, ginning and pressing 
$1.65, wear of tools $.62, marketing $.64, and other 
expenses $1.42? 

22. A man owns 5 horses. The first is worth $90, the 
second $125, the third $175, the fourth as much as the 
first and second, the fifth .as much as the second and 
fourth. What was the value of the 5 horses? 



26 



PRACTICAL ARITHMETIC 



23. The number of miles of railroad in the world in 
1900 was : North America 216,000, Europe 173,000, Asia 
36,000, South America and West Indies 28,000, Aus- 
tralasia 15,000, Africa 12,000. What was the total 
mileage ? 

Alabama, S 1,828,697 The adioininsT table 

Arkansas, S 1,311,564 . ^, "^ ^ , . 

California, P 1,485,053 gives the population 

Colorado . . . 539,700 of the States of the 

Connecticut, N.E. . . . 908,420 

Delaware, M 184,735 United States in 

Florida, S 528,542 -. Q^n 

Georgia, S 2,216,331 -^^""• 

Idaho 161,772 „, tji- j ^i. ^ 

Illinois, E.C 4,82i;550 ^4. Fmd the popula- 

Indiana, E.C 2,516,462 tion of the New Eng- 

Iowa,W.C 2,231,853 -, ^. . ■ ^- . j 

Kansas, W.C 1,470,495 land States, indicated 

Kentucky, E.C 2,147,174 bv N F 

Louisiana, S 1,381,625 -^ 

Maine, N. E 694,466 ,- rf-j ^Iio T^r.T.^^ 

Maryland, M 1,188;044 ^^- ^^"^^ *^^ P^P^" 

Massachusetts, N.E. . . 2,805,346 lation of the Middle 

Michigan, E.C 2,420,982 oj. 4. ■ j- ^ j i, ht 

Minnesota, W.C. . . . 1,751,394 States, indicated by M. 

Mississippi, S 1,551,270 „_ t^- i .i ^ 

Missouri, W.C 3;i06,665 ^6. Find the popula- 

Montana 243,329 tion of the Western 

Nebraska, W.C. . . . 1,066,300 ^ , , ^ ■ ■,. 

Nevada 42,335 Central States, indi- 

New Hampshire, N.E. . 411,588 patpri Vnr "W P 

New Jersey, M.. . . . 1,883,669 ^^^^'^ '^^ ^■^• 

New York, M 7,268,894 ,? Find the nonula- 

North Carolina, S. . . . 1,893,810 -^ ^^^ ^^^ popuia- 

North Dakota, W.C. . . 319,146 tion of the Southern 

Ohio, E. C 4,157,545 q. , • j- 4. j u 

Oklahoma, S 790^391 States, indicated by 

Oregon, P 413,536 S. 

Pennsylvania, M. . . . 6,302,115 

Rhode Island, N.E. . . . 428,556 28. Find the popula- 

South Carolina, S. . . . 1,340,316 . ^ ^ 

South Dakota, W.C. . . 401,570 tion of the Pacifio 

Tennessee, S 2,020,616 States indioatfld bv 

Texas, S 3,048,710 ^^^^^s, inaicacea Dy 

Utah 276,749 P. 



ADDITION 27 

Vermont N.E 343,641 29. Find the popula- 

Virgima, M 1,854,184 . . , 

Washington, P 518,103 tioii of the Eastern 

West Virginia, M. . . . 958,800 Central Statp^i inrli 

Wisconsin, E.C 2,069,042 ^^nrrai States, indi- 

Wyoming 92,531 cated by E.C. 

30. The remaining States are Plateau States. What is 
the population ? 

Except in leap year the days in the months number : 

January 31 31. How many days are there 

J, , „^ in a year that is not a leap 

April 30 year? 

M*y 31 32. The twenty-second of 

j^, gj February is how many days 

August 31 after January first ? 

September .... 30 33^ ^he fourth of July is 

October 31 •' 

November .... 30 '^ow many days after January 

December .... 31 first? 

34. The twenty-fifth of December is how many days 
after January first? 

SOME IMPORTANT DATES 

33. From the discovery of America by Columbus in 
1492 to the founding of St. Augustine 73 years elapsed. 
From the founding of St. Augustine to the settlement 
of Jamestown 42 years elapsed. What were the dates of 
these two settlements ? 

36. From the discovery of America in 1492 to the 
founding of New Amsterdam 122 years elapsed. From 
the founding of New Amsterdam to the landing of the 
Pilgrims 6 years elapsed. What were the dates of these 
two settlements ? 



28 



PRACTICAL ARITHMETIC 



37. From the first General Assembly in 1681 to the 
first Colonial Congress 84 years elapsed. From the first 
Colouial Congress to the second Colonial Congress 9 years 
elapsed. What were the dates of these two Congresses? 




Signing the Declaration of Independence 



38. From the first General Assembly in 1681 to the 
Declaration of Independence 95 years elapsed. From 
the Declaration of Independence to the adoption of the 
Articles of Confederation 5 years elapsed. What were 
the dates of these two events? 

39. From the first General Assembly in 1681 to the 
adoption of the Constitution 106 years elapsed. From 
the adoption of the Constitution to the election of the 
first President of the United States 2 years elapsed. 
What were the dates of these events? 



SUBTRACTION 

32. One dairy cow produces 9 pounds of butter in a 
week, another 5 pounds. How much more does one pro- 
duce than the other ? 

The process of finding how mucli greater one number 
is than another, or finding the difference between two 
numbers, is called Subtraction. 

33. The larger number, or the number from which 
another is subtracted, is called the Minuend. 

34. The smaller number, or the number subtracted, is 
called the Subtrahend. 

35. The result obtained in subtracting is called the 
Remainder or Difference. 

36. The sign of subtraction, — , is called Minus. When 
it is placed between two numbers, it means that the second 
number is to be subtracted from the first, e.g., 8 — 5=3 
is read, eight minus (less) five equals three. 

EXERCISE 17. — ORAL 

1-1= 2-2= 3-3= 

2-1= 3-2= 4-3= 

3-1= 4-2= 5-3= 

4-1= 5-2= 6-3= 

5-1= 6-2= 7-3= 

6-1= 7-2= 8-3= 

• 29 



30 PRACTICAL ARITHMETIC 



7-1 = 


8-2 = 


9-3 = 


8-1 = 


9-2 = 


10-3 = 


9-1 = 


10-2 = 


11-3 = 


10-1 = 


11-2 = 


12-3 = 


4:-4: = 


5-5 = 


6-6 = 


5-4 = 


6-5 = 


7-6 = 


6-4 = 


7-5 = 


8-6 = 


7-4 = 


8-5 = 


9-6 = 


8-4 = 


9-5 = 


10-6 = 


9-4 = 


10-5 = 


11-6 = 


10-4 = 


11-5 = 


12-6 = 


11-4 = 


12-5 = 


13-6 = 


12-4 = 


13-5 = 


14-6 = 


13-4 = 


14-5 = 


15-6 = 


7-7 = 


8-8 = 


9-9 = 


8-7 = 


9-8 = 


10-9 = 


9-7 = 


10-8 = 


11-9 = 


10-7 = 


11-8 = 


12-9 = 


11-7 = 


12-8 = 


13-9 = 


12-7 = 


13-8 = 


14-9 = 


13-7 = 


14-8 = 


15-9 = 


14-7 = 


15-8 = 


16-9 = 


15-7 = 


16-8 = 


17-9 = 


16-7 = 


17-8 = 


18-9 = 



Note. This subtraction table should be thoroughly studied 
by each pupil, and drill should be continued until the answers 
can be given quickly and correctly. 



SUBTRACTION 31 

EXERCISE 18. — ORAL 

Practice subtracting these numbers until the differ- 
ences can be told instantly. 





a 


b 


c 


d 


e 


f 


g 


h 


i 




1. 


4 


7 


6 


2 


4 


5 


6 


1 


8 


1. 




1 


1 


_2 


2 


_3 


J[ 


3 


1 


1 




2. 


2 


3 


9 


10 


3 


5 


4 


6 


10. 


2. 




1 


3 


J. 


2 


J. 


_2 


2 


1 


1 




3. 


7 


10 


5 


3 


4 


9 


6 


11 


8 


3. 




2 


3 


3 


_2 


_£ 


2 


_4 


2 


2 




4. 


9 


10 


7 


9 


5 


7 


11 


5 


8 


4. 




_3 


5 


3 


4 


A 


5 


_3 


_5 


4 




5. 


6 


8 


12 


13 


8 


7 


9 


6 


8 


5. 




_6 


6 


_3 


4 


JT 


4 


5 


5 


3 




6. 


10 


7 


10 


9 


11 


8 


9 


7 


14 


6. 




_4 


6 


8 


7 


4 


5 


6 


7 


6 




7. 


11 


14 


13 


8 


12 


12 


10 


9 


13 


7. 




5 


6 


5 


_8 


4 


JT 


6 


8 


7 




8. 


11 


15 


10 


12 


12 


15 


16 


16 


12 


8. 




8 


8 


7 


9 


5 


_9 


7 


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_8 




9. 


12 


13 


18 


15 


17 


15 


11 


14 


11 


9. 




6 


9 


9 


6 


9 


7 


_6 


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10. 


10 


14 


14 


16 


13 


17 


11 


14 


13 


10. 




9 


_7 


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9 


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8 


_9 


_8 


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a 


6 


c 


d 


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/ 


S' 


h 


i 





32 PRACTICAL ARITHMETIC 

BXBBCISB 19. — ORAL 

1. If a twig grew 6 ins. in 1906, and 4 ins. in 1907, 
which year produced the greater growth? How much 
greater ? 

2. What number taken from 10 leaves 2 ? 

3. What number with 6 makes 10 ? 

4. If a strawberry plant has 12 leaves and 4 are 
injured by insects, how many sound leaves are there on 
the plant ? 

5. If a limb on the north side of a tree measures 9 ft., 
and one on the south side measures 11 ft., which is the 
longer ? How much longer ? 

6. If the number of rainy and cloudy days in Septem- 
ber were 17, how many clear days were there in Sep- 
tember ? 

7. Subtract by threes from 99 to 0. 

8. Subtract by fours from 100 to 0. 

9. Subtract by sixes from 96 to 0. 

10. Subtract bj' sevens from 98 to 0. 

11. If the highest temperature for July in the Middle 
Atlantic States was 99 degrees, and the lowest tempera- 
ture 57 degrees, what was the range in temperature? 

12. The highest soil temperature at which wheat will 
grow is 104 degrees ; squash and corn grow at 115 
degrees. At how much higher temperature will squash 
and corn grow than wheat ? 

13. Melons grow best at a soil temperature of 99 
degrees, and clover at 70 degrees. How much higher 
temperature is required for melons than clover ? 



SUBTRACTION 33 

14. The boiling point of water is 212 degrees, the freez- 
ing point 32 degrees. What is the difference in degrees 
between the boiling and freezing points? 

15. A man wishes to start a small fruit garden. He 
has 115. to invest. The trellis and lattice cost 1 10. 
How much is left for the plants and trees ? 

16. If 2 pear trees cost 35 cts., 2 apple trees 25 cts., 
how much is left for smaller plants? 

17. If 6 doz. strawberry plants cost 25 cts., and 4 rasp- 
berry plants cost *.25, how much is still left of the 
original sum ? 

18. A normal child 6 yrs. old weighs 45 lbs., measures 
44 ins. in height, and has a chest measurement of 23 ins. 
A normal child of 9 yrs. weighs 60 lbs., measures 50 ins. 
in height, and has a chest measurement of 25 ins. What 
is the increase in weight in 3 yrs.? 

19. What is the increase in height in 3 yrs. ? 

20. What is the increase in chest measurement in 
3 yrs. ? 

37. From 875 take 446. 

875 Since we cannot take 6 iinits from 5 units we 

446 add one of the 7 tens to the 5 units, making 15 

429 units. We now have 6 units to be subtracted from 

15 units, which leaves 9 units to be written under the 

units' column. Since we have already taken 1 ten from the 7 

tens we have 6 tens remaining in tens' column. 4 tens from 6 

tens leaves 2 tens, which is written under tens' column; 4 

hundreds from 8 hundreds leaves 4 hundreds. The remainder, 

therefore, is 4 hundreds, 2 tens, 9 units, or 429. 



34 PRACTICAL ARITHMETIC 

38. From 584 take 296. 

584 Since we cannot take 6 units from 4 units we must 

296 take one of the 8 tens, which added to 4 units makes 

288 14 units. 6 units from 14 units leaves 8 units. Since 

we have already taken 1 ten from the 8 tens, we 

have 7 tens left. We cannot take 9 tens from 7 tens, so we 

must take 1 hundred from 6 hundreds, which added to 7 tens 

makes 17 tens. 9 tens from 17 tens leaves 8 tens. Since 

we have already taken 1 hundred from the 5 hundreds we 

have 4 hundreds left. 2 hundreds from 4 hundreds leaves 

2 hundreds. The remainder, therefore, is 2 hundreds, 8 tens, 

8 units, or 288. 

39. Add the remainder to the subtrahend in each of 
the last two examples. What do you observe ? 

The sum of the remainder and the subtrahend is equal 
to the minuend. Hence, to test the subtraction add the 
remainder and subtrahend together. If the sum equals 
the minuend, the work is correct. 

40. Rule for Subtraction. Write the subtrahend under 
the minuend, placing units under units and tens under 
tens, etc. Begin at the right and subtract each figure of 
the subtrahend from the corresponding figure of the min- 
uend, and write the remainder underneath. 

If any figure of the subtrahend is greater than the 
corresponding figure of the minuend, increase the figure 
of the minuend by taking one of the next higher order, 
which will be an increase of ten. Then diminish by 1 the 
order of the minuend from which the 1 was taken, and 
subtract. 

EXERCISE 20. — WRITTEN 

Subtract and prove : 

1. 52-26. 2. 37-28. 



SUBTRACTION 



35 



3. 94-58. 

4. 93-25. 

5. 92-68. 

6. 81-18. 

7. 70-36. 

8. 90-27. 

9. 50-13. 
10. 95-47. 



11. 786-235. 

12. 598-213. 

13. 647-238. 

14. 321-216. 

15. 976-247. 

16. 876-381. 

17. 358-149. 

18. 467-248. 





a 


b 


c 


1 


18729 


2628 


278 


2 


28694 


3979 


379 


3 


39231 


8642 


428 


4 


47326 


3981 


471 


5 


22821 


7986 


879 


6 


32542 


7842 


642 


7 


73625 


3765 


839 


8 


39832 


8429 


341 


9 


32421 


3764 


768 


10 


31321 


3428 


429 



The pupil should subtract sufficient of these problems to 
become accurate and rapid. 

19-28. From the first number in column b take each 
number in column c. 

29-118. From each other number in column h take 
each number in column c. 

119-128. From the first number in column a take each 
number in column h. 

129-218. From each other number in column a take 
each number in column h. 



SUBTEACTION OF UNITED STATES 
MONEY 

exercise 21. — oral 
Makixg Change 

1. I buy a book for 42 cts. ; how mucb change shall I 
receive from 50 cts. ? Make change in two ways. 

2. A yard of ribbon costs 12 cts., a spool of thread 
5 cts., a paper of pins 5 cts. How much change do I 
receive from a fifty-cent piece ? Make change in three 
ways. 

3. A yard of silk costs 63 cts., 1 doz. buttons 10 cts., 
a bolt of tape 5 cts. Make change for $1 in two ways. 

4. A copy of "Arabian Nights" costs $1.10. Make 
change for 12.00. 

5. Make change for $2.00 when you owe $1.75; $.15. 

6. Make change for $5.00 when you owe $1.49; $2.58. 

7. Make change for $5.00 when you owe $3.18; $2.16. 

8. Make change for $2.00 when you owe $1.23; $1.87. 

9. A pair of shoes costs $2.25, hat $1.00, tie 50 cts., 
4 handkerchiefs 72 cts. How much change does the 
merchant return for $5.00? 

10. Make change for $ 10.00 when you owe $ .81 ; $ 7. 84. 
41. Subtract $45,755 from $90.20. 
*Q0 200 Since the subtrahend has mills and there are no 

.rrjrr mills lu the minuend, a cipher is added to fill the 

4u. i DO , „ ..- 

— — — — ^ place 01 mills. The subtrahend is written under 
the minuend so that units of the same order shall 
36 



SUBTRACTION 37 

stand in the same column, and the decimal points be in a ver- 
tical line. Subtract as integers. The decimal point in the 
remainder should stand directly under the decimal points of 
the minuend and subtrahend. 

EXERCISE 22.— WRITTEN 

Subtract and prove: 

1. $4.24-111.10. 11. 11.00-1.75. 

2. 13.86 -#1.25. 12. 111.00 -$3.25. 

3. 14.50-. ¥3.20. 13. $90.99-180.25. 

4. 110.75- $8.41. 14. $77.42 -$65.94. 

5. $6.54 -$4.37. 15. $93.20 -$84.25. 

6. $9.27 -$8.16. 16. $525 -$177.02. 

7. $12.50 -$8.25. 17. $197 -$184.09. 

8. $17.28-18.25. 18. $3.333 -$2,999. 

9. $18.24 -$9.16. 19. $16.725 -$.50. 
10. $20.50 -$10.25. 20. $28.07 -$.125. 

EXERCISE 23.— WRITTEN 

1. Ill a day's milking of 769 lbs. of milk from a herd 
of Jersey cows there are 661 lbs. of water, 69 lbs. of 
solids-not-fat, and the remainder is butter-fat. How 
many pounds of butter-fat in the day's milking? 

2. In a day's milking of 769 lbs. from a herd of Hol- 
stein-Fresian cows there are 675 lbs. of water, 69 lbs. of 
solids-not-fat, and the remainder is butter-fat. How 
many pounds of butter-fat in the day's milking? How 
many pounds less of butter-fat than in problem 1 ? 

3. The 3d of February 1907 is the 34th day of the 



38 PRACTICAL ARITHMETIC 

year ; the 5th of June is the 156th day of the year. How 
many days between these dates ? 

4. The 10th of September is the 283d day of the year ; 
the 10th of June is the 191st day of the year. What is 
the difference in dates? 

5. The 22d of April is the 142d day of the year ; the 
31st of October is the 303d day of the year. What is the 
difference in dates? 

6. Jamestown, Va., was settled in 1607; the James- 
town Exposition, near Norfolk, Va., occurred in 1907. 
How many years elapsed between the dates ? 

7. The boiling point of water is 212 degrees. Water 
is at simmering temperature at 180 degrees. What is the 
difPerence in temperature? 

8. If a farmer kills a hog that weighs 369 lbs. when 
alive, how much will the dressed carcass weigh if it weighs 
82 lbs. less than the live weight ? 

9. A butcher killed a beef animal of good quality 
that weighed 1148 lbs. and an inferior one that weighed 
1179 lbs. What is the difference in the weight of the 
dressed carcasses of these beeves if the loss in weight of 
the first animal was 397 lbs. and of the second animal 
529 lbs.? 

10. If 4000 lbs. of ordinary fertilizer contains plant food 
as follows : phosphoric acid 320 lbs., nitrogen 80 lbs., and 
potash 80 lbs., how many pounds of plant food are there? 
How much that is not plant food ? 

11. In 4000 lbs. of cotton-seed hulls there are 444 lbs. 
of water and 2152 lbs. of indigestible matter. The re- 
mainder is digestible. How much is digestible ? 



SUBTRACTION 39 

12. In 4000 lbs. of corn there are 436 lbs. of water and 
408 lbs. of indigestible matter. The remainder is digest- 
ible. How many pounds of digestible matter are there? 

13. A man took 1500 lbs. of seed cotton to the gin and 
received a bale of lint weighing 493 lbs. How many 
pounds of seed should he also receive, all of the seed cot- 
ton that is not lint being seed? 

14. If to cultivate an acre of corn costs f 4.50, the 
fertilizers for it $3, harvesting $3.50, and other expenses 
f 1.00, and 35 bus. of corn worth §17.50, and a ton and 
a quarter of stover worth i 5, are produced, what is the 
farmer's profit? 

15. If 1083 lbs. of cotton are harvested from a fertil- 
ized field planted with selected seed, and 670 lbs. are 
harvested from an unfertilized field where unselected 
seed was used, what is the increase in yield due to fertili- 
zation and seed selection ? 

16. To grow a ton of oats requires 464 tons of water. 
A ton of corn requires 271 tons, potatoes require 385 tons, 
and clover 577 tons. How much more water is required 
by potatoes than by corn ? By clover than by oats ? By 
clover than by corn ? By clover than by potatoes ? By 
oats than by corn ? By oats than by potatoes ? 

17. If pat straw uses 163 lbs. of potash, 56 lbs. of ni- 
trogen, and 28 lbs. of phosphoric acid, and oat grain uses 
48 lbs. of potash, 176 lbs. of nitrogen, and 68 lbs. of 
phosphoric acid in every 10,000 lbs. of yield, which uses 
the most of each plant food, the straw or the grain? How 
much more of each ? 

18. In Michigan, soy beans with tubercles on their 



40 PRACTICAL ARITHMETIC 

roots yield 113 lbs. of nitrogen to the acre ; without 
tubercles 76 lbs. of nitrogen to the acre. How many 
pounds' increase in nitrogen was there when the tubercles 
were present ? 

19. Cow-peas with tubercles on their roots yielded 
139 lbs. of nitrogen and without tubercles 118 lbs. to the 
acre. What was the gain when tubercles were present ? 

20. A good clay soil contains 12,760 lbs. of potash, 
a good sandy soil 4840 lbs. of potash, to the acre, in a 
layer one foot deep. How much more potash is there in 
clay soil than in sandy soil per acre one foot deep ? 

HEIGHTS OF MOUNTAINS 

The heights of some of the highest mountains are : Mt. 
Aconcagua 28,082 ft., Mt. Blanc 15,744 ft., Mt. Everest 
29,002 ft., Mt. McKinley 20,464 ft., Mt. Mitchell 6711 ft. 

21. Mt. Mitchell is the highest mountain in the eastern 
United States. How much higher is Mt. McKinley than 
Mt. Mitchell ? 

22. Mt. Aconcagua is the highest mountain in the 
Americas. How much higher is Mt. Everest than Mt. 
Aconcagua ? 

23. Mt. Blanc is the highest mountain in the Alps. 
How much higher is Mt. Everest than Mt. Blanc ? 

24. How much higher is Mt. Aconcagua than Mt. 
McKinley ? 

25. The greatest known depth of the ocean is 27,930 ft. 
How many feet less is this than the height of Mt. Everest ? 



MULTIPLICATION 

42. If a blackbird destroys 3 cabbage worms in 1 hr., 
at tlie same rate how many cabbage worms will it destroy 
333333 in 2 hrs.? In 3 hrs.? In 4 hrs.? 
3 3 3 3 3 3 In 5 hrs.? In 6 hrs.? In 7 hrs. ? 
3 3 3 3 3 
3 3 3 8 
3 3 3 
3 3 
3 



6 9 12 15 18 21 



When several equal numbers are to be added, it is much 
shorter to obtain the result by the process known as Mul- 
tiplication. To multiply, however, we must learn the 
sums of the most common numbers added to themselves 
definite numbers of times. Thus in the problem above 
we see that 3 taken 2 times gives 6, taken 3 times gives 
9, etc. 

43. The number to be repeated is called the Multipli- 
cand. 

44. The number which indicates how many times the 
multiplicand is to be repeated is called the Multiplier. 

45. The result obtained by multiplying one number b}?- 
another is called the Product. 

46. The sign of multiplication is an inclined cross X . 
When placed between two numbers it is read " times," or 

41 



42 PRACTICAL ARITHMETIC 

"multiplied by." When the multiplier precedes the mul- 
tiplicand with the multiplication sign x between them, 
the sign is read " times " ; when the multiplicand pre- 
cedes, the sign is read "multiplied by," e.g., 3 x 8 = 24, is 
read 3 times 8 equals 24, or, regarding 8 as the multiplier, 
the expression is read, 3 multiplied by 8 equals 24. 

47. A number that is applied to any particular object 
is called a Concrete number, e.g., 1 bird, 3 caterpillars, 
48 hrs. 

48. A number that is iiot applied to a particular object 
is an Abstract number, e.g., 1, 3, 48. 

49. In multiplication the multiplier is always an ab- 
stract number. 

50. The most useful products are shown in the follow- 
ing tables. They should be committed to memory. 



1x1= 1 


1x2= 2 


1x3= 3 


2x1= 2 


2x2= 4 


2x3= 6 


3x1= 3 


3x2= 6 


3x3= 9 


4x1= 4 


4x2= 8 


4x3 = 12 


5x1= 5 


5x2 = 10 


5 X 3 = 15 


6x1= 6 


6x2 = 12 


6x3 = 18 


7x1= 7 


7 X 2 = 14 


7 X 3 = 21 


8x1= 8 


8x2 = 16 


8 X 3 = 24 


9x1= 9 


9x2 = 18 


9 X 3 = 27 


10 X 1 = 10 


10x2 = 20 


10 X 3 = 30 


1x4= 4 


1x5= 5 


1x6= 6 


2x4= 8 


2x5 = 10 


2x6 = 12 


3 X 4 = 12 


3x5 = 15 


3 X 6 = 18 


4x4 = 16 


4 X 5 = 20 


4 X 6 = 24 



MULTIPLICATION 43 



5x4 = 20 


5 X 5 = 25 


5x6 = 30 


6 X 4 = 24 


6 X 5 = 30 


6x6 = 36 


7x4=28 


7 X 5 = 35 


7 X 6 = 42 


8x4 = 32 


8 X 5 = 40 


8 X 6 = 48 


9 X 4 = 36 


9 X 5 = 45 


9 X 6 = 54 


10 X 4 = 40 


10 X 5 = 50 


10x6 = 60 


1x7= 7 


1x8=8 


1x9= 9 


2 X 7 = 14 


2 X 8 = 16 


2x9 = 18 


3 X 7 = 21 


3 X 8 = 24 


3x9=27 


4x7 = 28 


4 X 8 = 32 


4 X 9 = 36 


5 X 7 = 35 


5 X 8 = 40 


5 X 9 = 45 


6x7 = 42 


6 X 8 = 48 


6 X 9 = 54 


7 X 7 = 49 


7 X 8 = 56 


7x9 = 63 


8 X 7 = 56 


8 X 8 = 64 


8 X 9 = 72 


9 X 7 = 63 


9x8 = 72 


9 X 9 = 81 


10 X 7 = 70 


10 X 8 = 80 


10 X 9 = 90 


1x10= 10 


1x11= 11 


1x12= 12 


2x10= 20 


2x11= 22 


2x12= 24 


3x10= 30 


3x11= 33 


3x12= 36 


4x10= 40 


4x11= 44 


4x12= 48 


5x10= 50 


5x11= 55 


5x12= 60 


6x10= 60 


6x11= 6Q 


6x12= 72 


7x10= 70 


7x11= 77 


7x12= 84 


8x10= 80 


8x11= 88 


8x12= 96 


9x10= 90 


9x11= 99 


9x12 = 108 


10 X 10 = 100 


10x11 = 110 


10 X 12 = 120 



EXERCISE 24. — ORAL 

1. If it costs f 6 to spray 1 acre of potatoes, how much 



will it cost to spray 8 acres ? 



44 PRACTICAL ARITHMETIC 

2. If it costs f 3 to harvest an acre of corn, how much 
will it cost to harvest 7 acres ? 

3. If 1 acre of corn produces 9 tons of silage, how 
many tons will 6 acres produce ? 

4. If it costs 4 cents an acre to treat seed oats to pre- 
vent oat smut, what will it cost to treat the seed for 8 
acres ? 

5. If an acre of unfertilized land with unselected seed 
will produce 1 bale of cotton, how many bales will 9 acres 
produce ? 

6. If 1 acre of fertilized land with very carefully se- 
lected seed will produce 2 bales of cotton, how many bales 
will 9 acres produce ? 

7. At §50 a bale, what will be the value of the cotton 
in problem 5 ? 

8. At $50 a bale, what will be the value of the cotton 
in problem 6 ? 

9. A square field is 12 rods on a side. What is the 
distance around the field, or the perimeter? 

10. If it takes 7 lbs. of ordinary seed corn to plant an 
acre, how many pounds will it take to plant 8 A. ? 

11. What is the cost of 6 tons of coal at i 8 a ton ? 

12. If the school day is 5 hours long, how many school 
hours are there in a school week ? 

13. If a child sleeps 10 hours each night, how many 
hours does it sleep in 1 week ? 

14. If 10 hours are spent in sleep and 5 hours in school 
in each day of 24 hours, how many hours in a school week 
are left for play? 



MULTIPLICATION 45 

15. There are 12 inches in 1 foot. How many inches 
are there in 3 feet ? What name is given to a measure 3 
feet long ? 

16. If a man walks 3 miles an hour, how far will he go 
in 9 hours ? 

17. If a horse travels 6 miles an hour, how far will he 
go in 9 hours ? 

18. If a steamboat goes 9 miles an hour, how far will 
it go in 9 hours ? 

19. If a man on a bicycle rides 12 miles an hour, how 
far will he go in 9 hours ? 

20. If a freight train averages 15 miles an hour, how 
far will it go in 9 hours ? 

21. If an ocean liner goes 17 miles an hour, how far 
will it go in 9 hours ? 

22. If an automobile travels 20 miles an hour, how far 
will it go in 9 hours ? 

23. If an express train averages 35 miles an hour, how 
far will it go in 9 hours ? 

24. To properly cook a ham it should be kept at sim- 
mering heat 30 minutes for every pound of weight after 
first being plunged into boiling water and kept boiling for 
10 minutes. How long will it take to cook a 9-lb. ham ? 

25. With spool cotton at 6 cents a spool or 50 cents a 
dozfen, how many cents are gained by buying by the dozen 
rather than by the spool on a purchase of 5 dozen spools ? 

51. Find the product of 856 x 4. 

Write the multiplier 4 under the multiplicand 856, placing 
the units of the multiplier under units of the multiplicand, and 
begin at the right to multiply. 



46 PRACTICAL ARITHMETIC 

r^i-n 4 X 6 = 24. The 4 is written in units' column. The 
2 tens are to be added to the product of tens. 4x5 
tens = 20 tens. 20 tens plus the 2 tens, carried 



*'*-^* from the multiplication of units, gives 22 tens, or 2 
hundreds and 2 tens. 2 tens is written under tens' column and 
2 hundreds are to be added to hundreds' product. 4x8 
hundreds = 32 hundreds, which with 2 hundreds makes .34 
hundreds. 34 hundreds is written under hundreds' column. 
The product is 3424. 

EXERCISE 25. — WRITTEN 

Find the product of : 

1. 2 X 365. 18. 3 X 1845. 35. T x 37,863. 

2. 4 X 197. 19. 5 X 7543. 36. 6 x 31,245. 

3. 3 X 754. 20. 6 X 1896. 37. 8 x 43,036. 

4. 5 X 863. 21. 4 X 9806. 38. 5 x 68,734. 

5. 7 X 189. 22. 3 X 5431. 39. 2 x 81,896. 

6. 6 X 275. 23. 2 X 9864. 40. 8 x 52,783. 

7. 4x986. 24. 4x1896. 41. 9x28,357. 

8. 5 X 184. 25. 5 X 8652. 42. 7 x 48,021. 

9. 7 X 689. 26. 8 X 6541. 43. 8 x 52,163. 

10. 8 X 173. 27. 9 X 1864. 44. 4 x 59,136. 

11. 9 X 602. 28. 8 x 8250. 45. 2 x 24,386. 

12. 3 X 456. 29. 9 X 3475. 46. 9 x 12,854. 

13. 6x629. 30. 4x8364. 47. 7x47,829. 

14. 8 X 371. 31. 6 X 7928. 48. 9 x 79,836. 

15. 7x864. 32. 3x6471. 49. 8x64,281. 

16. 9 X 298. 33. 7 X 5498. so. 3 x 97,645. 

17. 3x672. 34. 9x3762. 51. 6x58,792. 



MULTIPLICATION 47 

52. What effect does it have upon a number to move it 
one place to the left in the period? 

Moving a figure one place to the left has the same effect 
as multiplying it by 10, e.g., 84 x 10 = 840. 

To multiply by 10, place a cipher at the right of the 
multiplicand, thus moving each figure one place to the 
left and increasing its value 10 times. To multiply by 
100, place two ciphers at the right of the multiplicand. 
To multiply by 1000, place three ciphers at the right of the 
multiplicand. 

EXERCISE 26.— WRITTEN 

1. Multiply 42 by 10, by 100, by 1000. 

2. Multiply 24 by 10, by 100, by 1000. 

3. Multiply 93 by 10, by 100, by 1000. 

4. Multiply 930 by 10, by 100, by 1000, by 10,000. 

5. Multiply 860 by 10, by 100, by 1000, by 10,000. 

53. Find the product of 842 x 40. 

Q J o The product is found by multiplying the multi- 

.f. plicand by 4 of the multiplier as if it stood alone 
and increasing the product ten times by placing a 
cipher at the right. 



33680 



EXERCISE 27. — WRITTEN 

1. Multiply 35 by 40, by 400, by 4000, by 400,000. 

2. Multiply 350 by 40, by 400, by 4000, by 400,000. 

3. Multiply 3500 by 3, by 30, by 300, by 3000, by 
30,000. 

4. Multiply 3500 by 6, by 60, by 600, by 6000, by 
60,000. 



48 PRACTICAL ARITHMETIC 

54. Rule for multiplying when either multiplier or 
multiplicand ends in ciphers. Multiply the multiplicand 
by the multiplier without regard to the ciphers, and annex 
as many ciphers at the right of the product as are found 
at the right of the multiplier and multiplicand. 

55. Multiply 4280 by 200. 

4280 Multiply as if the problem read 428 X 2, secur- 

n/^^ ing the product 856. In thus omitting the 



856000 



ciphers the multiplicand is decreased tenfold 



and the multiplier one hundred fold, and the 
product is therefore decreased 10 X 100 or 1000 fold. The 
product then is 1000 x 856 or 856,000. 

EXERCISE 28. — "WRITTEN 

Multiply : 

1. 876,420 by 3600. 7. 690,000 by 36,420. 

2. 960 by 4600. 8. 86,290 by 720. 

3. 87,640 by 300. 9. 370 by 6700. 

4. 79,842 by 34,000. lo. 296,380 by 3000. 

5. 88,967 by 360. li. 28,460 by 7200. 

6. 37,900 by 67,000. 12. 67,981 by 37,100. 

56. Find the product of 627 x 5864. 

To find the product of 5864 multiplied by 627 we must 
think of 627 as 6 hundreds plus 2 tens plus 7 units, or 
600 + 20 + 7. Multiplying 5864 by each of these numbers 
separately as in a, h, and c, we obtain the three partial products 
41,048, 117,280, and 3,618,400. The sum of these products is 
3,676,728. This method of securing the partial products by 
separate multiplications is needlessly long. Since we know 
that in multiplying by a number having ciphers at the right 





MULTIPLICATION 


a. 5864 


I. 5864 d. 5864 


600 


20 627 



3518400 

, 5864 

7 

41048 



117280 



41048 
11728 
35184 
3676728 



49 

we may disregard 
the ciphers, we may 
here write the par- 
tial products directly 
under each other as 
in the second opera- 
tion shown at d. 



The products obtained by the separate multiplications 
are called Partial Products. 



Multiply : 



EXERCISE 29.— WEITTEN 



1. 


842 by 56. 


9. 


3063 by 538. 


2. 


517 by 75. 


10. 


3769 by 645. 


3. 


829 by 88. 


11. 


8035 by 928. 


4. 


562 by 94. 


12. 


2380 by 763. 


5. 


755 by 48. 


13. 


4938 by 529. 


6. 


946 by 67. 


14. 


9123 by 372. 


7. 


258 by 99. 


15. 


5073 by 418. 


8. 


657 by 46. 


16. 


6392 by 239. 



57 



Find the product of 6004 x 1281. 

1281 

6004 Since the products corresponding to the zeros 



5124 in the multiplier will be zeros, they need not be 
7686 written in the partial products. 

7691124 

EXERCISE 30. — WRITTEN 



Multiply : 




1. 8375 by 206. 


3. 2684 by 702. 


2. 8295 by 2006. 


4. 9367 by 9006. 



60 PRACTICAL ARITHMETIC 

5. 2473 by 906. 9. 7876 by 903. 

6. 2482 by 7002. lO. 8345 by 9008. 

7. 2954 by 906. ii. 5878 by 809. 

8. 4375 by 603. 12. 7854 by 508. 

58. Rule for Multiplication. — Write the multiplier 
under the multiplicand, units under units, tens under 
tens, etc; Multiply the multiplicand by each figure of 
the multiplier. Place the right-hand figure of each par- 
tial product under the figure of the multiplier used to 
obtain it. Add the partial products. 

Since regarding either number as multiplier or multi- 
plicand does not affect the product, in practice the smaller 
is used as the multiplier. 

EXERCISE 31. —WRITTEN 

Multiply : 

1. 7564 by 73. 14. 8957 by 79. 27. 3264 by 287. 

2. 8715 by 86. is. 6428 by 64. 28. 8163 by 799. 

3. 4781 by 86. 16. 6753 by 97. 29. 2345 by 986. 

4. 3692 by 90. 17. 8429 by 68. 30. 9543 by 576. 

5. 5878 by 46. 18. 8867 by 29. 31. 7432 by 438. 

6. 4689 by 76. 19. 8456 by 25. 32. 6473 by 823. 

7. 5873 by 256. 20. 6397 by 86. 33. 9761 by 82. 

8. 6381 by 634. 21. 9876 by 38. 34. 8472 by S4. 

9. 9537 by 752. 22. 2785 by 89. 35. 9781 by 73. 

10. 2175 by 396. 23. 5432 by 92. 36. 9999 by 99. 

11. 7009 by 438. 24. 7654 by 47. 37. 8756 by 65. 

12. 8254 by 576. 25. 8765 by 59. 38. 9522 by 76. 

13. 7826 by 86. 26. 3528 by 463. 39. 7543 by 57. 



MULTIPLICATION 



51 



The pupil may use the following problems sufficiently 
to gain skill in multiplying. 

40-55. Multiply the number at small a in the diagram 
by each number in the larger circle. 

• 56—295. Multiply each of the other numbers in the 
smaller circle by each number in the larger circle. 

Note. The teacher may assign these problems by chance by making 
similar circles, pasting them upon pasteboard, and mounting the smaller 
one upon a pin so that it may revolve freely. 





^-^--^P 




~A ■ 


>v 








\ 




:/ 


1 

i 






ry 


Ny/O \ 

/r\%v 


a 


7> 


< 


^ 


\ 


^ SSifS 


y^^^oX \ 


/ 


/> 


>i 


48i46S 


\ 




'm fi'is'^^M 


1/' 


-^-^824 ^ 








1 >^ 

>7#/ 


^ 




^58738 


1 


X^^"^ 




Ji 




\ 


s 


1 


\k / 

\j 


/ Co 

/ ^ 




-3 \ 




y 





MULTIPLICATION OF UNITED STATES 
MONEY 

59. Multiply 195.35 by 25. 

195.35 

25 Multiply as in integral numbers, and point off 

47675 in the product as many places for cents as there 
19070 ^re places for cents in the multiplicand. 



12383.75 

EXERCISE 32. — WRITTEN 

Find the product of : 

1. 2. 3. 4. 

165.83 189.57 148.75 $46.98 
9 8 28 35 

5. 6. 7. 8. 

1640.25 $542.40 $864.19 $506.69 

.89 127 .95 1588 



Multiply : 

9. $43.95 by 875. • 14. $675.30 by 981. 

10. $640.50 by 846. is. $1250.25 by 806. 

11. $981.23 by 852. is. $3540.-30 by 905. 

12. $300.20 by 945. 17. $2859.65 by 79. 

13. $756.25 by 372. is. $875.90 by 350. 

52 



MULTIPLICATION 53 

EXBBOISE 33. — WRITTEN 

1. Since each State is represented in Congress by 2 
senators, how many senators are there in Congress ? 

2. A mechanic earns $2.75 a day. What will be his 
wages for a week ? For a month of 26 days ? 

3. A man earns $3.50 a day. What will be his wages 
for a week ? For 26 days ? 

4. If a hunter's coat and shoes cost him 16.50 each 
and his gun costs 4 times as much as his coat, what is 
the cost of his outfit ? 

5. If it requires 23 yards of carpet for a floor, what 
will be the cost at 11.25 a yard ? 

6. What will be the cost of 18 cords of wood at f 3.25 
a cord ? 

7. What will be the cost of 3 barrels of sugar weigh- 
ing 284 lbs. each at 6 cts. a pound ? 

8. How many feet of picture moulding will be required 
for a room 12 ft. long, 15 ft. wide ? 

9. What will moulding cost for the above room if two 
sizes are used, one at ceiling at 2 cts. a foot and a plate 
rail at 7 cts. a foot ? 

10. A storm moving eastward across the United States, 
travelling at the rate of 36 miles an hour, moves how far 
in 3 days ? 

11. If 1 cow drinks 73 lbs. of water daily, how many 
pounds of water will 16 cows drink ? 28 cows ? 69 cows ? 

12. If it costs 18.13 for labor and $7.39 for material 
for each acre, to spray a vineyard 6 times, what will it 
cost to spray 7 acres 6 times ? 



54 PRACTICAL ARITHMETIC 

13. If 100 gallons of Bordeaux mixture are sprayed upon 
a melon field to prevent blight, and to make this mixture 
6 lbs. of blue stone, at 7 cts. a pound, and 12 lbs. of lime, 
at 1 ct. a pound, are used, and the cost of labor is 33 cts., 
what will 1 spraying cost ? What will 6 sprayings cost ? 

14. If unsprayed melons all die, and sprayed melons 
yield 150 baskets to the acre, at 76 cts. a basket, what 
is the gain by sprajdng 8 acres of melons? 

15. If unsprayed grape-vines yield 1 lb. for each vine, 
arid sprayed vines yield 4 lbs. each, what is the gain by 
spraying an acre which yields 376 lbs. when not sprayed? 

16. If spraying potatoes 5 times increases the yield 
68 bushels per acre, and spraying 3 times increases the 
yield 32 bushels, what is the increase from the last 2 
sprayings? With potatoes at 65 cts. a bushel, what are 
the 2 extra sprayings worth to the farmer? 

17. If the best selected potato seed yields an average 
of 11,100 lbs. per acre and poor seed yields 8034 lbs. per 
acre, how much more will 9 acres yield when planted 
with good seed than with poor seed? 

18. If a dairy cow eats 40 lbs. of silage each day, how 
many pounds of silage will it take to feed 17 cows 180 
days? 

19. One field of wheat of 9 acres yields 22 bushels per 
acre, and another of the same size, due to better prepara- 
tion, yields 31 bushels an acre. What is the difference in 
the value of the wheat produced on the two fields when 
wheat is worth 87 cts. per bushel? 

20. One seven-acre field of cotton produces 215 lbs. of 
lint cotton and 430 lbs. of seed on each acre, while 



MULTIPLICATION 55 

another field of the same size produces 500 lbs. of lint and 
1000 lbs. of seed per acre. What is the difference in the 
value of the crop from the two fields when cotton is worth 
11 cts. a pound and seed 1 ct. a pound? 

21. If an unclean sample of clover seed contains 990 
weed seeds in each pound, how many weed seeds are 
there in each bushel weighing 60 lbs. ? 

22. A sample of unclean clover seed was found to con- 
tain 27,600 weed seeds in each pound. If 15 lbs. were 
sowed to an acre, how many weed seeds were planted on 
each acre? 

23. A sample of clover seed offered for sale contained 
338,300 weed seeds in each pound. How many weed 
seeds were there in each bushel of 60 lbs.? 

24. What is the value of an acre of celery yielding 
1500 dozen stalks at 26 cts. a dozen? If the annual grow- 
ing expense is $* 259, what is the profit per acre ? 

25. There are 21,780 cubic feet in the upper 6 inches 
of an acre of soil. If this soil weighs 79 lbs. per cubic 
foot, how much will the upper 6 inches of soil on an acre 
weigh ? 

26. A man bought a car-load of cattle, 25 in number, 
each animal weighing 961 lb., at 4 cts. a pound. After 
each had gained 889 lbs. in weight, they were sold for 
6 cts. a pound. What was his profit or loss if the feed 
consumed was worth $977, and the cost of labor to do the 
feeding 1125? 

27. A man bought 1728 acres of land at 167 an acre. 
He spent $3600 on improvements and then sold 79 acres at 



56 PRACTICAL ARITHMETIC 

$170 an acre, 160 acres at $165 an acre', 215 acres at 
$148 an acre, 450 acres at $132.18 an acre, and the rest 
at $45 an acre. How much did he gain or lose ? 

28. A common house-fly lays her eggs in broods of 
about 120 each. At this rate, how many flies may be 
expected from 29 overwintering flies during the first 
warm days of spring ? 

29. Mosquitoes lay eggs in masses of about 350 each. 
How many mosquitoes may be expected at the end of 
the hatching period from 9 such masses ? 

30. The white ant often lays as many as 80,000 eggs 
in a day. How many eggs may be expected from 30 lay- 
ing ants at tlie end of 4 days' laying ? 

31. A man in each of his working months earns $67.50 
and spends $28.37. What are his savings yearly, allow- 
ing one month of vacation during which he spends $56.97 
more than usual ? 

32. A man bought 39 strips of carpet, each 17 yards 
long, at 86 cts. a yard. What did they cost ? 

33. A teamster hauling 4 loads of sand a day, of 27 
cubic feet to the load, hauls how many cubic feet in 12 
days? 

34. Five boys purchase a camp outfit at the following 
prices: a 9-ft. tent for $5.80, two hammocks at 55 cts. 
each, five bathing suits at 55 cts. each, 1 clothes bag at 
60 cts., 1 junior camp stove at $1.74, one boat at $19, 
2 pairs of oars at $1 a pair, 4 fishing outfits at $1.89 
each. What was the cost of the outfit? Two boys paid 
toward the outfit $12.22. What was left for the other 
three to pay ? 



DIVISION 

60. If 3 gallons of milk yield 18 ounces of butter, how 
many ounces will 1 gallon yield? 

To solve this problem we must think of 18 ounces as 
separated into 3 equal parts. Separating 18 ounces into 
3 equal parts will give 6 ounces in each part. 

61. The process of separating a number into equal parts 
is called Division. 

62. The number to be divided, or the number to be 
separated into equal parts, is called the Dividend. 

63. The number that indicates into how many equal 
parts the dividend is to be separated, or the number by 
which the dividend is to be divided, is called the Divisor. 

64. The result obtained by Division is called the 
Quotient. 

To find the number of ounces of butter contained in 1 
gallon of milk we divided 18 ounces by 3 (not by 3 gal- 
lons) which gave 6 ounces. Three, the divisor in this 
problem, is an abstract number, and the term 3 gallons 
serves only to indicate the number of groups into which 
18 ounces is to be separated. 

65. When the dividend is concrete and the divisor is 
abstract, the quotient is like the dividend, e.g., 18 oz. -f- 3 

= 6 oz. 

57 



58 PRACTICAL ARITHMETIC 

66. When the dividend and divisor are concrete, they 
must be alike and the quotient will be abstract, e.g.^ 
18 oz. -=- 6 oz. = 3. 

67. Division is indicated by the sign, -^, or by writing 
the dividend above the divisor with a line between, thus 
18 -=- 3 = 6, or JgS. = 6, is read, 18 divided by 3 equals 6. 

68. When the division is not exact, the part of the 
dividend remaining is called the Remainder, e.g., 15 -r- 2 = 
7, with 1 as a remainder. 

69. When two or more numbers are multiplied together 
to produce a product, e.g., 3 x 6 = 18, the numbers so 
multiplied are called the Factors of the product. 

70. In the problem 18 -h 3, observe that we have the 
product 18 and one factor 3, to find the other factor. We 
may therefore think of division as the process of finding 
one factor when the product and the other factor are 
given. 

EXERCISE 34. — ORAL 

Find the quotients of tlie following and prove the divi- 
sion correct by multiplying the factors together : 



1. 


4-2 = 


because 


2x 


= 4. 


2. 


6-3 = 


because 


3x 


= 6. 


3. 


8h-4 = 


because 


4x 


= 8. 


4. 


18 -=-9 = 


because 


9x 


= 18. 


5. 


24 -=-6 = 


because 


6x 


= 24. 


6. 


42-7 = 


because 


7x 


= 42. 


7. 


40 -=-8 = 


because 


8x 


= 40. 


8. 


72^6 = 


because 


6x 


= 72. 





DIVISION 




9. 72^9 = 


because 9 x 


= 72, 


10. 63 -f- 7 = 


because 7 x 


= 63. 



59 



EXERCISE 35. — ORAL 

1. The year contains 4 seasons. How many months 
in each season ? 

2. Alfred the Great divided the day into 3 equal 
periods, for sleep, work, and recreation. How many 
hours were there in each period ? 

3. If f 1 is changed to ten-cent pieces, how many are 
there ? 

4. If $1 is changed to five-cent pieces, how many are 
there ? 

5. If f 1 is changed to twenty -five-cent pieces, how 
many are there? 

6. If fl is changed to twenty-five-cent, ten-cent, and 
five-cent pieces, in how many ways can the change be 
made? 

7. With lettuce plants set 11 in. apart, how many will 
be required for 1 row in a cold frame 88 in. long ? 

8. The rows are 10 in. apart. How many rows are 
there in a cold frame 60 in. wide ? 

9. In a fruit garden 165 ft. long, how many peach 
trees will be required to set a row, placing them 15 ft. 
apart ? 

10. How many rows can be set in a garden 90 ft. wide ? 

11. An English shilling equals nearly 25 cts. in our 
money? How many shillings in $1.50? 



60 PRACTICAL ARITHMETIC 

12. A French franc equals about 20 cts. in our money. 
How many francs in $3.00? 

13. A German mark equals about 24 cts. in our money. 
How many marks in |2.88? 

14. An Italian lira equals about 20 cts. in our money. 
How many lire in $5.60? 

15. A Dutch florin equals about 40 cts. in our money. 
How many florins in $3.60? 

16. An Austrian florin equals about 36 cts. in our 
money. How many florins in $1.80? 

17. At $ 72 a dozen for suits for sixteen-year-old boys, 
what is the cost of each suit? 

18. There are 7 days in 1 week; how many week's in 
28 days ? in 42 days ? in 98 days ? 

19. If a man earns $ 8 while a boy earns $ 3, how much 
will the boy earn while the man earns $48? 

20. If an adult man eats 360 grams of carbohydrates, 
120 grams of protein, and 60 grams of fats each day, how 
much does he average per meal ? 

21. If a laboring man eats 150 grams of protein, 99 
grams of fats, and 516 grams of carbohydrates each day, 
what is the average per meal ? 

22. If a man can do as much work as 3 boys, and it 
requires 48 boys 3 days to build a fence, how long will it 
require 8 men to build it ? 

23. If a man can hoe twice as much as a l)oy, and 4 
boys and 3 men hoe a field of 5 acres in a day, what 
amount does each hoe ? 



SHORT DIVISION 

71. When the divisor is so small that the work can be 
performed mentally, the process is called Short Division. 

72. Divide 9672 by 4. 

4)9672 The divisor is written at the left of the dividend 

2418 with a curved line between them and a line under- 
neath the dividend. To divide 9672 by 4, begin at 
the left and find how many times the divisor, 4, is contained 
in the first figure of the dividend. 4 is contained in 9 two 
times, with a remainder 1. Reduce the 1 to the next lower 
order, making 10, which with 6 makes 16 ; 4 is contained in 16 
four times. 4 is contained in 7 one time, with a remainder 
3. This remainder reduced to the next lower order makes 30, 
which with 2, the next figure of the dividend, makes 32 ; 4 is 
contained in 32 eight times. The quotient, therefore, is 2418. 

73. Divide 3651 by 7. 

7)3651 7 is not contained in the first 

521 with 4 remainder, figure of the dividend, 3, so the 
commonly written 4. 3 must be reduced to the next 

lower order, making 30, which 
with 6 makes 36. 7 is contained in 36 five times, with 1 re- 
mainder. Reduce 1 to next lower order, making 10, which 
with 5 makes 15. 7 is contained in 15 two times and 1 remain- 
der. 1 is reduced to next lower order, making 10, which with 
1 makes 11. 7 is contained in 11 one time, with 4 as remain- 
der. This final remainder is indicated with the quotient. 
The quotient, therefore, is 621, with 4 remainder. 

61 



62 



PRACTICAL ARITHMETIC 



Find the 

1. 376- 

2. 695- 

3. 459- 

4. 376 

5. 714 

6. 628 

7. 984-- 

8. 594- 

9. 4895 

10. 9656 

11. 7985 

12. 7983 

13. 8457 

14. 2708 



EXERCISE 36. — WRITTEN 

quotient of : 

h2. 15. 8736 -T- 7. 29. 56,216^-12. 

16. 7086^6. 30. 83,542 -f- 15. 

17. 8232-4. 31. 64,902-11. 

18. 8361^9. 32. 85,563 -=-14. 

19. 5643 -^ 8. 33. 37,642 -^ 12. 

20. 3716-^7. 34. 48,527-^-15. 

21. 5472^6. 35. 87,585-9. 

22. 7483 -f- 5. 36. 96,464 -=-22. 

23. 8721 -f- 7. 37. 83,691 -r- 12. 

24. 9212^9. 38. 77,585^11. 

25. 73,236-4-11. 39. 23,075-14. 

26. 24,631-4-12. 40. 89,576 -V- 11. 

27. 75,477^12. 41. 98,254-15. 

28. 36,286^21. 42. 61,082-4-21. 



4-5. 
4-9. 
4-5. 
4-4. 

4-7. 
4-8. 
4-7. 

-=-6 



^9 



6 



74. How many tens in 20? How many hundreds in 
200? How many thousands in 2000? 

To divide by 10, 100, 1000, etc., set off as many figures 
at the right of the dividend as there are ciphers in the 
divisor. The figures thus set off are the remainder. 
The other figures are the quotient, e.g., 45 -^ 10 = 4, with 5 
as remainder. 468 -4- 100 = 4, with 68 as a remainder. 



EXERCISE 37. -.ORAL 



1. 57,683 -=- 100. 

2. 76,493-4-100. 



3. 38,425^100. 

4. 54,580-100. 



DIVISION 63 

5. 42,676^-1000. 8. 57,826 -- 10,000. 

6. 26,257^1000. 9. 32,814-10,000. 

7. 14,637^1000. 10. 82,740^-10,000. 
75. Divide 4560 by 200. 

200 )4560 Cut off ciphers at the right of the 200, also 

221-^ two figures at the right of the dividend. Divid- 
ing 45 by 2 gives 22, with 1 remainder. The 
1, whicli represents 100, added to the 6, wliich represents 60, 
gives 160 remainder. 

When the divisor ends in one or more ciphers, cut these 
off, and also cut off an equal number of figures from the 
right of the dividend. Then divide by the figures re- 
maining. Place the figures cut off from the dividend 
at the right of the remainder, if there is a remainder, to 
form the true remainder. 

EXERCISE 38. — WRITTEN 

Find the quotient of : 



1. 


376^ 


-20. 


12. 


7534^ 


-300. 


2. 


285^ 


-50. 


13. 


35,456 -r 


-500. 


3. 


653^ 


-60. 


14. 


96,464 -f 


-800. 


4. 


981^ 


-40. 


15. 


58,775^ 


-700. 


5. 


9212- 


-80. 


16. 


28,976 -i 


-600. 


6. 


9064^ 


-70. 


17. 


92,123^ 


-400. 


7. 


887-^ 


-60. 


18. 


82,601 ^ 


-700. 


8. 


954- 


-50. 


19. 


42,563 ^ 


-800. 


9. 


3730- 


-90. 


20. 


30,600 -= 


-300. 


10. 


3645 -= 


-200. 


21. 


67,332 - 


-200. 


11. 


4328-= 


-300. 


22. 


85,563 H 


-400, 



LONG DIVISION 

76. Long division is the same as short division, with the 
exception that all the processes are written in full. The 
quotient is written over the dividend, the first figure of 
the quotient being written over the right-hand figure of 
the dividend used in obtaining it. 

77. Divide 32,962 by 49. 

It will be found helpful in the beginning tabi.e ^p Peoditots 

of the study of long division to form a table 1 Xt;9 = 49 

of products of the divisor with numbers from 2 x 49= 98 

1 to 9. The problem is arranged as in short 3 x 49 = 147 

division, with the exception that the quotient 4. v 49 = 196 

is written either above (or at the right of) . aq^qa^ 

the dividend. Since 49 is not contained in ~ 

32, we must use the first three figures of the o X "iJ = -94 

dividend, 329, for the first partial dividend. By 7 X 49 = 343 

consulting the table of products, we find that 8 x 49 = 392 

294 is the largest of the products that does 9 x 49= 441 
not exceed the partial dividend, 329. 

294 is the product of 6 x 49 ; hence, 

49 is contained in 329 six times. 6 is 



49)32962 written over the 9 of the dividend. 

^^^ The product of the 6 x 49, 294, is sub- 

'^^^ tracted from 329, v/hich leaves as a 

343 remainder 35. The next figure of the 

132 dividend, 6, is annexed to form the sec- 

98 ond partial dividend. 343 is the largest 

34 remainder, of the products that does not exceed 

this partial dividend, 366. 343 is the 

0,4 



DIVISION 65 

product of 7 X 49 ; hence, 49 is contained in 356 seven times. 
7 is written over the 6 of the dividend and 343, the product of 
7 X 49, is subtracted from 356, which leaves 13 remainder. 
The next figure of the quotient, 2, is annexed to form the third 
partial dividend, 132. 98 is the largest of the products that 
does not exceed this partial dividend, 132. 98 is the product 
of 2 X 49 ; hence, 49 is contained in 132 two times. 2 is writ- 
ten over 2 of the dividend and 98 is subtracted from 132, leav- 
ing 34 the final remainder. 

78. Divide 1,270,563 by 396. 

32081^-5- -'^fter some practice the quotient figures 
^^^ can be estimated without making the table 



-^ of products. The first partial dividend is 

il££_ 1270. 396 is contained in 1270 three times. 

'^-•^ 3x396 = 1188. 1188 subtracted from 1270 

'^^ leaves 82 remainder. Annexing 6 gives 

3363 the second partial dividend, 825. 396 is 

3168 contained in 825 two times. 2 x 396 = 792. 

195 792 subtracted from 825 leaves 33 re- 

mainder. Annexing 6 gives the third par- 
tial dividend, 336. 396 is not contained in 336, so a cipher is 
written over the 6 of the dividend and the next figure of the 
dividend, 3, is . annexed to 336 to form the next partial divi- 
dend, 3363. 396 is contained in 3363 eight times. 8 x 396 = 
3168. 3168 subtracted from 3363 gives 195, the final remainder. 

79. Rule for Long Division. 

I. Write the divisor at the left of the dividend with a 
curved line between them. For the first partial dividend 
take the fewest number of figures at the left of the divi- 
dend that will contain the divisor, and write the partial 
quotient over the right-hand figure of the partial dividend. 

II. Multiply the divisor, by this quotient, and write the 
product under the partial dividend used. 



66 PRACTICAL ARITHMETIC 

III. Subtract this product, and to the remainder annex 
the next figure of the dividend for the second partial 
dividend. 

IV. Divide as before, and continue the process until all 
the figures of the dividend have been used to make partial 
dividends. 

V. If there be a remainder, write it with the quotient. 
Proof. Find the product of the divisor and quotient, 

and to this product add the remainder, if any. If the 
work is correct, the result will equal the dividend. 





EXERCISE 39. 


— WB 


IITTBN 




Find the quotient of : 








1. 


5280-12. 


17. 


89,314 -; 


-86. 


2. 


1728-^12. 


18. 


54,963 ^ 


-863. 


3. 


1607 -f- 19. 


19. 


33,765 - 


-542. 


4. 


5347 - 21. 


20. 


84,568 -i 


-827. 


5. 


3987 ^ 94. 


21. 


74,938 ^ 


-357. 


6. 


6784-73. 


22. 


861,618^ 


-843. 


7. 


6548 - 89. 


23. 


98,125 -= 


-563. 


8. 


8789-65. 


24. 


84,629 - 


-189. 


9. 


5498 -=- 98. 


25. 


54,825 -J 


^254. 


10. 


3850 -^ 63. 


26. 


46,376 - 


-308. 


11. 


3987 -=- 91. 


27. 


879,384 H 


-508. 


12. 


4788-43. 


28. 


343,861 H 


-948. 


13. 


3402-81. 


29. 


324,924 - 


-357. 


14. 


6281^71. 


30. 


672,425 H 


-135. 


15. 


3485-873. 


31. 


861,254- 


h927. 


16. 


6842 - 78. 


32. 


938,764- 


h879. 



DIVISION 



67 





a 


6 


c 


1 


3762894 


42896 


329 


2 


3862847 


76298 


269 


3 


9683921 


42546 


873 


4 


1897892 


79832 


784 


5 


3984291 


62891 


672 


6 


8996823 


79684 


981 


7 


8672984 


62341 


679 


8 


6293478 


98641 


837 


9 


7986277 


82439 


568 


10 


1291382 


87897 


674 



The pupil should practise dividing sufficiently to become skilful. 

33-42. Divide the first number of column h by each 
number of column e. 

43-132. Divide each other number in column h by each 
number in column c. 

133-142. Divide the first number in column a by each 
number in column h. 

143-232. Divide each other number in column a by 
each number in column h. 



DIVISION OF UNITED STATES MONET 

80. Divide $741.32 by 86. 
$8.62 

oo^ijj l^l.oz Divide as in integral numbers, writing the 

688 first figure of the quotient over the right-hand 

533 figure of the first partial dividend. Place the 

516 decimal point in the quotient directly over the deci- 

JJ2 ™^ point in the dividend. 

172 

81. Divide $46.75 by $.25. 

187 
25)4675 

25 Change the dividend and divisor to cents which 

2^7 gives 4675 cents to be divided by 25 cents. The 
onA answer is 187. 

~175 

175 

BXEECISB 40. —WRITTEN 

Find the quotient of : 

1. $17.28^12. 6. $52.56^16. 

2. $17.28 ^$12. 7. $52.54 -$16. 

3. 17.28^.12. 8. $52.54 -.16. 

4. 856.90^41. 9. $438.90-21. 

5. 856.90 ^$41. 10. $438.90- $21. 

68 



DIVISION 69 

EXERCISE 41. — WRITTEN 

1. If 8 bushels of rye weigh 448 lbs., what is the 
weight of 1 bushel ? 

2. If 19 bushels of oats weigh 608 lbs., what is the 
weight of 1 bushel of oats ? 

3. If 27 bushels of wheat weigh 1620 lbs., what is the 
weight of a bushel of wheat ? 

4. If 32 bushels of corn weigh 1792 lbs., what is the 
weight of a bushel of corn ? 

5. If 37 bushels of peas Aveigh 2220 lbs., what is the 
weight of 1 bushel of peas ? 

6. How many boys' sweaters at 95 cts. can be bought 
for 16.65? 

7. A double plow harness costing $11.48 and a 
double carriage harness costing $45.92, how many plow 
harnesses can be had at the cost of 1 carriage harness ? 

8. If a beef animal weighs 960 lbs. at the beginning 
of the feeding period, and after being fed 162 days 
weighs 1284 lbs., how much did it gain a day ? 

9. If 40 lbs. of silage is the ration for a dairy cow, 
how many acres of corn will it take to produce silage for 
15 cows for 150 days, 1 acre of corn producing 18,000 lbs. 
of silage ? 

10. A base-ball outfit for the Asheboro High School 
Nine consists of the following articles : an American 
Association ball 70 cts., 9 Junior League bats at 25 cts. 
each, 1 catcher's mit fl.OO, 3 fielder's gloves at 55 cts., 
1 first-baseman's mit 90 cts., 4 infielder's gloves at 
30 cts., 1 amateur mask 50 cts., 9 pairs shoe plates 



70 PRACTICAL ARITHMETIC 

10 cts. per pair, catcher's breast protector fl.lO, 9 uni- 
forms at $1.25 each, 9 sweaters at $1.25 each. What 
part of the entire cost should each member pay ? 

11. The foot-ball eleven of Shelby ville Academy is 
equipped with the following articles : boy's Rugby foot- 
ball with bladder $1.50, inflater 15 cts., 11 jackets at 
60 cts. each, 11 pairs of pants at $1.00 eash, 9 pairs 
shin guards at 45 cts. per pair, 6 pairs shoulder pads at 
30 cts. per pair, 1 head harness at 75 cts. What part of 
the cost of the outfit' does each member pay ? 

12. The Asheboro High School Girls' Tennis Club 
ordered a tennis outfit as follows : 2 hardwood poles at 
75 cts. a pair, guy ropes and pins 23 cts. per set, court 
marker 95 cts., net $2.00, 2 back-stop nets $2.15 each. 
What will it cost to equip three courts ? What part will 
each member pay if the club is composed of 40 members ? 

13. The Croquet Club has 2 croquet sets at $2.50 a 
set. There are 16 members. What part of cost does 
each pay? 

14. If a man buys 1 ton of commercial fertilizer for $24 
and puts it on 4 acres, and another ton for $ 20 and puts 
it on 5 acres, how many additional pounds of cotton to 
the acre must he produce on the first field at 10 cts. a 
pound to pay for the greater cost of the fertilizer used 
thereon ? 

15. The following results for a period of 5 years' 
spraying Irish potatoes to prevent disease are recorded in 
New York : gain per acre due to spraying every 2 weeks, 
123, 118, 233, 119, 63 bushels; gain per acre due to 3 
sprayings, 98, 88, 191, 107, 32 bushels. What was the 



DIVISION 71 

average gain for the 5 years with 3 sprayings ? What was 
the average gain from spraying every 2 weeiis ? If potatoes 
average 57 cts. a bushel and spraying cost on an average 
77 cts. an acre each time, what was the average gain from 
spraying 3 times? 

16. If 5 gallons of spraying mixture be used to each 
tree in an apple orchard of 1000 trees and Paris green at 
20 cts. a pound be used, 1 lb. to 150 gals, of water, what 
would be the cost of the Paris green for 2 sprayings? 
What would it cost per tree? 

17. A pig weighing 50 lbs. cost 14. After eating 8 bus. 
of corn at 50 cts. a bushel and 400 lbs. of wheat middlings 
at 11 a hundred pounds, it weighs 250 lbs. At how much 
a pound must it be sold to make a net profit of f 3 ? 

18. What is the average of 79, 83, 160, 74, and 62? 

19. At three places in the Florida peninsula the num- 
ber of partly cloudy days in the year was 233, 145, 113, 
the number of cloudy days was 59, 74, 81. What was the 
average number of cloudy, partly cloud}', and clear days 
as shown by these observations? 

20. A man bought 782 acres of land for $98,762 and 
sold it at $18 an acre. Wliat was the average price paid? 
What was the average gain or loss per acre ? 

21. The deaths from consumption in the United States 
in 1900 were 111,059. W^hat was the average number of 
deaths for each day in the year (365 days) ? 

22. The deaths from typhoid fever in the United States 
for 1900 were 35,379. What was the average number 
daily ? 



CANCELLATION 

82. How many times is 3 x 6 contained in 12x6? 
How many times is 3 x 10 contained in 6 x 10? How 
many times is 6 x 7 contained in 12 x 7 ? 

83. Divide 24 x 12 by 6 x 12. 

24x12 = 288 6x12 = 72 288 h- 72 = 4. 

What factor is common to both dividend and divisor? 
If the factor 12 is struck out, or cancelled, from both divi- 
dend and divisor, does it affect the quotient? 

2iiil| = 24 or 24^6 = 4. 

6 X ;i;2 6 

Divide 5 x 27 x 4 by 18 x 2. 

3 3 Cancelling the common factor 2 from the 

5x^7x^ ^1- 4 of the dividend and the 2 of the divisor 

78x2 ~ '^' gives 2 in the dividend. Cancelling the 

2 common factor 9 from 18 gives 2; from 27 

gives 3. Cancel 2 from both divisor and 

dividend. Multiplying the remaining factors of the dividend 

gives the quotient, 15. 

84. Cancellation is the process of shortening work in 
division by removing or cancelling equal or common 
factors from the dividend and divisor. 

EXERCISE 42. — WRITTEN 

Solve by cancellation : 

1. Divide 7 x 6 x 16 by 6 x 8 x 7. 

72 



CANCELLATION 73 

2. Divide 11 x 27 x 30 by 9 x 15 x 3. 

3. Divide 15 x 48 x 70 x 11 x 40 by 30 x 16 x 7 x 22 x 50. 

4. Divide 84 x 18 x 5 by 91 x 4 x 15. 

5. Divide 27 x 12 x 35 x 14 by 9 x 3 x 5. 

6. Divide 48 x 35 x 42 x 54 by 12 x 7 x 6 x 9. 

7. Divide 63 x 36 x 48 x 96 x 27 by 81 x 9 x 12 x 48. 

8. Divide 420 x 68 x 88 x 22 by 210 x 11 x 44. 

9. Divide 42 x 35 x 56 x 4 x 12 by 28 x 49 x 14 x 10. 

10. Divide 17 x 9 x 12 x 11 x 28 by 34 x 6 x 72 x 6 x 22. 

11. Divide 24 x 15 x 8 x 4 x 7 by 14 x 8 x 6 x 4. 

12. Divide 20xl6x5x3x6by5x8x3xl0x6. 

13. 18 cows, each eating 4 lbs. of cotton-seed meal a 
day, can be fed how long on 360 lbs. of meal? 

14. 72 quarts of berries at 9 cts. a quart equal in value 
how many pounds of sugar at 6 cts. a pound? 

15. How long will it take a horse travelling 8 miles an 
hour to go as far as an express train goes in 3 hours at 
32 miles an hour ? 

16. If 42 bushels of wheat make 9 barrels of flour, how 
many bushels will it take to make 27 barrels? 

17. How many bushels of corn worth 49 cts. a bushel 
must be given in exchange for 63 bushels of oats worth 
35 cts. a bushel? 

18. How many bushels of oats worth 28 cts. a bushel 
must be grown on an acre to equal in value a crop of 56 
bushels of corn worth 42 cts. a bushel? 

19. A lumber mill cuts 60,000 ft. of lumber in 6 hours. 
How many feet will it cut in 3 days of 8 hours each ? 



74 PRACTICAL ARITHMETIC 

exercise 43. — "written 
Review Problems 

1. The population of Chicago in 1840 was 4470, in 
1870 it was 300,000, in 1900 it was 1,698,675. What was 
the yearly increase in population from 1840 to 1870? 
What was the yearly increase from 1870 to 1900 ? What 
was the daily increase ? 

2. The value of the hay crop raised in the United 
States for five years was as follows : 

What was the total value 
for five years ? What was the 
average value ? How much 
below the average was the 
value of the smallest crop ? 

3. The value of the corn exported from the United 
States for five years was as follows : 

1902 116,185,673. What was its total value? 

1903 140,540,673. What was its average value? 

1904 $30,071,334. What was the difference be- 

1905 147,446,921. tween the largest and the 

1906 162,061,856. smallest amount exported? 

4. A farmer has a small herd of 5 dairy cows which 

produce as follows: 

No. 1 = 396 lbs. butter a year, at 26 cts. a pound, cost of feed $59.00 
No. 2 = 323 lbs. butter a year, at 26 cts. a pound, cost of feed $57.50 
No. 3 = 257 lbs. butter a year, at 26 cts. a pound, cost of feed $55.67 
No. 4 = 176 lbs. butter a year, at 26 cts. a pound, cost of feed $52.38 
No. 5 = 147 lbs. butter a year, at 26 cts. a pound, cost of feed $49.84 



1902 . 


. . 1542,036,364, 


1903 . 


. . 1556,376,880. 


1904 . 


. . $529,107,625. 


1905 . 


. . $515,959,784. 


1906 . 


. . $592,539,671. 



REVIEW PROBLEMS 75 

What is the yearly profit on the herd ? What is the profit 
or loss ou each cow? 

If he sells Nos. 4 and 5 and buys instead 2 other cows 
which produce as follows: 

Xo. 6 = 298 lbs. butter a year at a cost for feed of $57.23 
Xo. 7 = 276 lbs. butter a year at a cost for feed of $54.50 

what will be his yearly profit ou the herd? on each cow? 

5. The value of the cotton exported from the United 
States for 5 years was as follows : 

1902 .... 1291,598,350. 

xA/ n«!>+ TUT" n CI -fhci ^-*-»fril iT-olna r\-t 

1903 . ,-..,_._. 

t^of.-) OAQ Of? I the exported cotton? What 



1904 . 

1905 . 

1906 . 



. !iS381,398,939. '^^' ^^^'^ ^""''""^^ ^"^"^^ 
. 1401,005,921. ^^^"^^ 



6. A farmer delivered to a creamery during May 
3674 lbs. of milk, during June 4876 lbs.', July 3929 lbs., 
August 3167 lbs., September 3067 lbs., October 2913 lbs. 
What was the total number of pounds during the half 
year? 

7. During November a farmer delivered to the cream- 
ery 2974 lbs. of milk, during December 2984 lbs., Janu- 
ary 2798 lbs., February 2890 lbs., March 3043 lbs., April 
3364 lbs. What was the total number of pounds deliv- 
ered during the latter half of the year? How much less 
was this than in the warmer half of the year? 

8. What number multiplied by 256 with 23 added to 
the product will give 5399? 

9. Light travels 186,680 miles a second. How far 
will it travel in 29 seconds? 



76 PRACTICAL ARITHMETIC 

10. Sound travels 1130 feet in a second. How far 
will it travel in 29 seconds ? 

11. It is, in round numbers, 25,000 miles around the 
earth. How many times will a light wave go round the 
earth in a second? 

12. What is the number nearest to 3980 which is di- 
visible by 234 without a remainder? 

13. In the United States in 1899, $49,099,936 was 
spent for fertilizers. This being used on 4,970,129 farms 
was an average of how many dollars' worth on each farm ? 

14. In 1880 the expenditure of the United States for 
fertilizers was $28,500,000, in 1890 it was $38,500,000, 
in 1900 it was $54,750,000. How much more was spent 
for fertilizers in 1900 than in 1880? in 1900 than in 
1890? in 1890 than in 1880? How much less in 1900 
than in 1880 and 1890 together? 

15. The shrinkage in weight of corn due to drying be- 
tween December and May is about 9 lbs. for every hun- 
dred pounds. What would be the loss in weight of 900 
bushels (1 bu. = 56 lbs.)? The price of corn advances on 
an average 4 cts. a bushel between December and May. 
Will this advance in price compensate for the loss due to 
shrinkage with corn in December at 57 cts. per bushel? 

16. The expenses of raising an acre of white pine from 
the seed may be stated as follows : 

Cost of seedlings, $2.00. Cost of land, $6.00. Trans- 
planting to nursery, $1.21. Transplanting to field, $5.45. 
Taxes, first decade, $1.69. Taxes, second decade, $3.04. 
Taxes, third decade, $4.39. Taxes, fourth decade, $5.74. 
What is the total cost ? 



REVIEW PROBLEMS 



77 




CUTS OE BEEF 

The above illustration shows butchers' cuts, their rela- 
tive weights, and Western retail prices ; live weight of 
animal 1550 lbs., dressed weight of carcass 1046 lbs. 

Cheap Cuts VALirABLE Cuts 

No. 1. Neck, 40 lbs. @ 4 cts. No. 3. Prime of Rib, 117 lbs. @ 16 

cts. 
No. 2. Chuck, 237 lbs. @ 7 cts. No. 4. Porterhouse Steak, 103 lbs. 

@ 22 cts. 
No. 8. Shank, 30 lbs. @ 2 cts. No. .5. Sirloin Steak, 87 lbs. @ 18 

cts. 
No. 9. Flank, 52 lbs. @ 5 cts. No. 6. Rump, 36 lbs. @ 10 cts. 
No. 10. Plate, 138 lbs. @ 5 cts. No. 7. Round Steak, 183 lbs. @ 
No. 11. Shin, 23 lbs. @ 4 cts. 10 cts. 



17. The difference between the live weight and the 
dressed weight is the waste in slaughtering. How much 
was it in the animal illustrated ? 



78 PRACTICAL ARITPIMETIC 

18. The parts of the carcass numbered 1, 2, 8, 9, 10, 
and 11 are in the forward and lower parts of the animal, 
and are less valuable. How many pounds are there in 
all these cheaper parts ? What is their total value ? 

19. The parts numbered 3, 4, 5, 6, and 7 are in the 
hind quarters and upper portion of the body, and are more 
valuable. How many pounds are there in all these parts? 
What is their total value ? 

20. What is the difference in the total weights of the 
cheaper and the more expensive cuts ? What is the dif- 
ference in their values ? 

21. What is the average value per pound of the entire 
carcass? What is the average value per pound of the 
cheaper outs? What of the more expensive cuts? 

22. One animal weighing 1550 lbs. produces a dressed 
carcass of 1046 lbs. that sells for 9 cts. a pound ; an in- 
ferior animal of the same live weight produces a carcass of 
990 lbs. that sells for 8 cts. a pound. How much greater 
is the value of the better animal ? 

POULTRY 

23. If 1 gallon of water glass mixed with 16 gallons 
of water makes a solution which will preserve 50 dozen 
eggs, what is the gain in putting up 25 dozen fresh eggs 
in summer when they are worth 15 cts. a dozen and keep- 
ing them until winter when they are worth 25 cts. a dozen? 

24. If a lot of 8 dozen eggs that weighs 9 lbs. sells for 
27 cts. a dozen, how much do they bring a pound? What 
will be the gain in selling another lot of 8 dozen eggs 
that weighs 14 lbs. for the same price per pound instead of 
the usual way of selling them at the same price per dozen ? 



EEVIEW PROBLEMS 79 

25. A flock of hens averages 12 dozen eggs for each hen 
yearly. If they each consume $1.45 worth of feed, what 
is left to pay for their care, losses from death, and profit, 
if the eggs bring an average price of "22 cts. a dozen? 

26. If to raise 73 chicks to 8 weeks of age costs : for 
eggs set $2.50, heat for incubators and brooders fl.OO, 
feed $3.87, what is the average cost per chick? 




27. If a flock of hens fed dry mash and grain produces 
216 dozen eggs at a cost of 11 cts. a dozen, and a second 
flock of the same number fed wet mash and grain pro- 
duces 163 dozen eggs at a cost of 10 cts. a dozen, how 
much greater is the profit from the first flock if eggs sell 
for 22 cts. a dozen ? 

28. If the total weight of the chicks in problem 26 be 
109 lbs., what is the average cost per pound ? 

29. If they are sold at 23 cts. each, what remains to 
pay for the labor and profit? 

30. By inquiry find the local prices and costs in your 
neighborhood, and substitute them in problems 25 and 26. 



80 PRACTICAL ARITHMETIC 



PREVENTION OF PLANT DISEASES 




Total Yield of Marketable Potatoes from Two Rows Sprayed 




Total Yield of Marketable Potatoes from Two Rows not Sprayed 

31. In treating seed oats to prevent oat smut, 1 ounce 
of formalin is used to every 3 gallons of water, and 1 gal- 
lon of this mixture suffices for 1 bushel of oats. How 
many ounces of formalin will be needed to treat 24 bushels 
of oats? 

32. Using 3 bushels of seed oats to the acre, what will 
be the cost of sufficient formalin to treat seed for 80 acres 
at 35 cts. for each 16 ounces ? 

33. The Bordeaux mixture consists of blue stone 5 lbs., 
lime 5 lbs., and water 60 gallons. With blue stone costing 
7 cts. a pound and lime at 1 ct. a pound, what will the 
materials for 150 gallons of Bordeaux mixture cost ? 

34. It requires about 150 gallons of Bordeaux mixture 
to spray an acre of Irish potatoes once. What will the 
materials for 3 sprayings cost? 



REVIEW PROBLEMS 81 

35. Spraying apple trees twice with Bordeaux-Paris- 
green mixture to prevent worminess costs 13 cts. for each 
tree. If this increases the value of the yield f 1.37 for 
each tree, what will be the gain by spraying an orchard of 
87 trees ? 

36. The cost of labor and materials for spraying an 
acre of grapes to prevent the black rot being as follows, 
what is the cost of each spraying and the total cost of 
labor and materials for the six sprayings? 

Cost op Material Cost of Labor Total Cost 

1st spraying .... $0.45 $1.13 

2cl spraying 0.68 1.13 

3d spraying 0:68 1.10 

4th spraying 1.86 1.47 

5th spraying 2.06 1.65 

6th spraying 2.06 1.65 

Total I^ IZI 

37. The average cost of spraying Irish potatoes to pre- 
vent blight being $5.18 an acre, and the average increase 
in value being $19.07 an acre, what is the average profit 
from spraying ? 

38. Six unsprayed apple trees yielded 188 sound apples 
and 4244 rotten apples. Six similar trees spra3'ed yielded 
8674 sound apples and 989 rotten ones. What was the gain 
for each tree in sound apples from spraying ? What was 
the decrease in rotten apples for each tree ? 

39. What would it cost to spray the potatoes and 
apples and to treat all the oat seed planted within a mile 
of your school? 

40. What would the profit be if it equalled per acre 
the increase indicated in the above problems ? 



82 PRACTICAL ARITHMETIC 




A Bountiful Harvest 



FARM CROPS 



41. The average yield of wheat for the United States 
for each acre in 1906 was about 15 bus., the price was 
67 cts. a bushel. What was the value of the yield per 
acre? 

42. The average yield in some States is about 10 bus., in 
others 32 bus. How much greater value per acre is pro- 
duced in the latter than in the former? 

43. If it costs $2.16 for fertilizer, 96 cts. for seed, 
37 cts. for housing, $1.20 for threshing, 76 cts. for 
marketing, and 12.81 for rent per acre in the United 
States, what is the average left to pay for labor and 
profit ? 

44. What is left for labor and profit in the low-yielding 

States? 

45. What is left for labor and profit in the higher- 
yielding States? 

46. If one farm yields 40 bus. an acre and another farm 
16 bus. an acre, each at a cost of $9.67, how much greater 



KEVIEW TROBLEMS 80 

is the value of the yield on the former farm, supposing the 
farms to consist of 79 acres each? How much greater 
is the profit? 

47. If a 3000-lb. crop of cow-pea hay per acre is grown 
on these fields, the stubble and roots will add 28 lbs. of 
nitrogen, worth 19 cts. a pound. What is the value of 
the nitrogen added? 

48. Find by inquiry the average yield of each of the 
above crops in your locality, and substitute your local 
value in the problems, and solve. 

SHIPPING 

Goods are shipped by express or freight, the former 
commonly being used for lighter articles or when speed 
is necessary. The freight rate varies with the articles 
shipped, there being some twelve or more classes. In the 
following table the class is indicated in parenthesis after 
the name of the article. The smallest charge made is usu- 
ally equal to that on 100 lbs. of the class of goods shipped. 

Empty barrels (6) Furniture, old, car-load lots 

Trunks of baggage (1) (6) 

Trunks limited to 1 5 a Vegetables : potatoes, 
hundred (D 1) onions, cabbage, etc. (6) 

Clothing (1) Bicycles, set up (1) 

New furniture, set up (1) Bicycles, not set up (2) 

New furniture, not set up Vegetables, canned, less 
(2) than car-load (2) 

Furniture, old, value limited Vegetables, canned, in ear- 
to $ 5 per 100 (4) load lots (4) 



84 PRACTICAL ARITHMETIC 

Grapes (1) Flour (6) 

Apples and pears in bas- Baled hay (D) 

kets (2) Plows, set up (2) 

Apples and pears in sacks Plows, not set up (4) 

or barrels (6) Power cutter, set up (1) 

Grain in bulk (D) Power cutter, not set up (3) 

The freight rate between two cities per 100 lbs. being : 
1st class 11.03, 2d 92 cts., 3d 79 cts., 4th 65 cts., 
5th 54 cts., 6th 43 cts., A 33 cts., B 39 cts., D 33 cts., 
E 54 cts., H 66 cts. 

Solve the following problems : 

49. What will be the freight on a shipment of bicycles, 
weight 200 lbs., set up ? Not set up ? In a shipment of 
bicycles weighing 500 lbs., what is the saving in freight if 
they be not set up ? 

50. How much cheaper is it to ship 1500 lbs. of new 
furniture not set up than to ship it set up ? 

51. How much cheaper is it to ship 1500 lbs. of old 
household furniture, value limited to 15 per hundred 
pounds in case of loss, than to ship the same weight of 
new furniture set up ? Than to ship the same weight 
of new furniture not set up ? 

52. What is the cost of shipping one car-load (20,000 
lbs.) of old furniture? How many pounds of the same 
goods shipped by the hundred will it take to cost the 
same for freight ? 

53. What is the difference in freight cost between 200 
lbs. of empty barrels and the same weight of trunks of 



KEVIEW PROBLEMS 85 

54. What is the difference in cost of freight on a ton 
(2000 lbs.} of canned vegetables and the same weight not 
canned ? 

55. What is the difference in cost between a car-load 
(24,000 lbs.) of canned vegetables and the same weight 
sent in two separate shipments, i.e., by the hundredweight? 

56. What is the difference in freight cost between 
1900 lbs. of apples in baskets and the same weigiit in 
barrels ? 

57. Which costs the most, the freight on 1700 lbs. of 
flour or on 1700 lbs. of wheat ? 

The express charge between the points for which freight 
rates were given above is 25 cts. for less than 1 lb., 35 
cts. from 1 to 2 lbs.,, 45 cts. from 2 to 3 lbs., 55 cts. from 
3 to 4 lbs., 60 cts. from 4 to 5 lbs., 70 cts. from 5 to 7 lbs., 
75 cts. from 7 +n 10 lbs., 85 cts. from 10 to 15 lbs., fl.OO 
from 15 to 20 Ib^., fl.lO from 20 to 25 lbs., 11.15 from 
25 to 50 lbs., f 2.30 from 50 to 100 lbs., and i|2.30 per 
hundred for weights greater than 100 lbs. 

58. What will be the difference of cost for a 200-lb. 
trunk shipped by express and by freight ? 

59. What will be the difference between freight and 
express charges on 300 lbs. of apples in baskets ? 

60. Which will be the cheaper way to ship a suit of 
clothes weighing, when boxed, 11 lbs.? How much 
cheaper ? 

61. Pupils may add problems concerning produce 
shipped to or from their nearest freight and express 
offices. 



DIVISOKS AND MULTIPLES 

85. Name two factors of 18, 25, 32, 81, 120. 
Name three factors of 18, 30, 45, 50, 66. 
Name a factor common to 12 and 36. 

If 3 is taken as one of the factors of 18, what is the 
other factor ? How is the second factor found ? 

The process of separating a number into its factors is 
called Factoring. 

86. An exact Divisor of a number is a factor of that 
number. 

87. A factor or a divisor that is common to two or 
more numbers is called a Common Divisor. 

EXERCISE 44. — ORAL 

Find a common divisor : 

1. 35, 45, 60. 5. 63, 72, 81. 9. 32, 48, 64. 

2. 21,35,70. 6. 45,24,54. lO. 27,36,75.- 

3. 12, 24, 36. 7. 15, 30, 36. ii. 12, 18, 22. 

4. 36, 28, 72. 8. 18, 24, 54. 12. 72, 81, 96. 

88. Name all the factors or exact divisors of 3, 7, 19. 
A number that has no factors or divisors except itself and 
1 is called a Prime Number, e.^., 7, 11, 19, are prime 
numbers. 

89. Factors that are prime numbers are called Prime 
Factors. 



DIVISORS AND MULTIPLES 87 

90. A number not a prime number is called a Com- 
posite Number. 

91. Which of the following numbers are exactly divisi- 
ble by 2 or have 2 as a factor : 2, 4, 6, 9, 11, 13, 14, 15, 
16, 17, 21, 22, 27, 30 ? 

92. Every number which contains the factor 2 is called 
an Even Number. 

93. Numbers that are not divisible by 2 are called Odd 
Numbers. 

94. Numbers that have no common factors are said to 
be prime to each other. 

EXERCISE 45. — WRITTEN 

1. Write a list of all prime numbers below 100, 

2. Write a list of all odd numbers below 100. 

3. Write all the exact divisors of all the numbers from 
1 to 50. 

4. Separate the following into prime factors : 4, 5, 7, 
8, 10, 12, 13, 14, 16, 18, 21, 24, 25, 30, 34, 36. 

5. Separate the prime, composite, even, and odd numbers 
in the following, and give reasons for your answers : 1, 6, 
7, 10, 11, 12, 14, 19, 21, 24, 26, 27, 32, 33. 

6. Write a list of the numbers from 2 to 50 that con- 
tain 2 as a factor. What do you note regarding the units' 
figure of each number? 

7. Write a list of the numbers from 5 to 100 that con- 
tain 5 as a factor. What do you note regarding the units' 
figure in each case? 



88 PKACTICAL ARITHMETIC 

8. Write a list of the numbers from 3 to 60 which 
contain 3 as a factor. What do you note regarding the 
sum of the figures or digits of each number? 

9. Write a list of the numbers from 9 to 90 that con- 
tain 9 as a factor, and find whether 9 is exactly contained 
in the sum of the digits of each of these numbers. 

95. A number is divisible : 

by 2 if the units' figure is 2, 4, 6, 8, or ; 

by 3 if the sum of its digits is divisible by 3; 

by 4 if the number represented by the two right-hand 

figures is so divisible ; 
by 5 if the units' figure is 5 or ; 
by 8 if the number represented by the three right-hand 

figures is so divisible ; 
by 9 if the sum of its digits is so divisible. 

96. Find the prime factors of 720. 
5 )720 

According to divisibility test 5 is a factor. 2 is a 
second, third, fourth, and fifth factor, ,3 is the last 
factor. Hence, the prime factors of 720 are 5, 2, 3, 
2, 2, 3, and 3. 



EXEECISB 46.— 

Find the prime factors of : 

1. 670.. 5. 420. 9. 

2. 981. 6. 462. 10. 

3. 310. 7. 741. 11. 

4. 2650. 8. 1575. 12. 



2)144 


2) 


72 


2) 


36 


2) 


18 


3) 


9 



WRITTEN 






385. 


13. 


321. 


297. 


14. 


335. 


2430. 


15. 


378. 


1215. 


16. 


10,935. 



DIVISORS AND MULTIPLES 89 

97. The greatest factor or divisor that is common to 
two or more numbers is called the Greatest Common 
Divisor (G.C. DO- 
SS. Find the G. C. D. of 24 and 30. 

04 _ 9 y ^ V 4 ^® ^'^^ ^^^^ *^® common factors of 24 

and 30 are 2 and 3. Multiplying these 
' common factors gives the Gr. C. D. There- 

fore, 2 X 3 = 6 is the G. C. D. 

99. Rule. To find the G. C. D. of two or more num- 
bers, separate the numbers into their prime factors and 
find the product of the prime factors that are common 
to all the numbers. 



EXERCISE 


47.— WRITTEN 


Find the G. C. D. : 




1. 14 98,112. 


6. 13, 91, 136. 


2. 60, 120, 150. 


7. 32, 48, 128. 


3. 28, 42, 36. 


8. 45, 72, 81. 


4. 24, 30, 36. 


9. 24, 80, 96. 


5. 21, 28, 77. 


10. 44, 77, 121. 



100. When it is required to find the G. C. D. of two or 
more numbers that cannot readily be separated into prime 
factors, the following method may be employed. 

Find the G. C. D. of 63 and 217. 

63)217(3 
189 

''^ff The G. CD. is 7. 

56 

7)28(4 
28 



90 PRACTICAL ARITHMETIC 

101. Rule. Divide the greater number by the smaller 
and the divisor by the remainder; continue the process 
until there is no remainder. The last divisor will be the 
G. C. D. 







BXBECISB 48.- 


- WRITTEN 


Find the G. C. 


D. 


of: 






1. 


144, 576. 






8. 


6004, 3318. 


2. 


720, 144. 






9. 


1820, 3367. 


3. 


98, 112. 






10. 


1485, 1155, 1750. 


4. 


720, 1728. 






11. 


1254, 2361, 8163. 


5. 


820, 697. 






12. 


125, 175, 1792. 


6. 


1086, 905. 






13. 


1024, 1280, 1792. 


7. 


1220, 201-3. 






14. 


315, 2267, 9012. 



102. If 6 is multiplied by 3, the product is 18; 18 is 
called a Multiple of 6 and 3. 

EXERCISE 49. — ORAL 

Name tvi^o multiples of : 

1. 7 and 5. 4. 8 and 2. 

2. 3 and 7. 5. 9 and 3. 

3. 6 and 3. 6. 10 and 4 

103. A multiple of each of two or more numbers is 
called a Common Multiple of the numbers. 

104. Of the common multiples of two or more numbers 
the least is called the Least Common Multiple (L. C. M.), 
e.g.^ 18 is a common multiple of 3 and 6, but 12 is the 
least common multiple of these numbers. 



7. 7 and 6. 


10. 3, 6, and 9. 


8. 8 and 5. 


11. 8, 6, and 4. 


9. 9 and 2. 


12. 9, 2, and 8. 



DIVISORS AND MULTIPLES 91 

105. Find the L. C. M. of 30 and 70. 

on _ y g „ r The prime factors of 30 are 2x3x5. 

70—0 r. 7 '^^® prime factors of 70 are 2x5x7. To 
obtain a number which will contain both 30 
and 70, the factors 2, 3, 5, 7, are selected, which multiplied to- 
gether give 210, the L. C. M. 

106. The following method of finding the L. C. M. of 
two or more numbers is also used. Find the L. C. J\I. of 
30, 70, 18. 



By multiplying together the final quotients 
and the divisors, 2x5x3x7x3, we get 
630, L. C. M. 



107. Rule. To find the L. C. M. of two or more num- 
bers, separate each number into its prime factors, and tak- 
ing each factor the greatest number of times that it appears 
in any one of the given numbers, find the product of these 
factors. 



2)30 


70 18 


5)15 


35 9 


3) 3 


7 9 







EXERCISE 50. 


— WRITTEN 


Find the L.C.M. 


of: 






1. 


5 and 15. 






9. 


21, 24, 26, 28. 


2. 


9 and 12. 






10. 


9, 10, 14, 15. 


3. 


21 and 36. 






11. 


7, 14, 56, 84. 


4. 


8, 16, 64. 






12. 


72, 66, 111. 


5. 


24, 30, 36. 






13. 


11, 22, 55, 110. 


6. 


9, 12, 50. 






14. 


8, 21, 28, 35. 


7. 


36, 54, 63, 






15. 


13, 15, 26, 39. 


8. 


17, 34, 51 . 






16. 


4, 21, 42, 63. 



DECIMAL FRACTIONS 

EXERCISE 51. — OEAL 

1. Name the smallest common silver coin in our money; 
name the largest silver coin. 

2. The smallest silver coin is equal to what part of the 
largest ? 

3. Name the smallest coin in our money. The smallest 
coin is equal to what part of the smallest silver coin? 
Of the largest silver coin ? 

4. Read the following as dollars, dimes, and cents: 
13.33, 14.44, $5.55, 16.66, f 7.77, 19.99. 

5. Read the following as dollars, tenths, and hun- 
dredths of a dollar: $8.33, $4.44, $5.55, $6.66, $7.77. 
$9.99. 

EXERCISE 52. — WRITTEN 

Write the following as cents, using the dollar sign : 

1. 55 hundredths of a dollar. 

2. 90 hundredths of a dollar. 

3. 36 hundredths of a dollar. 

4. 34 hundredths of a dollar. 

5. 25 hundredths of a dollar. 

6. 10 hundredths of a dollar. 

7. 1 dollar and 10 hundredths. 

8. 5 dollars and 15 hundredths. 

92 



DECIMAL FRACTIONS 93 

108. As dollars may be divided into tenths and hun- 
dredths, so units of anything may be divided. 

How many tenths of a thing are equal to 1 unit? 
To 10 units? To 100 units? 

109. The division of units into tenths, hundredths, or 
thousandths is called Decimal Division. 

110. The part of a unit obtained by decimal division 
is called a Decimal Fraction. Decimal fractions are 
commonly called Decimals. 

111. The period placed at the left of tenths, e.g., .2, is 
called the Decimal Point. 

112. Decimal fractions may also be expressed thus : 
.2 or two-tenths. It may be also written ■^-^. When so 
written, the decimal fraction is expressed in the form of 
a Common Fraction. 

113. The following table gives the names of the deci- 
mal places : 



•a 

.9 " ^ o 



5 ° 



a ""Ho 

2 j= S cs S 



no = J S cS 3 oj 

•OS * il "O Sj, si 

4672.198462 

EXERCISE 53. — OBAIj 



Read the following : 






1. 1.7. 4. 3.87. 


7. 2.9. 


10. 3.80. 


2. 6.12. 5. 84.67. 


8. 0.90. 


11. 24.06. 


3. 31.73. 6. 90.01. 


9. 6.7. 


12. 300.20, 



94 PKACTICAL ARITHMETIC 

EXERCISE 54. — ORAL 

Name the place at the right of tenths, at the right of 
hundredths, at the right of thousandths, the fourth place, 
the fifth, the sixth, the seventh. 

Read the following : 

1. 15.004. 4. 0.0001. 7. 50.504. lo. 98.7256. 

2. 25.102. 5. 1.4111. 8. 75.6281. ii. 100.2376. 

3. 30.675. 6. 10.1063. 9. 86.5467. 12. 105.20068. 

EXERCISE 55. — "WRITTEN 

Write in decimal form : 

1. Five-tenths, three-tenths, four-tenths, one and one- 
tenth . 

2. Six and eight thousandths, eight and forty-two 
thousandths, two ten-thousandths, ten millionths. 

3. One hundred forty-five thousandths, three hundred 
eighty-one thousandths, four ten-thousandths, two hun- 
dred and two hu.ndredths. 

4. Five and six-tenths, nine and one-tenth, seventy-five 
hundredths, four hundred and four thousandths. 

5. Write these common fractions as decimal fractions : 

_3_. _9_ _e^ _i _1_ 6 s 

10' 10' iTT' 10T5' 100' lOOO'T'OOOO- 

6. Distinguish between 0.300 and 0.00003. 

7. Express as common fractions : 0.25, 0.250, 0.2500. 

8. Annexing a cipher to a whole number increases its 
value how many times ? 

9. Does annexing a cipher to a decimal affect its value? 



ADDITION OF DECIMALS 

114. Add: 25.725,62.8,909.003,4.23681. 

25.725 

g2.8 ^^^ decimals as in the addition of United 

States money. Place the decimal points in a 
vertical line, and add as in integral numbers. 



909.003 
4.23681 



EXERCISE 56. — WRITTEN 

Find the sum of : 

1. 5.47 2. 7.87 3. 112.63 4. 41.039 

16.62 0.125 6.87 7.537 

5.097 19.00 152.00 5.03 

25.608 5.03 7.75 0.107 

5. 19.083, 0.96, 5.03, 27.107, 5.1464, 0.905. 

6. 489, 0.16, 0.49, 7.07, 5.0909, 0.0008. 

7. 37.204, 3.1459, 143.59, 3415.18. 

8. 6.2525, 62.525, 625.25, 6252.5. 

9. Express as decimals and add : -^% ^\%, -^%\, j;^\^o' 
h% 30^, 300^^0^. 

EXERCISE 57.— WRITTEN 

1. The amount of protein in pounds contained in 10 cts. 
worth of each of the following kinds of beef is as follows : 
tenderloin steak .064, sirloin steak .081, loin roast .090, 
rib roast .088, round steak, first cut., .130, round steak 

95 



96 PRACTICAL ARITHMETIC 

.135, chuck .129, rumiJ .114, shoulder .155, round, second 
cut, .205, neck .207, brisket .20, plate .230, flank .284, 
shank .256. I buy 10 cts. worth of each. Find the 
total amount of protein purchased ; how much money- 
do I spend? 

2. The amount of protein found in 10 cts. worth of 
each of the following kinds of pork is : smoked ham .071, 
bacon .065, smoked shoulder .108, fresh ham .112, fresh 
shoulder .120, ribs and loin .134, fat salt pork .019. If 
I buy 10 cts. worth of each, how much protein do I buy? 
At what cost? 

3. The amounts of protein in pounds found in 10 cts. 
worth of veal are as follows : cutlet .089, loin and rib 
.093, leg .098, shoulder and breast .18, chuck and neck 
.133, knuckle or shank .346, flank .424. Find the total 
amount of protein purchased if I buy 10 cts. worth of each 
of these cuts of veal. What does such a purchase cost ? 

4. The monthly rainfall at Davenport, la., a place of 
moderate rainfall, expressed in inches, was: 1.6, 1.6, 2.2, 

2.7, 4.4, 4.1, 3.7, 3.6, 3.2, 2.4, 1.8, 1.6. What was the 
rainfall for the year ? 

5. The monthly rainfall at IMobile, Ala. (heavy), was : 

4.8, 5.3, 7.4, 4.5, 4.2, 6.1, 6.7, 6.9, 4.9, 3.2, 3.5, 4.6. 
What was the yearly rainfall ? 

6. The monthly rainfall at Winnemora, Neb. (scant), 
was : 1.1, 0.9, 0.8, 0.9, 1.0, 0.6, 0.2, 0.2, 0.3, 0.5, 0.7, 1.2. 
What was the annual rainfall ? 

7. The monthly rainfall at Darjiling, India (excessive), 
was: 1, 1.5, 2, 6, 8, 16, 16, 16, 16, 6, 0.5, 0.5. What was 
the annual rainfall ? 



SUBTEACTION OF DECIMALS 

115. From 9.25 take 7.075. 

9.250 ^^ there are more decimal places in the subtra- 

_ „_- hend than in the minuend, annex ciphers until they 
— ^ have the same number of places. 

EXERCISE 58. — WRITTEN 

1. From 1.25 take 0.15. 7. From 25.25 take 2.525. 

2. From 7.75 take 1.95. 8. From 37.18 take 9.189. 

3. From 14.2 take 4.92. 9. From 1.25 take ■^^. 

4. From 14.2 take 4.92. lo. From -^ take -^. 

5. From 39. take 21.689. ll. From ^-f^-^ take j^-^. 

6. From 500 take 9.32. 12. From ^i^ take ^7. 

EXERCISE 59. — WRITTEN 

1. In 100 lbs. of wheat bran there are 15.4 lbs. of pro- 
tein, 62.9 lbs. of carbohydrates, 4 lbs. of fats, 5.8 lbs. of 
ash, and the balance is water. How much water is there ? 

2. If in 100 lbs. of milk there are 4.32 lbs. of fat, 3.34 
lbs. of protein, 5.7 lbs. of sugar, .74 lbs. of ash, and the 
balance is water, how much water is there? 

3. If in 100 lbs. of cream there are 23.8 lbs. of fat, 
4.12 lbs. of protein, 3.92 lbs. of sugar, 0.53 lb. of ash, and 
the balance is water, how much water is there ? 

97 



98 



PRACTICAL ARITHMETIC 



4. If in 100 lbs. of timothy hay there are 13.2 lbs. of 
water, 4.4 lbs. of ash, 7.4 lbs. of carbohydrates, 2.5 lbs. 
of fats and the remainder is protein, how much protein 
is there ? 

5. If in 100 lbs. of red-clover hay there are 15.3 lbs. 
of water, 6.2 lbs. of ash, 62.9 lbs. of carbohydrates, 3.3 
lbs. of fats, and the rest is protein, how much protein is 
there ? 

Nuts contain the following amounts of refuse and 
water in each pound. The refuse represents the shell and 
lining 













Refuse 


Watek 


Almonds 45 lb. 


.027 lb. 


Beechnuts 










.408 lb. 


.023 lb. 


Butternuts 










.864 lb. 


.006 lb. 


Cocoanuts 










.488 lb. 


.072 lb. 


Hickory nuts 










.622 lb. 


.014 lb. 


Pecans 










.532 lb. 


.014 lb. 


Walnuts . 










.741 lb. 


.006 lb. 


Peanuts . 










.245 lb. 


.069 lb. 



6. Which nuts contain most refuse ? Ho,w much more 
than those of least refuse ? 

7. Which nuts contain most water ? How much more 
than those of least water ? 

8. Which contain most nutritive matter ? The amount 
not water and refuse is nutritive matter. How much more 
than those of least nutritive matter ? 

9. Find the amount of nutritive matter in each kind 
of nut. 



MULTIPLICATION OF DECIMALS 

EXERCISE 60. — ORAL 

1. Read the following: .225, 2.25, 22.5, 225. How 
does moving the decimal point one place to the right 
affect the value of a number ? 

2. Read: .3720, 37.20, 3720. How does moving the 
decimal point two places to the right affect the value? 

3. Read: .973, 973. How does moving the decimal 
point three places to the right affect the value ? 

116. Moving the decimal point one place to the right 
has the effect of multiplying tlie number by 10, two places 
by 100, three places by 1000, etc. 

117. To multiply by 10, 100, 1000, etc., move the deci- 
mal point as many places to the right as there are ciphers 
in the multiplier, annexing ciphers at the right to com- 
plete the required number if necessary. 

EXERCISE 61. — ORAL 

1. Read the following: 675, 67.5, 6.75, .675. How 
does moving the decimal point one place to the left affect 
the value of the number ? 

2. Read: 22.70, 2270. How does moving the decimal 
point two places to the left affect the value ? 

3. Read: 325, .325. How does moving the decimal 
point three places to the left affect the value ? 

99 



100 PRACTICAL AKITHMETIC 

118. Moving the decimal point one place to the left has 
the effect of multiplying a number by one-tenth (0.1), 
two places by one one-hundredth (0.01), three places by 
one one-thousandth (0.001), etc. 

119. To multiply by 0.1, 0.01, or 0.001 move the deci- 
mal point as many places to the left as there are decimal 
places in the multiplier, prefixing ciphers if necessary to 
complete the required number of decimal places. 

EXERCISE 62. — ■WRITTEN 

Multiply : 

1. 49.68 by 10, by 100, by 1000. 

2. 6297.3 by 10, by 100, by 1000. 

3. 9.6847 by 10, by 100, by 1000. 

4. 429673.0 by 10, by 100, by 1000. 

5. 84910.0 by 10, by 100, by 1000. 

6. 49.68 by 0.1, by 0.01, by 0.001. 

7. 6297.3 by 0.1, by 0.01, by 0.001. 

8. 9.6847 by 0.1, by 0.01, by 0.001. 

9. 0.429673 by 0.1, by 0.01, by 0.001. 
10. 84910 by 0.1, by 0.01, by 0.001. 

120. Multiply 32.482 by 3. 

2 thousandths x 3 are 6 thousandths, the 6 is 

32.482 written under the thousandths. 8 hundredths X 3 

3 are 24 hundredths, which equals 2 tenths and 4 

97.446 hundredths. The hundredths are written under 

hundredths and the 2 tenths are to be added to 

tenths. 4 tenths x 3 are 12 tenths, which with 2 tenths are 14 

tenths, which equal 1 unit and 4 tenths. 2 units x 3 are 6 

units, which with 1 unit equal 7 units. 3 tens x 3 are 9 tens. 



DECIMAL FRACTIONS 101 

121. Multiply 'S2A82 by 0.3. 

Multiply by 3 as if it were a whole number, 

32.482 pointing off 3 places in the product for the 

0.3 thousandths in the multiplicand and an addi- 

9.7446 tional place to indicate that the multiplicand has 

been multiplied by tenths. The product then has 

4 decimal places. 

122. To multiply decimal fractions multiply as with 
whole numbers. Point off as many places as there are 
decimals in the multiplier and multiplicand together. If 
the product does not contain as man}'^ decimal places as 
are required, prefix enough ciphers to make the required 
number. 

EXERCISE 63. — WRITTEN 

Multiply : 

1. 96.0 by 0.3. 8. 0.236 by 8.93. 15. 184.2 x 0.098. 

2. 9.6 by 0.3. 9. 0.259 by 0.247. 16. 214.86x45.64. 

3. 0.96 by 0.3. 10. 349 by 0.46. 17. 37.55 x 0.00025. 

4. 132 by 2.47. ii. 4.39 x 0.74. 18. 873.0 x 0.675. 

5. 13.2 by 24.7. 12. 5 .6 x .056. 19. 214.76 x 1.25. 

6. 0.132 by 247.0. 13. 35.16 x 5.75. 20. 87.136 x 0.0042. 

7. 9.06 by 1.24. 14. 50.05x0.0095. 21. 897.28x2.009. 

EXERCISE 64. — WRITTEN 

1. If a bushel of corn on the ear weighs 70 lbs. and of 
each pound 0.2 is cobs, what is the weight of a bushel of 
shelled corn? 

2. If in 1 lb. of corn stover there is 0.6 lb. of stalks, 



102 PRACTICAL ARITHMETIC 

0.3 lb. of leaves, and 0.1 lb. of shucks, how many pounds 
of each are there in 2000 lbs. of stover? 

3. If in 1 lb. of commercial fertilizer there is 0.08 lb. of 
phosphoric acid, 0.025 lb. of nitrogen, and 0.035 lb. of 
potash, how many pounds of each are there in 100 lbs. 
of such commercial fertilizer ? How many pounds of each 
in 2000 lbs. ? 

4. A housekeeper's Saturday grocery order was as 
follows: 6 lbs. roast at f0.18 a pound, 3 lbs. rice at. 
$0.0825 a pound, 1 pk. sweet potatoes at $0.25 a peck, 
.5 lb. tapioca at $0.08 a pound, 1.25 lbs. cheese at 
$0.19 a pound, 10 lbs. graham flour at $0.03 a pound. 
Find total cost. 

5. The average wheat yield to the acre in Great Britain 
is 33.9 bus., in the United States 14.5 bus., in India 9.2 
bus., in Russia 10.2 bus. Russia grows 39,215,686 acres, 
the United States 33,766,233 acres, India 16,847,826 acres. 
If the yield per acre in the United States and Russia 
were brought up to that of Great Britain by skilful seed 
selection and tillage, what would be the increase to the 
world's wheat crop ? 

6. If the rainfall in India were sufficient, the yield per 
acre there might be equal to that in Great Britain. What 
would the total yield of India then be ? 

7. What does it cost to travel 198 miles at 2.5 cts. per 
mile? At 2.25 cts.? At 3.75 cts.? 

8. The distance round a wheel is 3.1416 times its 
height. What is the distance round a wheel 4.75 feet 
high ? Round a 28-in. wheel ? 



DIVISION OF DECIMALS 

123. Divide $40.00 by 110.00, 140.00 by 10 cts., 
$75.00 by 115.00, $75.00 by 15 cts. Compare the 
results. 

We have seen that United States money is written as a 
decimal fraction, e.^., $1 and 10 cts. is written $1.10. 

In the division of United States money when the 
divisor is represented by cents, both divisor and dividend 
are changed to cents, and the division is performed as 
with integers. 

124. Divide 8.75 by 2.5. 

3.5 2.5 multiplied by 10 is changed to the integer 25. 

25)87.5 8.75 multiplied by 10 is changed to 87.5. Divid- 

'j'g ing as in United States money, 87 -=- 25 = 3, with a 

remainder of 12. Adding .5 to the remainder gives 

12.5 for a new partial dividend. 12.5 -=- 25 = .6. 

Therefore, the quotient is 3.5. 

To divide a decimal fraction, multiply both dividend 
and divisor by 10, or such multiple of 10 as shall make 
the divisor an integer; then divide as in United States 
money. 

EXERCISE 65.— WRITTEN 

Find the quotient of : 

1. 7.75 -=-25. 3. 7.75 -=-.25. 5. 7.75 -.0025. 

2. 7.75-^2.5. 4. 7.75^.0-25. 6. 7.75^.00025. 

103 



12.5 
12.5 



104 PRACTICAL ARITHMETIC 

7. 17280-4-125. 9. 17280 ',-T- 1.25. xi. 17280 h- .001 25. 

8. 17280^-12.5. 10. 17280 4- .125. 12. 17280 ^- .0125. 

125. Divide 10.10 by 10, divide 100.100 by 100, divide 
1000.1000 by 1000. Compare these results. 

In preceding pages you have seen that moving a figure 
one place to the right in its period decreases its value 
tenfold. In like manner, the removal of the decimal 
point one place to the left decreases a number tenfold, or 
divides the number by 10. Hence, to divide a decimal by 
10, 100, 1000, etc., remove the decimal point as many places 
to the left as there are ciphers in the divisor. When 
necessary, add ciphers to complete the required number 
of places. 

BXEBCISB 66. —WRITTEN 

Find the quotient of : 

1. 3725.4 4-70. 4. 810.18 4-9000. 

2. 309.45 4-1500. 5. 810.18 4-0.009. 

3. 132.4^4000. 6. 7325.1 4- 1.045. 

126. When there is a remainder after using all the 
figures of the dividend, annex ciphers to the dividend 
and continue the division. For ordinary affairs in busi- 
ness it is not necessary to carry the division further than 
four or five decimal places. 

EXERCISE 67. — WRITTEN 

Find the quotient of : 

1. 92323.15 -f- 6.275. 4. 281.85 4-3.85. 

2. 281.8585 4-8.85. 5. 87.912 4-4.07. 

3. 725.406 4-6956. 6. 0.375 -5- .25. 



DECIMAL FRACTIONS 105 



7. 


317.25 -=-75. 




12. 


600982 -- 3.2909. 


8. 


0.0125^2.5. 




13. 


7.847^.03962. 


9. 


1361,5-1-500. 




14. 


849.27 -=-38.0099. 


10. 


50 -^ .25. 




15. 


3.42981-^2.86008. 


11. 


874.298^62. 


85. 


16. 


8498.762-- 678.9084, 



EXERCISE 68. — WRITTEN 

1. If 100 lbs. of milk yield 5.452 lbs. of butter, how 
much butter will 1 lb. yield? 

2. If a gallon of milk weighs 8.6 lbs., how much but- 
ter will 2 gallons of milk of the quality mentioned in the 
last problem produce? 

3. If the corn plants on an acre weigh 7450 lbs., and 
in each pound there are .417 lb. of ears and .583 lb. of 
stover, how many bushels of ear corn, allowing 70 lbs. to 
the bushel, are there, and how many pounds of stover? 

4. Seven pigs, averaging 28.10 lbs., gained in 6 weeks 
503 lbs. per acre of peanut pasture used. What was the 
gain of each animal for each day? If the increase was 
worth 6 cts. a pound, what value per acre was derived 
from the pasture ? 

5. Five pigs, aggregating 895 lbs., pastured 20 days 
on Spanish peanuts, weighed at the end of that time 1124 
lbs. What was the gain for each animal in the 20 days? 
What was the gain for each day ? At 6 cts. a pound, 
what was the increase in value ? 

EXERCISE 69. — WRITTEN 

The pupil should practise with decimals enough to 
attain proficiency. 



106 



PRACTICAL ARITHMETIC 





a 


6 


c 


d 


e 


/ 


9 


1 


379.421 


2.469 


24.378 


23.428 


2.267 


1.479 


h 


2 


387.463 


4.28 


368.0 


7.29 


0.39 


0.009 


i 


3 


289.4 


0.796 


398.42 


97.0 


78.4 


0.379 


i 


4 


63.0 


62.97 


798.4 


629.18 


82.007 


3.6298 


k 


5 


78.4 


17.843 


6829.45 


43.978 


67.08 


1.982 


I 


6 


8.629 


0.08976 


0.7842 


3692.0 


0.0079 


3.479 


m 


7 


0.0078 


0.42963 


67.0 


47.961 


7900.0 


0.062 


n 


8 


76.24 


0.0098 


8.0009 


692.0 


6239.5 


0.398 





9 


872.98 


- 7.627 


764.02 


798.42 


78.42 


3.429 


P 


10 


642.87 


8.429707 


7.9628 


68.394 


86.39 


6.729 


Q 




11 


12 


13 


14 


15 


16 





1-6. Add columns a, b, c, d, e,f. 

7-16. Add the numbers in line 1, 2, etc., to 10. 

17-27. Subtract from the first number in column d each 
number in column/. 

28-116. Subtract from each other number in column d 
each number in column/. 

117-216. Multiply each number in column o by each 
number in column e. 

217-316. Divide each number in column a by each num- 
ber in column b. 

exercise 70. — written 
Review Problems 
1. If a bushel of corn contains 5.88 lbs. of protein, 
40.15 lbs. of carbohydrates, and 3.024 lbs. of fats, what is 
a bushel of corn worth for feeding at 3.7 cts. a pound for 
protein, .5 ct. a pound for carbohydrates, and 3.1 cts. a 
pound for fats. 



REVIEW PROBLEMS 107 

2. The different items of cost to build a stave silo 12 ft. 
in diameter and 21 ft. high are as follows : hauling rock 
f 3, hauling sand $1, cement 4.75 barrels at f 2.85 per 
barrel, putting in concrete foundation, 1 man, 4 days at 
11.25 a day, lumber |5, staves 128.84, hauling lum- 
ber $3, nails 25 lbs. at 3 cts., nails 10 lbs. at 3| cts., 
hoops $21.95, bolts 45 cts., small bolts 30 cts., tar, 
gasoline, and brush !i5l.40, tar paper 2 rolls at •tl.37o, 
carpenter 6 days at #1.75 a day, labor 2 days at $1 a 
day. What was the total cost of building the silo? 

3. If a field of cotton yields 4793 lbs. of seed cotton 
and each poiuid yields .314 lb. of lint, how many pounds 
of seed and how many pounds of lint are there ? 

4. To make 1 lb. increase in weight in pigs pastured 
on peanuts required 1.77 lbs. of grain, when pastured on 
chufas 2.3 lbs. of grain, when on cow-peas 3.07 lbs. of 
grain, when on sweet potatoes, 3.13 lbs. of grain, when 
on sorghum 3.70 lbs. of grain. How many more pounds 
of grain were required when on chufas than when 
on peanut pasturage? How many more when on cow- 
peas than Avhen on peanuts? When on sorghum than 
when on peanuts ? When on sorghum than when on 
sweet potatoes? 

5. The following is the average yield of wheat per 
acre in the principal wheat-growing nations of the world : 
Great Britain 33.9 bushels, Germany 28.6, France 20.8, 
Hungary 18.4, Austria 19.6, United States 14.5, and Rus- 
sia, 10.2. How many acres would it require in each of 
the other countries mentioned to produce as much wheat 
as is produced on 1 acre in Great Britain? 



108 



PRACTICAL ARITHMETIC 



6. The following shows the cost and benefit from spray- 
ing Irish potatoes for several years in New York : 



Year 


Total Ackbs 

Sl'RAVBD 


Increase in Tield, 
Bushels pee Acre 


Cost op Spraying 
PER Acre 


Pkofit from 
Speating 


1903' 
1904 
1905 
1906 


61.2 
180.0 
160.7 
225.6 


57.0 
62.2 
46.5 
42.6 


$4.98 
4.98 
4.25 
5.18 


— 


Total 











What was the average cost of spraying per acre? 
Valuing potatoes at 57 cts. a bushel, what was the aver- 
age profit per acre from spraying? 

7. The items of expense for spraying 10.4 acres of 
potatoes 5 times are : 234 lbs. of copper sulphate at 7 cts., 
195 lbs. of prepared lime at 1.5 cts., 90 quarts of arsenite 
of soda solution at 25 cts., 70 hours' labor for man and 
horse at 30 cts., wear on tools, 16.50. What is the cost 
of spraying each acre for each application ? 

8. In 100 lbs. red-clover hay there are the following 
constituents: 15.3 lbs. water, 6.2 lbs. ash, 62.9 lbs. car- 
bohydrates, 3.8 lbs. fats, and the balance is protein. In 
100 lbs. of timothy hay there are 13.2 lbs. water, 4.4 
lbs. ash, 74 lbs. carbohydrates, 2.5 lbs. fats, and the 
balance is protein. How many more pounds of protein 
are there in 2000 lbs. of clover hay than in 2000 lbs. of 
timothy hay ? 

9. If 100 lbs. of green cow-peas contain 1.7 lbs. of 
ash, 2.4 lbs. of protein, 11.9 lbs. of carbohydrates, .4 lb. 



REVIEW PROBLEMS 109 

of fats, and the balance is water, how many pounds of 
water are there in 1000 lbs. of fresh cow-peas ? 

10. In buying redtop grass seed at 13.7 cts. a pound 
when only 77 lbs. in every 100 lbs. is good live seed, 
what is the price paid per pound for good seed ? 

11. With redtop seed at 8.54 cts. a pound containing 
11 lbs. of good seed in every 100 lbs., what is the price 
per pound of the good seed? 

12. With blue-grass seed at 14 cts. a pound containing 
60 lbs. of good seed in every 100 lbs., what is the price 
per pound of the good seed ? 

13. With blue-grass seed at 10 cts. a pound containing 
.4 lb. of good live seed to the hundred pounds, what is 
the price per pound of the good seed ? 

14. With timothy grass seed containing 96 lbs. per 
hundred of good seed bought at $1.60 a bushel, what is 
the price paid per bushel for good seed? 

15. If a cow produces 7446 lbs. of milk in a year and 
1 lb. of milk produces .059 lb. of butter, how many pounds 
of butter does the cow produce, and what is it worth at 
27 cts. a pound? 

16. How much does the butter cost per pound in value 
of feed, if she ate 12.4 cts. worth each day? 

17. Another cow gave 3400 lbs. of milk, and each pound 
of milk produced .0406 lb. of butter. Did this cow 
make a profit with butter at 27 cts. if the cost of feed 
was 11.2 cts. a day? 

18. If 1 pound of cotton-seed meal contains .0618 lb. 
of nitrogen, .018 lb. of potash, and. .028 lb. of phosphoric 



110 PRACTICAL ARITHMETIC 

acid, how much of each of these fertilizing materials does 
a ton, or 2000 lbs., of cotton-seed meal contain? "What is 
the ton of cotton-seed meal worth for fertilizing at 18 cts. 
a pound for nitrogen, 4 cts. for phosphoric acid, and 5 cts. 
for potash? 

19. If 1 pound of cotton-seed contains .031 lb. of nitro- 
gen, .013 lb. of phosphoric acid, .012 lb. of potash, what 
is the ton of seed worth at the same prices for fertilizing 
materials as in problem 18? 

20. The following are the plant-food constituents which 
a farmer sells from his farm in the products named : 





Nitrogen 


PuosPiroRic Acid 


Potash 


3000 lbs. milk . 


. 15.9 lbs. 


5.7 lbs. 


5.4 lbs 


liO lbs. butter . 


. 02.8 lbs. 


0.12 lb. 


0.35 lb. 


500 lbs. cotton lint . 


. 01.7 lbs. 


0.5 lb. 


2.3 lbs 


1000 lbs. cotton-seed 


. .31.0 lbs. 


13.0 lbs. 


12.0 lbs 


20 bus. wheat . 


28.32 lbs. 


9.48 lbs. 


6.0 lbs 


40 bus. corn 


. 40..>7 lbs. 


15.68 lbs. 


8.96 lbs 


1.5 tons timothy hay 


. 37.8 lbs. 


15.9 lbs. 


27.0 lbs. 



Valuing nitrogen at 18 cts. a pound, phosphoric acid at 
4 cts. a pound, and potash at 5 cts. a pound, what is the 
value of the fertilizing materials removed from the farm 
by the sale of each of these products in the amounts 
indicated ? 

COMPOSITION OF FOODS 

21. If for 10 cts. I can purchase .064 lb. of protein in 
tenderloin steak, how much protein do I obtain in 50 cts. 
worth of tenderloin ? 

22. If for 10 cts. I can purchase .185 lb. of protein in 



REVIEW PROBLEMS 



111 



round steak, in which do I get most protein for the money, 
in tenderloin or in round steak ? How niucli more ? 




A Good Loin Cut op Beef 

23. If for 10 cts. I can purchase .03 lb. of protein in 
oysters, how much protein do I obtain in 70 cts. worth of 
oysters ? In which of the above articles do I obtain most 
protein for my money ? 

24. In the following dairy products these amounts of 
protein may be purchased for 10 cts.: butter .004 lb., 
cheese .1631b., whole milk .110 lb., skimmed milk .20:5 
lb., cream .034 lb. How much protein in each may I 
obtain for 75 cts.? 



LEGUMES 

25. If each pound of vetch hay contains .17 lb. of nitro- 
gen, how many pounds of nitrogen are there in 2879 lbs. 
of vetch hay? Each pound of alfalfa contains .143 lb, 
of nitrogen. How many pounds are there in 2879 lbs. of 
alfalfa? Each pound of red clover contains .123 lb. of 



112 PRACTICAL ARITHMETIC 

nitrogen. How many pounds are there in 2879 lb. of red 
clover? Each pound of cow-pea hay contains .166 lb. of 
nitrogen. How many pounds are there in 2879 lbs. of cow- 
pea hay? What is the value of the nitrogen in each of 
the above instances at 19 cts. a pound? 

26. If 5953 lbs. of velvet-bean hay are grown on an 
acre, and in every pound of this hay there is .0221 lb. of 
nitrogen, how many pounds of nitrogen are gathered by 
the crop, and what is it worth at 18 cts. a pound? 

27. If there is .024 lb. of nitrogen in 1 lb. of cow-pea 
hay, and 3000 lbs. of h.a,j are made on an acre, what will 
be the value of the nitrogen collected by the crop, with 
nitrogen worth 18 cts. a pound, if for each pound of ni- 
trogen in the hay there is left in the stubble and roots 
.3 lb. of nitrogen? 

28. Crown Jewel potatoes dug in Virginia 80 days 
after planting yielded 170 bus., dug at 93 days after 
planting, the same variety gave 255 bus. What was the 
average increase daily during the additional period ? 

29. Beauty of Hebron potatoes dug in Virginia at 101 
days after planting showed an increase of 136 bus. over 
those dug 80 days after planting. What was the average 
increase per day during the additional time? 

30. Using nitrate of soda on clover, 300 lbs. to the 
acre, at §2.66 a hundred pounds, the yield was increased 
from 2.09 to 2.8 tons per acre, valued at 19 a ton in the 
field. Did the use of the fertilizer pay ? What was the 
gain or loss per acre ? 



COMMON FRACTIONS 

EXERCISE 71. — OEAL, 

1. How many weeks in a month ? One week is equal 
to what part of a month ? Two weeks are equal to what 
part of a month? Three weeks are equal to what part of 
a month ? 

2. One week is equal to what part of two months? 
One week is equal to what part of three months ? 

3. Two weeks are equal to what part of two months ? 
Two weeks are equal to what part of three months ? 

4. Three weeks are equal to what part of two months ? 
Three weeks are equal to what part of three months ? 

5. If a unit is divided into two equal parts, what is one 
part called? If a unit is divided into three equal parts, 
what is one part called ? If into four, six, ten ? 

127. One or more of the equal parts of a unit is called 
a Fraction. 

128. A fraction is expressed by two numbers, one writ- 
ten above the other, with a line between them ; e.g., one- 
fourth is expressed thus, \. 

129. Read the following : |-, \, \, Jg, ^^q, gV- What 
part of these fractions shows the number of parts into 
which the unit is divided? 

The number which shows into how many parts a unit 

113 



114 PRACTICAL ARITHMETIC 

is divided is called the Denominator ; e.g., in the fraction 
f, 6 is the denominator and shows that a unit has been 
divided into six equal parts. 

130. Which is greater, ^ or | ? 

What does the number above the line indicate ? 

The number which shows how many parts are taken 
is called tlie Numerator ; e.g., in the fraction |^, 3 is the 
numerator and shows that the fraction contains three 
of four equal parts. 

131. The numerator and denominator are called the 
Terms of a fraction. 

132. A fraction whose numerator is less than its 
denominator is called a Proper Fraction; e.g., |, ^, |, ■^, 
are proper fractions. 

A proper fraction is always less than a unit. 

133. A fraction in which the numerator is equal to or 
greater than the denominator is called an Improper Frac- 
tion; e.g., |, |, ^, are improper fractions. An improper 
fraction is always equal to or greater than a unit. 

134. A whole number and a fractional number written 
together is called a Mixed Number ; e.g., 3|, 1^ , are mixed 
numbers. 

BXBECISE 72.— OBAL 

Select proper fractions, improper fractions, and mixed 
numbers from the following : 

-^* 3' F' 6' 9" *• ''e' 2'' -'■"2' 5" 10' 3' 2' 9 

2 -t 1 34 1^ 5 5 la 8. J n 20 15 Q 1 5 6 
"*■ 4' 5' '^¥' 14" ^- 4' 16' 5' 25- **• 19' ? ' ^^2' IV 

3 15 IS 3 1 c 2_5. Q2 IflS 9 a 2_8 19 .£;i 16 
"*• 2 0' 15^' f' 3- °- '#' ^Y' •''"?' TO- ^- ■?9' '5"' ''2' 24- 



COMMON FRACTIONS 115 

EXERCISE 73. — WRITTEN 

Write as common fractions or mixed numbers : 

1. Thirt3^-one tenths. 

2. Fifty-six elevenths. 

3. Eight-nineteenths. 

4. Seven-fifteenths. 

5. Eight one-hundredths. 

6. Ninety and three-fourths. 

7. One hundred and forty-five forty-sixths. 

8. Seventy-seven and six-tenthsi 

9. Five hundred tentlis. 

10. Twenty-five tliirty-sixths. 

11. Nineteen and seven twenty-firsts. 

12. Twenty-one and eighteen nineteenths. 

13. One hundred twenty-five and one hundred twenty- 
four one hundred twenty-fifths. 



EXERCISE 


74. 


— WRITTEN 


Write in words : 






1- f^f A- 




6. 666f,25f 


2. if, If if- 




7. 8 7.121, $12.25f 


3- ihihi- 




8. $ 266. 26|, $19,181 



4. l|,25f,^i,. 9. If, _^, ^^a l-o^oji. 

5. 9^^, 150f 10. 3Vlf-\sl9f 

135. An improper fraction may be regarded as an indi- 
cated division, e.g., ^^ indicates that each of several units 
has been divided into 4 parts ; 13 of these parts are here 



1. V- 


4. iLI. 


7- If. 


10. 


ii- 


2. ^. 


5- ¥/• 


8. 3^1. 


11. 


W' 


3. -1/. 


6. \3.. 


9. ^M. 


12. 


6 93 
l20' 



116 PRACTICAL ARITHMETIC 

represented. To find how many units are represented by 
-3^5., "vve may regard 13 as the dividend and 4 as the divisor; 
13 T- 4 = 3 whole units and ^ of a unit. 

136. To change an improper fraction to a whole or 
mixed number, divide the numerator by the denominator. 

EXERCISE 75. — ■WRITTEN 

Change to whole or mixed numbers : 

13. -^f 

14. 11|1. 

15. 5^a. 

137. A whole number or a mixed number may be 
represented in the form of an improper fraction, e.g., 8 
may be expressed in halves, as J^ ; 8| may be expressed as 
halves, thus, ^^^. 

Since one unit contains 2 halves, 8 units contain ^. ^ 
and -J equals i-^. 

138. To change a mixed number to an improper frac- 
tion, multiply the whole number by the denominator and 
add the numerator ; write the sum over the denominator. 

EXERCISE 76. — WRITTEN 

Change to improper fractions : 

9. 17^^. 13. 45^. 

10. 12lf 14. 17f|. 

11. 72|f 15. 167f|. 

12. 25^. 16. 167||. 



1. 121. 


5. 


10^, 


2. 15f 


6. 


25i. 


3. 18|. 


7. 


331 


4. 45^. 


8. 


19i. 



COMMON FRACTIONS 117 

EXERCISE 77. — ORAL 

1. How many twelfths in one unit ? 

2. How many twelfths in two units ? 

3. How many twelfths in one-half unit ? 

4. How many twelfths in one-third unit ? 

5. What is true of the value of ^2 ^"^ 2 ^ What is 
true of the terms of the second fraction ? 

6. Does changing ^^ *o ^^^ lower terms, ^, change the 
value ? 

EXERCISE 78. — WRITTEN 

Change the following to lower terms : 

"• 21' 2 4' ^• 

7 IS li. 24 
'• 2T' 60' Tf- 

R 19 -6JL la. 
**• ¥"8'' 102' "rt- 

9 10 8 li l± 
^- 111' ^1' YO- 

TO IS. 22 11 
•^"" ?t' 6 6' 9 6* 

139. A fraction is reduced to its Lowest Terms when 
the terms are prime to each other. 

To reduce a fraction to lowest terms, select factors com- 
mon to both terms, and cancel. 



1. 


6' iV' A' iV 


2. 


9' if' 15" 


3. 


]%' 1' 2V 


4. 


^IS' 1' 1*6- 


S. 


■^(7' A' A- 





EXERCISE 79. 


— WRITTEN 






Reduce to lowest terms : 








1- II- 


5. m- 


9- il- 


13. 


^% 


2- i|. 


6. If. 


10. ,^. 


14. 


lit- 


3- U- 


7. ^Vl- 


11- Hf 


15. 


MI- 


*• u- 


8- ff 


12. 78^. 


16. 


MI- 



h 


h 


4. 


hh 


7. 


h i\- 


10. 


hi 


h 


tV- 


5. 


h "S- 


8. 


-hh 


11. 


1 1 

3' 6 


h 


h 


6. 


hh 


9. 


¥' 9" 


12. 


f' 9' 



118 1>RACTICAL ARITHMETIC 

EXERCISE 80. — ORAL 

1. Express ^ as 4ths. 6. Express ^, ^ as 8ths. 

2. Express f as Sths. 7. Express |, |, ^^ as-12ths. 

3. Express | as 12ths. 8. Express ^, |, | as 12ths. 

4. Express | as 14ths. 9. Express |, |, | as 24ths. 

5. Express f as 28ths. 10. Express ^, |, ^-^ as 20ths. 

EXERCISE 81. — AVRITTEN 

Express as fractions with the same denominator : 
1. 

2. 
3. 

140. If several fractions have the same denominator, 
they are said to be Similar Fractions, and the denominator 
is called a Common Denominator. 

141. If the common denominators are the smallest pos- 
sible, the fractions are said to have the Least Common 
Denominator (L. C. D.), e.ff., the fractions -^^ '^^^^ 1^2 ^^'^^ 
a common denominator 12, but they may be reduced to | 
and |, 4 being the L. C. D. 

142. Reduce ^, |, ||, to similar fractions with the least 
common denominator. 

The common denominator of ^, f, if, must be the least com- 
mon multiple of the denominators 3, 8, 12. 

We find that the L. C. D. of these nnmbers 
is 24. Change each fraction to 24ths by mul- 
tiplying each denominator by the factor that 
will give 24, and multiplying the numerator by 
the' same factor, thus : 



2)3 


8 12 


3)3 


4 6 


2)1 


4 2 


1 


2 1 



COMMON FRACTIONS 119 

To change 1 to 24ths, multiply both numerator and de- 
1x8 8 



nominator by 8 = 
To change | to 
nominator by 3 = 

To change ^| to 
nominator by 2 = 



3x8 2-i' 
To change | to 24ths, multiply both numerator and de- 

5 X 3 ^ 15 

8x3 24' 
To change 1| to 24ths, multiply both numerator and de- 

10 X 2 ^ 20 

12 X 2 24' 

143. In reducing fractions to a common denominator 
they are changed to Higher Terms. 

EXERCISE 82.— "WRITTEN 

Reduce to similar fractions : 

1 1 4- 3 -9- ii 5 5 _9_ n 3 J: 

■^- 2'?- ■*■ 21' ^0" °- S' 10- '• t' TT- 

^- 12' IZ- *■ 7' 2 1- °- 9' S- °- "5' 1(J' 20- 

EXERCISE 83. — WRITTEN 

Reduce to fractions having a L. V. D. : 

1 1 1 3_ 

^- ?' ^' 10- 

"• 2' S"' 12- 

o 3 4 2 
"*■ 5' T' 3- 

*• 8' 5' ?0- 

K 6 5_ _e 
^- 'SO' 15' 15" 

EXERCISE 84. — WRITTEN 

Change to improper fractions and reduce to L'. C. D. 

1. 12-1, 18f 5. 682^ 45}1. 

2. 2V„36,V 6. 42l|, 61ff. 

3. 72^, 26^\. 7. Sh%,2A^\. 

4. 24|, 3(11.?. 8. 16g\, 2111. 



6. 


12 1 
14¥' 132- 


7. 


2 22' ?^A- 


8. 


9 7 
25' "55- 


9. 


9 8 5 
IT' 9 9' T2 1 


10. 


A' i^' H- 



ADDITION OF FRACTIONS 

KXEROISE 85. — DEAL 

1. How many tenths in ^ + ^^? How many fifths? 

2. How many twelfths in ^^ + 1^2 ' How many 
fourths ? 

3. How many sixths in ^ + |^? How many ones? 

4. To find the sums of these fractions, what terms of 
the fractions are added? 

5. How much is 1 + 1? 1 + 1? l + J? 1+1? 

3 + 2 • 

6. To what kind of fractions must those above be 
changed before they can be added? 

144. Add|,f,3^. 

First find the L. C. D. The L. C. D. is 5 x 2 x 3 x 2 = 60. 
Eeducing each fraction to higher terms with 60 for a cohj- 
mon denominator, we have, 

4 X 12 ^ 48 6 X 10 ^ 50 9x5 ^45 

5x12 60 6x10 60 12 x 5 60 

ff + 1^ + 11 = Jg^. Eeducing J^ to a mixed number gives 

145. Add 31 + 6f 

The sum of 3 + 6 = 9. 

By finding the L. C. T>. of ^ and -J- and changing these frao- 
tions to higher termsj we get J^j + |-i = ff- 

120 



COMMON FRACTIONS 121 

Changing |J to a mixed number gives 1^^. 
Uniting the sums, 9 + l^j = lO^ij. 

146. To add fractions, reduce to similar fractions hav- 
ing the L. C. D., and add the numerators, placing the sum 
over the common denominator. The answer should al- 
ways be reduced to lowest terms. 



EXERCISE 


86.- 


- WRITTEN 


Find the sum of : 






1- hi- 




5. 6|,2f 


2- i,|. 




6. 9|,2|. 


3- hhi- 




7. I, 31 5f . 


*■ f'i'/r 




8. 2|, 9jL, S^^j, 



EXERCISE 87. — WRITTEN 

1. A boy spends f of his money for a suit of clothes, 
\ for an overcoat, ^ for a pair of shoes, and -^^ for a hat. 
What part of his money has he spent ? 

2. After making his purchases, he has left J of his 
money, which is i 4. How much had he at first? 

3. A girl's dress skirt is 26^ ins. long when finished; 
if \ in. is allowed for gathers at the top and 2^ ins. for the 
hem, how long must the material be cut for making? 

4. If she wishes to add a ruffle 3|- ins. wide, with an 
inch hem at the bottom, and a f-in. hem at the top, how 
wide must she cut the material for the rafSe? 

5. How many yards of fencing will be required to fence 
an irregularly shaped school yard 23-| yds., 42| yds., 40| 
yds., 27f yds. on the sides? 



SUBTRACTION OF FRACTIONS 

147. How much is f + |^? How much is | — ^? 

How much is f + -^-^ ? How much is | — ^■^? 

How much is ^ + ^^ '■ How much is | — yj^? 

To subtract fractions they must, as in addition, be 
changed to similar fractions. Subtract the numerator 
of the subtrahend from the numerator of the minuend to 
obtain the numerator of the difference, e.g., f — iV = t^ 



- iV or 1^- 
















EXERCISE 88.- 


ORAL 








Find the value 


of: 












1- l-l- 




*• H-tV 




7. 


A- 


-i- 


2- f-i- 




5- T^-i- 




8. 


A- 


-tV 


3- l-f 




6- H-l 




9. 


A- 


-f 



EXERCISE 89. — WRITTEN 

Find the value of : 



■h 



5 
15"- 



5. ^,-h 



6. 
7. 
8. 
9. 
10. 



f-^ 



11 

16 



12 



^• 



. 1 
1- 



2 

2"S"- 



11. 
12. 
13. 
14. 
15. 



2 5 

^ IJ- 

3'B ~ 13' 

2i_ a 

3 1 8 • 

A2._ 21 
49 '58" 



EXERCISE 90. — ORAL 

What fraction does x stand for in the following? 
1. i + 2;=f. 2. # + a; = 4. 



3. i-X=l. 



122 



COMMON FRACTIONS 123 



4. 


i-x = i. 


7. 


| + :r=i^. 


10. 


^-i = f- 


5. 


i + ^ = A- 


8. 


I--*'=1^- 


11. 


•i-f=6-- 


6. 


A-- = f 


9. 


4-1=^- 


12. 


^-^= 



148. Find the value of 13| - 9^. 

As in addition of fractions, the whole numbers and the 
fractions may be subtracted separately, but in the above 
problem we observe that the fraction ^ cannot be sub- 
tracted from the fraction -^ of the minuend. 

The problem may be restated thus, 12|-— 9^. 12—9 = 3. 

I = if- 2 = i\- tI" - T^o = iV- '^^^^ remainder, there- 
fore, is 3 and ■^^, ©r 3 j^. 

EXERCISE 91. -WRITTEN 

Add or subtract as indicated : 

1. 2|-1|. 6. 5f + 6^-3^V 

2. 3^-1-11 7. 525|-150if 

3. 9-4|. 8. 4:2 + dl + 10{^. 

4- 1 + 1 + A- 9- 9tV + 3A + 2|. 

5. 5-h6|. 10. 41-3. 

EXERCISE 92. — WRITTEN 

1. A boy spends ^ of his school days in the common 
school and | in the high school ; how much more of his 
boyhood does he spend in the common school than in the 
high school? 

2. If a boy sleeps I of his time and studies | of his 
time, how much time has he left for play? 

3. What fraction added to i^ -f | will make 2 ? 



124 PRACTICAL ARITHMETIC 

4. A normal child weighs at birth 7| lbs., at 1 year 20| 
lbs., at 2 years 26J lbs. What is the difference between 
its weight at birth and at end of first year ? What is the 
difference between its weight at end of first year and end 
of second year ? 

5. At birth a normal child measures in height 20| ins., 
at 1 year 29 ins., at 2 years 32-| ins. What is the differ- 
ence between its height at birth and at end of first year ? 
What is the difference between its height at birth and at 
end of second year? 

6. The organs of the human body are composed of 
water, as follows : bones ^, muscles ^y^', brain and spinal 
cord -1^, lungs r^^^^. How much more water is there in 
muscle than in bone ? In brain than in muscle ? In lungs 
than in muscles? 

7. The organs of the human body are composed of 
mineral matter, as follows : bones \^, muscles 2 |o' ^^^S^ 
loro' brain y-J^. How much more mineral matter is there 
in bone than in each of the other organs named ? 

8. The head of a normal child at 6 years of age 
measures 20|- ins., at 3 years 19| ins., at 2 years 19^ ins. 
Find the difference in measurement between the head of a 
child 6 years old and that of a child 3 years old ; between 
a 6-year-old child and a 2-year-old child; between a 3- 
year-old child and a 2-year-old child. 

9. The average boy of 8 years is ■ISy'g i'^^- ^^^^' ^^^^ 
average girl of 8 is 48^^^ ins. What is the difference in 
their heights? 

10. The average girl of 14 weighs 100^ lbs., the average 
boy 99|^. What is the difference ? 



MULTIPLICATION OF FRACTIONS 

EXERCISE 93. — ORAL 

1. How much is ^ of 6 inches ? ^ of 9 dollars? ^ of 10 
cents ? I of I ? 

• 2. How much is i of 12? ^of|? iofif? 

3. How many inches are there in a foot ? 

4. How many inches in | foot? In J of |- foot? 

5. In example 4 the result is what part of a foot? 

6. How much is I of | yard? I of | dollar? 

7. How much is -|- of ^ dollar? ^ of ^g dollar? 

8. How much is | of |- ? 

149. Multiplying any number by another number larger 
than 1 increases its value. When one fraction is multi- 
plied by another, the number of parts as shown by the 
denominator is increased, but the value of the fraction is 
decreased, e.ff., 2x3 = 6. -^ x ^ = J of |^ = ^. 

150. Multiply I by 1 = 1 of |. 

iof| = i. 

I of f = 2 X ^ or |. Hence, | multiplied by | = |. 

151. Multiply I by | = f off 

1 of 7 _ i of + 2 = -?~ 

I of Jj = 5 times Jj, or |f . 

152. To multiply a fraction by a fraction, find the 

125 





EXERCISE 94.- 


-ORAL 




id the pi 


roduct of : 








i-x|. 


6. 


|xf. 


11. 


ix|. 


*x|. 


7. 


ixf^. 


12. 


A X ^5^ 


ix,V 


8. 


fxf. 


13. 


|x|. 


ix|. 


9. 


|xif 


14. 


fxf. 


fxf. 


10. 


fxf 


15. 


|xi 



126 PRACTICAL ARITHJIETIC 

product of the numerators for the Numerator and the 
product of the denominators for the Denominator. 



1. 
2. 
3. 
4. 
5. 

153. Instead of multiplying the terms of the fraction 

together for the product, the process may be indicated, and 

the factors cancelled. 

Multiply I by |. 

2 

6 5 ^ x^ 3' 
3 

EXERCISE 95. — WRITTEN 

By cancellation find the product of : 

1 i- V fi 5 -5- V 12 Q J!_ V _S_ 

J.. 9 A ^. o. -jg A 25- »• 13 A 21' 

3. J X ^^. 7. J--2 X^f X ^. 11. gj X ;j9. 

4 11 V 21 R 11 X 3 T3 fi V 41 

*■ 12 X JS- 8. 21 X 2 5- "• g X -gy. 

154. Find the product of |- x 14. 

I of 14 = I of Jj4 = -\2 = -\i = 101, or by cancellation : 

7 
3X14_21_ 
ix 1~2~-'"*- 



COMMON rRACTIONS 127 

155. To find the product of a fraction and a whole 
number, regard tlie wliole number as an improper frac- 
tion with 1 as its denominator, and multiply the terms 
together ; or indicate the multiplication and cancel the 
common factors. 

EXERCISE 96. — ORAL 

Find the product of : 



1. 


15 xi. 


7. 


27 Xf. 


2. 


25 xi- 


8. 


1 X 20. 


3. 


10 X |. 


9. 


-1 X 16. 


4. 


21 x|. 


10. 


f x20. 


5. 


12 xf. 


11. 


f of 30. 


6. 


16 X |. 


12. 


f of 27. 



13. 


^\ Of 22. 


14. 


f of 12. 


15. 


18 xf. 


16. 


V- X 9. 


17. 


i X 12. 


18. 


1 of 15. 



156. Find the product of : 3x2; 3 x ^ ; 3 x 21. 

rind the product of 6 x 3i = 6 x 3 = 18, 6 x i = f = f , 
18 + | = 18f. 

To multiply a mixed number by a whole number, mul- 
tiply the whole and fractional parts separately, and add 
the products. 

157. Find the product of 2f x 1-^. 

o2v1i— syS- — i4 = 3-3, or 34 

To multiply a mixed number by a mixed number, re- 
duce each to an improper fraction and multiply the terms. 

EXERCISE 97. — WRITTEN 

Find the product of : 

1. 10x2i|. 3. 351x27. s. 16| x 121. 

2. 81 X 62f . 4. 331 X 181. 6. 18 x 331. 



128 PRACTICAI, ARITHMETIC 



7. 


27 X 421 


12. 


81 J^ X 561 


17. 


100 X 6^. 


8. 


16| X 28f . 


13. 


34 X 121 


18. 


86 X 41. 


9. 


9| X lOli. 


14. 


81x,V 


19. 


Ill X 111. 


10. 


35|- X 16. 


15. 


If of 512. 


20. 


35 X 8f . 


11. 


631 X 1. 


16. 


64 X 8f 


21. 


100 x5jV 



EXERCISE 98. — WRITTEN 

1. In 1 pint of whole (vinskimmed) milk -^-^ is water, 
jlg- fat, ^^ protein, gV carbohydrates. How much of each 
food constituent is there in 8 pints or 1 gallon ? 

2. In 1 pint of buttermilk -^^^ is water, ^^-^ fat, y|j 
protein, gV carbohydrates. How much of each food con- 
stituent is there in 8 pints or 1 gallon ? 

3. In 1 pint of skim milk -^ is water, ^^ protein, gV 
carbohydrates. How much of each food constituent is 
there in 1 gallon of skim milk? 

4. If a child of 4 to 6 years of age requires daily 1^ 
grams of protein, 1| grams of fats, and 5 grams of carbo- 
hydrates for each pound of weight, how much of each 
of these food constituents will be required for a child of 6 
years weighing 45 lbs. ? 

5. How much of each for a child of 4 years weigh- 
ing 35 lbs. ? 

6. If a boy of 10 or a girl of 8 years requires daily 1| 
grams of protein, | gram of fat, and 4^ grams of carbohy- 
drates for each pound of weight, how much of each con- 
stituent will be required for a boy of 10, weighing 67 lbs.? 

7. How much of each for a girl of , 8 years weighing 
55 lbs. ? 



DIVISION OF FRACTIONS 

158. How many times is ^ contained in 1? How 
many times is | contained in 1? 

Since ^ is contained in 1, or |, four times, | is contained in 
1, or I, ^ of four times, or -t times. 

How many times is | contained in 1 ? | is contained 
in 1, or |, one-third of 4 times, or |- times. 
How many times is ^ contained in 2? 
How many times is | contained in 2? 

Since ^ is contained in 2, or |, eight times, | is contained 
in 2, or |, | of 8 times, or f times. 

How many times is f contained in 2? | is contained 
in 2, or |, ^ of 8 times, or | times. 

EXERCISE 99. — DEAL 

1. How many times is ^ contained in 1? | in 1? 

2. How many times is | contained in 1? | in 1? 
f inl? 

3. How many times is ^ contained in 2 ? J in 2 ? | in 2 ? 

4. How many times is ^ contained in 3? -f in 3? 

159. When the product of two numbers is equal to 1, 
each of the two numbers is called the Reciprocal of the other, 
e.g., 3 X 1^= 1. Hence, 3 is the reciprocal of ^, and ^ is 
the reciprocal of 3. Again, ^ Xy = |-| = l. Hence, -| is 
the reciprocal of |-, and |- is tlie reciprocal of |-. 

129 



130 



PRACTICAL ARITHMETIC 



160. To multiply by the reciprocal of a number is the 
same as to divide by that number. Hence to divide a 
whole number by a fraction, or a fraction by a whole 
number, or a fraction by a fraction, multiply by its re- 
ciprocal. 

161. Divide | by f . 

Since, as we have seen, j- is contained in 1, seven times, 
f is contained in 1, i of seven times, or -J times. If i is con- 
tained in 1, |- times, it will be contained in |, ^ of f, or ^ or 
IJ-j- or 1-| times. 

162. Mixed numbers should be reduced to improper 
fractions before performing the division. 

When possible, use cancellation in the process. 



BXEECISE 100, 

Find the quotients of : 



-OEAIi 



1. 


16 ^i- 


8. 


-1^8. 


15. 


f^l- 


2. 


12^1 


9. 


,«^^100. 


16. 


A-f 


3. 


8-f- 


10. 


l|-l- 


17. 


^\-f 


4. 


144 ^i|. 


11. 


-I-'- 


18. 


If-i- 


5. 


i-f- 


12. 


21 -=-5. 


19. 


8^1. 


6. 


1^^- 


13. 


63^1 


20. 


17 ^ 11. 


7. 


l-G. 


14. 


3(5 ^|. 


21. 


36^1 






EXERCISE 101. — WRITTEN 




1. 


81^1 


6. ,3 


_i_ 1 

T • S- 


11. 4 


1-21. 


2. 


l?^f 


7. 2 


1^6 -5. 


12. If -4- 30. 


3. 


U^i- 


8. 2 


H^3G^6. 


13. I 


of|-|- 


4. 


144-132 


9. 8 


^f 


14. 1 


off^l. 


5. 


3.23^1. 


10. 9 


-f- 


15. i 


^lofi- 



COMMON FRACTIONS 131 

16. 3| of 71-^61 off 18. 240-Jj^|of|. 

17. 9^J^-off^i. 19. 3|ofl|^iofi. 

EXERCISE 102. — WRITTEN 

1. If a normal child of 7 years weighs 49^- lbs., and a 
child of 8 years weighs 54| lbs., what is the average 
monthly increase in weight? 

2. If a child of 7 years has a chest measurement of 
23J ins., and a child of 8 years lias a chest measurement 
of '2-l|- ins., what is the average monthly growth in chest 
measurement? 

3. If a child of 1 year weighs 20| lbs., and a child of 
10 years weighs 6Q^ lbs., what is the average yearly increase 
in weight? 

4. A merchant buys a bill of goods : cotton goods 
$250.50, silks ^5^125. 75, notions -¥75.80. He receives a 
discount of ^ of the bill for cash. What does he pay for 
the goods? 

5. A man at hard muscular labor requires 1^ times the 
food of a man at moderate muscular work. If a man at 
hard work consumes 11-| ounces of roast beef at a meal, 
how much roast beef is required for a man at moderate 
work? 

6. If a man at moderate work requires | the amount of 
food required for a boy from 10 to 12 years of age, and 
the food of a man at moderate work for supper consists of 
3 ozs. of bread, | oz. of butter, 3 ozs. of bananas, and 
2 ozs. of cake, how much of these foods is required by 
a boy of 12 years of age? 

7. If the man requires 5 times the amount of food 



132 PRACTICAL ARITHMETIC 

required by a child of 6 years of age, how much of these 
foods is required for the 6-year-old child ? 

COMPOUND AND COMPLEX FRACTIONS 

163. An indicated multiplication of a fraction is called 
a Compound Fraction, e,.g.^ f of f or | x f is a compound 
fraction. 

164. An indicated division of a fraction is sometimes 

2 3 

called a Complex Fraction, e.g., -2- and I are complex frac- 

tions,- and are read f divided by ^ and |- divided by 5. 
They are solved as are other examples in division of frac- 
tions. ' 

EXERCISE 103. — "WRITTEN 

Reduce to simple fractions : 

12 

1. ^- 



\' 


3. 


ii. 




5. 


12 




4. 


1 

6' 




6. 


15 


¥ofi% 

iof2i 




11. 


1^. 


of6i 




3-1 of 91 




12. 


2i- 







13. 



10. -^, TiTT- 12. ^^i y^- 14. 



7. 


M. 

27 


8. 


15^ 




10 


^Ofll,^^ 


M °t' n% 


Hi- 


-8 


29J^ 


-6 



FRACTIONAL RELATIONS OF NUMBERS 

165. What part of 6 is 3 ? What part of 10 is 5 ? 
Whatpartof 63 is9? 9 is g% of 63, or f 
To find what part the second of two numbers is of the 
first, divide the second by the first. 



COMMON FRACTIONS 133 

EXERCISE 104. — OEAL 

Find what part the second number is of the first : 



1. 


16,8. 


6. 


^%l■ 


11. 


|,12. 


2. 


82,9. 


7. 


101 51. 


12. 


A' 5. 


3. 


36,4. 


8. 


n^ i- 


13. 


9' 9* 


4. 


74, 18. 


9. 


8!, 2|. 


14. 


hi 


S. 


2h H- 


10. 


6|, 3|. 


15. 


i,7. 



166. 6 is I of what number? 

Since 6 is f of the number, ^ of the number is ^ of 6, or 3. 
If 3 is ^ of the number, the number must be 3 times 3, or 9. 
Hence, 6 is | of 9. 

167. To find a number when another number and its 
fractional relation to the unknown number are given, 
divide the given number by the numerator of the fraction 
and multiply by the denominator. 

EXERCISE 105. — ORAL 

1. 99 is I of what number? 7. 16 is | of what number? 

2. 8 is f of what number ? 8. 24 is | of what number ? 

3. 16 is I of what number ? 9. 20 is | of what number ? 

4. 15 is I of what number? 10. 21 is | of what number? 

5. 72 is 1^ of what number? li. 64 is | of what number? 

6. 81 is ^-^ of what number? 12. 54 is f of what number? 

13. Tomatoes at 11.75 per dozen cans cost how much 
per can ? 

14. Corn at 90 cts. per dozen cans costs how much per 
can? 



134 PRACTICAL ARITHMETIC 

15. Dried beef at #1.80 per dozen cans costs how much 
per can? 

16. A boy has 50 cts. He spends 30 cts. for a book, and 
10 cts. for a tablet. What part of his money has he left? 

17. A boy's spending money is $1.60. He spends | of 
it for a fielder's glove. What does the glove cost? 

18. If a half-ton of coal costs $4. 50, what will 5 tons cost? 

19. If the food required by a man at moderate work is 
expressed as 100 parts, how many parts are required by 
the following? 

a, man at light work requiring -^^ of the food of man at 

moderate work. 
h, woman at moderate work requiring ^ of the food of man 

at moderate work. 

20. How many parts are required by the following? 

a, child 6 to 9 years requiring -| of the food of a man at 
moderate work. 

b, child 2 to 5 years requiring ^ of the food of a man at 
moderate work. 

c, child under 2 years requiring -^-^ of the food of a man 
at moderate work. 

d, man at hard muscular work requiring 1^ of the food of 
a man at moderate work. 

21. A boy can walk | of a mile while an automobile 
goes 4 miles. How far will the automobile have gone 
when the boy has walked 5 miles? 

22. If four boys can mow the school lawn in 1^ hours, 
how long will it take one boy? How long will it take 
two boys? 



COMMON FRACTIONS 135 

168. How many cents in |^ of a dollar? J of 1 dollar is 
16| cts., therefore, | of a dollar multiplied by any number 
is the same as 16| cts. multiplied by that number. 

169. How many cents in ^ of a dollar? ^ of a dollar is 
12| cts., therefore, ^ of a dollar multiplied by any number 
is the same as 12| cts. multiplied by that number. 

170. The part of a number which will exactly divide it 
is called an Aliquot Part of that number. 

It is often easier to multiply or divide by ^ dollars, ^ 
dollars, or ^ dollars than to multiply or divide by 12^, 16|, 
or 334 cts. 

EXERCISE 106. — ORAL 

1. What will 18 pineapples cost at 16^ cts. apiece? 

2. At 12| cts. a yard, what will 12 yards of gingham 
cost? 

3. At 33J cts. apiece, what will 15 blank books cost ? 

4. At 25 cts. each, what will 16 pairs of stockings cost? 

EXERCISE 107. — WRITTEN 

1. 40 is what part of 100? 7. 621 is what part of 100? 

2. 60 is what part of 100? 8. 87-1 is what part of 100? 

3. 80 is what part of 100? 9. 66| is what part of 100? 

4. 75 is what part of 100? 10. 83| is what part of 100? 

5. 37| is what part of 100? ii. 41f is what part of 100? 

6. 31^ is what part of 100? 12. 58^ is what part of 100? 

REDUCTION OF DECIMAL FRACTIONS 

171. Express as common fractions and change to lowest 
terms: .4, .04, .004, .0004. 



136 PRACTICAL ARITHMETIC 

Express as common fractions and reduce to lowest terms .■ 
.25, .025, .0025. 

Express as common fractions and reduce to lowest terms : 
.300, .00003. 

172. To reduce a decimal to a common fraction, write 
the figures of the decimal for the numerator, with 1 and 
as many ciphers as there are decimal places in the decimal 
number for the denominator, and reduce this fraction to 
lowest terms. 

EXERCISE 108. — WRITTEN 

Reduce to common fractions in lowest terms or to mixed 
numbers: 



1. 


0.4. 


6. 


0.7. 11. 0.55. 


16. 1.25. 


2. 


0.5. 


7. 


0.135. 12. 1.05. 


17. 17.875. 


3. 


0.115. 


8. 


0.008. 13. 5.125. 


18. 25.135. 


4. 


0.125. 


9. 


0.375. 14. 10.50. 


19. 2.9375. 


5. 


0.6. 


10. 


0.10. 15. 2.75. 

EXERCISE 109. — OEAL 


20. 7.875. 


1. 


Express 


as a 


, decimal : l |, -^-^. 




2. 


Express 


as a 


, common fraction : 0.2, 


0.4, 0.5, 0.1. 


3. 


Express 


as decimals : |, |, |, |-, |, -| 




173. Change § 
3 3.0 

8 8 


to a decimal : 
-8)3.000. 
0.375 


1 = 0.375. 



174. To reduce a common fraction to a decimal, divide 
the numerator by the denominator, placing the decimal 
point and annexing as many ciphers as are necessary to 
complete the division. 



COMMON TRACTIONS 



137 



175. If the denominator of a common fraction has other 
prime factors than 2 or 5, the division of the numerator 
cannot be completed. In such cases it is customary to 
carry out the decimal to the fifth place and to place a plus 
sign after the decimal, thus 24.28978 +. 







^ 


-""^ 


~X' 


■-- 


"7\ 








/^ 


^ 


61- 


7^ 


/ 


r 


>. 


. 


/\ 


100.001 




___^ 


/ 


169 


7 
12 


/\ 


/ \ 

/ 26.78 ";: 


< 


\ 1.45 
6 \ 
11 \ 


i / 


1 

8 


> 


/ 

\ 


27.1 \ 


/m ^H 


t 


61 

82 

11 
18 


\o\P 




/ 


9 
16^^ 

3 
11 


\ 


42§ d\ 


\l 7^ 




h 

3 
8 


6 / 




\ 

)29 


9 
29 

21 

32 


y 


/ 786.42 / 

/ 


\ 1.00! 

\k 


)3 yc 

8.4291 


1 "* 


26 \ 
3? \ 


\ 




\ 
> 


H 7 
V 


^ 


6^ 


2^ 


y 








■--___I___^ 


H 


^ 


>^ 







EXERCISE 110. — WRITTEN 

1-16. Add the number found in e to each number in 
the outer circle. 

17-32. Subtract the number in b from each number in 
the outer circle. 



138 PRACTICAL ARITHMETIC 

33-48. Subtract the nuinbei* in p from each number in 
the outer circle in all cases where it is possible. 

49-112. Multiply the numbers at b, e, g, I by each num- 
ber in the outer circle. 

113-176. Divide each number in the outer circle by the 
numbers at 6, c, g, and i, 

EXEECISE HI. — WRITTEN 

Express as decimals, carrying the division to the fifth 
place in cases of inexact decimals : 

1. 
2. 
3. 
4. 
5. 



EXERCISE 112. — WRITTEN 
REVIEVi^ PROBLEMS 

1. 160 is f of vs^hat number? 

2. 144 is j^ of what number? 

3. 160 is 1^ of what number? 

4. 180 is |- of wliat number? 

5. 364 is ^ of what number? 

6. In repairing the waste pipes of a house 4 pieces are 
needed, — 3^ ft., 9| ft., 41 ft., and 17| ft. long. What is 
the total number of feet needed? 



if- 


6. 


JL. 
II' 


11. 


u- 


16. 


A' 


f 


7. 


iV- 


12. 


3|f 


17. 


A' 


9" 


8. 


_3_2_ 
111- 


13 


37|. 


18. 


i- 


M- 


9. 


5A- 


14. 


1261^ 


19. 


if 


lOA^ 


10. 


\i- 


IS. 


4H- 


20. 


f- 



REVIEW PROBLEMS 



139 



7. A six-sided chicken yard is 3| rods on one side, 41 
on another, 51 on another, 1 yL on another, 2| on the fifth 
side, and 4 rods on the sixth side. How many rods of 
fence will be required to enclose it ? 

8. If an apple tree bears 2678 apples and J drop, and 
^ of the remaining are wormy, what fraction of the apples 
originally present is good? How many apples are good? 
If the trees are sprayed to prevent worms, only about -^ 
will be wormy. What will the fractional gain from spray- 
ing be? How many apples are gained? 

9. What is the cost of spraying 197 apple trees for 
black rot at S^ cts. a tree for each application, spraying 
3 times? Adding 1-| cts. to cover cost of arsenite of lead 
used to prevent the codling moth, what is the cost? 

10. According to the Arkansas Experiment Station, | of 
an acre of peanut pasture produced 312 lbs. of pork, and 
the same area in corn produced 104 lbs. What fraction 
of the value of peanuts as a pork producer is possessed by 
corn ? 

11. Corn at different stages of growth contains water 
and dry matter in each ton, as follows : 



Fully tasselled .... 

Fully silked 

Kernels watery to full milk 
Kernels glazed .... 
Ripe 



COKN PER 

100 Acres 



90 tons 
129 tons 
163 tons 
161 tons 
11-2 tons 



Water per 
100 Acres 



82 tons 
113 tons 
140 tons 
125 tons 
102 tons 



Dry Matter 
PER 100 Acres 



8 tons 
15 tons 
23 tons 
36 tons 
40 tons 



What fraction of the corn is dry matter in each period? 



140 PRACTICAL ARITHMETIC 

How much greater is the fraction representing dry matter 
" ripe " than " fully tasselled " ? 

12. A crib of corn holds 10,976 lbs. of ear corn. How 
many bushels of shelled corn will it yield if ^ of the ear 
corn is grain and 56 lbs. of shelled corn make a bushel? 

13. If it requires 6| acres of corn to fill a 93-ton silo, 
how many acres will it require to fill a 60-ton silo? 

14. It is estimated that good roads to a farm increase 
its value about f 9^ an acre. What would this amount to 
on a 67-acre farm? 

15. Divide the number 81 into 2 parts such that ^ of 
the first shall be f of the second. 

16. A man by working 7|- hrs. a day can complete a 
piece of work in 11|^ days, how many hours must he work 
per day so that he will complete the work in 15 days? 

17. If a boy can do | as much as a man, how many days 
will he require to complete the work in the above problem, 
working the same number of hours as the man? 

CREAMING 

18. In skimming cream from shallow pans in the usual 
way, about ^500 of the skimmed milk is butter fat. Milk 
before skimming usually contains j^^q butter fat. What 
fraction of the original butter fat is lost in skimming? 

19. If a cow produces 256 lbs. of butter fat in a year, 
how much is lost in skimming? What is its value at 
23 cts. a pound? 

20. In setting milk in deep pails and using better skim- 
ming methods, the skimmed milk is only g^^ butter fat. 



EEVIEW PROBLEMS 



141 



What fraction of the original butter fat is lost? How- 
many pounds? What value? 

21. When a hand separator is used, skimmed milk is 
only g-j^ butter fat. What fraction of the butter fat is 
lost? How many pounds? What is its value? 




22. What fraction is saved by the separator that is losti 
by the shallow-pan method? What fraction is thus saved 
that is lost by deep setting? 

23. If a cow in a year gives 6278 lbs. of milk of which 
-^ is butter fat, and -^-^-^ of this amount be lost in sepa- 



142 PRACTICAL ARITHMETIC 

rating, and there be an increase of J in weight in the 
amount remaining (due to water, salt, etc., used in mak- 
ing the butter), what will be the butter yield? 

24. How many cows will a dairyman need in order to 
save enough butter in a year, by the use of a separator, 
to enable him to pay for a |65 separator? Use the facts 
given in problems 18, 19, and 21. 

25. In one herd the average of butter fat per cow 
was 285.62 lbs. If this were all converted into butter 
containing ^ fat, what would be the amount? The best 
cow in the herd gave 439.37 lbs. of butter fat. How 
much butter does that equal? 

26. Assuming that in problem 23 -I of the whole milk 
becomes skimmed milk and that it be ^q^q q" butter fat, and 
that f of the cream becomes buttermilk containing ^^ of 
butter fat, what is the loss in butter fat? What is its 
equivalent in butter ? 

27. The cost of feed to produce 100 lbs. of milk in New 
York was as follows from 19 different cows: f .62, |.61, 
$.46, 1.55, 1.49, $.89, $.82, f.62, $1.48, $.77, $.70, $1.07, 
$.74, $.85, $.75, $.81, $.59, $.53, $.44. What was the 
average cost per pound ? 

28. The cost for each pound of butter fat was $.115, 
$.155, $.18, $.225, $.175, $.16, $.13, $.16, $.17, $.14, $.12, 
$.26, $.125, $.14, $.185, $.21, $.27, $.15, $.225. What 
was the average cost of butter fat per pound ? 

29. If a tree 9 ins. in diameter yields only -| as much 
lumber as one 18 ins. in diameter, and the lumber of 
the smaller tree is worth only | as much per foot as that 
of the larger tree, what is the difference in the value of 



KEVIEW PROBLEMS 143 

two such trees, if the smaller one yields 132 ft. of lumber 
and it is worth 1| cts. a foot? 

30. If 1 lb. of butter is composed of j.^^-^ watei-, ||| 
butter fat, -gf^^ curd, and the balance salt, how much salt 
is there in 16 lbs. of butter? 

31. A hayseed mixture consists of 3 parts red clover 
and 7 parts tall oat grass. How many pounds of each are 
needed for 27 acres, using 35 lbs. to the acre? 

32. Another mixture is red top 3 parts, orchard grass 
4 parts, meadow fescue 2 parts, and red clover 1 part. 
Using 40 lbs. to the acre, how many pounds of each kind 
of seed are needed for 29 acres? 

33. A good pasture mixture is Kentucky blue-grass 2^- 
parts, white clover 1 part, perennial rye 3 parts, red fescue 
1 part, red top 2^ parts. Sowing 35 lbs. to the acre, how 
many pounds of each are needed for 26 acres ? 

34. If, in a score card for judging butter, ^-^ of the total 
points are given for perfect flavor, ^\ for grain, ^g- for 
color, and J^ for salting, what will be the numerical value 
assigned to each in a score card of which the total number 
of points is 100 ? 

35. A hog when alive weighs 312 lbs. and the dressed 
carcass weighs |- less ; what is the weight of the dressed 
carcass ? 

36. What is the difference in cost of a 2-2-50 (2 lbs. 
of bluestone, 2 lbs. of lime, 50 gallons of water) and a 
6-4-50 Bordeaux mixture with lime at 1^ cts. a pound, 
bluestone at 6| cts. a pound ? Using 150 gallons to the 
acre, what is the difference per acre in the cost of these 
two mixtures? 



144 PRACTICAL ARITHMETIC 

37. In an Arkansas orchard 6 apple trees sprayed to 
prevent the bitter rot yielded 8674 sound apples and 989 
diseased ones; on 3 unsprayed trees 188 sound apples 
and 4244 diseased ones. What fraction was sound in each 
case? Reduce to similar fractions for comparison. How 
many times greater is the yield of sound apples when 
sprayed than when not sprayed ? 

38. Two cows, Glista and Belva, were very similar in 
outward appearance, age, and weight. Glista required 
21 cts. worth of feed to produce 1 lb. of butter fat. 
Belva produced 1 lb. for 15|- cts. What fraction of the 
feed required by Glista was sufficient for Belva ? 

39. Seven samples of clover seed sold per bushel (60 lbs.) 
for: 15.50, §5.25, 15.00, 14.75, $4:.15, .$4.00, and 13.50. 
They contained, respectively: 55^, 4^5^^^, 55y2_.^ 55^, 48, 
52^3j_ and 27-^\ lbs. of good seed to the bushel. What 
was the price paid for a bushel of good seed in each case? 

40. Concrete is made of cement, sand, and aggregate 
(coarser material, gravel, crushed stone, etc.) in quanti- 
ties of 1 part to 2 parts to 4 parts. How many pounds 
of each material are required for 4000 lbs. of concrete ? 

41. Another mixture often used is 1 to 2J to 5. Em- 
ploying this mixture, how much of each material is needed 
to make 4000 lbs. of concrete? 

42. Using the quantities 1 to 3 to 6, how many pounds 
of each ingredient are needed to make 4000 lbs. of con- 
crete ? 

43. If the entire corn plants on an acre weigh 6800 lbs., 
what is the weight of grain, cobs, stalks, leaves, and 
shucks, if 2^0" of the plant be ears, and of these | be grain 



KEVIEW PROBLEMS 



145 



May 17, tgoS. 



New Vork .Ive. 

West 33d Street 

liiberty Street , . .' 

Phlla. (MUi&Cliestiiiit Sts.).. 

[lhavb 

Baltlmoro ((!uQ(lnSts.)+ . 

Relay .....,....> 

Hanover ..** 

DoTScy ^ 



Jessup 
An 



n»poll« June $ ■ . .arr. 



Annapclls+ .arr, 

Annapolis Ive, 



46. Ill nailing a i%-in. 
piece to a f-in. piece, with a 
3-penny nail, how much will 
the nail extend beyond the 
wood? 



AnnapolisJunctlon.lve, 

Savage 

Laurel £ 

Muirkirlc. 5 

Beltsville 

Branchvtlle 

H/attsvllle 

wash I ng- jKev Hsioii) g ar. 
ton X Station J+lv. 

Rockville 

Gaithersburg 

Boyd ". 

WashlnEton June ... 

BrunswicK +.. 

Weverten 

Harper's Fernr+ .... 
Shenandoah Juno+ . 

Kemeysville 

Martinsburg + . . v. . . . $ 

North MoUDtsun 

Cherry Run+ 

Hancock + $ 

Sir John's Run 5 

Woodmont 

Orleans Road 

Baird.... < 

Magnolia 

Paw Paw 

Okonoko 

Green Spring 

Patterson Creek 

Cumberland + S 

{arrive 



Mis. 



9.0 
11.5 

iS-8 
17.9 



A M 

tsoo 
516 
523 
528 
532 
538 



17.9 
19.4 
ai.3 
24-9 
27.1 
29-9 
33-4 
4ao 
40.0 
56-5 

fits 

69.1 
82.8 
S9.8 
92.7 
9S.6 
103.0 
106.5 
114.2 
121.6 
127.6 
137-0 
142.6 
147s 
'52.9 
159-8 
163.1 
168.0 
172.8 
178.3 
185.1 
192.2 



1*1 



and \ cobs ; and \\ be stover, and of this | is stalk, -^ 
leaves, and J^ shucks ? 

44. A 3-penny standard wire nail is 1\ ins. long, a 
4-penny nail IJ ins., a 5-penny nail 1| ins., a 6-penny 
nail 2 ins., an 8-penny nail 

2| ins., a 10-penny nail 3 ins., 
and a 20-penny nail 4 ins. 
What fraction of an inch in- 
crease in length is there for 
every pennyweight increase 
between 3 pennyweights and 
10 pennyweights ? 

45. If it is desired to nail 
a |-in. board to a IJ-in. 
board with as long a nail as 
possible but not allow the 
nail to come nearer than ^^g- 
in. of going through both 
pieces, how long a nail can 
be used ? 



5 38 
542 
546 
5 54 

V^ 
003 

6 

625 

AM 



IS 
A M 

fsao 
644 
653 
714 
729 
740 
752 
807 

8 14 
82s 
836 
848 
903 

9 20 

A H 



A M 

•6.51 
t7io 

725 
738 

804 
820 
A M 



47. In nailing a -J-in. piece 
to a 1-in. piece, with a 5- 

penny nail, how much will the nail lack of reaching 
through the wood ? In using a 6-penny nail, how much 
will it project beyond the wood? In each of the 



146 PRACTICAL ARITHMETIC 

above cases what will be the result if the nail be coun- 
tersunk -jJg in. ? 

48. The table on page 145 is a reproduction of a 
Baltimore and Ohio time-table showing the distances 
between stations in miles. 

How far is it from Baltimore to Washington? From 
Annapolis Junction to Washington ? Washington to 
Harper's Ferry? Harper's Ferry to Cumberland? Mar- 
tinsburg to Cumberland? Annapolis Junction to Mag- 
nolia ? 

49. What ■ would be the cost for each of these dis- 
tances at the following rates per mile, which are charged 
by some railroads: 2 cts., 2^ cts., 2| cts., and 3^ cts. ? 

50. If a farm is |^ in corn, ^f in wheat, -^^ in clover, 
1^ in oats, -^-^ in pasture, and the remaining 5 acres is occu- 
pied by houses, other buildings, etc., what is the size of 
the farm, and how many acres are in each crop? 

51. A man left to his son ^ of his estate, to one 
daughter |, to the other daughter the remainder, amount- 
ing to f 3268. What was the value of the estate? 

52. Walton caught | as many fish as Clara, who 
caught j- as many as Vernon, whose catch is 63. How 
many fish did Walton catch? 

53. A horse is worth 7 times the buggy. What part 
of the value of the horse is ^^ the value of the horse and 
buggy? 

54. It is estimated that about 1700,000,000 are lost 
annually in the United States through insect and fungous 
diseases ; | of this could be prevented by spraying. 
What amount could be saved by spraying? 



ACCOUNTS AND BILLS 

176. A Debt is that wliich one person owes to another. 

177. A Debtor is a person who owes. 

178. A Credit is that wliich is due one person from 
another. 

179. A Creditor is tlie person to whom the debt is due. 

180. An Account is a record of debits and credits. 

181. A Balance of an account is the difference between 
the sums of the debits and credits. 

182. A Bill describes the goods sold by giving quantity 
and price. 

183. The Footing of a bill is the total cost. 

184. A Receipt acknowledges the payment of a bill. 

A bill is receipted by the creditor's writing the words 
" Received Payment " and his signature. 

185. ORDERING GOODS 

Hendersonville, S.C, 
Sept. 10, 1908. 

Chisholm, Ward & Co., 

Market and Madison Sts., 
New York, N.Y. 
Dear Sirs : Please find enclosed 18.37, for which send 
me by express the following items : 

147 



148 



PRACTICAL ARITHMETIC 



Catalogue No. 


QCTANTITY 


Articles Wanted 


Price Each 


C. S. 40805 
B3137 
C6490 
B4692 


1 
1 
1 
1 


A^'ickless 2-burner Kerosene Stove 
Utility Wasliiiig-machine 
Eclipse Food Chopper 
Empire Clothes Wringer 


$3.13 

2.65 

.70 

1.89 



Yours truly, 

(Mrs.) James A. Monroe. 

186. An itemized bill of the above form is received by 
Mrs. Monroe with the full amount of the cost of the arti- 
cles stated and the words, "Received Payment," with the 
signature of the firm. 



EXERCISE 113. — WRITTEN 







Raleigh, N.C. 






Jan. 7, 1908. 


Adams, 








Bought 


of John G. Stroud. 


5 lbs. Coffee 




@$.30 


1 


20 lbs. Sugar 




@ .05| 




3 doz. Eggs 




@ .23 




1 lb. Cheese 




@ .15 




2 lbs. Butter 




@ .28 





Compute the amount of each item, place in a column at 
the right of the double line, add, and make a receipt. 

Mrs. C. J. Adams, wishing to stock her pantry for the 
first time, orders the supplies mentioned below. Make 
out each number as a separate order to any firm you wish, 



ACCOUNTS AND BILLS 149 

complete it as a bill, and write a receipt indicating its 
payment. 

2. Cereals: 1 bbl. flour |7 ; 10 lbs. graham flour @ 3 
cts. ; 10 lbs. corn meal @ 3 cts. ; 10 lbs. hominy @ 3J cts. ; 
4 pkgs. breakfast foods @ 10 cts. ; 1 pkg. corn starch 10 
cts. ; 10 lbs. rice @ 9 cts. ; 2 lbs. macaroni @ 15 cts. ; 3 
lbs. tapioca @ 7 cts. 

3. Sugars : 25 lbs. granulated sugar @ 6 cts. ; 5 lbs. 
cut loaf sugar @ 10 cts. ; 2 lbs. pulverized sugar @ 10 
cts. ; 10 lbs. brown sugar @ 5J cts. 

4. Canned vegetables : corn, 6 cans@ f 1.50 a dozen; 
peas, 6 cans @ $ 1.50 a dozen ; tomatoes, 12 cans @ $ 1.35 
a dozen. 

5. Canned fruits : peaches, 6 cans @ f 3 a dozen ; cher- 
ries, 2 cans @ 25 cts. ; plums, 2 cans @ 25 cts. 

6. Dried fruits : raisins, 2 lbs. @ 15 cts. ; currants, 
2 lbs. @ 13 cts. ; prunes, 5 lbs. @ 15 cts.; evaporated 
apricots, 2 lbs. @ 19 cts. 

7. Dried vegetables : dried black beans, 1 quart, 10 
cts. ; dried Lima beans, 5 quarts @ 15 cts. ; dried white 
beans, 1 peck, 75 cts. ; split peas, 2 quarts @ 10 cts. 

8. Canned meats : ham, 2 lbs. @ 30 cts. ; tongue, 2 
lbs. @ 30 cts. ; salmon, 2 cans @ 20 cts. 

9. Beverages : coffee, 1 lb., 35 cts.; tea, 1 lb., 75 cts.; 
cocoa, ^ lb. @ 88 cts.; chocolate, 1 lb., 35 cts. 

10. Sundries : 1 gal. vinegar, 25 cts. ; 1 gal. New 
Orleans molasses, 60 cts. ; baking soda, 2 lbs. @ 8 cts. ; 
cream of tartar, 1 lb., 50 cts.; baking powder, 1 lb., 54 
cts.; salt, 25 lbs., 25 cts.; white pepper, i lb. @ 50 cts. 



DENOMINATE NUMBERS 

187. How many inches are there in 1 foot ? Express 
2^ feet as feet and inches. 

A concrete number wliich represents one kind of unit is 
called a Simple Number ; e.g., 2^ ft. is a simple number. 

188. A concrete number which is expressed in differ- 
ent units is called a Compound Number, e.ff., 2 ft. 6 ins. is 
a compound number. 

189. Concrete numbers denoting units of measure are 
called Denominate Numbers, e.g., 2|- ft. is a denominate 
number. 

190. A denominate number composed of units of one 
denomination is called a Simple Denominate Number, e.g., 
2^- ft. is a simple denominate number. 

191. A denominate number composed of units of more 
than one denomination is called a Compound Denominate 
Number, e.g., 2 ft. 6 ins. is a compound denominate 
number. 

192. A unit of measure from which other units are 
derived is called a Standard Unit; e.g., the dollar is a 
standard unit of money, the pound is a standard unit of 
weight, the yard is a standard unit of measure of length. 

193. The process of changing the unit of a denominate 
number from one denomination to another without chang- 

150 



DENOMINATE NUMBERS 



151 



ing the value is called Reduction, 
e.g., changing 1 yd. to 36 ins. 

194. If the change be from a 
higher to a lower denomination, 
the process is called Descending 
Reduction ; if from a lower to a 
higher, it is called Ascending Re- 
duction, e.g., changing 1 yd. to 
36 ins. is descending reduction ; 
changing 24 ins. to 2 ft. is ascend- 
ing reduction. 

195. UNITS OF LENGTH 

A line has length only. Meas- 
ures that are used in measuring 
lines are called Linear measures. 

196. _ TABLE OF LINEAR 

MEASURES 

12 inches (ins.) = 1 foot (ft.) 
3 feet or 36 ins. = 1 yard (yd.) 
5|^ yards, or 1Q\ ft. = 1 rod (rd.) 
320 rods, or 5280 ft. = 1 mile 
(mi.) 

The folio-wing abbreviations are 
also commonly used : ' to represent 
feet and " to represent inches. 

EXERCISE 114. — ORAL 

1. How many inches are there 
in 5 ft.? In 10 ft.? 

2. How many feet are there in 
3 yds.? In 7 yds.? 



— 


« 


.-. — 
M — 
CO = 
^ = 
01 = 
0) = 

^ = 

00 = 


— 


— 


- 


— 


— 


lO 


— 


— 


- 


— 




Tfl 


— 






- 


— 




CO 


(0 = 

M — 


— . 




- 


^ 




(M 


— 


10 = 

CO = 

01 = 


— 


- 


— 


— 


iH 


— 


— 


- 


— 



152 PEACTICAL ARITHMETIC 

3. How many feet are there in 2 rds. ? In 4 rds. ? 

4. How many inches are there in 2 yds. ? In 2 ft. 3 ins. ? 

197. Reduce 12 yds. 2 ft. 8 ins. to inches. 

Since 3 ft. = l yd., in 12 yds. there are 12 x 3 ft. = 36 ft. 
36 ft. + 2 f t. = 38 ft. 

Since there are 12 ins. in a foot, in 38 ft. there are 38 x 12 
ins.=456 ins. 466 ins. +8 ins. =464 ins. Hence 12 yds. 2 ft. 
8 ins. =464 ins. 

198. To reduce a compound denominate number to 
lower units, multiply the number of the highest denomi- 
nation by the number of units required to change to the 
next lower denomination, and to the product add the 
number of units of this denomination given. Proceed in 
like manner with this result and each successive result 
obtained until the number is reduced to the required 
denomination. 

EXERCISE 115. — WRITTEN 

Reduce to inches: Reduce to feet : 

1. 2 yds. 2 ft. 6 ins. 5. 2 mis. 15 rds. 6 ft. 

2. 4 rds. 2 yds. 1 ft. 6. 3 mis. 30 rds. 15 ft. 

3. 25 rds. 12 ft. 4 ins. 7. 25 rds. 10 ft. 4 ins. 

4. I rds. 8. 3.875 mis. 

9. Measure the length, width, and height of your school- 
room, and express as feet, as inches, as yards, as rods, and 
as fraction of a mile. 

EXERCISE 116. — ORAL 

1. How many feet in 24 ins. ? In 36 ins.? In 18 ins. ? 

2. How many yards in 30 ft.? In 48 ft. ? In 36 ft. ? 



DENOMINATE NUMBEKS 153 

3. How many rods in 33 yds.? In 66 yds.? In 77 yds.? 

4. How many rods in 11 yds.? In 23 yds.? In 99 yds.? 

199. Reduce 250 ins. to yards, feet, and inches: 

Since 12 ins. equal 1 ft., J^ of 250 ins. = 20 = tlie number of 
feet, with 10 ins. remainder. Since 3 ft. = 1 yd., { of 20 = 
6 = number of yards, witli 2 ft. remainder. Hence, 250 ins. 
= 6 yds. 2 ft. 10 ins. 

200. To reduce a denominate number to an equivalent 
number of higher denomination, divide the given num- 
ber by the number representing the units of the next 
higher denomination. Proceed with this and each succes- 
sive quotient in like manner until the required denomi- 
nation is reached. The last quotient with the remainders 
will be the required compound denominate number. 

EXERCISE 117. — WRITTEN 

1. Reduce 950 ins. to feet. 

2. Reduce 496 ins. to feet, 

3. Reduce 8966 ins. to yards. 

4. Reduce 375 ft. to rods and yards. 

5. Reduce 42,560 yds. to rods and miles. 

6. Reduce 35'6|^ rds. to miles. 

201. METRIC UNITS OF MEASURE 

In many foreign countries and to an increasing ex- 
tent in our own country, another system gf measures called 
the Metric System is used. This system is founded upon 
10, as are decimal fractions, and is simpler and easier for 
purposes of computation than are other systems. 



154 



PRACTICAL ARITHMETIC 



202. METRIC LINEAR MEASURES 

10 millimeters (mm.) = 1 centimeter <^cm.) 
10 centimeters (cm.) = 100 mm. = 1 decimeter (dm.) 
10 decimeters = 100 cm. = 1000 mm. = 1 meter (m.) 

1000 m. = 1 kilometer (km.) 
The meter is the unit of measure corresponding to the 
yard. It is 39.37 ins. long. 1 km. = .62138 mi. 

EXERCISE 118. -ORAL 

1. What part of a meter is 1 centimeter? 3 cm.? 

2. What part of a meter is 1 millimeter? 6 mm.? 

3. What part of a meter is 100 millimeters? 500 mm.? 

4. Measure the length, width, and height of your school- 
room, and express as meters ; as centimeters. 

203. REPRESENTATION OF MAGNITUDES 

A clear conception of the relative sizes of numbers 
is often gained by representing the numbers by lines, let- 
ting the length of the line bear direct relation to the size 
of the number, e.g., the approximate amount of wheat 
produced in 1900 was: United States 520,000,000, Russia 
400,000,000, France 300,000,000 bushels. Letting a line 
\ in. long represent 50,000,000 bushels, a line 1^ ins. long 
would represent the yield of France, 2 ins. that of Russia, 
2| ins. that of the United States, thus: 

50 100 150 800 260 300 350 400 4B0 500 



UNITED STATES 

RUSSIA 

FRANCE 



DENOMINATE NUMBERS 



155 



EXERCISE 119. — WRITTEN 



100 



90 



1. Represent the coal production of the following coun- 
tries in metric tons. Let { in. equal 2n,000,000 metric 
tons. The production was as follows : The United States 
225,000,000, the United Kingdom 225,000,000, Germany 
155,000,000, Austria-Hungary 37,500,000, and France a 
trifle over 25,000,000 metric tons. 

2. Represent the silk pro- 
duction of the following 
countries, letting ^ in. rep- 
resent 1,000,000 pounds: 
China 14,000,000, Japan 
7,000,000, Italy 7,000,000, 
Turkey, France, Spain, and 
India together 3,000,000 lbs. 

3. Represent the cotton 
production, letting { in. 
equal 1,000,000 bales : 
The United States 10,250,- 
000, India 2,250,000, China 
1,250,000, Egypt 1,165,000. 

4. Represent the corn 
production in 1898, ^ in. 
representing 100,000,000 ssMay 83 
bushels. The production 
of the United States was 2,100,000,000 
countries about 700,000,000. 

204. Change in a quantity from time to time may be 
clearly shown by arranging, side by side, the lines repre- 



50 



40 



SO 



20 



10 



34 
Fig. a 



that of other 



166 



PRACTICAL ARITHMETIC 



senting the varying magnitudes so that they may be 
readily compared ; thus, the highest temperature for May 
22d, at a given place, was 75 degrees, the 23d 80 de- 
grees, the 24th 85 degrees, the 25tli 96 degrees, and the 
26th 76 degrees. Rejiresenting the temperature by ver- 
tical lines, 1 degree = 1 mm., at equal distances apart, 
and connecting the tops of these lines, we have figure A 
on the preceding page. This is called a Curve. The 
vertical lines are unnecessary, the curve alone being suf- 
ficient to picture the facts. 



I860 

soot 



1870 



1880 



1890 



190O 



iu 700 

I 

«D 

= 600 

O 500 

400 
g 300 
^ 200 

1 100 






Fig. B. — Curves showing the relative increase in population and in wheat 
production in the United States, wheat and population both expressed in 
millions. 



EXERCISE 120. — "WRITTEN 

1. Interpret in words the meaning of the curves shown 
in the above figure. 

2. The maximum price of corn per bushel in Chicago 
in May during 9 years was as follows : In 1893, 38 cts., 
in 1894, 55 cts., in 1895, 29 cts., in 1896, 25 cts., in 1897, 
37 cts., in 1898, 35 cts., in 1899, 40 cts., in 1900, 58 cts.. 



DENOMINATE NUMBERS 157 

in 1901, 65 cts. Show these values hj a curve, letting 
2 mm. represent 1 cent. Place the lines representing years 
1 cm. apart. 

3. The maximum v^holesale price of wheat per bushel 
in Chicago in 1905 was as follows: Januarj^ 11.21, Feb- 
ruary 11.24, March 11.19, April fl.l8. May 11.14, 
June 11.20, July 11.20, August 11.15, September 10.95, 
October 10.92, November |!0.92, December |0. 90. Show 
the changes in price by a curve, letting 1 cm. represent 1 
cent. Place the lines representing months 1 cm. apart. 

SURFACE MEASURE 

205. A surface has two dimensions. Length and Width. 

206. If a surface is flat and has four square corners, it 
is called a Rectangle. 

207. A rectangle with four equal sides is called a 
Square. 

208. The unit of surface is a square. A square inch 
is a square each side of which is 1 in. long. A square 
foot is a square each side of which is 1 ft. long. A 
square yard is a square each side of which is 1 yd. long. 

209. The Area of a surface is expressed by the number 
of square units it contains. 

BXEECISB 121. — ORAL 

1. A rectangle is 6 ft. long and 1 ft. wide. How 
many square feet are there in its surface? How many 
square feet if it is 2 ft. wide? 3 ft. wide? 6 ft. wide? 



158 



PRACTICAL ARITHMETIC 



2. How many square inches are there in a square 
whose sides are 5 ins.? 6 ins.? 8 ins.? 10 ins.? 12 ins.? 

3. How many square centimeters are there in a square 
whose sides are 6 cm. long? 7 cm. ? 9 cm. ? 18 cm. ? 

4. How many square rods in a school lot whose sides 
are 8 rods ? 9 rods ? 11 rods ? 13 rods ? 



210. 



SQUARE MEASURE 



144 square inches (sq. ins.) = 1 square foot (sq. ft.) 
9 square feet = 1 square yard (sq. yd.) 
30^ square yards = 1 square rod (sq. rd.) 
160 square rods = 1 acre (A.) 

640 acres = 1 square mile (sq. mi.) 



METRIC SQUARE MEASURE 

100 square rnillimeters (sq. mm.) = 1 square centi- 
meter (sq. cm.) 
100 square centimeters = 1 square deci- 
meter (sq. dm.) 
100 square decimeters = 1 square meter 

(sq. m.) 
10,000 sq. m. = 1 hectare = 2.4711 A. 



DENOMINATE NUMBERS 159 

EXBBCISB 122. — WRITTEN 

Reduce to square inches : Reduce to square yards : 

1. 13 sq. yds. 5 sq. ft. 6. 130 sq. rds. 12 sq. yds. 

2. 19 sq. rds. 7 sq. ft. 7. 2 sq. mis. 80 sq. rds. 

3. 26 sq. rds. 6 sq. ft. 8. 8 A. 5 sq. rds. 29 sq. ins. 

4. I sq. rd. 9. 5.47 A. 

5. ^ sq. m. to sq. cm. 10. 86.4 sq. m. to sq. mm. 

11. Measure the area of tlie floor, and eacli of the four 
walls of your schoolroom, and express as square feet ; as 
square yards. 

EXERCISE 123. — WRITTEN 

Reduce to higher denominations : 

1. 6740 sq. ins. 4. 22,160 sq. ft. 7. 12,346 sq. rds. 

2. 984 sq. ins. 5. 9678 sq. yds. 8. 39,271 sq. rds. 

3. 540 sq. ram. 6. 6782 sq. cm. 9. 3240 sq. cm. 

SURVEYORS' MEASURES 

211. Surveyors in measuring use a Chain consisting 
of 100 links ; its length is 4 rds., or 66 ft. 

212. TABLE OF SURVEYORS' LINEAR MEASURE 

7.92 inches =1 link (1.) 
25 links = 1 rod (rd.) 
4 rods = 100 1. = 1 chain (ch.) 
80 chains = 1 mile (mi.) 



160 PRACTICAL ARITHMETIC 

213. TABLE OF SURVEYORS' SQUARE MEASURE 

16 square rods = 1 square chain (sq. oh.) 
10 square chains = 1 acre (A.) 

640 acres = 1 square mile (sq. mi.) 
1 square mile= 1 section (sec.) 
36 sections = 1 township. 

BXEECISE 124. — WRITTEN 

1. Reduce 1560 sq. yds. to chains. 

2. Reduce 960 sq. chs. to acres. 

3. Reduce 67,820 ins. to chains. 

4. Reduce | mi. to chains. 

5. Reduce 60 chs. to feet ; to inches. 

6. Measure the distance around your school yard. Ex- 
press in chains ; in links ; in feet ; in rods ; in yards. If 
rectangular, how many square chains does it equal ? What 
fraction of an acre ? 

MEASURES OF VOLUME 

214. A body that has length, width, and thickness is 
called a Solid. 

215. If the rectangles forming the faces of a solid are 
squares, the solid is called a Cube. 

216. The number of solid units that a body contains is 
called the Solid Contents or Volume. 

EXERCISE 125. — ORAL 

1. How many cubic inches are there in a rectangular 
solid 1 in. long, 1 in. wide, and 1 in. thick ? 



DENOMINATE NUMBERS 



161 



2. How many cubic feet are there in a solid 1 ft. long, 
1 ft. wide, and 1 ft. thick ? How many cubic inches ? 
What is the name of such a solid? 

3. How many cubic yards are there in a solid 1 yd. 
long, 1 yd. wide, and 1 yd. thick? How many cubic 
feet ? Name such a solid. 



IIIIIIIIIII' 



217. UNITS OF VOLUME, OR CUBIC MEASURE 

1728 cubic inches (cu. ins.) = 1 cubic foot (cu. ft.) 
27 cubic feet = 1 cubic yard (cu. yd. ) 
1^ cubic feet = 1 bu. (approximately) 



218. 



METRIC CUBIC MEASURE 



1000 cubic millimeters = 1 cubic centimeter (cc.) 
1000 cubic centimeters = 1 cubic decimeter (cdm.) 
1000 cubic decimeters = 1 cubic meter (cbm.) 



EXERCISE 126. —WRITTEN 

Reduce to cubic inches : 

1. 10 cu. ft. 14.5 cu. ins. 3. -^ cu. yd. 



2. 46 cu. ft. 149 cu. ins. 



4. I cu. ft. 



162 PRACTICAL ARITHMETIC 

5. 45 cu. yds. 18 cu. ft. 

6. 8 cu. yds. 16 cu. ft. 425 cu. ins. 

7. 29 cu. yds. 12 cu. ft. 1-J cu, ins. 

8. 15 cu. yds. 1234 cu. ins. 

9. 72 cu. yds. 25 cu. ft. 

10. 15 cu. yds. 16 cu. ft. 
Reduce to cubic centimeters : 

11. 15 cbm. 5 cdm. 10 cc. 13. 200 cbm. 125 cdm. 

12. 300 cbm. 150 cdm. 14. 275 cbm. 165 cdm. 15 cc. 

EXERCISE 127.— "WRITTEN 

Reduce to units of liigher denominations : 

1. 12,865 cu. ins. 4. 4256 cu. ins. 

2. 924 cu. ft. 5. 98,764 cu. ins. 

3. 6573 cu. ins. 6. 325 cu. ft. 

7. How many cubic yards in your schoolroom ? How 
many cubic feet? Cubic inches? 

8. How many cubic centimeters in your schoolroom? 
How many cubic meters ? 

219. DRY MEASURE 

2 pints (pts.)= 1 quart (qt.) 
8 quarts = 1 peck (pk-) 
4 pecks = 1 bushel (bu.) 

A bushel contains 2150.42 cubic inches. 

The dry quart contains 67.2 cubic inches., 

A Heaped Bushel, which equals about 1^ Stricken Bushels, 



DENOMINATE NUMBEKS 



163 



is used in measuring potatoes, apples, and other large vege 
tables, also for lime, coal, and other bulky substances. 




EXERCISE 128. — ORAL 

1. How many pints in 5 qts.? In 7 qts.? In 2 pks. ? 
In 1 bu.? In 2 bus.? 

2. How many quarts in 3 pks.? In 3 bus.? In 1 bu. ? 
In 12 bus.? 

3. How many bushels in 20 pks.? In 25 pks.? In 36 
pks.? In 16 qts.? 

4. How many pints in 1 bu. 2 qts. 1 pt.? 



EXERCISE 129. — WRITTEN 

Reduce to pints : Reduce to higher units : 

1. 5 bus. 3 pks. 5 qts. 4. 2254 qts. 

2. 5 bus. 2 pks. 3 qts. | pt. 5. 3360 pts. 

3. .625 pk. 6. 4800 pks. 



U'A 



PKACTICAL ARITHMETIC 



Reduce the following to fractions of a bushel. Express 
both as decimals and as common fractions : 

7. -f^ pt. 8. f qt. 9. I pk. 10. 2 pks. 8 qts. 

11. Get a bushel of sand or grain and a quart measure, 
and practise estimating quarts, pints, and pecks to see 
who can make the most accurate estimates at sight. 



220. 



LIQUID MEASURE 




4 gills (gis.) = 1 pint (pt.) 
2 pints = 1 quart (qt.) 
4 quarts = 1 gallon (gal.) 

A gallon contains 231 cubic inches. 

31^ gals, are usually •considered a barrel, and 2 barrels a 
hogshead. 

221. METRIC LIQUID MEASURE 

10 milliliters (ml.) = 1 centiliter (cl.) 
10 centiliters = 1 deciliter (dl.) 
10 deciliters = 1 liter (1.) 

1 milliliter = 1 cubic centimeter. 1 milliliter of water weighs 
1 gram. 



DENOMINATE NUMBERS 165 

EXBBCISB 130. — ORAL 

1. How many gills are there in 6 pts. ? In 10 pts. ? 

2. How many gills are there in 5 qts. ? In 8 qts. ? 

3. How many pints are there in 8 qts. ? In 12 qts. ? 

4. How many quarts are there in 60 pts. ? In 45 pts. ? 

5. How many milliliters are there in 3 1.? How many 
cubic centimeters in 7 1. ? 

EXEBCISE 131. — WRITTEN 

Reduce to units of lower denomination : 

1. 12 gals. 2 qts. 1 pt. 5. 14 gals. 2 qts. 1 pt. 1 gi. 

2. 25 gals. 1 qt. 1 pt. 2 gis. 6. 45 gals. 2 qts. 1 pt. 3 gis. 

3. I gal. 7. .225 gal. 

4. I gal. 8. J_. gal. 
Reduce : 

9. 12 liters to deciliters. 10. -^ liter to milliliters. 

With a pail of water and pint and quart measures, be- 
come familiar with all of these units. 

EXERCISE 132. — WRITTEN 

Reduce to units of higher denomination : 

1. 145 pts. 8. I gi. to fraction of quart. 

2. 424 gis. 9. 1 qt. 1 pt. to decimal of gallon. 

3. 380 pts. 10. 786 qts. to bbl. and fraction. 

4. 1984 gis. 11. 6.7 gis. to decimal of gallon. 

5. 1286 qts. 12. 29 cu. ft. to gallons. 

6. 1254 pts. 13. 1728 pts. to hogsheads and fraction. 

7. -j-9j deciliter to 14. 7| gals, to decimal of barrel. 

liter. 



166 
222. 



PRACTICAL ARITHMETIC 

MEASURES OF WEIGHT 
Avoirdupois Weight 




16 drams (drs.) = 1 ounce (oz.) 
16 ounces = 1 pound (lb.) 
100 pounds = 1 hundredweight (cwt.) 
20 hundredweight .= 2000 lbs. = 1 ton (T.) 
1 avoirdupois pound = 7000 grains. 

A cubic foot of water weighs 62.42 pounds. 

The ton of 2000 lbs. is sometimes called a Short Ton, the 
Long Ton being 2240 lbs. The long ton is used in measuring 
coal at the mines. 

500 cu. ft. of hay in loads, or 



400 cu. ft. of hay in the mow 



= 1 ton (approximately) 



223. 



METRIC UNITS OF WEIGHT 




Kilo 



im^ 



10 milligrams (nig.) = 1 centigram (eg.) 
10 centigrams = 1 decigram (dg.) 
10 decigrams = 1 gram (g.) 
1000 grams = 1 kilogram (kilo or k.) 



DENOMINATE NUMBERS 167 

A gram weighs 15.432 grains ; it equals the weight of a 
cubic centimeter of water. 

1 pound = .45+ kilogram. 

EXERCISE 133. — DEAL 

1. How many ounces are there in 6 lbs. ? In 9 lbs.? 

2. How many ounces are there in 5 cwts. ? In 7 cwts. ? 

3. How many ounces are there in T. ? In 8 cwts. ? 

4. How many pounds are there in 44 ozs.? In 100 cwts.? 

5. How many tons are there in 60 cwts. ? In 100 cwts.? 

BXBECISE 134. — WRITTEN 

Reduce : 

1. 3 cwts. 21 lbs. 6 ozs. to ounces. . 

2. 10 T. 50 cwts. 15 lbs. to pounds. 

3. I T. to pounds. 4. 5 g. 10 dg. to milligrams. 

5. .375 T. to hundredweights. 

6. ^Q T. to pounds. 

7. 17 cwts. 15 lbs. 3 ozs. to ounces. 

8. 2 T. 10 cwts. 25 lbs. to pounds. 

9. .675 cwt. to pounds. 11. 21 lbs. 6 ozs. to grams. 
10. .5 T. to hundredweights. 12. 26 g. to grains. 

EXERCISE 135. — WRITTEN 

Reduce to units of higher denominations : 

1. 2500 ozs. 4. 5275 lbs. 7. 15,674 cwts. 

2. 9546 ozs. 5. 4250 ozs. 8. 2654 grs. to lbs. 

3. 1056 mg. 6. 5420 mg. 9. 5460 grs. to g. 



168 PRACTICAL ARITHMETIC 

10. Tie up packages of sand or grain of various weights, 
and practise lifting them until you can judge weight with 
some accuracy. 

224. MEASURES OF TIME 




60 seconds (sees.) = 1 minute (min.) 
60 minutes = 1 hour (1 hr.) 
24 hours = 1 day (da.) 
7 days = 1 week (wk.) 
12 months (mos.) = 1 year (yr.) 

" Thirty days hath September, 
April, June, and November, 
All the others thirty-one 
Except the second month alone, 
Which hath but four and twenty-four 
Till Leap Year gives it one day more." 

The common year has 365 days, or 52 weeks and 1 day. 
The leap year has 366 days. Years whose numbers are divisi- 
ble by 4 and not by 100, or by 400, are leap years. 

A decade consists of 10 years ; a score, 20 years, and a cen- 
tury, 100 years. 

EXERCISE 136. — ORAL 

1. How many seconds are there in 3 mins.? In 10 
mins.? In 15 mins. ? In 15 mins. 20 sees. ? 



DENOMINATE NUMBERS 169 

2. How many minutes are there in 2 hrs. ? In 6 hrs. ? 
In 6J hrs. ? In 8^ hrs. ? 

3. Howmany hours inS days? In 4i- days? In 5| days? 

4. How many days in 2 wks. ? In 5|- wks. ? In 5 wks. ? 
In 5 days? 

5. How many days in 2 years? In 2 leap years? 

EXERCISE 137. — WRITTEN 

Reduce to units of lower Reduce to units of higher 

denomination : denomination : 

1. 6 hrs. 25 mins. 10 sees. 5. 2460 mins. 

2. 10 days 5 hrs. 12 mins. 6. 142.2 hrs. 

3. f day. 7. 89,764 sees. 

4. 867 days. 8. |- hr. to fraction of a da}'. 
9. Practise estimating a second and a minute until 

you can do so with some accuracy. 

ANGLE MEASURE 

225. A Circle is a plain surface bounded by a curved 
line, the circumference, every point of which is equally 
distant from a point within, called the Centre. 

226. A straight line drawn through the centre of a 
circle from one point in the circumference to another is 
called the Diameter of the circle. 

227. A Section of the circumference is called an Arc. 

228. The diameter exactly divides the circle. 

229. One-half the diameter is the Radius. 



170 



PRACTICAL ARITHMETIC 



A 



C 



230. The difference in the direction of two lines that 
meet is called an Angle. 

231. A line which cuts an- 
other line making with it two 
equal adjacent angles is said to 
be Perpendicular to the other 
line, e.g., the line AB is per- B 
pendicular to the line CB. The two angles made by the 
line AB with the line CB are equal. Each of the angles 
so made is called a Right Angle, e.g., the angles ABQ 

and ABB are right angles. 

232. The circumference 
of a circle is measured in 
Degrees. There are 360 
degrees in a whole circum- 

^08ti— J ^ I Lo a ference. Degrees are not 

of uniform length, but 
vary with the circumference of the circle, e.g., the cir- 
cumference of the circle A measures 360 degrees as does 
also the circumference of the circle B. Degrees are 
divided into minutes and seconds. 




233. TABLE or ANGLE MEASURE 

60 seconds (") = 1 minute (') 
60 minutes = 1 degree (°) 
360 degrees = 1 circle. 

EXERCISE 138. — ORAL 

1. How many degrees are there in a circumference? 

cir- 



In a half circumference? 
cumference? 



In I circumference? 



In 



DENOMINATE NUMBERS 171 

2. If one line is drawn perpendicular to another, how 
many degrees are there in each angle so made? How 
many degrees in the two angles? 

3. How many degrees are there in a right angle? 
What is the difference between a right angle and an 
angle of 60°? Of 90°? Of 100°? Of 120°? 

4. What part of aright angle is 45°? 30°? 

5. How many minutes in 6°? 8°? 24°? 

6. How many seconds in 3'? 5'? 1°, 6', 6"? 

EXERCISE 139. — ■WRITTEN 

1. Draw an angle of 45 degrees ; 90 degrees ; 120 de- 
grees ; 180 degrees. 

2. Reduce 40° 20' 20 " to seconds. 

3. Reduce 43,200" to degrees. Draw an angle having 
the number of degrees found. 

4. Determine the number of degrees of " pitch " of 
some roof that is accessible to you. 

234. COUNTING 

12 things = 1 dozen (doz.) 
12 dozen = 1 gross (gr.) 
12 gross = 1 great gross (g. gr.) 
20 things = 1 score. 
24 sheets of paper = 1 quire. 

EXERCISE 140. — ORAL 

1. A crate contains 492 eggs; how many dozen? 

2. A single card contains 24 hooks and eyes. How 
many gross are there on 48 cards? 

3. How many years are three score and ten? 



172 PRACTICAL ARITHMETIC 

ADDITION AND SUBTRACTION 
EXERCISE 141. — ORAL 

Add: 

1. 12 ft. 1 in. 2. 7 days 1 hr. 3. 12 lbs. 5 ozs. 
13 ft. 9 ins . 8 days 12 hrs. 16 lbs. 9 ozs. 

4. 120° 14' 12" 5. 20 rds. 4 yds. 1 ft. in. 
10° 15' 30'' 10 rds. 1 yds. ft. 6 ins . 

235. 

16 lbs. 4 ozs. Addition and subtraction of com- 

25 lbs. 3 ozs. pound numbers is performed in the 

18 lbs 12 07S same manner as with simple numbers, 

FQ 1, ^ — T^ ; the only difference being that units of 

oy IDS. i-v ozs.^ or Til • 1 



60 lbs. and 3 ozs. 



compound numbers have a varying scale 
of value, while with simple numbers the 
scale is uniformly ten. 

Add the numbers of eacb denomination separately, then 
reduce the sums to the highest units possible. 

EXERCISE 142. — WRITTEN 

Add: 

1. 12 lbs. 12 ozs. 4. 13 bus. 3 pks. 5 qts. 

18 lbs. 10 ozs. 25 bus. 4 pks. 4 qts. 

9 bus. 1 pk. 1 qt. 1 pt. 
54 bus. 2 pks. 1 qt. 

5. 18 gals. 1 qt. 1 pt. 
68 gals. 1 qt. 

25 gals. 3 qts. 1 pt. 

13 gals. 1 qt. 1 pt. 



2. 73 rds. 


5 ft. 


18 rds. 


9 ft. 


3. 12 lbs. 


8 ozs. 


25 lbs. 


6 ozs. 



DENOMINATE NUMBERS 173 

BXBRCISB 143. — OBAIi 

Subtract : 

1. 15 ft. 9 ins. 3. 150° 16' 16" 

9 ft. 4 ins. 100° 8' 10'' 

2. 27 T. 12 cwts. 11 lbs. 4. 3 yds. 31 ft. 

1 T. 10 cwts. 10 lbs . 1 yd. 2 ft. 6 ins. 

236. Subtract: 

45 bus. 3 pks. 1 qt. pt. In the first right-hand col- 

39 bus. 1 pk. qt. 1 pt. ^^^ we have 1 pt. to be sub- 
tracted from pt., which is 
impossible. Taking 1 qt. from the quarts column and chang- 
ing it to pints gives 2 pts. 1 pt. subtracted from 2 pts. leaves 

1 pt. Completing the subtraction the remainder is 6 bus. 

2 pks. 1 pt. 

Subtract as simple numbers. Increase when necessary 
the number representing any denomination by taking one 
unit from the next higher denomination. 

BXBRCISB 144. - WRITTBN 

Subtract : 

1. 12 hhds. 10 gals. 3 qts. 4. 76 mis. 8f rds. 
10 hhds. 50 gals. 1 qt. 19 mis. 9 rds. 

2. 50 yds. 8 ins. 
30 yds. 10 ins . 

3. 25 rds. 3 yds. li ft. 
10 rds. 1 yd. 2 ft. 

237. DIFFERENCE BETWEEN TWO DATES 

Find the difference between the dates March 6 and 
July 4: 



5. 


12 m. 6 dm. 4 cm. 




9 m. 9 dm. 8 cm. 


6. 


14 1. 8 dl. 5 cl. 




5 1. 9 dl. 8 cl. 



Yes. 


Mos. 


Days 


1871 


4 


1 


1815 


7 


15 



174 PRACTICAL ARITHMETIC 

The number of days in March after the 6th is 25 ■ 
The number of days in April is 30 

The number of days in May is 31 

The number of days in June is 30 

The number of days in July before the 5th is 4 

Total is 120 
The difference of dates is 120 days. 

To find the difference between two short dates, the 
exact number of days in each month is taken. 

238. Find the difference between the dates April 1, 
1871 and July 15, 1845 : 

Write the dates as in subtraction of 

compound numbers, representing the 

number of years, months, and days in 

columns. 
25 8 16 

To find the difference between two dates of longer period, 
that is, covering a period of more than a year, 30 days are 
considered a month. 

BXEBCISE 145, — ■WRITTEN 

1. Find the difference of dates between July 4, 1776 
and May 20, 1776. 

2. Find the difference between April 19, 1774 and 
October 12, 1492. 

MULTIPLICATION 
BXEBCISE 148. -ORAL 

Multiply : 

1. 4 ft. 2 ins. by 2. 3. 12 lbs. 4 ozs. by '3. 

2. 6 yds. 1 ft. 3 ins. by 2. 4. 49 pks. 2 qts. by 4. 



DENOMINATE NUMBERS 175 

239. Multiply 30 gals. 3 qts. 1 pt. by 6. 
30 gals. 3 Qts. 1 pt. 6 X 1 pt. = 6 pts., or 3 qts. 6 x 3 

qts., or 5 gals, and 1 qt. 6 x 30 gals. 



185 gals. Iqt. Opt. ^^g^ ^^^^^ ^gO g^jg. + g g^^l3_ ^ 
185 gals. The product is 185 gals, and 1 qt. 

Multiply separately the number representing each de- 
nomination. Reduce each product to units of the next 
higher denomination and add to the product of that 
denomination. 

EXERCISE 147. — WRITTEN 

Multiply : 

1. 15 bus. 3 pks. 2 qts. by 8. 

2. 56 ft. 61 ins. by 96. 

3. 4 T. 25 cwts. 10 lbs. 9 ozs. by 28. 

4. 46 mis. 3 ft. by 27. 

5. 121 lbs. 4 ozs. by 34. 

6. 46 gals. 2 qts. 1 pt. by 12.5. 

7. 15 m. 6 dm. 8 cm. by 25. 

8. 25 1. 3 dl. by .34. 

9. 18 g. 4 dg. 6 eg. by 12. 

10. 2 sq. mis. 80 sq. rds. 6 sq. yds. by .245. 

11. 3 sees. 50 A. 7 sq. chs. by 364. 

12. 15 cu. yds. 19 cu. ft. 108 cu. ins. by 2.75. 

DIVISION 
EXERCISE 148. — ORAL 

Divide: 

1. 12 ft. 6 ins. by 2. 3. 54 gals. 3 qts. by 3. 

2. 35 lbs. 14 ozs. by 7. 4. 60 ft. by 12 ft. 



176 PRACTICAL ARITHMETIC 

5. 108 yds. 3 ft. 6 ins. by 9. 

6. 54° 20' 36" by 6. 

7. 25 hrs. 30 mins. 20 sees, by 10. 

8. 144 sq. ft. 72 sq. ins. by 9. 

9. 48 bus. 2 pks. 3 qts. by 3. 

10. 174 yds. by 6 yds. 

11. 136 yds. 2 ft. by 5. 

12. 154 bus. 3 pks. 2 qts. by 4. 

240. Divide 25 gals. 2 qts. 1 pt. by 4. 

4 )25 gals. 2 qts. 1 pt. \ of 25 gals. = 6 gals, with 

6 gals. 1 qt. 1\ pts. 1 remainder. 1 gal. = 4 qts. 4 

qts. + 2 qts. = 6 qts. ^ of 6 
qts. = 1 qt. and 2 qts. remainder. 2 qts. = 4 pts. 1 pt. + 4 
pts. = 5 pts. ^ oi 5 pts. = 1^ pts. 

Divide separately the number representing each denomi- 
nation. If there is a remainder, reduce it to the next 
lower denomination and add to the number representing 
that denomination. 

241. Divide 18 lbs. 6 ozs. by 8 lbs. 3 ozs. 

■ 18 lbs. = 256 ozs. + 6 ozs. = 262 ozs. 
8 lbs. = 128 ozs. + 3 ozs. = 131 ozs. 
262 ozs. ^ 131 ozs. = 2. 

In order to divide one compound number by another, 
both compound numbers must be reduced to simple num- 
bers of the same denomination. 

242. Observe that in division of denominate numbers 
when the divisor and dividend are concrete, the quotient 
is abstract, e.ff., 131 ozs. is contained in 262 ozs. two times. 



DENOMINATE NUMBERS 



177 



EXERCISE 149. — WRITTEN 

Divide : 

1. 245 mis. 120 rds. by 8. 

2. 945 ft. 6 ins. by 12. 

3. 2 lbs. 7 ozs. 14 grs. by 5. 

4. 12 yrs. 6 mos. 5 days by 2 yrs. 4 mos. 5 days. 

5. 32 gals. 2 qts. by 5 gals. 1 qt. 1 pt. 

6. 

7. 

8. 

9. 

10. 



10 1. 3 dl. 5 cl. by 2 1. 1 dl. 

15 m. 8 dm. 6 cm. by 10 m. 2 cm. 

25 g. 3 dg. by 12 g. 

6984 ins. by 127. 

8 A. 25 sq. rds. 3 sq. ft. by 9.5. 



11. 1155 sq. rds. 10 sq. Is. by 2.5. 



EXERCISE 150. — WRITTEN 





a 


h 


c 


1 


64 


23 


24 


2 


72 


16 


19 


3 


93 


19 


16 


4 


11 


78 


12 


S 


2 


72 


19 


6 


98 


18 


78 


7 


16 


21 


42 


8 


18 


42 


73 


9 


27 


18 


64 


10 


24 


7 


77 



1. If the numbers in line 1 a, J, c, represent respec- 
tively tons, hundredweight, and pounds, how many pounds 



178 PRACTICAL ARITHMETIC 

and how many hundredweight do they equal ? How 
many tons and fraction? 

2-10. Solve problems based on lines 2 to 10 as in 
No. 1. 

11-20. If the numbers in columns «, b, c represent 
respectively miles, rods, and yards, how many yards do 
the numbers in each line 'equal? Rods and fraction? 
Miles and fraction ? 

21. If the numbers in line 1 a, b. c represent yards, 
feet, and inches, respectively, how many inches do they 
equal ? Feet and fraction ? Yards and fraction ? 

22-30. Solve each other line as in No. 21. 

31. If the numbers in line 1 a, 5, c represent bushels, 
pecks, and quarts, respectively, how many quarts do they 
equal? Pecks and fraction ? Bushels and fraction? 

32-40. Solve each other line as in No. 31. 

41. If the numbers in line 1 a, 5, e represent respec- 
tively centuries, years, and days, how many days do they 
equal? Years and fraction? Centuries and fraction? 

42-50. Solve each other line as in No. 41. 

51. If the numbers in line 1 a, J, c represent respec- 
tively hours, minutes, and seconds, how many seconds do 
they equal ? Minutes and fraction ? Hours and fraction ? 

52-60. Solve each other line as in No. 51. 

61. If the numbers in line 1 a, i, e represent respec- 
tively barrels, gallons, and quarts, how many quarts do 
they equal? How many barrels and fraction? 

62-70. Solve each other line as in No. 61. 



REVIEW PROBLEMS 179 

71. If the numbers in line 1 a, b, e represent respec- 
tively square miles, acres, and square rods, how many 
square rods do they equal ? Acres and fraction ? Square 
miles and fraction ? 

72-80. Solve eacli other line as in No. 71. 

81-90. If each number in a represents grams, how many 
pounds does each equal ? 

91-100. If each number in a represents meters, how 
many inches does each equal ? How many yards ? 

101-110. If each number in a represents yards, how 
many meters does each equal ? 

111-120. If each number in a represents pounds, how 
many grams does each equal? 

EXERCISE 151. — WRITTEN 

Review Peoblems 

1. If a man bu3's 373 lbs. of seed corn at $2 a bushel, 
and plants 4 qts. to the acre, how many acres can be planted 
with this seed, and how much will it cost to the acre ? 

2. A dairyman producing 80 gals, of milk delivers ^ of 
it in pint bottles, ^ of it in quart bottles. How many 
bottles of each size are needed for one delivery ? 

3. Two bushels of peaches are preserved and kept in 
quart cans. Allowing -J for shrinkage, how many cans 
are needed? 

4. A barrel of vinegar is sold, half in pints, half in 
quarts. How many of each are sold? 



180 PRACTICAL ARITHMETIC 

5. Twenty bushels of garden peas are sold in quart 
boxes. How many boxes are required? 

6. In building a fence 80 rds. long, 4 boards high, with 
boards 16 ft. long and posts 8 ft. apart, using 2 nails at 
every point where a board is nailed to a post, how many 
pounds of tenpenny nails will be needed, allowing 69 nails 
to the pound ? 

7. Wind with a velocity of 1 mile an hour (barely 
observable) exerts a pressure of .005 lb. to the square 
foot. What is the pressure of such a wind on ' a tight 
board fence 1 rd. long, 5 ft. high ? 

8. With a velocity of 8 miles (a pleasant wind) the 
pressure is .32 lb. to the square foot. What is the press- 
ure on the fence mentioned in the last problem ? 

9. With a velocity of 80 mis. an hour (a hurricane) ' 
the pressure is 32 lbs. to the square foot. What is the 
pressure on the fence of problem 7? 

10. If each tea bush yields 3 ozs. of tea each year, how 
many bushes will be required to yield 18 lbs.? 

11. If a pound of tea will make 400 cups, how many 
tea plants will be needed to furnish 1 cup each day for a 
year for each member of a family of nine ? 

12. A square piece of land is 81 chs. on a side. What 
is its perimeter? 

13. A city block is 625 ft. on a side. How many chains 
on one side ? How many square chains in a block? 

14. How many acres are there in a rectangular enclos- 
ure 1 mi. long and -I mi. wide? 



REVIEW PROBLEMS 181 

15. A rectangular farm contains 100 A. It is 80 rds. 
on one side. How long is the other side? 

16. Reduce 2482 sq. rds. to square chains. 

17. At i960 a mile, what is the cost of making a road 
4 mis. and 43 chs. long? 

18. At $4.90 a square chain, what is the cost of 27 A. 
43 sq. rds. of land? 

19. The pressure of the air is 14 lbs. per square inch. 
What is the air pressure on a table top 38" x 76"? 

20. The longest day in Stockholm is 18 hrs. 30 mins., 
in London 16 hrs. 32 mins., in Paris 16 hrs., in Boston 15 
hrs. 16 mins., in Washington 14 hrs. 62 mins. How much 
longer is the longest Stockholm day than that of each of 
the other cities? 

21. The shortest day in Stockholm is 5 hrs. 54 mins., 
London 7 hrs. 44 mins., Paris 8 hrs. 10 mins., Boston 8 
hrs. 58 mins. How much shorter is the shortest Stockholm 
day than that of each of the other cities ? 

22. How many cubic feet of dirt must be moved in 
digging a ditch 18" wide, 2' 6" deep, 79 rds. long? How 
many cubic yards? 

23. What will it cost to excavate a cellar 18' long, 
14' wide and 6' 3" deep at f.42 per cubic yard of dirt? 

24. How many bushels will a bin hold if it is 5' wide, 
7' long, 4' deep ? 

25. A wagon bed 10', 8" long, 3' wide, and 19" deep 
holds how many bushels? How many bushels will it 
hold with a 6-in. top-box added? How much with a 9-in. 
top-box? 



182 



PRACTICAL ARITHMETIC 



26. If a bushel of soft coal weighs 80 lbs., how deep 
must such a wagon bed be to contain 1 ton? 

27. How deep a bin 7' long, 4' 7" wide must be built 
to hold 3|- tons of soft coal? 

28. A solid piece of timber 8" x 9" x 16' contains how 
many cubic feet ? 

29. A cubic foot of seasoned mahogany weighs 65.1 lbs., 
of hickory 58.8-1 lbs., of pitch pine 47.44 lbs., of cedar 
42.7 lbs., of hemlock 25.53 lbs., of white pine 21.72 lbs., 
of ash 39.19 lbs. What is the weight of a piece of each 
of the above woods of the size mentioned in problem 28? 

30. If a cubic foot of soil weighs 87 lbs., what is the 
weight of the soil of 1 sq. yd., 1 ft. in depth? Of 1 sq. 
rd., 1 ft. in depth? Of 1 A., 1 ft. in depth? 

31. The following table shows the number of pounds of 
the three important elements of plant food in a ton of 
four different soils : 





Nitrogen 


Phosphoric 
Acid 


Potash 


Loam 

Clay 

Drift 

Sand 


7 lbs. 
3 lbs. 
3 lbs. 
lib. 


3 lbs. 
3 lbs. 

i\h. 
2 lbs. 


8 lbs. 

15 lbs. 

6 lbs. 

5 lbs. 





How much of each of these plant foods is there in an 
acre 1 ft. in depth? 

32. In each bushel of the following crops there is the 
amount of the three chief plant foods indicated by the 
following table : 



REVIEW PROBLEMS 



183 



Plant Food 


NiTROGKN- 


PlIOSlMIORKl AOID 


Potash 


Wheat 


20 ozs. 


8 ozs. 


5 OZS. 


Rye 


17 ozs. 


9 (izs. 


5 OZS. 


Shelled corn 


14 ozs. 


5 ozs. 


3 OZS. 


Barley 


12 ozs. 


6 ozs. 


4 OZS. 


Oats 


10 ozs. 


3 ozs. 


2 ozs. 


Potatoes 


3 ozs. 


1 oz. 


4 ozs. 



How many pounds of each of these is taken from the 
field with 65 bus. of crop? 

33. What fraction of an acre is a garden 8 rds. 4 ft. 
long, 6 rds. 1 yd. wide? 

34. How many square feet are there in a floor 15 ft. 
3 ins. long by 12 ft. 9 ins. wide ? 

35. How many square j^ards are there in a ceiling 
27 ft. 4 ins. long, 16 ft. 7 ins. wide? 

36. If corn is planted in rows 3 ft. 6 ins. apart and the 
pla,nts are 13 ins. apart in the row, how many corn plants 
will there be in a field 30 rds. 3 yds. 2 ft. 9 ins. long by 
27 rds. 4 yds. 1 ft. 8 ins. wide? 

37. How many square feet are allotted to each plant 
in problem 36? 

38. In 1856 the steamship Persia crossed the ocean 
between Queenstown and New York, a distance of 2800 
miles, in 9 days 1 hr. 45 mins. What was the average 
distance per day ? 

39. In 1894 the Lucania making the same trip crossed 
in 5 days 7 hrs. 23 mins. What was the average rate per 
hour? What was the gain in time of crossing over that of 
the Persia? 



184 PRACTICAL ARITHMETIC 

40. Through how many degrees does the hour hand 
of a clock pass from 6 A.M. to 3 p.m.? From 12 M. to 
3.30 P.M. ? From 9 p.m. to 10 p.m.? 

41. Through how many degrees does the minute hand 
pass from 6.15 to 6.30? From 5.45 to 6? 

THREAD AND CLOTH 

42. A calico cloth 27 ins. wide is made with 64 length- 
wise threads (warp) to the inch. How many linear yards 
of warp are there in a piece of calico 3| yds. long? In a 
square yard of calico? 

43. Cloth made with 84 crosswise (filling) threads to 
the inch has how many yards of filling in 3 yds. of cloth 
28 ins. wide? 

44. A standard wrapping reel is 4 ft. 6 ins. in circum- 
ference. How many times will it turn in wrapping 840 
yds. of thread? 

45. A cloth 30 ins. wide with 80 " ends " (lengthwise 
threads) to the inch has how many ends? 

46. A cloth 30 ins. wide consists of alternate close and 
open stripes. The close stripes, | in. wide, have 60 ends 
in -^ in. The open stripes have 96 ends in a 1-in. stripe. 
What is the average number of ends per inch ? What is 
the total number in cloth 28 ins. wide ? 

47. Cloth made with 84 threads of filling to the inch 
has how many to the yard ? 

48. A gentleman's cotton handkerchief 18" X 18" 
weighs I oz. How many can be made from 450 lbs. of 
cotton, not allowing for waste? 



REVIEW PROBLEMS 185 

49. A lady's handkerchief is one-fourth smaller. How 
many can be made from 450 lbs. of cotton ? 

50. A bale of cotton weighs 500 lbs. Bagging and 
ties weigh 25 lbs. This cotton loses f-^ during the 
process of making the warp and filling threads. How 
many handkerchiefs can be made from the bale if a 
handkerchief weighs | of an ounce? 

51. The warp threads in a handkerchief weigh .43 oz. 
The filling threads in same handkerchief weigh .32 oz. 
How many pounds of cotton will be used for warp threads 
and how many pounds for filling threads ? 



52. Wilbur Wright of Ohio is reported to have flown 
on his aeroplane, in France, on Aug. 8, 1908, a distance 
of 3 kilometers in 1 min. 46 sees. What was the rate in 
miles per minute? 

53. A man purchases 2520 lbs. of corn and feeds 2 qts. 
and 1 pt. three times a day to his horse. How long will 
the corn last? (56 lbs. of corn = 1 bu.} 

54. A dairyman produces 50 gals, of milk. Half of 
this is delivered to customers taking 1 pt. each, ^-^ to cus- 
tomers taking 2 qts. each, the remainder to customers 
taking 1 qt. each. How many customers are there? 

55. A quart of beans weighs 80 ozs. How many pounds 
are there in a bushel of beans ? 

56. For a grain bin 6'xl5|^'x5' how much carbon 
di-sulfide will be required to kill weevils, allowing 1 lb. 
to every 1000 cu. ft. of space? What will this cost at 
29^ per pound ? 



MEASUREMENTS 

243. A plane figure having four straight sides is called 
a Quadrilateral. 

244. A plane figure having four straight sides and its 
opposite sides parallel is called a Parallelogram. 




A QUADRILATEBAL A PARALLELOGRAM A TRAPEZOID 

245. A quadrilateral which has only one pair of its 
opposite sides parallel is called a Trapezoid. 

246. A parallelogram the angles of which are right 
angles is called a Rectangle. 

247. A plane figure bounded bj- three straight lines and 
having three angles is called a Triangle. 




A Rectangle A Triangle Base and Altitude 

248. The line upon which a figure seems to rest is 
called the Base. 

186 



MEASURKMENTS 187 

249. The perpendicular distance between the base and 
the highest opposite point is called the Altitude. 

250. The straight lines joining the opposite angles of a 
parallelogram are called its Diagonals. 





Diagonals Equilateral Triangle Isosceles Triangle 

251. Polygon is the name given to any figure bounded 
by straight lines. 

252. The Perimeter of a polygon is the distance 
around it. 

253. A triangle whose three sides are equal, is called an 
Equilateral Triangle. 

254. A triangle, two of whose sides are equal, is called 
an Isosceles Triangle. 




Right Triangle Acute Angle Obtuse Angle 

255. A triangle having one right angle is called a 
Right Triangle. 

256. An angle less than a right angle is called an Acute 
Angle. 



188 



PRACTICAL ARITHMETIC 



257. An angle greater than a right angle is called an 
Obtuse Angle. 

EXERCISE 152.— ORAL 

1. What is the perimeter of a square lOJ ft. on a 
side? 

2. What is the perimeter of a rectangle two sides of 
which are 12|^ ft. and 6^ ft. respectively? 

3. What is the perimeter of a quadrilateral whose sides 
are 10, 12, 6, and 8 inches? 

4. What is the perimeter of an equilateral triangle 25 
ft. on a side ? 

5. What is the perimeter of a triangle whose sides are 
21ft., 3|ft., and 6 ft.? 

6. A triangle has a perimeter of 120 ins. ; one side 
measures 30 ins., another IJ times this number of inches. 
What is the length of the third side ? 

7. The base of an isosceles triangle is 12 ft. ; the perim- 
eter is 42 ft. What is the length of each of the equal 
sides ? 

BXEECISE 153. — ORAL 

1. How many square inches are there in a rectangle 

10 ins. long and 1 in. wide? 



How many rows of square 

inches are there in the 

figure ? 

2. How many rows of 

square inches are there in a 
rectangle 10 ins. long and 2 ins. wide ? How many square 
inches are there in a row ? In two rows ? How many 




MEASUREMENTS 



189 



rows of square inches are there in a rectangle 10 ins. long 
and 3 ins. wide? How many square inches in a row? 
In three rows ? 

3. How many square inches are there in a rectangle 
10 ins. long, 5 ins. wide ? In a rectangle 10 ins. long, 10 
ins. wide ? 

258. In finding the area or surface of a rectangle, we 
must think of the surface in rows of square inches, which 
will give the number of times the square inches in one 
row is to be taken, e.g., if a square measures 10 ins., there 
are, as may be seen, 10 rows of square inches of 10 sq. ins. 
each, or 100 sq. ins. 

Hence, the area of a rectangle equals the product of the 
length by the width. 

EXERCISE 154. —ORAL 

State the areas of the following rectangles : 

7. 7 ins. X 9 ins. 
5. 9 ft. X 61 ft. 8. 4 ft. X 6 ins. 
3. 10 ft. X 4 ft. 6. 3 m. X 1^ m. 9. 1 yd. x 10 ft. 



1. 5 ins. X 10 ins. 4. 8 ins. x 8|- ins. 



2. 4 ft. X 6i ft. 



EXERCISE 155.- 

1. What is the re- 



-ORAL 




lation of triangle a to 
rectangle A ? 

2. What is the rela- 
tion of triangle h to 
rectangle B ? 

3. What is the relation of triangle c to (7? 

From the above, what is true of the area of a triangle ? 





190 PRACTICAL ARITHMETIC 

4. Give the areas of the following triangles : base 4 ins., 
height 6 ins. ; base 9 ins., height 12 ins. ; base 3 ft., height 
4ft.; base 3ft., height 3 ft. 

259. The area of a triangle equals J the product of the 
base by the altitude. 

EXERCISE 156. — WRITTEN 

State the areas of the following triangles : 
1. Base 45 ft., altitude 30 ft. 
■ 2. Base 16 ft., altitude 12 ft. 

3. Base 87 ft., altitude 28 ft. 

4. Base 40 ft., altitude 26 ft. 

5. Base 67 ft., altitude 55 ft. 

260. If you CLit off the triangle a from the parallelo- 
gram X and place the line ho so that 



X \ ^^ exactly coincides with de, what kind 

^e of figure have you ? What is true 

of the area of the first figure as compared with the 
second ? 

EXERCISE 157. — ORAL 

Give the area of the following parallelograms : 

1. Base 12 ins., height 9 ins. 

2. Base 14 ins., height 6 ins. 

3. Base 18 ins., height 12 ins. 

4. Base 15 m., height 6 m. 

5. Base 17 ins., height 17 ins. 

261. The area of a parallelogram is equal to the prod- 
uct of the base by the height. 



MEASUREMENTS 191 

EXERCISE 158. — "WBITTEN 

Find the areas of the following parallelograms : 

1. Base 18.4 ins., height 9.2 ins. 

2. Base 17| ft., height 16.5 ins. 

3. Base 34 m., height 20 cm. 

4. Base 16 ft. 6 ins., height 12 ft. 4 ins. 

5. Base 171.4 ft., height 34.9 ft. 

6. Base 3.75 ft., height 4.25 ft. 

7. Base 35 m., height 9 cm. 

8. Base 345.2 rds., height 6 yds. 

fj 9 



-X 




d^ 



262. If you cut the trapezoid X through the line ef 
and place the two sections so that the lines cf and df coin- 
cide, what kind of figure have you ? 

Is the area of the second figure the same as the area of 
XI How long is the figure made froin the trapezoid? 
How high is it? To find the area of a trapezoid, what 
dimensions must be given? 

EXERCISE 159. — ORAL 

Find the area of the following trapezoids : 

1. The parallel sides are 10 ins. and 12 ins., height 6 ins. 

2. The parallel sides are 6 ins. and 4 ins., height 4 ins. 

3. The parallel sides are 12 ins. and 9 ins., height 8 ins. 



192 PKACTICAL ARITHMETIC 

4. The parallel sides are 16 ins. and 12 ins., height 9 ins. 

263. The area of a trapezoid is equal to the sum of the 
two parallel sides multiplied by J the height. 

EXERCISE 160. — WRITTEN 

Find the area of the following trapezoids : 

1. Parallel sides, 96 rds. and 180 rds., height 108 rds. 

2. Parallel sides, 45 rds. and 95 rds., height 64 rds. 

3. Parallel sides, 120 ft. and 90 ft., height 40 ft. 

4. Parallel sides, 60 m. and 90 m., height 44 m. 

5. Parallel sides, 135.5 m. and 34 m., height 110 m. 

6. Parallel sides, 62 yds. and 80 yds., height 112^ yds. 

264. It has been found that the circumference of a 
circle is approximately 8^ times the diameter. 

Find the circumference of circles with the following 
diameters : 

1. 7 ins. 4. 21 ins. 7. 0.7 m. 10. 45 ft. 

2. 14 ins. 5. 77 ins. 8. 14 cm. 11. 84 ft. 

3. 49 ins. 6. 0.28 in. 9. 14.7 cm. 12. 105 ft. 

265. To find the circumference of a circle, multiply the 
diameter by 3^, or more accurately by 3.1416. 

EXERCISE IBI. — WRITTEN 

Find accurately the circumferences of the following cir- 
cles; also find their approximate circumferences. Note 
the difference. in results by the two methods. 

1. Diameter 16 ft. 4. Radius 9 ft. 

2. Diameter 21 ft. 5. Radius 12 m. 

3. Diameter 19 ft. 6. Radius 45 rds. 



MEASUREMENTS 



193 



EXERCISE 162. —WRITTEN 

Find the diameters of circles having the following 
circumferences : 

1. 426 ft. 4. 1400 rds. 7. 318 m. 

2. 218 ft. 5. 1676 yds. 8. 164 m. 

3. 670 ft. 6. 115.6 rds. 9. 92.45 ins. 

266. If you divide the circle shown in the figure by 
cutting the line ah, then cutting each half circle into many 
small triangles by 
cutting along 
each radius, it 
will be seen that 
the many trian- 
gles joined, as is 
suggested in figure y, will approximate in area a parallelo- 
gram with a length equal to one-half the circumference 
of the circle and a height equal to the radius of the circle. 

The area of a circle is found by multiplying one-half 
the circumference by the radius, or by multiplying the 
square of the radius by 3.1416. 




EXERCISE 163. — WRITTEN 

Find the areas of circles with a : 



1. Circumference of 242 ft. 

2. Circumference of 110 ins. 

3. Circumference of 154 ft. 

4. Circumference of 96 yds. 

5. Circumference of 3.75 ft. 

6. Circumference of 18 yds. 



7. Diameter of 77 ft. 

8. Diameter of 35 m. 

9. Diameter of 49 rds. 

10. Diameter of 146 ft. 

11. Diameter of |^ ft. 

12. Diameter of 54 rds. 



194 



PRACTICAL ARITHMETIC 



EXERCISE 164. — WRITTEN 

Find the areas of circles having a radiugr of : 

1. 8 ins. 3. 4 ft. 5. 9 m. 7. 4 rds. 

2. 10 ins. 4. 16 ft. 6. 8 m. 8. 5 rds. 

SOLIDS 

267. A solid has three dimensions, • — Width, Length, 
and Thickness. 

268. A solid that has six rectangular sides or faces is 
called a Rectangular Solid. 

269. A solid that has six square faces is called a Cube. 

270. A cubic inch is a solid, the faces of which are each 
one inch square. What is a cubic foot? What is a 
cubic yard? 

BXEECISE 165. — ORAL 

1. In a solid 12 ins. long, 1 in. wide, and 1 in. thick, 
how many rows of cubic inches are there? How many 
cubic inches are there ? 



SI 

Figure 1 



I'igure 2 





Figure 3 Figure 4 

2. In a solid 12 ins. long, 2 ins. wide, 2 ins. thick, how 
many layers of cubic inches are there ?. How many rows 



MEASUREMENTS 195 

of cubic inches are there in one layer ? How many cubic 
inches are there in one layer ? How many cubic inches 
are there in 2 layers ? 

3. In a solid 12 ins. long, 12 ins. wide, 2 ins. thick, how 
many layers are there ? How many rows are there in one 
layer ?. How many cubic inches are there in one row ? 
How many cubic inches are there in one layer ? How 
many cubic inches are there in two layers ? 

4. In a solid 12 ins. long, 12 ins. Avide, 12 ins. thick, how 
many layers are there ? How many rows are there in a 
layer? How many cubic inches are there in one row? 
How many cubic inches are there in a layer ? How many 
cubic inches are there in 12 layers ? 

5. In a solid 4 ins. long, 4 ins. wide, and 4 ins. thick, 
how many cubic inches are there in the length of the 
solid? How many rows of cubic inches in the width? 
How many cubic inches in each layer ? How many 
layers in the solid? How many cubic inches in the solid? 

In examples 6, 7, 8, answer all the questions made in 
example 5. 

6. In a solid 4 ins. by 5 ins. by 6 ins. ? 

7. In a solid 2 ins. by 3 ins. by 12 ins. ? 

8. In a solid 6 ins. by 8 ins. by 10 ins. ? 

271. To find the volume of a cube, we must think of it 
iis a solid having a length equal to the number of units in 
its length and a width equal to that of the rows of cubic 
units in its width, and a thickness equal to the number 
of layers of cubic units in its thickness. 



196 



PRACTICAL ARITHMETIC 



272. The volume of a rectangular solid equals the prod- 
uct of the three dimensions similarly expressed. 

BXBBCISB 166. — WRITTEN 

1. How many cubic inches are there in a box 16 ins. 
long, 8 ins. wide, and 9 ins. deep? 

2. How many cubic feet of masonry are there in a wall 
120 ft. long, 2 ft. wide, and 4 ft. high? 

3. How many gallons of water will a tank 5|- ft. long, 
4 J ft. wide, and 2^ ft. deep contain? 

4. How many cubic yards of soil will be excavated in 
making a ditch 12 ft. long, 2 ft. wide, and 3 ft. deep? 

5. How many liters of air are there in a room IS^ m. 
long, 9^ m. wide, and 3 m. high? 

6. The box of a one-horse express wagon is T 2" by 3' 
2|" by 8". Find the capacity. 

7. A two-horse farm wagon is 11' 6" x 3' x 10^". 
Find the capacity. 



THE CYLINDER 

273. A cylinder is a solid 
having for its ends two equal 
circles joined by a uniformly 
curved surface, called its lat- 
eral surface. 

274. A cylinder may be 
seen in the form of a rectangu- 
lar solid with a length equal 

to the length of the cylinder, a width equal to one-half 




MEASUREMENTS 



197 



the circumference of the circular base, a thickness equal 
to the radius of the circular base. 

275. Hence, to find the volume of a cylinder, multiply 
the number of square units in the base by the height. 



vjy 



276. The lateral surface of a cylinder 
may be seen in the form of a rectangle, 
with a length equal to the circumference 
of the circular base and a width equal to 
the height of the cylinder. 

277. Hence, to find the area of the 
lateral surface of a cylinder, multiply 
the length of the circumference of the circular base by 
the height of the cylinder. 

EXERCISE 167.— WRITTEN 

Find the volume of the following cylinders : 

1. Area of base 126 sq. ins., height 16| ins. 

2. Area of base 72 sq. ins., height 44.56 ins. 

3. Area of base 81 sq. ins., height 16 fins. 

4. Area of base 84 sq. ins., height 42| ins. 

EXERCISE 168. — WRITTEN 

Find the lateral surfaces of the following cylinders : 

1. Circumference of base 40 ins., height 45 ins. 

2. Circumference of base 24 ins., height 25 ins. 

3. Circumference of base 66| ins., height 27 ins. 

4. Circumference of base 14f ins. height 641 ins. 



PEACTICAL MEASUREMENTS 

PLASTERING, PAINTING, PAVING 

278. In estimating labor of latliing, plastering, painting, 
and paving, the square yard is taken as the unit. In mak- 
ing estimates for plastering, one-half the areas of doors, 
windows, and other openings is deducted from the total 
area, and the result expressed to the nearest square yard. 

EXERCISE 169. — ORAL 

1. What is the perimeter of a room 12 ft. x 14 ft.? 

2. If the room is 8 ft. high, what is the area of the 
4 walls, making no allowance for the openings in them? 

3. What is the area of the ceiling? 

4. What will be the cost of plastering this room at 
25 cts. a square yard? 

EXERCISE 170. — WRITTEN 

In this exercise exclude closets, and make no allowances 
for windows or doors. 

1. To plaster 100 sq. yds. of surface requires 1 barrel 
of lime, 3 barrels of sand, and 1 bushel of hair. Find the 
amount of these materials required to plaster each bed- 
room of the house shown in the two accompanying dia- 
grams, also living room, dining room, and kitchen. 

2. What will it cost to lath and plaster the living 
room, kitchen, and dining room of tlie lower floor with 
pulp plaster at a cost of 60 cts. a square yard ? 

198 



PRACTICAL MEASUREMENTS 



199 



3. To lath and plaster the i bedrooms of the upper 
floor with ordinary plastering will cost 25 cts. a square 
yard. Estimate the cost. 



Pitch 10 ft. 




4. Estimate the number of gallons of paint required 
to give two outside coats to a house 32 ft. long, 32 ft. 
wide, 18 ft. high, the gable ends of the roof forming 
700 sq. ft. of surface. One gallon of paint covers 
300 sq. ft. of surface, 2 coats. 



200 



PRACTICAL AEITHMETIC 



5. At f 1.25 a gallon, what would be the cost of paint- 
ing this house? 

6. It requires 1.16 barrels of cement, 0.44 cu. yd. of 
sand, 0.88 cu. yd. of gravel to make a cubic yard of con- 



Pitch 8 ft. 




Crete. How much cement will it require to concrete the 
basement floor of a house, 21 ft. x 18 ft., to a depth of 
3 ins. ? 

7. If 1 cubic yard of concrete costs $3.31, what will 
be the cost of material in the last problem? 



PRACTICAL MEASUREMENTS 



201 



CARPETING 

279. Carpets are usually 1 yd. or | yd. wide. 
Brussels and velvet carpeting is | yd. wide and is 
usually sold with a border varying from 22 to 27 ins. in 
width. Ingrain carpets are 1 yd. wide. Matting is 
usually 1 yd. wide. Linoleum and oil-cloth are sold by 
the square yard. The short loops of wool seen in 
Brussels carpet are made by the use of wires over which 
the wool is thrown in weaving. The number of wires 
(usually between 5 and 10 to the inch) used in weaving 
varies with the price of the carpet and the fineness of the 
wool. 

EXERCISE 171. — OBAIj 

1. How many loops of wool are there in a piece of 5-wire 
Brussels carpet | yd. wide and 5 ins. long? 

2. How many loops of wool in an 8-wire Brussels car- 
pet I yd. wide and 5 ins. long ? 

280. In determining the number of yards of carpet 
required for a floor, the 
number of strips should be 
found, the fractional part 
of a strip being regarded as 
a full strip. Often it is 
necessary to allow for match- 
ing and shrinking; 3 inches 
are also allowed on each end 
of each strip for turning in. Borders are fitted at each 
corner, hence the perimeter of the room indicates the 
length of border required ; see figure. 



I I 




202 PRACTICAL ARITHMETIC 

If a floor is 12 ft. wide and the carpet f yd. wide, it will 
require 5^ strips. Since | strip cannot be bought, 6 strips 
must be bought. If the room is 18 ft. long, it will require 6 
strips 18 ft. long, or 36 yds. If 9 ins. must be allowed for 
matching the figure, 9 ins. must be added to each strip, except- 
ing one, since it is not necessary to allow for matching the 
first strip. Three inches additional must be allowed for turn- 
ing under. If a 22-in. border is used, only 3^|- strips of carpet 
are actually used, but 4 strips must be bought. 

BXBBCISE 172. — ORAL 

1. How many strips of f yd. carpeting are required to 
carpet a room 12^ ft. wide? 

2. The room is 14 ft. long. How many yards, without 
border, are required, allowing 12 ins. for matching? 

3. A room is 12 ft. x 18 ft. How many strips of | yd. 
carpeting are required? 

4. How many yards allowing ^ yd. for matching? 

EXERCISE 173. — WRITTEN 

Find how many yards of carpet are needed for the fol- 
lowing rooms : 

1. 15 ft. X 18 ft. 6 ins.: use 27-in. carpet, allow 9 ins. 
for matching and use border -I yd. wide. 

2. 16' X 18' : use carpet 1 yd. wide, and allow ^ yd. 
for matching, turning in, and shrinkage. 

3. The living room and hall of the house shown by 
diagram on page 199 : use a 10-wire body Brussels carpet 
1^ yd. wide, with 22|-ins. border, which requires 9 ins. for 
matching and turning in, and costs 11.50 a yard, with 
10 cts. a yard extra for making. 



PRACTICAL MEASUREMENTS 203 

4. The dining room is covered with an Axminster rug, 
8^ ft. X 10|^ ft. at $1 a square yard. What is the price of 
the rug? How much floor space is left at each side of 
the rug when the rug is laid in the centre of the room ? 

5. What will it cost to stain the floor around the rug 
if 1 qt. of stain is sufficient for 125 sq. ft., the stain cost- 
ing 50 cts. a quart ? 

6. The kitchen floor is covered with linoleum which 
comes only in 2-yd. and 4-yd. widths at f 1 a square yard. 
What is its cost? 

7. The bedrooms are carpeted as follows : No. 1 with 
plain ingrain carpet 1 j'd. wide, strips lengthwise. Al- 
lowing 6 ins. on each width for turning in and 3 ins. on 
each width for shrinkage after it is cut, what is the cost 
at 63 cts. a yard, allowing 3 cts. per yard additional for 
making? 

8. Bedroom No. 2 with China matting 1 yd. wide at 
34 cts. a yard, strips lengthwise? 

9. Bedroom No. 3 with Japanese matting 1 yd. wide 
at 21 cts. a yard? 

10. Bedroom No. 4 with Sanitas washable carpet 36 ins. 
wide at 25 cts. a yard, strips lengthwise? 

PAPERING 

281. Wall paper is usually 18 ins. wide and is sold by 
the roll. A single roll is 8 yds. long, a double roll 16 
yds. Borders are from 3 ins. upward in width. 

Deduction is not made for borders, since no allowance 
is made for matching. Some paper-hangers measure the 
surface above the base-board, and deduct for windows 



204 PRACTICAL ARITHMETIC 

and doors, allowing | roll for each door or window. It 
is also customary to find the number of square feet in 
the walls and ceiling, deduct for doors and windows, and 
divide by 70, to find the number of double rolls required. 

EXERCISE 174. — OBAIi 

1. How many square feet of wall paper are there in a 
single roll? 

2. How many square feet of wall paper are there in a 
double roll? 

3. If a room measures 12 ft. x 12 ft. and 9 ft. high, 
how many single rolls of wall paper will be required, 
making no allowances? 

4. How many double rolls are required for the same 
room? 

5. Allowing for 2 windows 6 ft. x 3 ft. and a door 
7|^ X 4 ft., how many square feet are there left to be 
papered? 

6. How many single rolls are required after making 
this deduction, making no allowance for matching? 

7. How many double rolls? 

BXBECISE 175. — WRITTEN 

1. How many rolls of paper will be required to paper 
the living room of the house shown in the diagram on 
page 199, the base-board 9" wide, there being 3 windows 
3' X 6', 1 window 6' x 6', one fireplace 7' x 6', and 1 door 
7' x 4', alcove not papered ? 

a. Estimate accurately by the number of square feet. 

h. Estimate, allowing -| roll for each opening. 



PRACTICAL MEASUREMENTS 205 

c. Estimate by dividing total number of square feet by 
70, after deducting for the doors and windows. 

2. How much will the paper cost at 50 cts. a double roll ? 
(Use answer c above.) How much will it cost to paper 
the ceiling at 20 cts. a double roll ? What will picture 
moulding cost at 3-| cts. a foot, no allowance for openings? 

3. The dining room has 2 windows 6 ft. x 3 ft., one, 

6 ft. X 6 ft., one opening 6 ft. x 7 ft., and two doors 

7 ft. x 4 ft., buffet not papered. If the wall paper costs 
30 cts. a double roll and the ceiling paper, 20 cts. a double 
roll, with no border, but with picture moulding at 2J cts. 
a foot, how much is the total cost? 

Each bedroom has 2 windows 6 ft. x 3 ft. and 1 door 
7 ft. X 3 ft., ceilings and closets not papered. 

4. Find the cost of bedroom No. 3 with paper at 25 cts. 
a double roll, picture moulding IJ cts. a foot. 

5. Find the cost of papering room No. 4 with sanitary 
wall paper at 30 cts. a double roll, 4-in. border at 2 cts. a 
yard, ceiling papered at the same price. 

282. MASONRY AND BRICKWORK 

Brickwork is usually estimated by the thousand brick. 
The unit of measure for walls built of stone is the perch. 

Twenty-two bricks of common size laid in mortar are 
reckoned for each cubic foot of wall. Common brick 
measure 8x2x4 ins. The mortar occupies \ in. in thick- 
ness between bricks. A perch measures 16^' x 1|' X 1' 
and equals 24| cubic feet. In practice a perch is under- 
stood to be 25 cubic feet, 



206 PRACTICAL ARITHMETIC 

It requires for each square foot of wall : 

7 bricks, if the wall is 1 brick in thickness. 
15 bricks, if the wall is 2 bricks in thickness. 
22 bricks, if the wall is 3 bricks in thickness. 

In estimating work, deductions are not usually made 
for openings of less than 100 sq. ft. area. In estimating 
materials, deduct for openings. 

BXERCISB 178. — ORAL 

1. How many bricks are required for a wall 10 ft. 
long, 5 ft. high, 1 brick thick ? 2 bricks thick ? 3 bricks 
thick ? 

2. How many bricks are required for a wall 1 brick 
thick, for a cellar 10 ft. x 12 ft., not allowing for open- 
ings? 2 bricks thick? 3 
bricks thick ? 

3. How manj'^ perch of 
stone are required for a wall 
50 ft. long, 10 ft. high, 1 ft. 
4 ins. thick? 
To find the number of bricks required for a wall, mul- 
tiply the number of square feet by 7, 15, 22, or 29 accord- 
ing as the wall is 1, 2, 3, or 4 bricks thick. 

EXERCISE 177. — WRITTEN 

1. If a cellar is 18' x 24' x 9', inside dimensions, how 
many bricks are used in walling it 2 bricks thick? 

2. How many perches of stone are required for the 
walls of a cellar 18' x 24' x 9', 6", the wall 18" thick? 




PRACTICAL MEASUREMENTS 207 

3. Find cost of construction in problems 1 and 2 with 
bricks at $8.50 per M and labor 13.00 per M, allowing no 
deductions for openings, stone costing 118.00 per perch 
and f 1.50 per perch for labor. 

4. How many bricks will be required to wall a house 
36' long, 30' wide outside, and 34' high, including the 
cellar, the wall to be 2 bricks thick? No allowance for 
openings. 

5. The cellar and rear walls of the house of problem 4 
are of common brick, the cellar dimensions being 36' 
X 30', 6" X 9', the openings 1 door 6' x 3', 2 windows 
3' X 1^', 2 windows 6' x 3'. What is the cost of the brick 
at 18.45 per M ? Of the labor at $3 per M? 

283, WOOD MEASURE 

A cord of wood is 8 ft. long, 4 ft. wide, and 4 ft. high. 

128 cu. ft. = 1 cord. 16 cu. ft. = 1 cord foot. 

EXERCISE 178. — ORAL 

1. A pile of wood is 8 ft. long, 4 ft. wide, 2 ft. high. 
What part of a cord is it? 

2. A pile of wood is 
96 ft. long, 4 ft. wide, 4 
ft. high. How many 
cords are there? 

3. Another pile is 12 

ft. long, 4 ft. wide, 4 ft. high. How much wood is there 
in the pile? 

EXERCISE 179. — WRITTEN 

1. How many cord feet are there in a pile of wood 96 
ft. long, 16 ft, wide, 12 ft. high? 




208 PRACTICAL ARITHMETIC 

2. How many cords can be piled in a woodhouse 12 ft. 
X 16-1- ft. X Hi ft.? 

3. Find the number of cord feet in a pile of wood 100 
ft. long, 25 ft. wide, 25 ft. high. Find the number of 
cords. 

BOARD MEASURE 

284. Lumber is bought and sold by Board Measure. 

285. The unit of Board Measure is the Board Foot, 
which is 1 ft. long, 1 ft. wide, and 1 in. thick. Boards 
less than 1 in. in thickness are reckoned as though they 
were 1 in. thick. Boards more than 1 in. thick are 
sold according to the number of board feet in them, e.g., 
a board 10' long, 1' wide, 2" thick, contains 20 board feet. 

EXBBCISE 180. — OEAIj 

Find the number of board feet in the following : 

1. 10 boards 1" x 12" x 8'. 4. 10 boards 2" x 9" x 10'. 

2. 10boardsl"x|"xll'. 5. 10 boards 1^" x 6" x 8'. 

3. 10 boards 1" X f" X 18'. 6. 10 boards If" x 9" x 14'. 

EXERCISE 181. — "WRITTEN 

Find the number of board feet in the following : 

1. 12 planks 3" x 8" x 12'. 

2. 14 planks 2|" x 9" x 18'. 

3. 18 planks 1^" X 12" x 12'. 

4. 24 planks If" x 26" x 16'. 

5. 60 planks If" x 4" x 12'. 

6. How much flooring 18' long, 4" wide, If" thick 



PRACTICAL MEASUREMENTS 209 

must be bought to floor a room 18' x 12' ? What will 
the flooring cost at |60 per M ? 

ROUND LOGS 

286. Round logs are sold by the number of board feet 
that can be cut from them. To find the number of board 
feet in a log, subtract twice the diameter in inches from 
the square of the diameter ; |^ of the remainder will be 
the number of board feet in 10 linear feet of the log. 

Find the number of board feet in a log 18' long, 12" in 
diameter. 

122 _ (2 X 12) = 144 - 24 = 120 

|l of 120 = 63 

If of 63 = 113.4 board feet. 

EXERCISE 182. — WRITTEN 

Find the number of board feet in the following : 

1. In a log 12' long, 10" in diameter. 

2. In a log 18' long, 15" in diameter. 

3. In a log 14' long, 18" in diameter. 

4. In a log 15' long, 22" in diameter. 

MEASURING TEMPERATURE 

287. Temperature is commonly measured in this coun- 
try in degrees by Fahrenheit's thermometer. The 32- 
degree mark is placed at the freezing-point of water, 
the 212-degree mark at the boiling-point of water. The 
interval between the freezing-point and the boiling-point 
is divided into 180 equal degrees. Another thermometer 
used in many other countries and in most scientifc work 



210 



PRACTICAL ARITHMETIC 



is the Centigrade, with zero at the freezing-point, 100 
degrees at the boiling-point. Below zero is indicated by 

the — sign. Above zero is indicated by the 

-(- sign or by no sign. 



EXERCISE 183. — ORAL 

Unless otherwise stated, Fahrenheit de- 
grees are to be understood in the following 
problems : 

1. When the temperature of the air is 40 
degrees, how much above freezing is it? 

2. When water is at 180 degrees, how 
much below boiling is it? 

3. The body temperature of a person is 
normally 98.6 degrees. A temperature of 99 
degrees or more indicates fever. What is 
the range between normal temperature and 
fever temperature? 

4. A body temperature of 108 degrees usually indicates 
approaching death. What is the range between normal tem- 
perature and the death point? Only rarely does the body 
temperature fall below 92 degrees and life continue. What 
is the range of temperature ? 

5. How many degrees Centigrade equal 180 degrees 
Fahrenheit? 

6. How many degrees Fahrenheit equal 1 degree Centi- 
grade ? 

7. How many degrees Centigrade equal 1 degree 
Fahrenheit? 



PRACTICAL MEASUREMENTS 211 

BXEECISE 184. — 'WRITTEN 

1. Change 10° F. to C; change 10° C. to F. 

2. Devise a rule for changing from Fahrenheit to Centi- 
grade. 

3. Devise a rule for changing from Centigrade to 
Fahrenheit ? 

LONGITUDE AND TIME 
BXEECISE 185. — ORAL 

1. The earth appears to be flat. If it were really flat, 
what would be true concerning the time of sunrise on 
every part of the earth's surface? 

2. What would be true of sunset under the same con- 
ditions? What are the facts concerning the time of sun- 
rise and sunset upon different parts of the earth's surface? 

3. Which city has sunrise first, New York or Chicago? 
Why? Chicago or San Francisco? Why? 

4. What places upon the earth have sunrise at the 
same time? What places have noon at the same time? 
What places have midnight at the same time? 

288. A meridian is an imaginary line running north 
and south from pole to pole. All places upon the same 
meridian have their midday or noon at the same moment, 
i.e., they are touched by the vertical rays of the sun at 
the same time. 

289. The distance east or west from a given meridian 
is called Longitude. 



212 PRACTICAL ARITHMETIC 

EXERCISE 186.— ORAL 

1. Through how many degrees does the earth rotate 
from sunrise until the sun is in the zenith? 

2. Through how many degrees does the earth rotate 
from sunrise to sunset ? Through how many degrees does 
a point upon the earth pass in a complete rotation ? 

3. Since the earth turns on its axis through 360 degrees 
in 1 day of 24 hours, through how many degrees does it 
turn in 1 hour ? 

290. Longitude is measured by degrees. The merid- 
ians from which longitude is commonly reckoned are 
two, one of which passes through Washington, D.C., one 
through Greenwich, England. 

291. The given meridian from which longitude is gen- 
erally reckoned is called the Prime Meridian. Longitude 
is reckoned east and west of the prime meridian to 180 
degrees. West longitude is designated by the letter 
"W." and east longitude by the letter "E." 

EXERCISE 187. — ORAL, 

1. When it is sunrise at Baltimore, how long will it be 
before it is sunrise at a place 15 degrees west of Balti- 
more? 30 degrees west? 45 degrees west? 

2. When it is noon at St. Louis, how long will it be 
before it is noon at a place 15 degrees west of St. Louis? 

3. If I travel eastward, will my watch become too slow 
or too fast ? If I travel westward, will my watch become 
too slow or too fast ? 



PRACTICAL MEASUREMENTS 213 

292. Since the earth turning upon its axis once in 24 
hours, passes through 360 degrees in that time, the follow- 
ing table may be deduced : 

Longitude Timb 

360° corresponds to 24 hours. 
15° corresponds to 1 hour. 
15' corresponds to 1 minute. 
15" corresponds to 1 second. 

1° corresponds to 4 minutes. 

1' corresponds to 4 seconds. 

293. Two places are 40° 15' 30" apart. What is the 
difference in time between them ? 

Since places 16° distant 

15 )40° 15' 30" from each other have a dif- 

2 hrs. 41 mins. 2 sees, ference of 1 hr. in time, and 

since places 15' apart have a 

difference of 1 min. in time, 

and since places 16" apart have a difference of 1 sec. in time, 

jig- of the numbers representing degrees, minutes, and seconds 

will give the difference in time in hours, minutes, and seconds. 

BXBRCISB 188. — WRITTEN 

1. The difference in longitude between two places is 
46 degrees, 20 minutes, 35 seconds. What is the difference 
in time? 

2. Washington is 77° 3' from Greenwich. What is 
the difference in time? 

The longitude of the following cities is : 

Washington, 77° 3' 0" W. 
New York, 74° 3" W 

Paris, 2° 20' 22" E. 



214 PRACTICAL ARITHMETIC 

San Francisco, 122° 24' 15" W. 
Peking, 116° 27' 30" E. 

Constantinople, 28° 59' E. 

Berlin, 13° 23' 43" E. 

Find the difference in time between : 

3. Washington and Peking. 

4. New York and San Francisco. 

5. Washington and Constantinople. 

6. New York and Paris. 

7. San Francisco and Berlin. 

294. The difference in time between two places is 5 hrs. 

30 mins. 25 sees. What is the difference in longitude? 

ri on ■ oc Since there are 15 times as many 

5 hrs. 30 mms. lo sees. , . ■, , ^. 

-. r degrees, mmutes, and seconds of 

'- longitude as there are hom's, min- 
utes, and seconds of time, 15 times 
the number representing the difference in time will give the 
difference of longitude in degrees, minutes, and seconds. 

BXBBCISE 189. -WRITTEN 

1. The difference in time between two places is 10 hrs. 
16 mins. 24 sees. What is the difference in longitude? 

Find the difference in longitude between the following 
places and Greenwich, the difference in time being: 

2. Athens, Greece, 1 hr. 34 mins. 54.9 sees. E. 

3. Calcutta, 5 hrs. 53 mins. 20.7 sees. E. 

4. Chicago, 5 hrs. 50 mins. 26.7 sees. W. 

5. St. Petersburg, 2 hrs. 1 min. 13.5 sees. E. 

6. What is the difference in longitude between St. 
Petersburg and Chicago? 



PRACTICAL MEASUREMENTS 215 

7. When it is noon at Greenwich, it is 6.09 A. jr. at 
Chicago. What is the longitude of Cliicago? 

8. Wlien it is 6.09 a.m. at Chicago, it is 3.50 a.m. at 
San Francisco. What is the difference in longitude? 

STANDARD TIME 

295. To use the exact sun time for each place brings 
about so many complications that another method has 
been devised by which the world is divided into 24 time- 




Standard Time Map 

belts, all places within the same belt using the same time. 
The time meridians of the time-belts of the United States 
are those of 75°, 90°, 105°, and 120°, as is shown in the 
accompanying map. Accordingly, the United States and 
Canada are divided into four belts extending north and 
south. All places in the same belt have the same time 
regardless of their exact longitude. In practice, these 



216 PRACTICAL ARITHMETIC 

belts do not have regular boundaries ; but the points of 
change are determined rather by the position of important 
cities. Time determined in this manner is known as 
Standard Time. 

EXERCISE 190. — OEAL 

1. When it is noon at Greenwich, what time is it at 
New York, estimating the longitude at New York as 75"? 

2. When it is 6 a.m. at New York, what time is it at 
Chicago ? ' At Denver ? At San Francisco ? 

EXERCISE 191.— WRITTEN 

1. What is the difference between standard and local 
time at Chicago ? 

2. The longitude of Pittsburg is 80° 2' 0". What is 
the difference between standard and local time there? 

3. What is the difference between standard and local 
time at New Orleans, longitude 90° 3' 28.5" ? 

4. The longitudes of St. Louis, Richmond, Denver, and 
Boston are respectively : 90° 15' 15" W., 77° 26' 4" W., 
104° 59' 33" W., 71° 3' 30" W. At what time, standard, 
will an electric time signal sent from Washington at 
noon reach them ? At what local time ? 

REVIEW PROBLEMS 
EXERCISE 192. — WRITTEN 

1. How many barrels of water will a trough hold, if it 
is 7 ft. long, 2 ft. wide, 16 ins. deep? 

2. If a windmill pumps 2 gals, and 8 qts. each minute 
and pumps 4 hrs. in a day, how many cows will it supply 
if each cow consumes 1.5 cu. ft. of water daily? 



REVIEW PROBLEMS 217 

3. How many pounds of water does each cow consume 
if one gallon weighs 8.35 lbs.? 

4. A pound of timothy seed conta,ins 1,170,500 seeds. 
Sowing 16 lbs. to the acre, how many seeds are sown to 
the acre ? How many seeds are there in an ounce ? 

5. What is the value of a rectangular field 23 chs. 2 rds. 
17 Iks. 6 ins. long by 17 chs. 3 rds. 18 Iks. 7 ins. wide at 
137.50 an acre? 

6. There are 15 steps on the hall stairs. The tread is 
12", the rise 7|-". What Avill sufficient stair carpet cost 
at 62 cts. a yard, allowing Jq extra carpet for the pro- 
jection of the tread ? 

7. In raising Irish potatoes three grades of seed were 
used : 1st, seed from the best hills to be found ; 2d, seed 
from ordinary hills ; 3d, seed from the very poor hills. 
The yields for each 100 hills planted with these seed were: 
ordinary seed 136 llw. 1-t ozs., best seed 172 lbs. 8 ozs., 
poor seed 75 lbs. 10 ozs. What was the average yield per 
hill? What was the increase in yield from seed No. 1 over 
that of No. 2? Of seed No. 2 over seed No. 3 ? 

8. Sprayed grapes yielded 4 lbs. 5.8 ozs. to the row. 
Unsprayed grapes yielded 1 lb. 1.5 ozs. to the row. What 
was the gain per row in pounds from spraying? 

9. Sprayed grapes yielded 3 lbs. 4.3 ozs. more per row 
than unsprayed grapes. What was the difference in 
yield on 17| rows ? 

10. Western Yellow Pine in Colorado, 20 years old, 
measured 1.2 ins. in diameter ; at 80 years, 2.9 ; at 40, 4.9 ; 
at 50, 6.8; at 60, 8.6; at 70, 10.2; at 80, 11.7; at 90, 
12.8; at 100, 13.8; at 110, 14.7; at 120, 15.5. What 



218 PRACTICAL ARITHMETIC 

was its circumference at each of these ages? How much 
did the diameter increase from the fourth to the fifth 
decade ? How mucli the circumf ereiice ? How much did 
both the diameter and the circumference increase from the 
eleventli to the twelfth decade? 

IX. An ordinary milk pail is llj ins. in diameter at the 
top; another pail has an opening only 7 ins. in diameter. 
What is the difference in the areas of the openings? If 
seven billion bacteria fall into the milk in the first pail in 
15 mins., at the same rate how many would fall into the 
other pail in the same time ? 

12. Planting 7 ozs. of tomato seeds to the acre, how 
many pounds are needed for 19 A. ? 

13. Sowing 3 pks. of cow-peas to the acre, how many 
bushels of seed are needed for 40 A. ? 

14. Bordeaux mixture consists of 5 lbs. of bluestone, 
5 lbs. of lime, and 50 gals, of water. Applying this to 
potatoes at the rate of 150 gals, of mixture to the acre, 
for each application, and making 3 applications: a. How 
many gallons will be needed on 40 A. ? 6. How many 
barrels? c. What will the bluestone cost at 6 cts. a 
pound? d. What will the lime cost at \\ cts. a pound? 

15. To produce 1 T. of oats requires 376 T. of water. 
How many cubic feet of water are needed? How many 
barrels? How many hogsheads? How many quarts? 

16. To produce a ton of wheat requires 338 T. of water. 
Solve for all the items of the last problem. 

17. To produce a ton of dry matter, the average crop 
plant requires 325 T. of water. Solve as in problem 15. 



REVIEW PROBLEMS 219 

18. A man sells 7 customers 1 pt. each of syrup at 5 
cts. a pint, 9 customers 1| qts. each at 10 cts. a quart, and 
13 others 1 gal. each at 35 cts. a gallon. How much a 
gallon did he average for his syrup? 

19. A horse moving at 2:40 gait, moves how far in 1 
sec. ? At a 2: 10 gait? At a 3-nnn. gait? At a 4-min. gait ? 

20. What is the cost of materials for 1 cu. yd. of con- 
crete made of 1.16 bbls. of cement @ |2, 0.44 cu. yd. 
of sand @ 75 cts., 0.88 cu. yd. of gravel @ 75 cts. ? If 
20 posts 6" X 6" at the bottom, 6" x 8" at the top, and 7' 
long, can be made from 1 cu. yd. of concrete, what will 
the materials cost per post? 

21. Adding 6 cts. for 28 ft. of 0.16-in. steel wire @ 3 
cts. a pound, what is the total cost for materials per post? 

22. A well is 7 ft. in diameter. Wliat is its circumfer- 
ence? If it contains 6 ft. of water, how many gallons 
are there? 

23. A tree has a circumference of 12 ft. What is its 
diameter? If 8 ft., what is the diameter? 

24. The triangular end of a house gable is 37 ft. on 
its base, and 16 ft. from the base line to apex. What is 
its area in square feet? 

25. A triangular garden has a base of 90 ft. and an 
altitude of 75 ft. What fraction of an acre is it? 

26. A cistern is 12 ft. deep and has a diameter of 8 ft. 
What is the volume of the cistern? How many gallons 
of water will it hold? 

27. The water pipes on a house measure 13 ins. outside 



220 PRACTICAL ARITHMETIC 

circumference. There are 200 ft. of piping on the house. 
What is the surface of this piping ? 

28. How many cubic feet are there in a cylindrical 
tank 12 ft. in diameter and 20 ft. deep? How many 
gallons? How much does the water in it weigh when it 
is full? How many square feet in its outer surface, ex- 
clusive of bottom? How many gallons of water does it 
contain for each foot in depth? 

29. How many feet of picture moulding are needed for 
a room 17' 6" long and 9' 9" wide? 

30. AVhat is the length of the tire of a wheel 4 ft. in 
diameter? Of a wheel 3^- ft. in diameter? 

31. Mr. Akers owned a rectangular piece of land, the 
north and south sides of which were each 42 rds. long. 
The east and west sides were each 38 rds. long. Two 
railroads cut off portions of it ; one took all west of a line 
beginning at the N.W. corner and running S.E. to a 
point 14 rds. east of the S. W. corner. The other took 
all east of a line beginning at a point 12 rds. south of the 
N. E. corner and running S. W. to a point 8 rds. west of 
the S.E. corner. Draw a map of the land as cut off by 
the railroads. The railroad owners bought the land cut 
off by their roads at $150 an acre. How much did it 
cost ? How much land was left in the tract ? 

32. How much lumber will be required for 80 rds. of 
fence 4 boards high, each board 6 ins. wide ? How much 
lumber will be required to make a tight board fence the 
same length and 5 ft. high, nailing the boards to two 2" 

X 4" scantling? No allowance for waste in either case. 

33. How many yards of 27-in. velvet carpet with 22-in. 



REVIEW PROBLEMS 221 

border will be required to carpet a society hall 42 ft. 
long, 36 ft. wide, having one rectanglar alcove at each 
end? Each alcove is 5 ft. deep and 20^ ft. wide. Esti- 
mate the amount with strips of carpet running lengthwise. 

34. Estimate with strips running crosswise. 

35. What will carpet and border cost at $ 1.25 a yard ? 

36. How much paper will be needed to paper the walls 
and ceiling of this hall, there being 4 windows 9| x 6 ft. 
and the pitch of the ceiling being 14 ft.? The alcove 
ceilings are papered, but the alcove walls are finished in 
hard-wood panels, and require no paper. 

37. The paper for walls costs 95 cts. per double roll, 
for ceiling 25 cts. per double roll, picture moulding 7 cts. 
a foot, no moulding being used in the alcove. What is 
the cost ? 

38. Estimate in meters the height of Mt. Everest 29,002 
ft.. Pikes Peak 14,111 ft., Mt. Blanc 15,744 ft., and Mt. 
Aconcagua 23,082 ft. 

39. What number of bricks is needed for a wall 4^ ft. 
high, 3 bricks thick, around an enclosure 14 x 23 ft.? 

40. How many cubic yards of concrete are required to 
make a circular wall 8 ins. thick around the top of a well, 
the wall to be 29 ins. high and 5 ft. 3 ins. inside diameter ? 

41. How many cubic yards of concrete are needed to 
make a semicircular walk in front of a schoolhouse, the 
walk to be 4 ft. 3 ins. wide, 27 ft. long on its shorter side, 
and the concrete to be laid 4 ins. thick ? 

42. A farmer uses a potato crate 19|" x 13" x 12" to 
contain a bushel of potatoes, 60 lbs. How much does 



222 PRACTICAL AKITHMETIC 

this bushel of potatoes exceed in size the standard bushel 
of dry measure ? 

43. A crate 22" x llf" X 14|" contains how many- 
such bushels ? How many standard dry bushels ? 

44. A tank of a spraying machine is in. the form of a 
half-cylinder resting on its convex side, 5 ft. long and 2 ft. 
6| ins. in diameter, inside measurement. What is its 
capacity? If it were shortened 5 ins. and increased in 
height 3| ins. without further curving of the sides, what 
would the capacity be ? 

45. The usual 40-qt. milk can is 12-|- ins., inside di- 
ameter. How many inches tall need it be if of uniform 
diameter ? What fraction of an inch in depth equals 1 qt.? 

46. In the usual 50-qt. milk can, 1 qt. occupies .375 
in. in depth. What is the diameter of the can ? 

SILOS AND SILAGE 

47. The base of a, silo is 16 ft. in diameter. What is 
its circumference? If 26 ft., what is its circumference? 

48. Find the capacity, in tons, of a silo 10 ft. in diame- 
ter and 20 ft. high, if a cubic foot of silage from such a 
silo weighs 30 lbs. 

49. How many tons of silage will this silo contain, if, 
after it has settled, the silage is 5 feet from the top ? 

50. Find how many tons of silage a silo will hold, that 
is 20 feet in diameter and 32 feet deep, if in such a silo 
a cubic foot of silage weighs 40 pounds. 

51. How many tons of silage will there be in this silo, 
if, after it has settled, the silage is 7 feet from the top? 



REVIEW PROBLEMS 



223 



52. If 43 COWS be fed 37 lbs. each of silage per day, 
how long will the contents of this silo last ? 

53. In order that the silage may settle sufficiently to 
insure its preservation, a silo should not be less than 
30 ft. deep. What di- 
ameter must it have to 
hold enough silage to 
feed 25 cows 40 lbs. per 
day for 185 days, if the 
silage weighs 38 lbs. to 
the cubic foot? 

54. How many acres 
of corn will it take to 
furnish a feed of 35 
pounds per day each to 
a herd of 32 cows for 
150 days, each acre yield- 
ing 12 tons of silage ? 
What must be the diameter of the silo necessary to hold 
this silage, if the height of the silo is 32 feet, and 1 cubic 
foot of silage weighs 40 pounds? 

55. The corn on a field of 18 acres when ready for 
cutting arid shocking or for putting in the silo weighs 
9 tons per acre, of which ^ is water. If by cutting and 
shocking the corn, there is a loss in dry matter of ^^^, and 
by putting it in a silo there is a loss of dry matter of Jg-, 
what is the value of the feed gained by putting the crop 
in the silo, if the dry matter in silage is worth .71 of a 
cent per pound ? 

56. How many acres of corn will it require to produce 




22-4 PRACTICAL ARITHMETIC 

the silage to feed 18 cows 37- pounds per day for 184 
days, if each acre produces 13 tons of silage corn? 

DRESSMAKING 

57. How many yards of 36-in. material will be required 
to make a shirt-waist, if the tucked front measures 24 ins. 
before tucking and the two backs 12 ins. before tucking ; 
the front length from shoulder measuring 18 ins. and two 
backs 16 ins.; sleeves 16 ins. long before finishing and 
18 ins. wide in the widest place? Cuffs, collars, belts are 
found in pieces cut from strips. See diagram. 

58. How many yards of insertion will be required for 
this waist for 4 strips the length of the front, 4 strips 
for the back, one piece for the neck 12 ins., and two 
pieces for the sleeves 8 ins. each? 

59. How many yards will be required for a nine-gore 
skirt of the same linen if gores average 5 ins. wide at the 
top, and 15 ins. wide at the bottom, the length of 
each gore being 38 ins. when finished with a 3-in. hem, 
and allowing 1 in. at the top for finishing? 

60. How much insertion will be required for two rows 
5 and 8 inches from the bottom of the skirt, if the gores 
for the bottom row average 13 ins. and second row 12 ins. ? 

61. At 50 cts. for linen and 15 cts. a yard for insertion, 
1 doz. buttons at 10 cts., 1 bolt of tape at 5 cts., what 
will the dress cost? 

62. The lining and finishings for a dress are called the 
findings. What will findings consisting of the following 
items cost : 2 J yds. of waist lining at 15 cts., 6 yds. skirt 
lining at 25 cts., 2 spools silk at 10 cts., 1 spool cotton 



REVIEW PROBLEMS 

5 cts., 1 bolt braid 10 cts., 1 card hooks 
and eyes 10 cts., 1 bolt silk binding 10 
cts., 1 yd. featherbone 5 cts., 1 pr. 
shields 35 cts. ? 

63. Find the cost of a Panama-cloth 
dress ; 8 yds. of material at 89 cts. a 
yard, with findings at price given in 
last problem. 

64. What will the dress cost if a 
professional shopper charges 10 cts. 
on each dollar for buying the above 
materials and a dressmaker charges f 8 
for making the dress? 

65. If, for the cotton skirt lining, 
a silk lining be substituted which will 
require 10 yds. of silk at 59 cts. a yard, 
what will the dress cost? What will 
be the shopper's fee? 



66. Races are run at the 
Olympic games at Athens 
over distances of 100 meters, 
400 meters, 800 meters, 1500 
meters. How many j'-ards 
in each of these distances ? 

C7. The best time for 
these races prior to 1908 
was respectively 10|- sees., 
49|^ sees., 1 min. 56 sees., 
and 4 mins. 5| sees. What 
was the speed per yard in 
each race ? 




FOLD OF GOODS 



226 PRACTICAL ARITHMETIC 

68. Some races run in the Public Schools' Athletic 
League, high school events, are 100 yds., 440 yds., 880 
yds., and 1 mi. What is the diiference between these dis- 
tances and those mentioned in problem 66 ? 

69. The time for these races was respectively 10| sees., 
53 sees., 2 mins. 7| sees., and 4 mins. 59| sees. What 
was the speed per yard ? 

70. Some Olympic records are : running long jump 
24 ft. 1 in. ; running high 6 ft. 2^ ins.; pole vault 11 ft. 
6 ins. P. S. A. L. high school records for the same events 
are respectively: 21 ft., 5 ft. 6 ins., 9 ft. 9 ins. By what 
fraction does the P. S. A. L. high school record fall short 
of the Olympic record in these events ? 

71. The steamship Lusitania, in July, 1908, made an 
average speed of 25.01 knots an hour. One knot equals 
6086.7 ft. What was the average speed in miles per day? 

72. The Lusitania covered the distance from Daunt's 
Rock to Sandy Hook lighthouse in 4 das. 20 hrs. and 15 
mins. What is the distance? 

73. What is the speed per second of the circumference 
of a grindstone 4 ins. in diameter, run at 30 revolutions 
per minute? 

74. Allowing 5 sq. ft. of floor space to each fowl, what 
may the dimensions of a henhouse be to accommodate 100 
fowls? If one side be 14 ft. what will the other dimen- 
sion be? With lumber at $15 per M, what will the 
boards for sides and ends cost if 5 ft. 6 ins. high when 
built square ? When built 14 ft. wide? How much does 
the extra light and ventilation secured by the narrower 
form of house cost? 



PERCENTAGE 

296. If a spraying mixture contains 98 parts water, 1 
part lime, and 1 part bluestone, how many parts are there 
in the mixture? How many hundredths of the mixture 
are water? How many hundredths are lime? How many 
hundredths are bluestone? 

Of a number of seeds tested, one out of every ten fails 
to grow. How many fail to gi'ow out of every hundred? 
How many hundredths fail to grow? 

The number of hundredths of a number is commonly 
expressed by the term per cent. 

Out of 100 oak leaves examined, 60 were injured by 
insects. What per cent were injured by insects ? What 
per cent were uninjured? 

297. The term per cent is expressed by the sign %, e.g., 
8 % is read 8 per cent. 

298. A given per cent, or a given number of hun- 
dredths, of a number may be expressed as a whole number 
with the per cent sign, as a decimal, or as a common frac- 
tion, e.g., 1 per cent may be written 1 %, .01, or ^-J-g-. 8 
per cent may be written 8 %, .08, or j-f-iy 





EXERCISE 


193 


. - WRITTEN 




Express as 


decimals : 








1. 4%. 


4. 15%. 




7. 6f%. 


10. 62-1%. 


2. 6%. 


5. 75%. 




8. 5f%. 


11. 8-31%. 


3. 5%. 


6. 41%. 




9. mo. 


12. 115%, 



227 



228 PRACTICAL ARITHMETIC 

13. 125^%. 16. 2.25%. 19. .4%. 

14. 250%. 17. 6.4%. 20. .04%. 

15. 631%. 18. 9.34%. 21. .004%! 

299. Express 25%, 2.5%, | %, as common fractions in 
lowest terms : 

25%=TVu = i- 

1 

1 pi„ ~i 1 

'i JO — iTo ~ TiriT- 

EXBBCISB 194. — "WRITTEN 

Express as common fractions in lowest terms: 

1. 12%, .12%. 6. 16f%, 1%. 11. 150%, .15%. 

2. 25%, .25%. 7. 3.31%, 1%. 12. 625%, 6.25%. 

3. 42%, .42%. 8. 621%, 1%. 13. 375%, 3.75%. 

4. 55%, .55%. 9. 83^%, f%. 14. 1%, 1.2%. 

5. 75%, .75%. 10. 121%,!%. 15. 1%, .05%. 

300. Express | %, ^%, j^^%, as decimals of a per cent, 
and as decimals : 

i%=.6%=.005. 

i % = .2 % = .002. 

t\%=.2%=.002. 

exercise 195. — written 

Express the following as decimals, and as decimals of a 
per cent : 

10. ^%. 

11. 1%. 

12. ^%. 



1- \1o. 


4- \1o. 


7. 1% 


2. \1o. 


5- \1o. 


8. i% 


3. \1o. 


6. 1%. 


9- \1o 



fERCENTAGE 229 

13. ^%. 15. f%. 17. f%. 19. 1%. 

14. i%. 16. T^%. 18. 1%. 20. 1%. 

301. Important per cents to be remembered : 

1 = 100%. 1 = 15%. i=m%. tV = 6|%. 

1 = 50%. i = 20%. 1 = 371%. ^-, = 5%. 

i = 33i%. 1 = 60%. 1 = 621%. 2^ = 4%. 

f=66|%. i = 16f%. t = 87i%. ^V = 2%. 

i = 25%. 1 = 831%. J^=10%. 1^0 = 1%. 

EXERCISE 196. — ORAL 

Find: 

1. 10 % of 50. 6. 371 % of 48. ii. 16| % of 66. 

2. 25 % of 80. 7. 871 % of 72. 12. 62-1 ^^ of 64. 

3. 60 % of 300. 8. 5 % of 125. 13. 60 % of 10. 

4. 121 % of 72. 9. 2 % of 200. i4. 83^ % of 42« 

5. 16| % of 90. 10. 831 % of 96. 15. 5 % of 120. 

EXERCISE 197. — WRITTEN 

Find: 

1. 75 % of 1280. 8. 66f % of 5432. 

2. ^% of 5420. 9. 4.2% of 2437. 

3. 2.5% of 2655. 10. 42% of 8432. 

4. 871 % of 6424. 11. § % of 9812. 

5. 4% of 2254. 12. 381% of 5431. 

6. 1% of 8243. 13. 4.5% of 5240. 

7. 831% of 9846. 14. 8.9% of 1872. 

302. The number of which so many hundredths or a 
certain per cent is to be taken is called the Base. 



230 PRACTICAL ARITHMETIC 

303. The number indicating how many hundredths of 
the base are to be taken expresses the Rate or Rate Per 
Cent. 

304. The result obtained by taking the number of hun- 
dredths of the base indicated by the rate is the Per- 
centage. 

Find 9 % of 50 : 

50 is the base. 
.09 is the rate. 
4.5 is the percentage. 

305. Three kinds of problems occur in percentage: 

1. Those in which base and rate are known and per- 
centage is to be found. 

2. Those in which base and percentage are known and 
rate is to be found. 

3. Those in which rate and percentage. are known and 
base is to be found. 

306. Case One. Given the base and the rate to find 
the percentage. 

In testing a certain ore it was found that 25 % of it was 
iron. How much iron was contained in 496 lbs. of ore? Since 
25<fo =^, the percentage is most readily obtained by taking | 
of 496, which is 124. Hence, 124 lbs. was iron. 

In testing an ore it was found that 29 % of it was iron. 
How much iron was there in 469 lbs. of ore? 

Since 29% or -^ is not conveniently used as a common 
fraction, it is best to express it as a decimal, .29. 469 x .29 = 
136.01 lbs. Hence 136.01 lbs. was iron. 



PERCENTAGE 231 

Knowing the base and rate to find the percentage. 
Multiply the base by the rate expressed either as a com- 
mon or as a decimal fraction. 

EXERCISE 198. — ORAL 

1. Find 5 % of 80 ; 120 ; 40 ; 200 ; 180 ; 160 ; 20. 

2. Find 4% of 75; 125; 150; 175; 50; 25. 

3. Find 10 % of 40 ; 110 ; 140 ; 90 ; 70 ; 860 ; 10. 

4. Find 20% of 30; 75 ; 90; 65; 95; 100; 25; 5; 10. 

5. Find 25 % of 20 ; 40 ; 80 ; 60 ; 12 ; 8 ; 10 ; 4. 

6. Find I % of 100 ; 200 ; 50. 

EXERCISE 199. — -WRITTEN 

Solve the following, using the rate both as a decimal 
and as a common fraction : 

1. Find 7% of 425; of 67.3; of 526; of 9642; of 87.9. 

2. Find 14% of 48.8; of 68; of 125.6; of 7981. 

3. Find 6^% of 32; of 96.32; of 128.64; of 842. 

4. Find 19 % of 38 ; of 99 ; of 132 ; of 869 ; of 7684. 

5. Find 72 % of I ; of fy ; of J^ ; of -^\ ; of If. 

6. What is 15% of $5.20? of *13.50? of |75? of 
$8764.75? 

7. What is 4 % of | of an acre of land ? 

8. What is 13% of 96 sq. ch^. 48 sq. rds. of land? 

9. What is 37% of 1 sq. mi. 168 sq. rds. of land? 

10. Find 129% of 76; of 128; of 7842.1. 

11. Find 300 % of 84 ; of 78.2 ; of 3. 

12. Find .3% of 782; of 6498. 



232 PRACTICAL ARITHMETIC 

13. Find .17% of 6842; of 17; of 386.7. 

14. Find .06% of 98; of 782; of 6428. 

15. A owned f of a mill and sold 33^% of his share. 
What part of the mill did he sell, and what part does 
he still own? 

307. Case Two. Given the base and the percentage to 
find the rate. 

What per cent of 85 is 17? 

Dividing 17 by 85, we have ^ = \. 

^ of any number is 20 % of that number, therefore 17 is 
20 % of 85. 

Since the percentage is found by multiplying the base 
by the rate, the rate may be found by dividing the 
percentage by the base. 
_ What per cent of 85 is 17.85? 

^ 

85)17.85 Dividing 17.85 by 85, we have .21 = 21 %. 
I'^QO Therefore, 17.85 is .21, or 21 hundredths, or 

85 21 % of 85. 
85 

BXEECISB 200. — ORAL 

1. What per cent of 50 is 25? Is 10? 

2. What per cent of 1^.00 is |125? Is $2.50? 

3. Whatper cent of 112.50 is $3.00? Is 12.75? 

4. What per cent of 172.50 is $15.50? Is $17.40? 
3. What per cent of 96 is 31? Is 27? 

6. What per cent of 122 is 6.1? Is 9.76? 



PERCENTAGE 233 

BXBECISB 201. — WRITTEN 

1. What per cent of 86 is 24? Is 8? Is 1? Is ^? 

2. What per cent of 7862 is 18? Is 986? Is 12? Is 7? 

3. Wliatper cent of 7847 is 67? Is 7614? Is 96? 

4. Whatper cent of 848is 424? Is 212? Is 106? 

5. What per cent of 1 is ^ ? Is f ? Is .08? 

6. A man whose salary is f 182 a month pays 126.40 
for board, and $5.28 for amusement. What per cent of 
his salary remaining after his board is paid, does he pay 
for amusement? 

7. A workingman's day is 10 hours long. He spends 
^ of the remaining hours in sleep. What per cent of his 
time is given to sleep? What per cent to other pursuits? 

8. A farmer held cotton bought of a renter; the price 
declined 12%, then rose 15% ; he then sold. What per 
cent did he gain on the transaction ? 

9. If a merchant's scales weigh 14 ozs. for a pound, 
what per cent does the purchaser lose? 

10. If the retail merchant's fair profit is equivalent to 
3 ounces and the scales are as in the above example, what 
per cent more does the buyer pay than if he were to buy 
from wholesale houses? 

11. What per cent of a number is 33^% of 6 % of it? 

308. Case Three. Given the rate and the percentage 
to find the base. 

29 is 20 % of what number ? 

20 % = TW) or h 29 is therefore i of the base ; the base is 



234 PRACTICAL ARITHMETIC 

29 -H -^ = 29 X f , or 29 multiplied by 5, or 145, or expressing 
20 % as a decimal = .20 = .2, and dividing we have, 

■2 )29.0 
145. 

The second method is preferable when the rate cannot 
readily be expressed as a fraction. 

Since the percentage is the product of the rate and the 
base, the base may be found by dividing the percentage 
by the rate expressed as a decimal. 

EXERCISE 202. — OBAL 

1. 8 is 5% of what number? 10% of what number? 

2. 8 is 20% of what number? 25% of what number? 

3. 12 is 12^ % of what number? 75% of what number? 

4. 12.50 is 16|% of what? 33^% of what? 

5. 6 ft. 10 ins. is 66| % of what? 331% of what? 

6. 21 ft. 7 ins. is 871-% of what? 

7. 16 gals. 4 qts. 2 pts. is 87-i-% of what? 

BXBECISB 203.— "WRITTEN 

1. 44.1 is 105% of what number? 90% of what 
number ? 

2. 60 is 125% of what number? 75% of what number? 

3. 96 is 30% of what number? 18% of what number? 

4. 47 is 8% of what number? 20% of what number? 

5. 776 is 60% of what number? 83% of what number? 

6. 6 is 16% of what number? 90% of what number? 

7. 87 is .05 % of what number? 178 % of what number? 



PERCENTAGE 235 

309. When the base is added to the percentage, the sum 
is known as the Amount. 

310. When the percentage is subtracted from the base, 
the remainder is called the Difference. 

311. The rent of a farm is §68.20 and this is an advance 
of 10 "Jo over the previous year. What was the rent the 
previous year? 

100 "Jo = rent the previous year. 

10 % = advance this year. 
110 % = r? ()8.20. 

1% = .62. 
100% = $62. 

Hence, % 62 was the rent of the farm for the previous year. 

A regiment returns from battle with 1197 men, whicli 
is 5 % less than it started with. How many men were in 
the regiment when the battle began? 

100 % = nmnber started with. 
6 % = number lost. 
95% =1197. 
1%=12.6. 
100 % = 1260. 

To find the base when the rate and amount are given, 
divide the amount by 1 plus the rate expressed as a 
decimal. 

To find the base when the rate and difference are given, 
divide the difference by 1 minus the rate expressed as a 
decimal. 

EXERCISE 204. — ORAL 

1. Amount 110, rate 10 ; find the base. 

2. Amount 150, rate 50 ; find the base. 



23G 



PRACTICAL ARITHMETIC 



3. Amount 75, rate 50 ; find the base. 

4. What number plus 7 % of itself equals 214 ? 

5. What number minus 10 % of itself equals 90? 

EXERCISE 205. — WRITTEN 





Base 


Peecentase 


Eate 


Amount 


DiFFEEEHOE 


1 


17.62 


.75 


7% 


647 


784 


2 


1784.2 


1.50 


5i% 


829 


679 


3 


368.0 


7.84 


27% 


36.89 


87.24 


4 


42.879 


26.75 


219% 


726.47 


629.84 


5 


6784.0 


179.50 


0.6% 


99i 


88J 


6 


20090.0 


16A 


r/o 


642^ 


79if 


7 


6425.7 


A 


0.08% 


i 


t\ 


8 


84| 


6f 


0.009% 


0.06 


0.098 


9 


9 


0.074 


0.01 


8.09 


9.99/t 


10 


.0086 


6.28 


0.6 


7.09 


6.4J 



The pupil should practise with these problems enough to 
attaiu skill, accuracy, and certainty. 

1-10. Using the base in line 1, find the percentage with 
the rate given in each line from 1 to 10. 

11-40. Using bases in lines 2, 3, and 4, find percent- 
ages with each rate given. 

41-80. Using the percentages in lines 4, 5, 6, and 7, 
with each rate given, find the bases. 

81-120. Using the bases given in lines 3, 4, 5, and 6, 
with each percentage given, find the rates. 

121-160. Using the amounts given in lines 6, 7, 8, and 
9, find the bases with each rate given. 

161-200. Using the differences given in lines 1, 2, 3, and 
4, find the bases with each rate given. 



PERCENTAGE 237 

EXERCISE 206. — WRITTEN 
FARMING IN THE UNITED STATES 

1. In 1900, 7.1 % of the farms, or 407,012 farms, were 
between 10 and 20 A. in area. How many farms were 
there in the United States then ? 

2. Of 29,285,922 working inhabitants in the United 
States in. 1900, 10,438,217 were engaged in agriculture, 
7,112,987 in manufacturing, and 1,264,735 in professional 
service. What per cent was engaged in each of these 
pursuits ? 

3. $3,560,198,191, the value of the farm buildings of 
the United States, is 21.4 % of the total farm value. What 
is the total farm value? 

4. Of the 5,739,657 farms in the United States in 1900 
54.9% were worked by their owners, 13.1% by cash 
tenants, and 22.2% by share tenants. How many farms 
were worked in each of these ways? 

5. In 1900, 1,366,167 of the 5,739,657 farms of the 
United States were between 50 and 100 A. in area. 
What per cent of farms were of this size ? 47,276 were over 
1000 A. in area. What per cent did they constitute? 

6. In 1900 24.8% of the farms in the United States 
were between 100 A. and 175 A. in area. How many 
farms of this size were there? 21.9% were between 20 
and 50 A. How many were there of this latter class? 

7. In 1900 there were 9,349,922 men and boys engaged 
in farming in the United States, 20.1 % more than in 1890. 
At the same rate of increase, how many farmers will there 
be in 1910? 



238 PKACTICAL ARITHMETIC 

8. In 1894 there were 2712 Agricultural College 
students in the United States; in 1899, 5035. What was 
the per cent of increase for these five years? 

9. The value of the fertilizers used in the United 
States in 1899 was 149,099,939. If by home mixing of 
fertilizers and more intelligent use 23 % of this could be 
saved, what would be the saving to the farmers of the 
United States? 

IMPORTANCE OF GOOD SEED 

10. A certain number of tobacco plants raised from 
heavy seed produced 12.5 lbs. of tobacco; an equal num- 
ber of plants raised from light 
seed gave only 6.4 lbs. What 
was the per cent of gain by the 
use of heavier seed? 

11. With ordinary tobacco 
seed yielding 816 lbs. of tobacco 
per acre, and heavy seed yield- 
ing 29 % more, what would be 
the number of pounds of gain 
on an acre, if heavy seed were used? Tobacco selling at 
8 cts. a pound, what is the gain in value ? 

12. If a machine to separate heavy seed (see picture) 
costs 18 and the labor of such separation costs 5 cts. for 
seed for an acre, what would be the profit per acre the 
first year, supposing 7 A. were to be raised? 

13. What would be the per cent of profit the second 
year on the same acreage? There is no cost for the 
machine the second year. 




TERCENTAGE 239 

14. It is estimated that by using only the best varieties 
of corn and selecting the seed by the best-known methods, 
the corn crop of the United States might be increased 10 %, 
or 1116,662,647, in value. What is the present value of 
the corn crop? 

15. What could be its value if the best methods of seed 
selection were used? 

16. Light and heavy seeds were tested for germinating 
power. It was found that with lettuce, 44 % of the light 
seed germinated, 88 <fc of the heavy seed germinated ; 
onions, 38 % of the light seed germinated, 85 % of the 
heavy. What was the per cent of increase of the heavy 
seeds over light seeds in germinating power in each case ? 

17. If selected heavy cotton-seed yield 8.25% more 
than ordinary cotton-seed, what will be the value of the 
increase in yield on 600 A., averaging |- of a bale to the 
acre with the unselected seed, when cotton sells at $56 a 
bale? 

18. If cow-pea stubble plowed under increases the cot- 
ton crop of the following year 47%, and the cotton crop 
was originally |- of a bale to tlie acre, what is the money 
value of the stubble to the farmer, witli cotton at $55 a 
bale? 

19. Heavy cotton-seed produces better plants than does 
light seed. On 20 rows at Lamar, S.C., heavy seed 
yielded 1047| lbs. of cotton ; ordinary seed yielded 944 
lbs. What was the per cent of gain by the use of heavy 
seeds ? 

20. On another trial, heavy seed gave 1164 lbs. of 



240 PRACTICAL AKITHMETIC 

cotton; ordinary seed 1075 lbs. What would the gain 
from the use of heavy seed amount to on a 500-acre plan- 
tation averaging -^ of a bale per acre ? (500 lbs. equals 1 
bale.) 

21. What would be the value gained, with cotton at 
11^ cts. per pound ? What could the planter afford to 
pay to have seed separated, and still make 12 % upon the 
investment ? 

22. Which is most economical to buy, a. Red clover 
seed at 15.20 per 100 lbs. containing only 48.06% of real 
clover seeds and only 38 <fo of them alive ; or i. Seed at 
$6.10 per 100 lbs. with 46.24% of real clover seed, 27.5% 
of which are alive ; or c. Seed at 17.20 per 100 lbs. with 
73.8% real clover seed, 89% of which are alive? 

23. One lot of redtop seed at f 5.00 per bushel con- 
tained 77.4% of good seed; another lot at fl.lO per 
bushel contained 10.48% of good seed. Which was the 
cheaper? How much was paid per bushel for good seed 
in each case? 

PREVENTION OF PLANT DISEASES 

24. In using 1 oz. of formally to 3 gals, of water as 
a steep for oat seed to prevent smut, what per cent of 
formalin is used? (1 gal. of water weighs 8J lbs.) 

25. How many pounds, of formalin will be needed for 
25 A., allowing 1 gal. of mixture to each bushel of oats 
and 2 bus. of oats to the acre ? At 38 cts. a pound, what 
will it cost ? 

26. Formalin, being 40% formaldehyde, what per cent 
of formaldehyde is there in a l-oz.-to-3-gal. mixture? 



PERCENTAGE 



241 



27. The average net profit from spraying potatoes in 
experiments carried out during 1906 was 113.89 per 
acre ; the net profit from similar experiments in 1905 was 
120.04, in 1904 $24.06, in 1903 123.43. What was the 
average benefit for all these years? What would such 
amount to on 40 A.? 

28. Apple trees sprayed and not sprayed for the pre- 
vention of worminess yielded as follows : 





Total 
Yield 


Windfalls 


Picked Fruit 


Total 
Number 

OF 

Apples 


Per- 
cent 

OP 

Sound 
Fruit 




Wormy 


Not 
wormy 


Total 


Wormy 


Not 
wormy 


Total 


Sprayed r 
Treel 
Tree 2 
Tree 3 


Bushels 
U 

13.25 
13.75 


No. 
20 
11 
26 


No. 


No. 

188 

102 

78 


No. 
153 
129 
206 


No. 
1754 
1605 
1.562 


No. 






Total 




















Unsprayed : 
Treel 
Tree 2 
Trees 


11.75 
6.875 
5.50 


464 
224 
315 




502 
248 
404 


1258 
697 
564 


383 
488 
428 








Total 





















Copy table and fill each blank. 

29. A block of 69 sprayed trees yielded : merchantable 
fruit, 255 bus. ; culls, including windfalls, 36.5 bus. What 
was the per cent of merchantable fruit? 

30. The crop from 10 unsprayed Winesap trees was : 
salable fruit, 6.75 bus. ; culls, including windfalls, 10.25 
bus. What was the per cent of salable fruit? 

31. The use of Bordeaux mixture to prevent the downy 
mildew of cucumbers in New York State at an expen- 
diture of 19.50 an acre increased the profit 1163.50 



242 PRACTICAL ARITHMETIC 

an acre. What was the per cent of gain on the amount 
invested? 

32. Three trees affected with bitter rot yielded 21.1 
bus. of apples, 188 sound apples and 4244 diseased apples. 
Six similar trees, sprayed to prevent the rot, yielded 101.3 
bus., 8674 sound and 989 diseased. What was the per 
cent of increase in bushels by spraying? In sound apples? 
Spraying costs each time 3| cts. per tree. They were 
sprayed 3 times. What was the cost of spraying? What 
was the profit with apples at 85 cts. a bushel? 

33. A man plants two fields of 10 A. each with corn. 
In A he uses seed corn selected in the field ; in B he 
uses seed selected in the barn. The cost of fertilizers 
and labor for each field was flO an acre. Field A 
produced 45 bus. and field B, 36 bus. an acre. The man 
sold the corn at $.60 a bushel. Allowing f4 an acre for 
rent of land, what was the profit on each field? What 
per cent was gained by selecting seed in the field? 

34. Two farmers plant 5 A. each in peanuts, using 
the same kind of seed. Mr. A spends f 1.50 for lime, 
$3.00 for commercial fertilizer, and $2.00 for land plaster 
to the acre. Mr. B uses the same as the above, except the 
lime. Rent of land and cost of labor was $7.00 an acre for 
each. Mr. A made 1500 lbs. and Mr. B 1000 lbs. of 
peanuts an acre, which they sold at 3 cts. a pound. 
How much more did Mr. A get for his crop than Mr. B ? 
What per cent was made on the money invested in lime? 

ROOT TUBERCLES 

35. Cow-peas with tubercles upon their roots yield 
139.29 lbs. of nitrogen, without tubercles 118.45 lbs.; 



PERCENTAGE 



243 



soy beans with tubercles 113.55 lbs., without 75.98 lbs. 
What is the per cent of additional nitrogen with each of 
these crops when tubercles are present? 

36. If 100 lbs. of cow-pea tops contain: nitrogen 1.84 
lbs., phosphoric acid .67 lbs., potash 1.29 lbs.; and 100 lbs. 
of cow-pea roots contain: nitrogen 1.47 lbs., phosphoric 
acid .67 lbs. and potash 1.43 lbs., — what per cent of each 
of these foods is in the root ? What per cent in the tops ? 
In a harvest of 3.2 T. per acre, how much nitrogen is re- 
moved ? How much potash ? How much phosphoric acid ? 

37. The following amounts of fertilizers in each 100 
lbs. of dry substance were found in leguminous crops. 



Plant and 
Part 


NiTEOOEN 


Phosphoric 
AniD 


Potash 


Red clover 

Tops 

Roots 

Alfalfa 

Tops 

Roots 

Crimson clover .... 

Tops 

Roots 

Cow-pea 

Tops 

Roots 


Pounds 

2.28 
2.74 

2.89 
2.04 

2.72 
1.50 

2.79 
1.46 


Pounds 

0.72 
0.84 

0.53 
0.43 

1.10 

0.47 

0.57 
0.16 


Pounds 

1.40 
0.82 

1.46 
0.48 

1.56 
1.02 

2.00 

.77 



In each crop what per cent of the top is nitrogen? 
What per cent phosphoric acid? What per cent potash? 
What per cent of the roots is nitrogen? What per cent 
potash? What per cent phosphoric acid? By what per 
cent does the nitrogen of red clover exceed that of cow- 



peas 



244 



PRACTICAL ARITHMETIC 



COMMERCIAL FERTILIZERS 

312. Commercial fertilizers are used for the nitrogen, 
phosphoric acid, and potash they contain. The nitrogen, 

phosphoric acid, and potash are 
obtained from different sub- 
stances. Some of these sub- 
stances contain one, some two, 
and some all of these plant 
foods. The substances used 
for supplying nitrogen, phos- 
phoric acid, and potash in com- 
mercial fertilizers contain dif- 
erent per cents of these plant 
foods. The composition of 
some of these substances is 
quite uniform or constant, while in others the per cent of 
nitrogen, phosphoric acid, and potash varies considerably. 



200 POUNDS 

AMMONIATED^ 

FERTIUZER 

MANUFACTURED BY 

JOHN DOE i. CO 
ATLANTA GA. 

GUARANTEED ANALYSIS^ 
AVAILABLE PHOSPHOR- ^ 
IC ACID 8 PERCENT 
NITROGEN 3 
POTASH 3 




EXERCISE 207.— WRITTEN 

1- If ammonia is 82.4% nitrogen, how many pounds 
of nitrogen are there in a ton of fertilizer that has 2% of 
ammonia ? 

2. If there is 1 lb. of nitrogen in 1.214 lbs. of ammonia, 
how many pounds of nitrogen will there be in a ton of 
commercial fertilizer which has 6.07% of ammonia? 

3. What per cent of nitrogen has a fertilizer which has 
3.642% of ammonia? 

4. What per cent of ammonia has a fertilizer that has 
2 % of nitrogen ? 



PERCENTAGE 245 

5. If a ton of cotton-seed contains 60 lbs. of nitrogen, 
what per cent of cotton-seed is nitrogen '? 

6. If cotton-seed meal contains 6.2% nitrogen, 2.8% 
phosphoric acid, 1.8% potash, how many pounds of each 
are there in a ton of cotton-seed meal ? What is the ton 
worth for fertilizer, valuing nitrogen at 19 cts. per pound, 
phosphoric acid at 4-| cts., and potash at 5 cts. ? 

7. If cotton-seed meal has 7.5% of ammonia, how 
many pounds of nitrogen will there be in a ton of cotton- 
seed meal? How much will the nitrogen be worth at 18 
cts. per pound? How much, when the cotton-seed meal 
has 8% ammonia? 

8. If there are 124 lbs. of nitrogen in a ton of 
cotton-seed meal, what per cent of cotton-seed meal is 
nitrogen ? 

9. If there is 15.8% of nitrogen in nitrate of soda, 
how many pounds of nitrogen are there in a ton of 
nitrate of soda. What will the ton of nitrate of soda be 
worth, valuing nitrogen at 18 cts. per pound? 

10. If a ton of cotton-seed contains 26 lbs. of phosphoric 
acid, what per cent of cotton-seed is phosphoric acid? 

11. If there are 14 lbs. of nitrogen in 17 lbs. of 
ammonia, and 15.8 lbs. of nitrogen in 100 lbs. of nitrate 
of soda, how many pounds of ammonia will it take to 
furnish as much nitrogen as 1 T. of nitrate of soda? 

12. If a farmer mixes a fertilizer so as to contain 800 
lbs. of a 16 % acid phosphate to the ton, what per cent of 
phosphoric acid will his fertilizer contain ? 

13. A farmer is offered a ton of 16 % acid phosphate 



246 PRACTICAL ARITHMETIC 

at 112.75 a ton, 14% acid phosphate at $12.00 a ton, or 
a ton of 12% acid phosphate for $11.00. Which is the 
cheapest, and liow much cheaper, valuing phosphoric acid 
at 4 cts. a pound? 

14. Which is cheaper, a ton of a 2-8-2 fertilizer (i.e., 
one containing 2 % of nitrogen, 8 % of phosphoric acid, and 
2 % of potash) at $18, or a ton of a 3-8-3 fertilizer (i.e., one 
containing 3 % of nitrogen, 8 % of phosphoric acid, and 3 % 
of potash) at $22, valuing nitrogen at 20 cts. per pound, 
phosphoric acid at 4-| cts. per pound, and potash at 5 cts. 
per pound? 

15. If there are 250 lbs. of potash in a ton of kainit, 
what per cent of potash is there in kainit? 

16. If a ton of cotton-seed contains 24 lbs. of potash, 
what per cent of cotton-seed is potash? 

17. Sulphate of potash contains 4 times as much potash 
as kainit contains. What per cent of sulphate of potash is 
potash, if there are 48 lbs. of potash in 384 lbs. of kainit? 

18. If there are 1000 lbs. of potash in a ton of muriate 
of potash, what per cent of muriate of potash is potash? , 

19. If there are 36 lbs. of potash in a ton of cotton-seed 
meal, what per cent of cotton-seed meal is potash? 

20. If kainit contains 12|^% of potash, and muriate of 
potash contains 50 % potash, how many pounds of kainit 
will it take to supply as much potash as there is in 40 lbs, 
of muriate of potash? 

21. If a ton of dried blood contains 280 lbs. of nitrogen, 
what per cent of dried blood is nitrogen? 



PERCENTAGE 247 

22. If a ton of fish scrap contains 180 lbs. of nitrogen, 
wliat per cent is nitrogen? 

23. If fish scrap contains 8.25% of nitrogen and 6% of 
phosphoric acid, what is a ton of fish scrap wortli, allow- 
ing 20 ots. per pound for nitrogen and 4 cts. per pound 
for phosphoric acid? 

24. If a ton of wood ashes contains 120 lbs. of potash, 
what per cent of wood ashes is potash? If a ton contains 
130 lbs. of potash, what per cent of wood ashes is potash? 

25. If there are 140 lbs. of phosphoric acid in a ton of 
fish scrap, what per cent of fish scrap is phosphoric acid? 

26. If there are 320 lbs. of phosphoric acid in a ton of 
acid phosphate, what per cent of acid phosphate is phos- 
phoric acid? If there are 280 lbs., what per cent is phos- 
phoric acid? If 240 lbs., what per cent is phosphoric 
acid? If 200 lbs., what per cent is phosphoric acid? 

27. If there are 56 lbs. of phosphoric acid in a ton of 
cotton-seed meal, what per cent of cotton-seed meal is 
phosphoric acid? 

28. What is a ton of acid phosphate analyzing 16 % 
phosphoric acid worth, when phosphoric acid is worth 
4 cts. a pound? 

29. How much is a ton worth when it analyzes 14%, 
12%, 10%, and 8% respectively? 

30. If there are 329.4 lbs. of nitrogen in a ton of 
nitrate of soda, what per cent of nitrate of soda is 
nitrogen ? 

The composition of many fertilizing materials varies 
considerably, but the following is a fair average: 



248 



PRACTICAL ARITHMETIC 



COMPOSITION OF FERTILIZING MATERIALS 



Acid phosphate 

Acid phosphate 

Acid phosphate 

Giound phosphate rock . . . 

Tobacco stems 

Sulphate of potash (high grade) 

Muriate of potash 

Nitrate of potash 

Kainit .■ 

Wood ashes (unleached) . . 

Cotton-seed meal 

Cotton seed 

Tankage (concentrated) . . . 
Dried blood (high grade) . . 

Fish scrap 

Nitrate of soda 

Sulphate of ammonia .... 



Per Cent of 


Per Cent of 


Nitrogen 


Potash 


1.5 


5 




50 




50 


13 


45 




12.5 




6 


6.2 


1.8 


3 


1.2 


12 




14 




9 




15.6 




20.5 





Per Cent op 

Phosphoric 

AoiD 



16 
14 
13 
32 
2 



1.5 
2.8 
1.3 
1.5 



31. If in making a ton of fertilizer containing 3.2235% 
of nitrogen, 9.099% of phosphoric acid, and 3.5815% of 
potash, 100 lbs. of nitrate of soda are used, what number 
of pounds of cotton-seed meal, 16% acid phosphate, and 
of muriate of potash must be used ? 

32. What per cent of nitrogen, phosphoric acid, and 
potash will there be in a ton of fertilizer composed as 
follows: 1000 lbs. of 16% acid phosphate, 700 lbs. of 
cotton-seed meal, 100 lbs. of nitrate of soda, and 200 lbs. 
of muriate of potash? 

33. What will be the per cent of nitrogen, phosphoric 
acid, and potash in a fertilizer composed of the following 



PERCENTAGE 



249 



materials : 800 lbs. of cotton-seed meal, 800 lbs. of 16 % 
acid phosphate, 400 lbs. of kainit ? 

34. How many pounds of nitrogen, phosphoric acid, and 
potash will the ton of fertilizer mentioned in the last prob- 
lem contain, and what will it be worth at 18 cts. a pound 
for nitrogen, 4-| cts. a pound for phosphoric acid, and 5 cts. 
a pound for potash, adding |5 for mixing, bags, and 

freight ? 

FEEDS AND FEEDING 

313. If corn contains 10.3 % of protein and 76 % of this 
protein is digestible, what per cent of digestible protein is 
there in corn? 

If corn contains 72.5% of carbohydrates and 92% of 
these are digestible, what per cent of digestible carbohy- 
drates is there in corn? 

If 5 % of corn is fats and 86 % of these fats are digest- 
ible, what per cent of digestible fat is there in corn? 

314. Table of digestible nutrients in certain feeds. 



Feeds 

Corn 

Oats 

Wheat bran . . 
Wheat middlings 
Cotton-seed meal 
Timothy hay . . 
Red-clover hay 
Cow-pea hay . . 
Alfalfa hay . . . 
Corn stover . . . 
Corn silage . . . 
Skim milk . . . 



Per Cent op 
Protein 



Per Cent op 
Carbohydkates 



Per Cent 
OF Fats 



7.8 

9.22 

12.2 

12.8 

37.2 

2.8 

6.8 

10.8 

11.10 

1.7 

0.9 

90 



66.7 
47.3 
39.2 
53.0 
16.9 
43.4 
35.8 
38.6 
39.6 
32.4 
11.3 
5.2 



4.3 
4.2 
2.7 
3.4 
12.2 
1.4 
1.7 
1.1 
1.2 
0.7 
0.7 
0.3 



250 



PRACTICAL ARITHMETIC 



315. A Ration is the amount of feed given to an animal 
during 24 hrs. 

316. A Balanced Ration is one which contains the dif- 
ferent nutrients in sucli amounts as best to meet the needs 
of the animal being fed. 

317. Scientists have formulated balanced rations or the 
nutritive requirements of the various kinds of farm ani- 
mals at different stages of growth and when being fed 
for different purposes, calculated for 1000 lbs. live 
weight. These are known as Feeding Standards, and are 
used as guides in practical feeding in compounding 
rations. 

318. The following table shows the amounts of digest- 
ible nutrients in feeding standards, calculated for 1000 
lbs. live weight : 

FEEDING STANDARDS 



Kind of Animal 


DiGESTiiiLE Nutrients 


Protein 


Carbohy- 
drates 


Fats 


Fattening cattle (first period) . . . 
Fattening cattle (second period) . . 
Fattening cattle (third period) . . 

Horse (heavy work) 

Horse (light work) 

Dairy cow (giving 16i lbs. milk daily) 
Dairy cow (giving 22 lbs. milk daily) 
Fattening swine (first period) . . . 
Fattening swine (second period) . . 
Fattening swine (third period) . . 
Growing cattle (6 to 12 mos. old) 
Growing swine (3 to 5 mos. old) . . 


Poimds 

2.5 
3.0 
2.7 
2.5 
1.5 
2.0 
2.5 
4.5 
4.0 
2.7 
3.5 
5.0 


Pounds 

15.0 
14.5 
15.0 
13.3 
9.5 
11.0 
13.0 
25.0 
24.0 
18.0 
12.8 
23.1 


Pounds 
0.5 
0.7 
0.7 
0.8 

0.4 
0.4 
0.5 
0.7 
0.5 
0.4 
1.5 
0.8 



PERCENTAGE • 251 

When feeds rich in protein are high in price, the 
amount of protein may be reduced 10 % without injury 
to the ration. 

319. How nearly will the following ration meet the 
" Feeding Standard " requirements of a dairy cow giving 
22 lbs. of milk daily? 

Ration No. 1. 35 lbs. corn silage, 8 lbs. cow-pea hay, 6 
lbs. corn stover, 3 lbs. cotton-seed meal, 4 lbs. corn. 

To find total protein in ration : 

By reference to table on page 249 it is found that corn 
silage contains .9 per cent of digestible protein. If there is .9 
per cent of protein in corn silage, there is .9 lb. in 100 lbs. ; there- 
fore, in 1 lb. of silage there is .9 -=- 100 = .009 lb. If in 1 lb. 
of silage there is .009 lb. of protein, in 35 lbs. there is 35 x .009 
= .315 lb. of protein. 

Ration : 

35 lbs. silage = 35 x .009 = .315 lb. protein 

8 lbs. cow-pea hay = 8 x .108 = .864 lb. protein 
6 lbs. corn stover ' = 6 x .017= .102 lb. protein 

3 lbs. cotton-seed meal = 3 x .372 = 1.116 lbs. protein 

4 lbs. corn = 4 x .078 = .312 lb. protein 

Total = 2.709 lbs. protein 

By reference to the table of feeding standards, page 250, it 
is found that a dairy cow giving 22 lbs. milk a day should 
receive 2.5 lbs. of protein. In the ration above we have found 
that she receives 2.709 lbs. The ration therefore contains 
.209 lb. more protein than is required. 

To find total carbohydrates in ration : 

By reference to table (page 249), it is found that corn silage 
contains 11.3 per cent of digestible carbohydrates. If there is 
11.3 per cent of carboliydrates in corn silage, there are 11.3 lbs 



252 • PRACTICAL ARITHMETIC 

in 100 lbs. ; therefore, in 1 lb. of silage there are 11.3 -f- 100 = 

.113 lb. of carbohydrates. If in 1 lb. of silage there is .113 lb. 

of carbohydrates, in 35 lbs. of silage there are 35 X .113=3.995 

lbs. of carbohydrates. 

35 lbs. silage = 35 x .113 = 3.995 lbs. carbohydrates 

8 lbs. cow-pea hay = 8 x .386 =3.088 lbs. carbohydrates 
6 lbs. corn stover = 6 X .324 = 1.914 lbs. carbohydrates 

3 lbs. cotton-seed meal = 3 x -169 = .507 lb. carbohydrates 

4 lbs. corn = 4 x .667 = 2.668 lbs, carbohydrates 

Total = 12.162 lbs. carbohydrates 

By reference to the table of feeding standards (page 250), 
it is found that a dairy cow giving 22 lbs. of fnilk a day needs 
13 lbs. of carbohydrates. In the ration above she receives 
12.162 lbs. The ration therefore lacks .832 lb. of carbo- 
hydrates. 

To find total fats in ration : 

By reference to table, it is found that corn silage contains 
.7 per cent of digestible fats. If there is .7 per cent of fats in 
corn silage, there is .7 lb. in 100 lbs. ; therefore, in 1 lb. of 
silage there is .7 -f- 100 = .007 lb. of fats. If in 1 lb. of silage 
there is .007 lb. of fats, in 35 lbs. there is 35 x .007 = .245 lb. 
of fats. 

35 lbs. silage = 35 x .007 = .245 lb. fats 

8 lbs. cow-pea hay = 8 x .011 = .088 lb. fats 
6 lbs. corn stover = 6 x .007 = .042 lb. fats 

3 lbs. cotton-seed meal = 3 x .122 = .366 lb. fats 

4 lbs. corn = 4 X .043 = ^172 lb. fats 

Total = .913 lb. fats 

By reference to table of feeding standards, it is found that 
a dairy cow giving 22 lbs. of milk a day needs .5 lb. of fats. 
In the ration above, there is .913 lb. of fats, or an excess of 
.413 lb. 

In a similar manner the amounts of protein, carbohydrates, 
and fats in the different feeds in any ration may be computed. 



PERCENTAGE 253 

320. TABLE SHOWING PRICES OF FEEDS 



Feeds 



Estimated 
Price 



Local Price 



Corn, per bu 

Oats, per bu 

^Vheat bran, per T. . . 
Wheat middlings, per T. 
Cotton-seed meal, per T. 
Timothy hay, per T. 
Red-clover hay, per T. . 
Cow-pea hay, per T. . . 
AKalfa hay, per T. . . 
Corn stover, per T. . . 
Corn silage, per T. 
Skim milk, per cwt. . . 



I 0.49 

0.37 

18.00 

19.00 

30.00 

12.00 

12.00 

12.00 

12.00 

5.00 

3.00 

0.20 



Pupils should ascertain local prices of such feeds as are 
used in their neighborhood, and complete column three. 

EXERCISE 208.— "WRITTEN 

1. Wherein will the following ration fail, according 
to the feeding standard, in meeting the requirements of 
a dairy cow giving 16.5 lbs. milk a day ? 

Ration No. 2. 35 lbs. corn silage, 10 lbs. corn stover, 
5 lbs. corn, 5 lbs. wheat bran. 

2. Construct a ration from the feeds used in your 
locality (if given in the table) that will better meet the 
requirements of this cow, and calculate and compare the 
cost of this ration with the one given. 

3. Wherein and how much will the following rations 
fail, according to the feeding standard, to meet the needs 
of a horse doing hard work? 



254 PRACTICAL ARITHMETIC 

Ration No 3. 10 lbs. corn stover, 6 lbs. cow-pea hay, 
11 lbs. corn, 2 lbs. cotton-seed meal. 

Ration No. 4. 15 lbs. timothy hay, 14 lbs. corn. 

Ration No. 5. 15 lbs. timothy hay, 16 lbs. oats. 

Ration No. 6. 4 lbs. timothy hay, 10 lbs. alfalfa, 7 lbs. 
corn, 8 lbs. oats. 

4. It is seen that ration No. 3 is much nearer the 
requirements of sach a horse than ration No. 4. Which 
is cheaper? 

5. "Wherein will the following ration fail, according 
to the feeding standard^ in meeting the needs of a horse 
doing light work ? 

Ration No. 7. 7 lbs. corn stover, 8 lbs. alfalfa hay, 
6 lbs. corn. 

6. If a draught horse weighing 1500 lbs. requires 37^-% 
more nutrients than one weighing 1000 lbs., what will be 
the weight of the different nutrients required daily by 
such a horse when doing hard work? (For nutritive 
requirements for a 1000-lb. horse, see table of feeding 
standards, page 250.) 

7. Construct a ration that will approximate the needs of 
such a draught horse, and compare its cost with a similarly 
composed ration for a 1000-lb. horse. 

8. Wherein will the following ration fail to meet the 
requirements of a fattening beef animal during the third 
portion of the feeding period ? 

Ration No. 8. 35 lbs. corn silage, 15 lbs. corn stover, 
4.5 lbs. cotton-seed meal, 6 lbs. corn. 

9. How nearly will the following meet his needs dur- 
ing the second part of the feeding period ? 



PERCENTAGE 255 

Ration No. 9. 15 lbs. corn stover, 10 lbs. clover hay, 
1 lbs. cotton-seed meal, 8 lbs. corn. 

10. Wherein will the following ration fail to meet his 
requirements during the first part of the feeding period? 

Ration No. 10. 15 lbs. corn stover, 10 lbs. timothy 
hay, lo lbs. corn. 

11. Find the weights of the different nutrients that 
would be required daily by a beef animal weighing 750 
lbs. for each of the three fattening periods, if the same 
amounts of nutrients are required for eachlOO-lb. live 
weight as for each 100 lbs. of a 1000-lb. aifimal. 

12. If pigs during the second part of the fattening 
period require daily for 1000 lbs. live weight, 4 lbs. 
protein, 24 lbs. carbohydrates, and .5 lb. fats, wherein 
will the following ration fail to meet their needs? 

Ration No. 11. 24 lbs. corn, 10 lbs. wheat middlings, 
25 lbs. skim milk. 

13. Wherein will 40 lbs. of corn fail to meet their re- 
quirements? 

14. Wherein will 20 lbs. of corn,, and 20 lbs. of wheat 
middlings fail to meet their requirements ? 

15. Ascertain the rations being fed to the various kinds 
of animals in your locality, and compare them with the 
feeding standards given in table, page 250. Compare 
cost at local prices. 

16. Ascertain local prices of feeds and construct rations 
that will come near to the requirements of the feeding 
standards for each of the animals for which sample rations 
have been given. Compute cost of each. 



PROFIT AND LOSS 

EXERCISE 209. — ORAL 

1. I bought a book for $1 and sold it for 10% more 
than I paid. What was the selling price? 

2. When 10% is gained, what part is gained? 

3. A grocer sold butter for 30 cts. a pound that cost 
20 cts. What was his per cent of gain? 

4. Damaged goods bought at |125 were sold for $100. 
What was the per cent of loss? 

5. If 1120 is the cost price and 16|-% is the gain, what 
is the selling price ? 

321. The per cent of gain or loss in a business transac- 
tion is always reckoned on the cost or the sum invested. 

322. A merchant buys goods for $125 and sells them 
for $110. Does he gain or lose by the transaction? 

$ 125 = cost 
$ 110 = selling price 
$126- f 110= f 15 loss 
$15 -=-$126= 12% loss. 

• 

EXERCISE 210. — "WRITTEN 

1. A crate of berries, worth $6.40, was delayed in ship- 
ping and was sold at a loss of 25 % . What was the loss 
on the crate. 

256 



PERCENTAGE 257 

2. A man bought a team for $280 and sold it at 15% 
profit. What did he gain? 

3. A man bought merchandise for $472, and in sell- 
ing gained $67. What was the per cent of gain? 

4. A storekeeper bought goods for $679.50 and sold 
them for $665.00. What was the per cent of loss? 

5. A quantity of dress goods sold for $67 at a loss of 
15%. What did it cost? 

6. A transaction nets 18| % profit. How much must 
be invested to gain $650? 

7. A steamboat sold for $117,600, 12% more than it 
cost. What did it cost? 

EARM PROFITS 

8. With wheat yielding 20 bus. to the acre at 75 cts. 
a bushel, the land, 66| A. at $40 an acre, costing in 
rent 5 % of its value, and the cost of raising the crop 
amounting to $6 an acre, what is the profit? What is 
the per cent of profit ? 

9. With potatoes yielding 200 bus. to the acre at 40 
cts. a bushel, the land 12-|^ A. at $ 50, costing in rent 
5 % of its value, and the cost of raising amounting to 
$ 20 an acre, what is the profit ? What is the per cent 
of profit ? 

10. With onions yielding 500 bus. at 50 cts. a bushel, 
the land 4 A. at $ 100 an acre, costing in rent 5 % of 
its value, and the cost of raising amounting to $100 an 
acre, what is the profit ? What is the per cent of profit ? 



258 PKACTICAL ARITHMETIC 

11. Suppose in problem 8 the crop weighs 4 T. ; in 
problem 9, 40 T. ; in problem 10, 50 T. ; and the farm 
being 5 mis. from town, marketing costs 12.50 a ton. 
How much will the results in each of the last three prob- 
lems be changed, if you consider cost of marketing ? 

12. Suppose wheat be raised under the conditions of 
problem 8, on land valued as that in problem 10, but with 
the yield increased 50 % above that in problem 8. What 
Avill be the profit or loss ? 

13. Suppose onions to be raised under the conditions 
of problem 10, on land valued as that of problem 8, with 
a production decreased 75 % below that of problem 10. 
What will be the profit or loss ? 

14. When well-sorted apples bring $2.00 a barrel and 
poorly sorted apples f 1.50 a barrel, what will be the 
profit on sorting 13 bbls. of apples, if in sorting, 2 bbls. 
of culls worth f 1.00 a barrel be taken out ? Estimate the 
labor of sorting at 75 cts. What is the per cent of profit 
upon the investment ? (Note that the expense of sorting 
is the only item of expense in the investment.) 

15. Suppose there were no sale for the culls and they 
are wasted. What will then be the profit of sorting ? 



16. If a miller buys wheat at 86 cts. a bushel and in 
grinding obtains 72 % of flour, what per cent profit does he 
make in selling flour at $ 5.85 a barrel (196 lbs.), if the cost 
of milling is ifl.Sl per barrel of flour and he gets 33| cts. 
for the by-products ? 

17. At what per cent above cost must I sell | of a city 
lot so that I may retain ^ of it for ray own use, free of cost ? 



PERCENTAGE 259 

18. With a farm worth $4000, buildings 1 1000, teams 
and tools 11000, and with total sales amounting to $1500, 
allowing for use of the money 5 %, depreciation in team 
and tools 10 %, depreciation and repairs on buildings 5 %, 
taxes and insurance f 50, labor f 200, supplies $ 200, what 
is the profit ? What per cent is paid on the investment? 

19. If by $300 additional labor the total sales can be 
increased to $2000, what is then the net profit? What 
the per cent of profit? What the net profit on the $300 
additional labor ? What the per cent of profit on this ? 

20. If I sell -| of an article for the price which I paid 
for the whole article, what per cent have I gained ? 

21. A merchant marks his goods at 25 % above cost. 
At what per cent below the marked price must he sell to 
make 17^ % ? 

22. At what price above cost must this merchant mark 
his goods so that after he has deducted 15 % from the 
marked price, he will still have remaining a profit of 121 ^? 

23. A buys an engine for $125. He trades this for 
another piece of machinery, and receives in addition 20 % 
of the cost of the first in money. The second piece of 
machinery is sold for $ 90. Has he gained or lost on his 
investment, and what per cent ? 



COMMISSION 

EXERCISE 211. — ORAL 

1. A trucker sliips 100 baskets of lettuce at fS a 
basket, and payg 8 % to the commission merchant for 
selling. What does he pay for selling? 

2. What are the net proceeds from the shipment? 

3. A real estate agent receives 3 % for collecting rents. 
If his collections amount to #500 in a month, what is his 
percentage ? 

323. A person who buys or sells goods, or transacts 
business for another, is called a Commission Merchant, 
Agent, or Broker. 

324. The pay is usually reckoned at a certain per cent 
of the price, and is called a Commission or Brokerage. 

325. The sum left after the commission and other 
expenses have been paid is called the Net Proceeds. 

EXERCISE 212. — "WRITTEN 

1. What will be an agent's commission for collecting 
rents amounting to $ 675 at 2| % commission ? 

2. If an agent charges Sj'fo for handling supplies for 
an orphanage, and his commission amounts to f 750, what 
was the amount of supplies purchased? 

260 



PERCKNTAGE 261 

3. A man has $1250.00 to invest with a land company. 
He pays his agent $40.75 for making the investment. 
Wliat was the rate charged by the agent? 

4. A clerk in a city store receives a salary of $1200 
a year ; in addition he receives a commission of 2 % on 
all goods he sells. If he receives $1500 for the year, what 
is the amount of his sales ? 

5. An agent receives $67.84 commission on sales. At 
5 ojo what was the amount sold ? 

6. A lawyer collected a debt of $96 at 18% commis- 
sion. What did he receive? 

7. What is the commission on 20 crates of eggs at 
$4.50 a crate, commission 10^? On 250 T. of cabbages at 
$3.30 a ton, commission 8% ? 

8. If a farmer ships 38 baskets of beans to a commis- 
sion merchant in Baltimore, who sells them for $1.25 a 
basket, how much money should the farmer receive if 
the merchant charges 8% commission for selling, and 
pays 40 cts. freight per basket? 

9. A strawberry grower ships 27 crates of straw- 
berries to a commission merchant in New York City, who 
sells them for $3.25 a crate. After deducting his com- 
mission, paying drayage of 3 cts. a crate, and refrigerator 
car charges of 75 cts. a crate, he remits $59.67 to the 
grower. What per cent commission did he charge? 

10. A farmer ships 34 crates of cabbages to a commis- 
sion merchant in Philadelphia, who sells them for $1.50 
a crate. How much should the merchant send the farmer 
after deducting 8| % commission, paying drayage charges 
of 5 cts. a crate and freight charges of 50 cts. a crate ? 



262 PRACTICAL ARITHMETIC 

11. A live-stock dealer ships a car-load of 27 cattle 
weighing 1437 lbs. each to Chicago, and the commission 
man sells them for $5.75 per cwt. After paying $1.00 
switching charges on the car, $5.00 yardage, 600 lbs. hay 
at iflO.OO a ton, 400 lbs. corn at 50 cts. a bushel (1 bu. = 
56 lbs.), $59.00 freight, and charging 50 cts. a head for 
selling, what will be the amount of net proceeds sent 
to the shipper? 

12. What per cent of the gross receipts are the total 
charges connected with selling the cattle in problem 11 ? 

13. If this same car-load of cattle had been shipped to 
Richmond, Va., and the freight charges and selling price 
had been the same, what would have been the net pro- 
ceeds returned to the shipper, if the other charges had 
been as follows? Commission for selling 4%, 600 lbs. 
hay at $20 per ton, 400 lbs. corn at $1 a bushel, yard- 
age $10. 

14. What per cent on gross receipts are the charges 
connected with selling the cattle in problem 13 ? 

15. If a grower ships 27 bbls. of potatoes to a com- 
mission merchant in Philadelpliia, who sells them for 
$2.75 a barrel, pays 50 cts. a barrel freight, 5 cts. a barrel 
drayage, and remits $53.46 to the grower, what per cent 
commission did the agent charge for selling? 

16. A publisher sells at auction for various customers 
rare books which bring respectively: $125.50, $62.25, 
$187.50, $285.00, $845.25, $35.50, $48.75, $88.00, 
$672.00, and $950.50. If he charges 8% commission, 
what does he receive for tlie transaction ? 



COMMERCIAL DISCOUNT 

EXERCISE 213. — ORAL 

1. If a merchant buys a bill of goods marked f 500 
and receives 10 % reduction for paying cash, what does 
he pay? 

2. A school liistory costs 50 cts. If 25 % is allowed 
for an old text-book taken in exchange, how much cash 
is paid for the new history? 

3. If a grocer allows 10 % from his bill for cash, what 
amount will he deduct from a bill of l|25? 

326. A deduction from the price or value of anything 
is called a Commercial Discount. 

Manufacturers and dealers in merchandise often issue 
a Price List from which certain discounts are allowed. 

327. Prices published in catalogues known as List 
Prices are often subject to discounts. 

328. Sometimes several discounts are allowed to the 
buyer. In cases of this kind the first discount is to be 
deducted, then the second computed upon the remainder 
and deducted, and so on for each discount; e.g., when 
40%, 10%, and 5% discounts are allowed from a bill of 
goods, the 40% is first deducted, then 10% from the 
remainder, and then 5% is deducted from the last re- 
mainder. The amount remaining after deducting the 
discounts is the Net Price or Net Amount. 

263 



264 



PRACTICAL ARITHMETIC 



EXERCISE 214— WRITTEN 

1. A chemist buys a bill of laboratory supplies from 
A. H. Newsom & Co., New York. He is allowed 50% 
and 10% discount from list price and 5% off for cash. 
What is the discount on an original bill of f 350 ? 

2. Mr. A's grocery bill for the month was $34.75; 



his cash discount was 12.78. 
was allowed for cash ? 



What per cent of discount 



3. A discount of 10 % is offered on all purchases dur- 
ing a certain season and 5 % additional for cash. What 
is the discount on a bill of .$249.60? On $ 678.00 ? 

4. The bill of a certain gas company reads : 

" The following discount will be allowed if this bill is paid 
at the office of the company on or before the fifteenth instant : 

100 to 2000 cubic feet, monthly, 
$ 1.26 per 1000 feet. 

Over 2000 to 6000 cubic feet, 
monthly, $ 1.25 per 1000 feet less 
5%. 

Over 5000 to 10,000 cubic feet, 
monthly, $ 1.25 per 1000 feet less 
10%. 

Over 10,000 to 15,000 cubic feet, monthly, $1.26 per 1000 
feet less 15 % . 

Over 15,000 to 20,000 cubic feet, monthly, |1.25 per 1000 
feet less 20%. 

20,000 cubic feet or over, monthly, light and fuel, f 1.25 per 
1000 feet less 25%." 

What is the net cost of the following amounts of gas : 
1990 cu. ft. ? 2100 cu. ft. ? 3500 cu. ft. ? 4900 cu. ft. ? 
6100 cu. ft.? 9000 cu. ft.? 9900 cu. ft.? 10,000 cu. ft.? 




INSURANCE 

EXERCISE 215, — OBAL 

1. What will be the cost of insuring a building worth 
$6000 for |- its value at 40 cts. on a hundred dollars? 

2. A merchant insures his store valued at $5000 for | 
its value at 1%. What does it cost him? 

3. I pay i96 annually for a life insurance of $4000. 
What is the rate per thousand? 

329. Insurance is the promise of indemnity for personal 
and property losses. 

330. Insurance is of two kinds — Property: fire, hail, 
tornado, etc. ; Personal : life, accident, health. 

331. The written contract between the insurance com- 
pany and the person insured is called the Policy. 

332. The Premium is the sum paid for the insurance. 

EXERCISE 216. — WRITTEN 
LIFE INSURANCE 

1. What is the premium on a 14000 policy at $28 per 
$1000? 

2. If a $1000 policy of life insurance costs the insured 
$32.16 each year, what will be the total cost of a $4000 
policy for 20 yrs. ? 

265 



266 PRACTICAL ARITHMETIC 

The rates per $ 1000 on a policy in a certain company- 
are : at 20 yrs. of age, 114.96; at 30, $19.06; at 40, 
$26.07 ; at 50, $38.92 ; at 60, $63.42. 

3. What would be the cost of a $4000 policy per year 
if taken at 20 yrs. of age? What if taken at each of the 
other years given? 

4. If taken at 20 yrs., what would be the total cost if 
carried 20 yrs. ? What would it be if taken at each of 
the other ages and carried for 20 yrs. ? 

5. What is the difference in premiums, per thousand, 
between a policy for a man of 20 yrs. and a policy for a 
man of 40? Of 60? 

6. A participating 20-yr. endowment policy is one 
which pays the insured the face of the policy at the end of 
20 yrs., and in addition thereto profits or dividends. If this 
policy costs $48.10 each j'ear and the profit at the end of 
the 20 yrs. is $316.00, what per cent of the total premiums 
is this profit ? 

PROPERTY INSURANCE 

7. Insurance on a shingle-roofed dwelling with a 
water supply and fire protection costing 50 cts. on $100 
for one year, what is the cost of insurance to the amount 
of $4500? 

8. If it costs twice as much to carry the insurance 
3 yrs. as it does to carry it 1 yr., what will be the cost 
per year in the last problem if the owner insures for a 
period of 3 yrs. ? 

9. If it costs three times as much to insure for a term 
of 5 yrs. as for 1 yr., what is the rate per year in prob- 
lem 7 if taken for a term of 5 yrs. ? 



PERCENTAGE 267 

10. Each dwelling within 30 ft. adds 15 cts. per f 100 
to tlie cost of insurance. What will the insurance in 
problem 7 cost if there is a building 29 ft. 6 ins. to the 
right of this dwelling and another 32 ft. to the left? 
What will it be if there is a dwelling 30 ft. to the right 
and another 30 ft. to the left? 

11. Suppose the dwelling of problem 7 were slate in- 
stead of shingle roof. The rate then might be 40 cts. per 
f 100. How much less would the insurance be? 

12. Suppose the dwelling instead of being in a city 
well protected from fire were in a city with no fire protec- 
tion, the rate might then be 75 cts. per $100 under the 
conditions of problem 7. What would be the cost per 
year ? 

13. The rates on certain classes of unprotected property 
are very high. Saw-mills sometimes cost 14 % yearly. 
What would be the premium for 1 yr. on a $3500 saw- 
mill insured for | value ? 

14. What per cent of the face of the policy is the yearly 
premium in problem 7 ? 

15. The insurance rate in the country being 1 %, what 
is the premium on the insurance of a barn with contents 
valued at $2700, if the property is insured for | of its 
value? 

16. What is the premium on a country dwelling valued 
at $6400 at the same rate, if the property is insured for J 
of its value? 

17. The rate being |%, or 75 cts., on the hundred, if 
the buildings are metal roofed, what is then the premium 
in problem 16 ? 



TAXES 

EXEBCISB 217. — ORAL 

1. If a man pays annually for public purposes 2% of 
the value of his property, which is f 7000, what amount 
does he pay ? 

2. Mr. A pays for public purposes 2% on his real 
estate, valued at $-4000, 2J% on money in bank, which is 
$1000. What amount does he pay for public purposes? 

3. If a man pays annually $200 upon real estate for 
public purposes, which is 2% of its value, what is the 
value of his property? 

333. Taxes are required from individuals for the sup- 
port of the government and for other public purposes. 

334. Land, buildings, and other fixed property is 
called Real Estate. 

335. ^lovable property, as household goods, clothing, 
jewelry, mortgages, live-stock, machinery, etc., is Per- 
sonal Property. 

336. The valuation of property for taxation is made by 
Assessors, or Tax Listers. Taxes are levied at a certain 
rate or per cent on the assessed valuation of the property. 

337. A Tax Collector is an officer who collects the taxes. 
He usually receives a percentage of the taxes collected. 

268 



PERCENTAGE 269 

EXERCISE 218. — WRITTEN 

1. A farm valued at $6750 near a city is assessed at | 
its value. The tax rate being .7%, what are the taxes? 

2. The city boundary is extended so as to include one- 
half of this farm. The city tax rate being 2.49%, what 
is the increase in taxes? 

3. A man owning $4200 worth of personal property, 
living in the city, pays what taxes at the above rate? 

4. With the same property what are his taxes if out- 
side the city limits? 

5. An income tax of 1 % on all annual incomes over 
#1000 is collected in some states. What is the income tax 
of a man receiving a salary of $1200? Of $2400? Of 
$3500? What is it if his salary be $2400 and he earns 
$ 250 additional by extra labor ? 

6. The rate being .6 %, what are the taxes on 160 A. of 
timber land assessed at $9.38 per acre? At $16.88? At 
$24.38? At $31.88? 

7. If a man owns $8700 worth of property valued for 
taxes at |, and the rate for state and county taxes is 1.05 %, 
the city or local rate is 1.25%, poll tax is $2.00, and he 
has an income of $2700, on which he pays an income tax 
of 1 % on all over $1000, what will be his taxes? 

8. If a school district having an assessed property 
valuation of $200,000, maintains a public school 7 mos. 
at a cost of $720, and could maintain it 2 mos. more at 
an additional cost of $180, what will be the increase in 
the taxes of a man owning property valued for taxation 



270 PRACTICAL ARITHMETIC 

at $2600, if a special tax is voted for maintaining the 
school 2 additional months? 

9. A man owns property in the city worth $9750. 
The valuation for taxation is | and the rate 2.15%. He 
receives $776 rent for this property. 

He also owns farm property of the same value, which is 
valued the same for taxes, but the rate is .9%. The rent 
obtained for this property is $682.50. On which does he 
receive the larger net profit, and how much more ? 

10. If a state having an assessed valuation of $393,571, - 
982 increases its appropriation for the support of its Agri- 
cultural College from $100,000 to $150,000 per year, what 
will be the increase in taxes of a man who owns property 
valued for taxes at $3500? 

11. If the assessed valuation of the property in a county 
is $14,844,364 and the total state and county taxes amount 
to $185,554.55, what is the tax rate, stated in per cent 
and as mills on the dollar? 

12. If the assessed valuation of the property in a county 
is $15,452,776 and the total state and county taxes col- 
lected amount to $245,931.64, what is the rate of taxation 
if there be 7552 polls on which there is a tax of $1.87 
each? 

DUTIES OR CUSTOMS 

338. A charge is fixed by the government upon goods 
imported from other countries. Such charges are called 
Duties. 

339. When the duty is a certain per cent of the cost 
of the goods, it is called an Ad Valorem Duty. 



PERCENTAGE 271 

340. When the duty is fixed without regard to the 
value of the goods, it is called a Specific Duty. 

341. This table gives the customs duties according to 
the Tariff Act of 1897 on several articles imported into 
the United States : 

Apples, 25 cts. per bu. Coffee, free. 

Barley, 30 cts. per bu. Diamonds, 60 % ad val. 

Beef, 2 cts. per lb. Eggs, 5 cts. per doz. 

Bottled beer, 40 cts. per gal. Hay, $i per ton. 

Bonnets, 60% ad val. Horses, f 30 per head. 

Books, 25 % ad val. Jewelry, 60 % ad val. 

Books for public libraries. Potatoes, 25 cts. per bu. 

free. Wool, 11 cts. per lb. 

Cheese, 6 cts. per lb. Woolen clothing 40 cts. 
Cigars, $4.50 per lb. and per lb. and 60% ad val. 

25% ad val. 

EXERCISE 219. — WRITTEN 

1. What is the dutj' on 360 lbs. of cheese ? 

2. What is the duty on 400 lbs. of cheese costing 8 cts. 
per pound? 

3. What is the duty on 12000 worth of diamonds? 

4. What is the duty on a consignment of 3 head of 
horses valued at $350 each? 

5. What is the duty on a car-load of 9 T. of hay worth 
18 a ton? 

6. What is the duty on 4 lbs. of cigars valued at |4 
a pound? 

7. What is the duty on 4 lbs. of cigars valued at |8 a 
pound? 



PRACTICAL ARITHMETIC 



8. Pupils should make ten similar problems concerning 
the articles given in the table that are used in their homes. 

342. COMPOSITION OF FOODS 



Foods 


Kefuse 


Water 


Peotei.n 


Fat 


Carbo- 
hydrates 


Asir 


Beef flank . . 


Per Cent 

5.5 


Per Cent 
56.1 


Per Cent 
18.6 


Per Cent 
19.9 


Per Cent 


Per Cent 
0.8 


Salt pork . . . 
Pickled tongue . 
Bacon .... 


6 

8.7 


7.9 
58.9 

18.4 


1.9 

11.9 
9.5 


86.2 

19.2 
59.4 




3.9 

4.8 

4.5 


Veal cutlet . . 


3.4 


68.3 


20.1 


7.5 




1 


Fish . . . 


44.7 


40.4 


10.2 


4.2 




0.7 


Chicken . . . 


25.9 


47.1 


13.7 


12.3 




0.7 


Ham .... 


12.2 


35.8 


14.5 


33.2 




4.2 


Jlilk .... 




87 


3.3 


4 


5 


0.7 


Cheese .... 




34.2 


25.9 


33.7 


2.4 


3.8 


Butter .... 




11 


1 


85 




3 


Eggs .... 
Flour .... 


11.2 


65.5 
12 


13.1 
11.4 


9.3 

1 


75.1 


0.9 
0.5 


Oatmeal . . . 




7.3 


16.1 


7.2 


67.5 


1.9 


Corn meal . . 




12.5 


9.2 


1.9 


75.4 


1 


Apples .... 
Bananas . . . 


25 
35 


63.3 
48.9 


0.3 

0.8 


0.3 
0.4 


10.8 
14.3 


0.3 
0.6 


Bread .... 




35.3 


9.2 


1.3 


53.1 


1.1 


Sugar .... 
Potatoes . . . 


20 


62.6 


1.8 


0.1 


100 
14.7 


0.8 


Cabbage . . . 
Lettuce . . . 


15 
15 


77.7 
80.5 


1.4 
1 


0.2 
0.2 


4.8 
2.5 


0.9 
0.8 


Peas .... 




74.6 


7 


0.5 


16.9 


1 


String beans 


7 


83 


2.1 


0.3 


6.9 


0.7 


Turnips . . . 
Squash . . . 
Dried beans . . 
Canned tomatoes 
Rice .... 


30 
50 


62.7 

44.2 

12.6 

94 

12.3 


0.9 
0.7 
22.5 
1,2 
8 


0.1 

0.2 
1.8 
(1.2 
0.3 


5.7 
4.5 

59.6 
4 

79 


0.6 
0.4 
3.5 
0.6 
0.4 


Sweet potatoes 
Plain cake . . 


20 


55.2 
19.9 


1.4 
6.3 


0.8 
9 


21.9 
63.3 


0.9 
1.5 



PERCENTAGE 



273 



343. 



TABLE OF DIGESTIBILITY OF FOODS 



Meats and fish . . . 

Eggs 

Dairy products . . . 

Cereals 

Sugars 

Dried peas and beans 
Vegetables . . . . 
Fruits 



Protein 



Ptr Cent 

97 
97 
97 
85 

78 
83 



Fats 



Per Cent 
95 
95 
95 
90 

90 
90 
90 



Carbo- 
hydrates 



Per Cent 



98 



97 
95 
90 



EXERCISE 220. — WRITTEN 

1. The human body is composed of: ash 6%, protein 
18 %, fats 15 %, carbohydrates about 1 %. The remainder 
is water. A man weighing 150 lbs. has how many 
pounds of water in his body tissues? 

2. A man weighing 150 lbs. has how many pounds of 
fat? The fat equals what per cent of the water? 

3. A man weighing 150 lbs. has how many pounds of 
protein? The fat equals what per cent of the protein? 

4. The carbohydrates equal what per cent of the pro- 
tein ? 

5. Since 97 % of the protein of meat and fish is 
digestible, how many ounces are digestible in 2 lbs. of 
beef flank? 

6. Since 95% of the fats of meat and fish is digestible, 
how many ounces are digestible in 1 lb. of fish? 

7. Since 98 % of the carbohydrates of meat and fish is 
digestible, how many ounces are digestible in 3 lbs. of veal? 



274 



PRACTICAL ARITHMETIC 



Find the number of ounces of water, refuse, and digest- 
ible protein, fats, and carbohydrates in the following : 

8. 1 lb. of bread. 9. 1 lb. of chicken. lo. 1 lb. of 
milk. 11. 1 lb. of corn bread. 12. 1 lb. of potatoes. 
13. 1 lb. of cabbage. 14. 1 lb. of turnips. 15. lib. of ham. 
16. 1 lb. of rice. 17. 1 lb. of apples. 18. 1 lb. of cheese. 

The following food materials were consumed in one 
day by a family of four grown persons, two men and two 
women, at moderately hard work: 



Food Materials 



BREAKFAST 

Oatmeal . 

Milk . . 

Sugar . 
Veal cutlet 

Bread . . 

Butter . 

Coffee . . 



DINNER 

Roast beef (flank) 
Potatoes . . . 
Sweet potatoes . 
Bread .... 



Pounds 



2 


12 

12 



Food Materials 



DINNER 

Butter . 
Rice pudding 

Rice . . 

Eggs . . 

Milk . . 

Sugar 

Tea . . . 



SL'PPER 

Bread . . 

Butter . 

Bananas . 

Cake . . 



PoUN'lS 



Ounces 



4 
4 
6 
3 


12 
3 

12 

8 



19. Find the amount of digestible protein, carbohy- 
drates, and fats per person in the three meals. 

20. Estimating 453.6 grams to a pound, compare with 
food standards, as follows : man requiring protein 100 
grams, carbohydrates 400 grams, fats- 60 grams ; woman 
requiring protein 90 grams, carbohydrates 350 grams, fats 
40 grams. Wherein is the ration excessive ? Wherein 
deficient ? 



INTEKEST 

What per cent of 100 is 6 ? 
What per cent of f 1 is 6 cts. ? 

If $6 is charged for the use of f 100, what per cent of 
the sum loaned is the sum charged? 

344. The money charged for the use of money is called 
Interest. 

345. The money loaned is called the Principal. 

346. The per cent which the interest is of the princii^al 
is the Rate of Interest. 

347. The principal plus the interest is called the 
Amount. 

348. Many states have established a fixed rate of 
interest, an excess of which it is unlawful to accept. 
This fixed rate is known as the Legal Rate of interest. 

349. Usury is interest charged in excess of that 
allowed by law, or the legal rate. 

350. Interest is usually calculated by taking a certain 
rate per cent of the principal for one year. 

351. The time for which interest is to be reckoned is 
calculated in years and days. When over a year, both 
years and daj^s are used, and when under a year, days 

275 



276 PRACTICAL ARITHMETIC 

only. In both cases the exact number of days is counted, 
if exact interest is desired. 

352. In practice, however, when money is loaned for 
less than a year interest is usually reckoned on a basis 
of 30 days to the month, and 12 months, or 360 days, 
to the year, instead of 365 days as when exact interest is 
computed. 

If 1500 is loaned from May 1, 1906, to Aug. 1, 1907, 
the exact time is 1 year and 92 days, but in business, 
interest is usually reckoned for 1 year and 3 months, or 
1^ years, instead of for l/g^ years. The United States 
government and some banks, however, use the exact 
method, and in the above example would reckon interest 
ior 1^6^^ years. 

353. When money is loaned for a certain number of 
months, or when interest is payable monthly, calendar 
months are meant. 

EXERCISE 221. — ORAL 

Find the interest on the following sums for the times 
and rates specified : 

1. $5 for 1 year at 4% ; at 5% ; at 6%. 

2. 125 for 1 year at 3 % ; at 6 % ; at 8 %. 

3. 150 for 1 year at 4 % ; at 6 % ; at 7 %. 

4. $300 for 2 years at 4 % ; at 7 % ; at 9 %. 

5. $600 for 1 year and 6 months at 4% ; at 6 %. 

6. 1800 for 1 year and 3 months at 6 % ; at 8 %. 

7. $400 for 2 years at 6 % ; at 8 % ; for 2 years and 
3 'months at 8 % ; at 10 %. 



INTEREST 277 

8. 11200 for 1 year at 8%; for 3 years at 7%; for 
6 months at 9 % ; for 3 months at 5 %. 

354. Find the interest on $375.25 at 6% for 2 years. 

The interest for 1 year is 6% of 375.25, or, 375.26 X .06 = 
22.515 = $22,515. 

For 2 years the interest is $22,515 x 2 = $46.03. 

Find the interest on $450 for 3 years, 4 months, and 
15 days at 8% per year? 

The interest for 1 year is 450 x .08 = 36.00 = $36.00 
The interest for 3 years is $36 x 3 = $ 108.00 

The interest for 4 months is j\, or |, of $ 36 = 12.00 

The interest for 15 days is ^f, or i) of J^ = ^^ of $ 36 = 1.50 
' Therefore, the total interest is $ 121.50 

355. To find the interest for a given time, find the 
interest for 1 year and multiply by the number of years 
or fraction of a year. 

EXERCISE 222. — WRITTEN 

Find the interest and amount : 

1. 1 275.25 for 1 yr. 3 mos. 20 days at 8 %. 

2. $345 for 2 yrs. 6 mos. 15 days at 6 %. 

3. 1 435 for 3 yrs. 11 mos. at 5 %. 

4. $ 850 for 1 yr. 8 mos. 15 days at 5-| %. 

5. I 340 from June 1, 1906, to Sept. 15, 1908, at 6 %. 

6. $ 450 from Sept. 10, 1905, to Dec. 25, 1907, at 8 %. 

7. I 815.27 from Jan. 10, 1905, to Oct. 1, 1908, at 10 %. 

8. $427.25 from Nov. 5, 1906, to Jan. 20, 1908, at 6 %. 

9. $ 650 from April 10, 1908, to Oct. 10, 1908, at 4 %. 
10. 1 347.50 from Feb. 5, 1908, to Sept. 10, 1908, at 6 %. 



1^78 



PRACTICAL ARITHMETIC 



BXEECISB 223. —WRITTEN 

Find the exact interest on : 

1. 1200 from July 1, 1905, to Aug. 7, 1907, at 6%. 

2. 1450 from July 3, 1907, to May 31, 1908, at 8 %. 

3. $775 from Dec. 9, 1905, to Feb. 17, 1908, at 6 %. 

4. 1 2550 from May 21, 1907, to Dec. 13, 1907, at 4J %. 

5. % 90 from Aug. 10, 1906, to Nov. 10, 1906, at 7 %. 

6. 11750 from Jan. 24, 1906, to Feb. 16, 1907, at 5 %. 

7. 1335 from July 1, 1900, to June 19, 1903, at 6 %. 

8. 1 3750.50 from Jan. 29, 1899, to Feb. 29, 1908, at 6 /o. 

356. For convenience in finding the correct or exact 
time, the following table is frequently used by bankers and 
others : 





Jan. 


Feb. 


Mar. 


April 


May 


June 


July 


Aug-. 


Sept. 


.Oct. 


Nov. 


Dec. 


January . . 


365 


31 


59 


90 


120 


151 


181 


212 


243 


273 


304 


334 


"February 


334 


365 


28 


59 


89 


120 


150 


181 


212 


242 


273 


303 


March . . 


306 


387 


365 


31 


61 


92 


122 


153 


184 


214 


245 


275 


April . . . 


275 


306 


334 


.365 


30 


61 


91 


122 


153 


183 


214 


244 


May . . . 


245 


276 


304 


335 


365 


31 


61 


92 


123 


153 


184 


214 


June . . . 


214 


245 


273 


304 


334 


365 


30 


61 


92 


122 


153 


183 


July . . . 


184 


215 


243 


274 


304 


335 


365 


31 


62 


92 


123 


153 


August . . 


153 


184 


212 


243 


273 


304 


334 


365 


31 


61 


92 


122 


September . 


122 


153 


181 


212 


242 


273 


303 


334 


365 


30 


61 


91 


October . . 


92 


123 


151 


182 


212 


243 


273 


304 


335 


365 


31 


61 


November . 


61 


92 


120 


151 


181 


212 


242 


273 


304 


334 


365 


30 


December . 


31 


62 


90 


121 


151 


182 


212 


243 


274 


304 


335 


365 



The exact number of days from any particular day of any 
month to the corresponding day of any other month, within 1 
year, is found opposite the first month and under the second. 
If the day of the month is not the same in the two months, 



INTEREST 279 

the difference may be added or subtracted as the case may 
require, e.g., from July 10, to Dec. 10 is 163 days. Erom 
July 10 to Dec. 23 is 153 + 13 = 166 days. From July 31 to 
Dec. 20 is 153 - 11 days = 142 days. 

357. On many calendars used in business offices the 
days of the years are numbered consecutively through the 
months, and in calculating interest for periods less than a 
year, business men frequently take the number of the day 
on which interest begins and subtract it from the number 
of the day when it is due ; e.g., June 18, 1908, is the 170th 
day of the year, and Nov. 12 is the 317tli day, therefore 
from June 18 to Nov. 12 is 317-170 = 147 days. 

SIX PER CENT METHOD 

358. What is the interest on $1 at 6 % for 1 month? 
For one day ? 

If the interest on $ 1 for 12 mos. is $ .06, the interest on $ 1 
for 1 mo. is j\ of $ .06 = $ .005, and the interest on $ 1 for 
1 da. is ^ of $ .005 = $ .000^. 

Thus: 

The interest on f 1 for 1 yr. at 6 % = f .06. 
The interest on $1 for 1 mo. at 6 % = f .005. 
The interest on $1 for 1 da. at 6 % = f .OOOf 

What is the interest on $360.40 at 6% for 2 yrs. 8 mos. 

18 days? 

The interest on f 1 for 2 yrs. is | .06 x 2 = f .12 

The interest on $1 for 8 mos. is $.005x8= .04 
The interest on $ 1 for 18 days is $ .000^ x 18 = .003 
The interest on $ 1 for 2 yrs. 8 mos. 18 days = $ .163 
The interest on $ 360.40 for 2 yrs. 8 mos. 18 days = $ 360.40 
X .163 = $58.7452, or f 58.75. 



280 PRACTICAL ARITHMETIC 

359. To find the interest on any sum at 6 % for a given 
number of years, months, and days, multiply 6 cts. by the 
number of years ; . 5 cts. by the number of months ; and 
1^ of a mill by the number of days. Find the sum of these 
and multiply this sum by the principal. 

EXERCISE 224. - "WRITTEN 

Find the interest by the six per cent method on: 

1. $475.40 for 1 yr. 2 mos. 6 days, at 6%. 

2. 1820 from June 1, 1904, to Oct. 12, 1905, at 6%. 

3. $528.60 for 3 yrs. 8 mos. 18 days at 6 %. 

4. 1360.50 for 3 yrs. 9 mos. 24 days at 6 %. 

5. $750 from May 12, 1901, to April 18, 1903, at 6%. 

360. Short-time loans are frequently made for 3, 4, 6, 
8, or more months : 

Since the interest on $1 for 1 mo. at 6 % is $.005, or 
^ ct., to find the interest on any sum at 6% for time 
expressed in months, move the decimal point two places to 
the left in the principal and multiply by one -half the 
number of months. 

The interest on $320.50 for 6 mos. is 3.205 x 3 = 9.615 
= $9,615. 

361. Loans made for three months or less are usually 
made for 30, 60, or 90 days : 

Since the interest on $1 for 1 da. at 6 % is ^ of a mill, to 
find the interest on any sum for time expressed in days, 
move the decimal point three places to the left in the 
principal and multiply by | the number of days. 



INTEREST 281 

The interest on 1160.75 for 30 days is .16075 x } of 30 
= .16075 X 5 = .80375 = $.80375, or 80 cts. 

EXERCISE 225. — WRITTEN 

Find the interest at 6% on : 

1. 1325 for 8 mos. 6. 1 945 for 30 days. 

2. $785 for 6 mos. 7. 11500 for 60 days. 

3. $957 for 9 mos. 8. $525 for 90 days. 

4. $2450 for 7 mos. 9. 1 343 for 30 days. 

5. $375 for 11 mos. 10. $250 for 90 days. 

362. The six per cent method may be used for finding 
the interest at other rates, as follows : 

2 % is f, or |, of 6 %, therefore, take ^ of the interest at 6 %. 

3 % is f, or -^j of 6 %, therefore, take -J of the interest at 6 %. 

4 % is ^, or f, of 6 %, therefore, take | of the interest at 6 %. 

4i-% is — 2^, or J of 6 %, therefore, take f of the interest at 

6 %, or subtract I of the interest at 6 %. 

5 % is f of 6 %, therefore, take f of the interest at 6 %, or 
subtract ^ of the interest at 6 %. 

7 % is I of 6 %, therefore, take ^ of the interest at 6 %, or 
add ^ of the interest at 6 %. 

■71 

J i cf„ is ~^! or I of 6 %, therefore, take -J of the interest at 
6%, or add J of the interest at 6 %. 

363. The six per cent method being based on 12 months, 
or 360 days, to tlie year, of course, does not find tlie exact 
interest. 

EXERCISE 226.— WRITTEN 

Find the interest by the six per cent method on : 
1. $ 250 for 1 yr. 3 mos. at 2 %. 



282 PRACTICAL ARITHMETIC 

2. 1335 from July 10, 1903, to June 20, 1905, at 3%. 

3. 1 945 for 2 yrs. 4 mos. 20 days at 4 %. 

4. 11350 from Dec. 12, 1905, to Feb. 1, 1907, at 41%. 

5. 1725 for 1 yr. 7 mos. 13 days at 5%. 

6. $ 2450 from Aug. 15, 1905, to Nov. 20, 1908, at 7 %. 

7. $ 183 for 2 yrs. 5 mos. 23 days at 7J %. 

8. 1420 from July 20, 1898, to June 5, 1901, at 8 %. 

364. It is seen that in computing interest there are four 
factors involved : time, rate per cent, principal and inter- 
est, or principal and amount, or interest and amount. 

Any one of these factors can be found if the other' three 
be given, but in business the principal, rate per cent, and 
time are usually given and the interest, or interest and 
amount, are required to be found. 

365. It may be necessary to find the principal, rate, or 
time when only two of these and the interest, or the 
amount, are given. 

366. To find the principal, when the rate, time, and 
interest or amount are given : 

What principal Avill produce fl5 interest in 2 yrs. 
6 mos. at 6 % ? 

Interest on f 1 for 1 yr. at 6 % = $.06. 

Interest on $ 1 for 2^ yrs. .at 6 % = f .06 X 2i = f .15 

Hence, principal required = — — = $ 100. 

.15 

What principal at 6 9^ interest for 2 yrs. 6 mos. will 
amount to f 115 ? 

A principal of f 1 at 6 % for 1 yr. = $ .06 interest. 



INTEREST 283^ 

A principal of $ 1 at 6 % for 2| yrs. = $ .06 X 2^ = $ .15 
interest. 

A principal of $ 1 at 6 % interest for 2i yrs. amounts to 

principal 1 1 + interest $ .15 = $ 1.15. 

$115 

Hence, principal required = ~ = f 100. 

$1.15 

EXERCISE 227. — WRITTEN 

Find the principal that will bring : 

1. 1450 interest in 3 yrs. at 6 %. 

2. 172.74 interest in 3 yrs. 9 mos. at 2^%. 

3. 111.33 interest from July 5, 1904, to Feb. 9, 1905, 
at 4%. 

4. 118.72 interest in 5 mos. 27 days at 5^%. 

EXERCISE 228. — WRITTEN 

Find the principal that will amount to : 

1. 11283.33 at 5 % interest for 3 yrs. 4 mos. 

2. 1 1303.41 at 6 % interest for 60 days. 

3. 1 25.76 at % interest for 33 days. 

4. $ 94.31 at 6 % interest for 1 yr. 7 mos. 21 days. 

367. To find the rate per cent, when the time, princi- 
pal, and the interest or the amount are given: 

At what rate per cent will $100.00 produce 124.50 
interest in 3 yrs. 6 mos. ? 

The interest on f 1 for 1 yr. at 1 % = f .01. 
The interest on f 1 for 3^ yrs. at 1 % = f .035. 
The interest on 1 100 for 31 yrs. at 1 % = $ 3.50. 

Hence, the rate is f2450 ^ ^ ^^ 
3.50 



284 PRACTICAL ARITHMETIC 

EXERCISE 229. — WRITTEN 

Find the rate per cent : 

1. When the interest on 1 2300 for 1 yr. is 1138. 

2. When the interest on f 675.88 for 5 yrs. is $118.28. 

3. When 16130 at interest from June 6 to Nov. 24 
amounts to $6237.28. 

4. When $1050 at interest from Sept. 21, 1904, to 
March 5, 1905, amounts to $1069.15. 

368. To find the time, when the rate, principal, and the 
interest or the amount are given: 

In what time will $100, at 6%, bring $21 interest? 
The interest on $ 1 at 6 % for 1 yr. = | .06. The interest 
on $ 1 for the unknown time = $ 21 ^ 100 = $ .21. 

$.21 
.06 



Hence, the unknown time = '^^ = 3|- yrs. 



EXERCISE 230.— WRITTEN 

Find the time in which : 

1. The interest on $1500 will be $180 at 4%. 

2. The interest on $8520 will be $1746.60 at 6%. 

3. The interest on $17,040 will be $3493.20 at 6%. 

4. $238.74 at 4i% will amount to $308.20. 

369. In the foregoing solutions the unit in finding the 
principal was $1 ; the unit in finding the time was 1 year, 
and in finding the rate the unit was 1 per cent. Hence, 
to find the principal, time, or rate, when the other factors 
are given, divide the given interest by the interest ob- 
tained by using the unit as the required factor. 



STOCKS AND BONDS 

370. When two or more persons form an organization 
under the laws of the state to conduct business as one 
body, the organization is called a Company, Stock Company, 
or Corporation. 

371. The money contributed for the purpose of carry- 
ing on the business of a company is known as its Capital, 
Capital Stock, or Stock. 

372. Tlie stock of a company is divided into a number 
of equal parts known as Shares, or Shares of Stock. 

373. A person holding or owning one or more shares of 
stock is known as a Stockholder. 

374. The document or certificate issued to each stock- 
holder showing the number of shares he owns, is called a 
Certificate of Stock. 

375. A Bond is a written promise or obligation of a cor- 
poration, or a government, to pay a specified sum of 
money at a certain time, with interest at regular stated 
intervals and at a certain rate. 

376. The original, certificate, or face value of a stock is 
its Par Value. The price for which it sells is its Market 
Value. When the market value is greater than its par 
value, the stock is said to be at a premium, and when it 

285 



286 PRACnCAL ARITHMETIC 

sells for less than the face or par value, it is at a Discount 
or Below Par. 

377. The profits of a company which are divided among 
the stockholders according to the stock which they hold 
are known as the Dividends. 

378. The capital stock of a corporation is sometimes 
divided into two kinds : Preferred and Common. A divi- 
dend is usually guaranteed on the preferred stock, and in 
such case must be paid before any dividend is paid on the 
common stock. 

379. Persons who buy and sell stocks and bonds are 
called Stock Brokers, or Brokers, and their commission is 
called Brokerage. Brokerage is computed on the par 
value of the stock. 

380. Small certificates of interest, called Coupons, are 
usually attached to bonds. These coupons are promises 
to pay interest at a certain time at a specified rate. If 
this interest is not paid when due, the interest itself draws 
interest at the legal rate. 

381. Large numbers of different stocks and bonds are 
regularly on the market, and are bought arid sold exten- 
sively. The following are a few with the quotations 
given in a daily newspaper June 27, 1908 : 

The figures indicate the price in dollars per share or bond. 
The par value is usually f 100, but in some cases it may be $50, 
or some other value. In the following problems f 100 is the 
par value of the stocks or bonds in question, unless otherwise 
stated ; 





INTEREST 


287 


Stocks 




Bonds 




L. & N. . . 


. 103^- 


U. S. 4's ... 


121i 


Am. Copper . 


■ 66f 


Minn. & St. L. 4's 


76 


B. & 0. 


. 86 


Mo. K. & Tex. . 


96i 


Ch. & N. W. . 


. 150 


B. & 0. 4's . . . 


98^ 


111. Cent. . . 


. 130| 


Col. Mid. 4's . . 


63 



382. If I pay a broker ^ % commission to buy 9 shares 
of L. and N. R.R. stock worth on the market 103^, what 
will be the total cost? 

$ 100 = par value of 1 share. 
I % of f 100 = f .126 = commission on 1 share. 
$ .125 + $ 103^ = f 103.625 = cost of 1 share. 
$ 103.625 X 9 = $932,625 = cost of 9 shares. 

383. Find the annual income from 327 shares of stock 
which pays a semiannual dividend of 3| % ? 

3^ % of $ 100 = $ 3.50 = semiannual interest on 1 share, 
f 3.50 X 2 = $ 7.00 = annual interest on 1 share. 
327 X f 7 = f 2289 = income on 327 shares. 

384. What rate of interest on money invested shall I 
receive if I buy S.A.L. R.R. bonds at 53|^, which pay 4% 
interest, brokerage ;|- % ? 

4 % of f 100 = $4 = income from 1 share. 

-\% ot^ 100 = 1 .25 = brokerage on 1 share. 

$ .25 + $ 53| = $ 53.75 = cost of 1 share. 

$.53.75 invested brings $4 in interest. 

$ 53.75 at 1 % = $ .5375. 

$ 4 -=- .5375 = 7.5"^ = 7|- % = rate of interest on money invested. 

EXERCISE 231. — WRITTEN 

1. Find the cost of 18 shares American Copper at 66^, 
brokerage ^%. 



•288 PRACTICAL ARITHMETIC 

2. Find the cost of 27 shares of stock (par value $ 50) 
at 34|, brokerage ^%. 

3. Find the amount realized from the sale of 32 shares 
of B. & O. R.R. stock at 86, brokerage ^%. 

4. Find the amount realized from the sale of 9 §500 
U. S. bonds, at 113|, brokerage ^%. 

5. How many shares of stock having a par value of 
$50 and a market value of $67.50, can be bought for 
$4869, brokerage |%? 

6. How many U. S. $100 bonds must I sell at 107| to 
raise sufficient money to pay a debt of $3432.80, broker- 
age |%? 

7. How much income will $3600 Standard Oil stock, 
paying 36 % dividend, yield ? 

8. What is the profit in buying 26 shares of Chicago 
and N. W. R.R. stock at 150 and selling for 159, broker- 
age on each transaction ^ % ? 

9. What is the gain in buying 37 shares of stock (par 
value $50) at 49-|- and selling at 62^, brokerage on each 
transaction -j % ? 

10. What sum must be invested in U. S. 4's at 118|, 
brokerage ^%, to yield an income of $160? 

11. What sum must be invested in P. R.R. stock at 
92| of par value, paying 3| % half yearly, to give an in- 
come of $ 630, brokerage ^%? 

12. What income will be obtained from the investment 
of $5287.50 in stock at 105J, paying 3% semiannually, 
brokerage | % ? 

13. A man bought Illinois Central R.R. stock at 137| 



. INTEREST 289 

and sold it for 1421, making a profit of $512.50. How 
many shares did lie buy, brokerage ^ % in each transaction? 

14. A man buys 200 shares of Colorado Midland R.R. 
stock, paying 4%, at 63 and holds it 2 years, receiving 2 
dividends, and sells it at 78. Money being worth 6 % per 
annum and brokerage -^^ on each transaction, how much 
did he gain? 

15. Which is the best investment : 7 % stock at 127^, 
5 (Jo bonds at 82J, or money loaned at 6 % ? 

16. If a man buys U. S. 4 % bonds at 116|, what per 
cent does he receive on his investment ? 

17. Which pays better, a 5 % stock at 90 or a 7 % bond 
at 130? How much better? 

18. A man has 13800 to invest. Which wilt yield the 
larger income, 5% stock at 95, or 5J% bonds at par? 
How much larger ? 

NEGOTIABLE PAPERS 
385. A written order to a bank to pay money, from one 
having money deposited in such bank, is called a Check. 



Ji'o.--337- J^ewYorh,...Ci'wc}. 6, ..,190 8 

The Corn Exchange Bank 

FIFTH AVENUE BRANCH 

Pay to ^. (S, B'uyuyyi& or order 

(Z. /"f. M-aAJMi^ V &0- 



A Bank Check 



290 



PRACTICAL ARITHMETIC 



386. A check may be made payable to Payee or to 
Bearer, in which case it may be collected by auy one ; or 
to Payee or order. If made payable to "order," it must 
be indorsed by the person to whose order it is made pay- 
able. A check may be " indorsed in blank," when the 
person to whose order it is made payable writes only 
his name across the back of the check as in A ; or he 
may make a special indorsement, as in B. 




A. Indorsed in Blank 



S'au to tk& o-vcIea, o-l 

/'ftn-vu j.akni'Cyn, 
^eA>\a£, l/O-Lttia.yyh^ 



B. Special Indorsement 



387. A Certified Check is one upon which the cashier of 
a bank has written, in red ink, the word " Certified," with 
date, name of bank, and his name as cashier. This makes 
the bank responsible for its payment. 



DRAFTS 

388. A written order to one person- to pay a specified 
sum of money to another person at a certain time is called* 
a Draft, or Bill of Exchange. 

389. The person who makes the order is called the 
Drawer of the draft ; the person who is ordered to pay is 
the Drawee ; and the person to whom the money is to be 
paid is the Payee. 



INTEREST 291 

390. A draft which is paj'able whenever presented to 
the drawee is called a Sight Draft. 

391. A draft payable after date or at a certain time 
after sight is a Time Draft. 



JVo. __f/., Atlanta, Ga.,..Mel. f,-..190 8 

Pay to the order of 
3'k& ^ovn ^cK^kanaSt ffa,nA, ol c^e^w- Z/o-ik $260 

■c■^^^vc^•^^■>^^^c^•^i«>■ /i-wncll&ct c/t/^i^^^i-^T^^^^^^^-^^r^ Dollars. 

To T. T. Sands, 
Jfeiv York. 



A Draft 

392. A time draft must be presented to the drawee or 
person who is to pay, who must accept the draft by writ- 
ing across its face the word " Accepted," together with 
the date and his signature. 

393. A draft by one bank upon another in which it has 
a deposit is a Bank Draft. 

PROMISSORY NOTES 

394. A written promise to pay a certain sum of money 
at a specified time after date is called a Promissory Note. 

395. The person who signs a note and thereby promises 
to pay is the Maker of the note. The Payee is the person 
to whom the promise to pay is made. 



292 PRACTICAL ARITHMETIC 

396. A note signed by one person only is called an 
Individual Note. 

397. A note signed by two or more persons is a Joint 
Note. 

398. A note is usually written so as to include the 
payment of interest at a specified rate for the time of the 
note. 



3'kvt^ •yyuyyCth^-- -after date.. -o^^.. promise to jiay to 

tlze order of. /%5a^ra-. ^to-n& a/yicl /'f&vvi&k 

at the Xational City Bank, of Jfew York, with interest 
at six per cent. 
Value received. 

Jfo.. .■¥-/-. I>ue...fa,rv. /, /f^f_._ 



A Promissory Note 

399. When no rate is mentioned, a note bears interest 
at the legal rate of the state in which it is payable. 

400. A note may be made payable to the payee or 
bearer, to the payee only, or to the order of the payee. 
Notes are indorsed in blank or to special persons, as with 
checks. The indorser of a note is I'esponsible for its 
payment unless the words " Without Recourse " precede 
his signature. 



INTEREST 293 

401. The Day of Maturity of a note is the day on which 
it becomes due or the last day of the time for which it is 
drawn. In some states after the note becomes due, three 
days are allowed for its payment. These three days are 
known as Days of Grace. 

BANK DISCOUNT 

402. Bankers and others make a certain deduction 
from a note or draft for paying it before it is due. This 
deduction or charge is the simple interest on the face of 
the note or draft from the date on which it is paid to the 
date of maturity. This charge or deduction is known as 
Bank Discount. 

403. The Proceeds of a note or draft is the amount of 
the note or draft less the discount and exchange. 

404. The paying or transferring of money by means of 
cheeks, drafts, or money orders is called Exchange. The 
charge made by banks and other institutions for issuing 
or cashing these checks, drafts, or money orders is also 
called Exchange. The rate of exchange varies from ^ to 
1^ of 1%, or may be a certain fixed amount for different 
sums. 

EXERCISE 232. — WRITTEN 

1. A draft for 1 320 is sold by a bank in Raleigh,- N.C., 
on a New York bank, rate ^fo. What is the exchange ? 

2. A draft for $125 is sold by a bank in New Orleans, 
La., on a bank in Chicago, 111., rate |%. What is the 
exchange ? 

3. A United States postal money order for $76 costs 



29i PKACTICAL ARITHMETIC 

30 ets., and one for $100 can be bought at the same price. 
What is the rate per cent on each ? 

4. Which is cheaper, a draft on a New York bank for 
f 40 at ^ %, or a U. S. money order for the same amount at 
a cost of 15 cts. ? 

5. If a bank in Chicago, 111., charges 15 cts. for a 
draft for f 100 on a New York bank, what is the rate of 
exchange charged? 

405. A note for |100 at 6% interest drawn July 15, 
1905, due 9 months after date, is presented to a bank Oct. 
15, 1905, for discount. Find the discount and the pro- 
ceeds. 

The discount is the simple interest on $ 100 at 6 % from 
Oct. 15, the day it is discounted, to maturity. The note is 
drawn July 15, 1905, for 9 months, and is, therefore, due April 
15, 1906. From Oct. 15, 1905, to April 15, 1906 = 6 months. 

The interest on $ 100 at 6 % for 1 year = f 6. 

The interest on $100 at 6% for 6 months = ^ of |6 = 
f 3 = the discount. 

$ 100 - $3 = $ 97 = the proceeds. 

BXEECISB 233. — WRITTEN 

1. Find the discount on a note for f 480 dated Sept. 
15, 1905, and payable in 90 days, if discounted Sept. 30, 
1905, at 5%. 

2. Find the proceeds of a note for 1375, dated May 5, 
1907, payable Aug. 20, 1908, at 6 % interest, if discounted 
by a bank July 15, 1907. 

3. Find the discount on a note for 12250, drawn 
Jan. 1, 1905, for 4 months at 8% interest, discounted 
Jan. 15, 1905. 



INTEREST 295 

Find the discount and the proceeds on the following : 

4. 1342.00. Raleigh, N.C, Jan. 25, 1907. 
Seven mouths after date I promise to pay to the order 

of Samuel Wolfe three hundred forty -two dollars, with 

interest at. six per cent, for value received. 

James Baird. 
Discounted Feb. 10, 1907. 

5. 1785.00. Atlanta, Ga., July 1, 1905. 
Ninety daj's after date I promise to paj' John Williams, 

or order, seven hundred eighty-five dollars, for value 

received. 

William Jones. 
Discounted July 10, 1905, at 7%. 

6. I wish to pay for a car-load of cattle which cost 1860, 
but must give my note to the bank for 90 days to obtain 
the money. For how much must I draw the note to 
obtain this amount if it is discounted at 10 per cent ? 

7. I sell fifty acres of land for f 62.50 an acre, on a 
cash basis, but the purchaser is not able to pay the money, 
and offers instead his note for 6 months at 8 % interest. 
For how much must the note be drawn that I may receive 
the cash price after discounting the note at the bank? 

8. I sell a car-load of cattle, taking in payment a prom- 
issory note for 60 days. After discounting the note at 
the bank at 5 per cent, I have 11487.50. For how much 
did I sell the cattle? 

9. Write a promissory note for 90 days, with yourself 
as payee. Properly indorse it and find the bank discount 
and proceeds at the legal rate of interest in your state 
on the day it is drawn. 



PAETIAL PAYMENTS 

406. A payment made on a note which is not equal to 
tlie principal and the interest then due is known as a 
Partial Payment. 

407. When such partial payments are made, the amount 
paid and the date, with the signature of the person receiv- 
ing the payment, are indorsed on the back of the note. 

Received on the within note : 
$S20, March 1, 1904 

jo-kn j. fcm&i, 

$1SB, April 15, 1905 

jo-hn f. jo-n&O' 
$85, June 20, 1906 

UNITED STATES RULE 

408. The rule adopted by the United States Supreme 
Court for finding the amounts due on notes when partial 
payments have been made, has been adopted as the legal 
method hy most states, and is as follows : 

Find the amount of the principal to the time when the 
payment or the sum of the payments equals or exceeds 
the interest due ; from this amount subtract the payment 
or the sum of the payments; treat the remainder as a 
new principal, and proceed as before. 

296 



INTEEEST 297 

409. A note for 1 935, drawn Jan. 1, 1903, due one year 
from date, at 6 per cent interest, has the following in- 
dorsements on it: March 1, 1904, 1320; April 15, 1905, 
135; June 20, 1906, 1 85. 

What was the balance due Sept. 1, 1906 ? 

Solution by United States Eule 

Principal Jan. 1, 1903 = $ 935.00 

Interest from Jan. 1, 1903, to March 1, 1904 = 65.45 

Amount March 1, 1904 = $ 1000.45 

First payment March 1, 1904 = 320.00 

New principal March 1, 1904 = $ 680.45 

Interest from March 1, 1904, to April 16, 1905 = 45.93 
(Since the interest due April 15, 1905, is greater 

than the payment made, no new principal is 

calculated.) 

Interest from March 1, 1904, to June 20, 1906 = 94.13 

Amount June 20, 1906 = $ 774.58 

Payments deducted June 20, 1906 ($ 35 + $ 85) = 120.00 

New principal June 20, 1906 = | 654.58 

Interest from June 20, 1906, to Sept. 1, 1906 = 7.64 

Amount due Sept. 1, 1906 = f 662.22 

MERCHANTS' RULE 

410. For calculating the amount due on accounts and 
notes bearing interest, on which partial payments have 
been made, merchants often use what is known as the 
Merchants' Rule. It is not as accurate as the United 
States method and is not legal, but for short periods, one 
year or less, it gives nearly the same results, and is easier. 
It is as follows: 1. Find the amount due on the original 
principal to the time final settlement is made. 2. Find 
the amount of each payment from the date it was made 



298 PRACTICAL ARITHMETIC 

to date of final settlement. 3. Subtract the sum of the 
amounts of the payments from the amount of the original 
principal at the time of final settlement. 

If used for periods greater than one year, find the 
balance due at the end of each year by the rule above 
stated, and take this balance as a new principal. 

411. Find the correct settlement on Feb. 15, 1908, on a 
note for |100 dated March 1, 1907, at 6 % interest, with' 
the following indorsements : May 1, 1907, $ 20 ; July 15, 
1907,150; Jan. 1,1907,120. 

Solution by the Merchants' Rule 

Amount of principal for 11^ mo. = $ 105.75 

Amount of $ 20 for 91 mos. = $ 20.95 
Amount of f 60 for 7 mos. = $ 51.76 
Amount of $ 20 for 1| mos. = $ 20.16 

= $ 92.85 
Correct settlement = $ 12.90 

412. In a few states other rules are used. In such states 
the teacher should furnish the pupils with the special rule 
in use, and have the following problems solved by this 
special rule as well as by the rules indicated. 

EXERCISE 234. — WRITTEN 

Find the balance due on date of settlement by the 
United States Rule : 

1. A note for ;$300 at 6% is dated March 1, 1905, and 
has the following indorsements: July 1, 1905, -f 50; Sept. 
1, 1905, 130; Jan. 1, 1906, $100. How much is due 
June 1, 1906 ? 



INTEREST 299 

2. A note for fSOO dated i\[ay 1, 1901, at 6% interest, 
has f 50 partial payments indorsed on it every 6 months 
from date to Nov. 1, 1905. What is the correct settle- 
ment Feb. 1, 1906? 

3. A note is settled 4 years after date. Its face value 
is $400, and it draws 8% interest. It has $150 paid on 
it 1 year and 8 months before final settlement. How 
much is required to settle the note? 

4. A note for $800 dated April 10, 1901, has the follow- 
ing indorsements: June 20, 1901, $30; July 10, 1901, 
$50; Dec. 1, 1901, $20; May 25, 1902, $25; Sept. 10, 
1902, $100. How much was due Jan. 20, 1903, at 7% 
interest ? 

Find the amounts necessary to settle the following 
notes, by both the United States and the Merchants' Rules, 
and compare results : 

5. A note for $320 dated July 15, 1906, at 6 % interest, 
is indorsed as follows: Sept. 25, 1906, $80; Dec. 1, 1906, 
$40; Jan. 1, 1907, $50; June 1, 1907, $10. How much 
was due July 1,1908? 

6. A note for $150 dated May 10, 1906, for one year, 
at 6% interest, has indorsed on it payments of $25 every 
three months. How much will be required to settle bal- 
ance of note on the date it falls due ? 

7. An account amounting to $375, due Jan. 1, 1904, is 
settled May 15, 1905. The following amounts had been 
paid on it: March 1, 1904, $75; Jiine 15, 1904, $30; Sept. 
10, 1904, $80; Jan. 15, 1905, $100. How much was re- 
quired to pay the balance, with interest at 6%? 



300 PRACTICAL ARITHMETIC 

8. On Jan. 1, 1904, A owes B 1650, on which he agrees 
to pay 6 % interest and make a payment of f 75 every three 
months and the balance Jan. 1, 1905. When the balance 
is due, A is unable to pay it, and B charges him 8 % inter- 
est until paid. If A pays 185 Feb. 1, 1905, and f 135 on 
July 10, 1905, how much money must he raise to pay the 
balance Sept. 20, 1905? 

COMPOtWD INTEREST 

413. When the interest as it falls due is added to the 
principal, and the amount forms a new principal on which 
interest is paid, the owner receives Compound Interest. 

414. Compound interest on notes is not now generally 
allowed by law, but savings-banks allow compound inter- 
est on balances remaining on deposit for a certain definite 
interest term. Interest may be compounded annually, 
semi-annually, or quarterly. Unless otherwise stated, it 
is usually compounded annually. 

415. What is the compound interest on f 100 for 3 
years at 6 %? 

$ 100 == first principal. 

f 100 X .06 = $ 6 = first interest. 

$ 100 -I- $ 6 = f 106 = second principal at end of 1 year. 

f 106 X .06 = $ 6.36 = second interest. 

$ 106 -|- $ 6.36 = $ 112.36 = third principal at end of 2 years. • 

f 112.36 X .06 = $ 6.7416 = third interest. 

$ 112.36 -I- I 6.7416 = f 119.10 = amount at end of 3 years. 

Therefore $119.10 - .f 100 = $19.10 = compound interest 
on f 100 for 3 years at 6%. 



INTEREST 301 

EXERCISE 235. — WRITTEN 

Find the compound interest and compound amount on 
the following : 

1. $375 for 4 yrs. at 4%. 

2. $125 for 3 yrs. 6 mos. at 5 %. 

3. $650 for 5 yrs, at 6 %. 

4. $2300 for 3 yrs. at 6%. 

5. $1875 for 4 yrs. at 8%. 

6. $3250 for 6 yrs. at 6%. 

7. $4325 for 3 yrs. at 5%. 

8. $7575 for 7 yrs. at 5 %. 

Find the amount and interest compounded semi-annually 
on the following : 

9. $500 for 2 yrs. 6 mos. at 6 %. 

10. $ 250 for 2 yrs. 6 mos. at 7 %. 

11. $ 1750 for 1 yr. 9 mos. at 8 %. 

12. $2225 for 3 yrs. 6 mos. at 5 %. 

13. $ 3575 for 3 yrs. 9 mos. at 6 %. 

14. If a man deposits $2500 in a savings-bank, which 
pays 4% semiannually, and leaves it for 2 yrs. 6 mos., 
will he have more or less money than if he had loaned it 
at simple interest for the same time at 4^ % ? 

15. How much money did I have to my credit Jan. 1, 
1908, if I made deposits as follows in a savings-bank, pay- 
ing 4 % interest and compounding it Jan. 1 and July 1 : 
July 1, 1906, 1200; Aug. 1, 1906, $75; Dec. 1, 1906, 
$150 ; May 10, 1907, $100; and July 1, 1907, $ 185. 



EATIO 

416. How many weeks are there in one month? What 
part of one month is one week? What is the relation of 
one week to one month ? 

417. This relation is expressed in fractional form, ^. 
It may also be expressed thus, 1: 4, which is read 1 to 4. 

The relation of two numbers of the same kind as ex- 
pressed by division is called the Ratio of the first to the 
second. 

418. The two numbers of a ratio are called its Terms. 

EXERCISE 236. — ORAL 

Express the following common fractions in the form of 
ratios : 

1. i- 4. 4. 7. I. 



?• •*• 3 



2. f 5. f. 8. 1. 

3. i. 6. i. 9. 1. 



1 



Express the following ratios as fractions : 

10. 3:10. 12. 8:9. 14. 1:15. 

11. 10:3. 13. 12:11. 15. 15:1. 

419. The first term of tlie ratio is called the Antecedent. 
The second term is the Consequent. 

302 



RATIO 303 

420. Two quantities of different kinds cannot form the 
terms of a ratio. A ratio is always abstract, and the 
terms may be written as abstract numbers. 

421. Multiply, also divide, both terms of the ratio 4 : 
6 by 2. 

Multiplying, we have 8 : 12; dividing, we have 2:3. If we 
express as a fraction the value of each ratio so obtained, we see 
that multiplying or dividing has not changed the value of the 
ratio. 

Multiplying or dividing both terms of a ratio by the 
same number does not change its value. 

422. In order to compare readily two or more ratios, it 
is convenient to reduce the ratios to such forms that the 
first terms of the ratios to be compared shall be the same, 
usually 1. 

423. Reduce 7 : 28 to a ratio having 1 for its first term : 
Dividing both terms by 7, we have 1 : 4. To obtain a 

ratio with one for its first term, divide the second term by 
the first term ; take the quotient as the second term and 
1 as the first term of this new ratio. 

EXBRCISB 237. — WRITTEN 

Reduce each of the following to a ratio having 1 for its 
first term : 



1. 


12 : 24. 


6. 


16; 


;39. 


11. 


.1:3. 


16. 


1:2. 


2. 


3:9. 


7. 


19: 


:72. 


12. 


.9:6. 


17. 


j:ll. 


3. 


6:60. 


8. 


11; 


:23. 


13. 


.784:9. 


18. 


T^ = 24. 


4. 


7:21. 


9. 


24 


:98. 


14. 


.62:11. 


19. 


j.?y:9642. 


5. 


9:81. 


10. 


96; 


;700. 


15. 


.7:6. 


20. 


tV9=1>2V 



304 PRACTICAL ARITHMETIC 

The following numbers express the density of popula- 
tion per square mile in various countries. Compare the 
population of the Uuited States with that of other coun- 
tries in the form of ratios, using the number represent- 
ing the population of the United States as the first term 
in every case. Reduce all the ratios so that the first term 
shall be 1. 

United States 25, Great Britain and Ireland 344, France 
188, Germany 288, Italy 293, Belgium 609, Switzerland 
208, Canada 1. 

THE NUTRITIVE RATIO 

424. What is the ratio of 2.5 lbs. to 16.25 lbs., with the 
first term reduced to 1 ? 

What is the ratio between 1.5 lbs. protein and 10.5 lbs. 
carbohydrates and fats ? Reduce to a ratio having 1 for 
its first term. 

425. Find the nutritive ratio of the following standard 
ration for a dairy cow : 2.5 lbs. of digestible protein, 13 lbs. 
of digestible carbohydrates, and .5 lb. of digestible fats : 

The fats in a ration are 2.4 times more valuable than the 
carbohydrates. To reduce the fats in this ration to the value 
of carbohydrates, the number expressing the amount of fats, 
.5, must be multiplied by 2.4. .5 x 2.4 = 1.2. Adding this to 
the number expressing carbohydrates, we have 1.2 + 13 = 14.2, 
the value of the carbohydrates and fats taken together. The 
nutritive ratio of this standard dairy ration is, therefore, as 
2.5 is to 14.2, or, reducing the first term to 1, we have 1 : 5.68. 
The nutritive ratio is therefore 1 : 5.68. 

426. The Nutritive Ratio of a ration is the ratio of 
the weight of the digestible protein to the sum of the 



RATIO 305 

weights of the carbohydrates plus 2.4 times the sum of 
the weights of the fats. 

Digestible protein : (2.4 x fats) + carbohydrates. 

427. A Balanced Ration is one having the correct nutri- 
tive ratio for the particular animal and purposes for 
which it is being fed. 

438. A Narrow Ration is one in which the proportion 
of protein to carbohydrates and fats is greater than the 
standard requirements. 

429. A Wide Ration is one in which the proportion of 
protein to the carbohydrates and fats is less than the 
standard requirements. 

EXERCISE 238. — WRITTEN 

1. A ration consisting of 10 lbs. of corn and 20 lbs. of 
timothy hay contains 1.35 lbs. of digestible protein, 15.35 
lbs. of carbohydrates, and .71 lb. of fats. What is the 
nutritive ratio? 

2. A ration consisting of 10 lbs. of corn and 20 lbs. of 
alfalfa hay contains 2.99 lbs. of digestible protein, 14.57 
lbs. of carbohydrates, and .67 lb. of fats. What is the 
nutritive ratio ? 

3. A ration consisting of 8 lbs. of corn, 1 lb. of cotton- 
seed meal, 12 lbs. of alfalfa hay, and 20 lbs. of corn silage 
contains 2.50 lbs. of digestible protein, 12.52 lbs. of digest- 
ible carbohydrates, and .75 lb. of fats. What is the 
nutritive ratio ? Compare these three rations with the 
feeding standard for a cow giving 22 lbs. of milk a day. 
(See page 250.) Which is too narrow? Which is too 



306 PRACTICAL ARITHMETIC 

wide? Which most nearly meets the requirements of the 
standard? 

4. If a ration consisting of 10 lbs. of corn and 20 Ihs. of 
red-clover hay contains 2.15 lbs. of digestible protein, 
13.83 lbs. of digestible carbohydrates, and .77 lb. of digest- 
ible fats, what is the nutritive ratio ? 

5. If a ration for dairy cows, consisting of 7 lbs. of 
corn and cob meal, 1.5 lbs. of cotton-seed meal, 10 lbs. of 
clover hay, and 40 lbs. of corn silage contains 2.14 lbs. 
of protein, 13.02 lbs. of carbohydrates, and .93 lb. of fats, 
what is the nutritive ratio? 

6. A ration consisting of 20 lbs. of corn, 5 lbs. of tim- 
othy hay, and 5 lbs. of corn stover contains 1.8 lbs. of 
protein, 17.13 lbs. of carbohydrates, and .96 lb. of fats. 
What is the nutritive ratio? Is this too wide or too 
narrow a ration for a fattening beef animal for the third 
period? -(See page 250.) 

7. Determine the nutritive ratio of the feeding stand- 
ards in the table on page 250. 

8-18. Find the nutritive ratio of rations Nos. 1 to 11, 
on pages 251 to 255. 

Find the nutritive ratio of the following rations: 

19. Red-clover hay, 12 lbs., corn stover, 15 lbs., corn, 
12 lbs. 

20. Corn silage, 40 lbs., red-clover hay, 5 lbs., corn 
stover, 5 lbs., corn, 6 lbs., cotton-seed meal, 3 lbs. 

SPECIFIC GRAVITY 

430. The Specific Gravity of a substance is the ratio of 
its weight to the weight of an equal volume of water. 



RATIO 



307 



431. To find the specific gravity of a substance, state 
the ratio of its weight to that of an equal volume of water, 
reducing this ratio so that the second term shall be 1. 



EXERCISE 239 — WRITTEN 

Find the specific gravity of each of these substances, tlie 
weight of which is given per cubic foot : 

1. Water, 62.42 lbs. 

2. Cast iron, 449.86 lbs. 

3. Cast copper, 548.55 lbs. 

4. Cast lead, 708.59 lbs. 



Ice, 



58.04 lbs. 10. Clay, 



6. Cork, 14.9808 lbs. 

7. Maple wood, 46.815 lbs. 

8. Ebony, 83.0186 lbs. 

9. Butter, 58.6748 lbs. 
74.904 lbs. 



Find the weight per cubic foot of the following sub- 
stances, the specific gravities of which are given : 



11. 


Ash wood, 


.84. 


24. 


Paraffin, 


.874. 


12. 


Mercury, 


13.598. 


25. 


Glycerine, 


1.26. 


13. 


Glass, 


2.89. 


26. 


Milk, 


1.031. 


14. 


Cider, 


1.02. 


27. 


Petroleum, 


.836. 


15. 


Sea- water. 


1.03. 


28. 


Olive oil. 


.915. 


16. 


Silver, 


10.47. 


29. 


Sulphur, 


2.043. 


17. 


Gold, 


19.26. 


30. 


Anthracite, 


1.8. 


18. 


Steel, 


7.816. 


31. 


Elm wood 


.8. 


19. 


Tin, 


7.291. 


32. 


Oak wood, 


.845. 


20. 


Flint glass. 


3.-329. 


33. 


Yellow pine wood, .657. 


21. 


Platinum, 


22.069. 


34. 


Poplar wood. 


.389. 


22. 


Copper, 


8.878. 


35. 


Beech wood, 


.852. 


23. 


Aluminum, 


2.68. 









PROPORTION 

432. When two ratios are equal, the four terms form 
a Proportion, e.g.^ 2:4::8:16 are in proportion, since 
f equal Jg. 

433. A proportion, therefore, is an expression of equal- 
ity between two ratios and is written by placing the sign 
of equality or the double colon between the two ratios. 
The proportion 2 : 4 : : 8 : 16, or 2:4=8:16, is read, 2 is to 
4 as 8 is to 16. 

434. The first and last terms of a proportion are called 
the Extremes, and the two middle terms are the Means. 

435. When four numbers are in proportion, the product 
of the extremes equals the product of the means. This 
constitutes the test of the proportion. 

EXERCISE 240. — ORAL 

Complete the following statements of proportions : 

1. 2: 4:: 3:? 5. 6:?:: 5: 10. 

2. ?:4::4:8. 6. 2.8 : 5.6 :: ? : 4.8. 

3. 6: 9:: 12:? 7. 9:24::?: 8. 

4. 5: 15:: 6:? 8. 1.2 : ? : : 2 : 4. 

436. Find the missing term in the following propor- 
tion : 

? • 8 1 • • 1 9,^- ^ '^^^ product of the extremes equalling 
the product of the means, 8.1 X 1.25 = 5 
SOS 



PROPORTION . 309 

times the unknown number. The unknown number is 

8.1 X 1.25 

therefore — ^ — . Solving this example by cancellation, 

o 

.25 
we have 8.1 x l-?^ _2qk 

The completed proportion, therefore, is 2.05 : 8.1 : : 1.25 : 5. 



EXERCISE 241. — WRITTEN 

Find the missing terms in the following proportions : 

1. ?: 136:: 84: 336. 5. 17.4 : 191.1 :: 11.5: ? 

2. 12: 144::?: 1728. 6. ?: 6.25 :: .75 : 8.36. 

3. 15:?:: 6: 82. 7. ?: 18:: 45: 32. 

4. 22: 5:: 35:? 8. 18.2 :?:: 7.3 : 9.1. 

437. If 10 bus. of apples cost 17.60, what will 15 bus. 
of apples cost ? 

This problem may be stated and solved as a proportion 
since we have two ratios, one between the number of bushels 
of apples in the first instance and the number of bushels in the 
second instance, 10 : 15 ; the other between the amount paid in 
the first instance and the amount paid in the second instance 
$ 7.50 and f ?. The price of apples remaining the same, these 
two ratios are equal. Therefore, we have 

10 bus. :15 bus.:: $7.50:$? 

Since unlike quantities cannot be multiplied, we may substi- 
tute abstract numbers instead of the first two terms, which will 
not affect the value of the ratio. We then have 

10 : 15 : : f 7.50 : $ ? Solving, we have $12.25, the cost of 
the 15 bus. of apples. 

Arrange the three known quantities and the unknown 



310 PRACTICAL ARITHMETIC 

quantity of the problem in the form of two ratios which 
shall be equal. Solve as a proportion. 

BXEBCISB 242. — WRITTEN 

1. If 25 lbs. of sugar cost $1.50, what will 75 lbs. 
cost ? 

2. If 6 tons of hay cost $ 72, what will 36 tons cost ? 

3. If a railroad ticket good for 80 miles costs $1.80, 
what will a ticket good for 60 miles cost ? 

4. If a railroad ticket for 64 miles at 2| cts. a mile 
costs $1.76, what will a ticket for 17 miles cost at the 
same rate ? 

5. If it costs 14.01 cts. to spray 3 acres 3 times, how 
much will it cost to spray 21 acres 3 times ? 

6. If the net profit from spraying 6 acres of potatoes 
is $ 138, what is the profit from spraying 33 acres ? 

7. If at a certain moment a post 32 ft. high casts a 
shadow 48 ft. long, how long is the shadow of a tree which 
is 48 ft. high? 

8. At the same moment how tall is a tree that casts 
a shadow 32 ft. long ? 

9. Measure the height of a post in your neighborhood 
and the length of its shadow; also, at the same time, 
measure the length of the shadow of any tall object, and 
by means of these measurements calculate the height of 
the tall object. 

10. The height of a tall object is also often measured, 
as is shown in the accompanying figure, using a triangle 
of which UD = DC. The sides of the triangle are in the 



PROPORTION 



311 




proportion AB :GD:: BE : I)E. Exclusive of the height 
of the triangle from the ground, what is the height of the 
tree, if the distance EB 
is 64 ft.? 

H. If in 15 lbs. of 
oats there are 13.35 lbs. 
of dry matter, 1.395 lbs. 
of protein, 7.125 lbs. of 
carbohydrates, and .54 lb. 
of fats, how many pounds 
of each of these are there 
in 2000 lbs. of oats ? 

12. If in 5 lbs. of cow- 
pea vine hay there are 
4.4 lbs. of dry matter, .465 lb. of protein, 1.92 lbs. of 
carbohydrates, and .06 lb. of fats, how many pounds of 
each are there in 2000 lbs. of cow-pea vine hay? 

13. If in alfalfa hay there is 10.6% of digestible pro- 
tein, how much protein is there in 2500 lbs. of alfalfa 
hay? 

LEVERS 

438. In considering le- 
vers, three things must be 
recognized : (1) the Power 
applied to do the work or 
overcome the resistance ; 
(2) the Weight or the re- 
sistance to be overcome ; 
and (3) the immovable 
point on which the lever turns, called the Fulcrum. 




312 



PRACTICAL ARITHMETIC 



In the figure on page 311 where is the weight ? Where 
is the power ? What is the fulcrum? 

439. A lever can always be divided into two parts : 
(1) the distance from the weight to the fulcrum, called 
the Weight Arm ; (2) the distance from the power to the 
fulcrum, called the Power Arm. 

In the figure how long is the power arm? How long 
is the weight arm ? 

440. The factors of a lever are always in proportion, 

thus: 

Power arm : Weight arm : : Weight : Power, 

or, abbreviating. 

Pa :Wa : : W: P 



EXERCISE 243. — ORAL 

1. In the figure on page 311 how many pounds must 
the man exert to lift the stone if it weighs 30 lbs. ? 
90 lbs. ? 

2. If the man exerts a power of 3 lbs., how heavy a 
stone can he lift? If he exerts 9 lbs. ? 100 lbs. ? 3^ lbs. ? 

3. If the power arm is 9 ft. and the weight arm 1 ft., 
what will be the answers to No. 1? To No. 2? 

4. In this figure where is the power? Where the ful- 
crum? Where the 
weight (resistance)? 
Will a wire be cut more 

^ easily near the tip of the 

'"""■' ~ ' shear blades, or near the 

base ? Why ? What is the power arm ? The weight 
arm ? 




PROPORTION 

5. In this figure what is the length of power arm? 
weight arm ? 



313 
Of 




6. With a pressure of 80 lbs., how much resistance 
can be overcome ? 



EXERCISE 244. — WRITTEN 

1. In raising a stone weighing 1400 lbs. with a weight 
arm 1 ft. long, how long must the power arm be to enable 
a man who can exert only 200 lbs. of power to do the 
work? If the weight arm is reduced to 9 ins., how long 
need the power arm be ? 

2. How much does the weight of a 156-lb. man, on 
the end of the power arm, fall short of raising a stone 
weighing 1200 lbs. with a lever having a power arm of 
4 ft. and a weight arm of 1 ft.? 

3. With a wagon-jack of the dimensions indicated, how 
much power is needed to lift 
the rear end of a loaded 
wagon, the rear end, loaded, 
weighing 1600 lbs.? 

4. With steelyards as in 
the figure on page 314, with 
a weight (a) of 8 ozs., how 
far from the fulcrum must this weight be to balance 18 
lbs. ? 25 lbs. ? 16 lbs. ? 




314 



PRACTICAL ARITHMETIC 




5. In fishing John lield the large end of the pole sta- 
tionary in the left hand. The right hand was 2 ft. 9 ins. 

farther up the pole, which 
was 12 ft. long. With his 
right hand it took a force 
of 8 ozs. to sustain the fish. 
What did it weigh ? 
Draw a diagram to aid in 
stea solving this problem. 

6. In drawing a nail with a hammer the distance from 
the fulcrum to the nail is 2 ins., from fulcrum to hands is 
11 ins. How much direct pull is exerted upon the nail if 
it requires 95 lbs. of pull 
upon the hammer handle to 
extract it ? 

7. A boy weighing 96 
lbs. is swinging on a gate, 
having 2 hinges, 12 ft. from 
the hinges. It is 3 ft. 4 ins. 
from one hinge to the other. 
How ,much pull does the 
boy's weight exert upon the upper hinge ? How much 
does it push upon the lower hinge ? Draw a diagram 
before attempting to solve. Compare with the last 
problem. 

8. Two men carry a weight of 195 lbs. suspended on 
a pole between them. If the weight is 6 ft. from one 
man and 9 ft. from the other, how many pounds does 
each carry ? In order that one may carry ^ of the weight 
where must the weight be hung? 




PROPORTION 31c 



COMPOUND PROPORTION 



441. If 18 men working (j hrs. per day can dig a canal 
50 ft. long in 25 days, how many men working 10 hrs. per 
day can dig a canal 80 ft. long in 8 days ? 

This problem can be separated into simple proportions 
and solved as follows : 

If 18 men can dig a canal in 25 days, how many men are re- 
quired to dig the same canal in 8 days ? This is expressed in 
proportion. (1) Solving, we get ^j^ men. Tlie canal is, how- 
ziN a ok 18 9 ®^''^'^'' ^"^ ^^- ^°"S instead 
' 50 80 - - of 50 ft. long. If... 

)y^ 10 • 6 • • 90^ ■" ™^^ ^^^ ^^° ^ °^^^^^ ^^ ^*' 

„ ' y ..y ^r m „, lo'ia; ill 8 davs, how many 
8 X no X 10 18 X ifi X90 ■ A ^ A- 

— ^ ^, =: ^^^ ^ *^^^ ^ . ^ men are required to dig a 

canal 80 ft. long in 8 
days ? This is expressed 
in proportion. (2) Solv- 
ing, we get 90 men. The 
previous statements have been made under tlie assumption that 
the men were to worlt 6 hrs. per day instead of 10 hrs. If 90 
men can dig a canal 80 ft. long in 8 days, working 6 hrs. per 
day, how many men will be required to dig a canal 80 ft. long 
in 8 days, working 10 hrs. per day ? This is stated in pro- 
portion. (3) Solving, we get 54 men, which is tlie final answer. 
This method of procedure may be shortened. IMultiplying the 
completed proportions, 1, 2, and 3 together, term by term, we 
obtain a new proportion, which, expressed as a ratio, is shown 
in 4. We see that the answers obtained from the first two pro- 
portions cancel, leaving the second member a simple ratio. The 
ratio may now be expressed as a proportion, as is shown in 5, 
and solved, as follows : 

10 3 
23X80X0X18 




18 : ? men. 



8 X 50 X 10 



: 54 men. 



316 PRACTICAL ARITHMETIC 

The fact that the first two answers cancel shows that it was 
unnecessary to obtain them to arrive at the final answer. 

Rule 1. Place the unknown quantity as the fourth 
term of the proportion. 

2. Place as the third term of the proportion the quan- 
tity given in the problem expressing the same kind of 
thing as the unknown quantity. 

3. Take each of the other ratios separately, and arrange 
according to their relation to the ratio already stated. 

4. The product of all the means divided by the product 
of all the extremes, except the unknown one, will give the 
answer. 

442. The product of two or more simple ratios is a 
Compound Ratio. 

443. A proportion in which either or both ratios are 
compound is a Compound Proportion. 

EXERCISE 245, — WRITTEN 

1. If 17 men working 7 hrs. a day can build a bridge 
in 22 days, how many men working 10 hrs. a day will it 
take to build the bridge in 4 days ? 

2. If 3 men can milk 35 cows in 1.5 hrs., how many 
men will it take to milk 65 cows in J hr. ? 

3. If 3 teams working 5 hrs. a day can haul dirt as 
fast as 5 men can excavate it, how many teams working 
7 hrs. a day are required to haul dirt as fast as 15 men 
can excavate it ? 

4. If 6 men can draw and house 32 tons of hay in 2 
days, how many men are needed to draw and house 14 
tons in 6 hrs. ? 



PROPORTION 317 

5. If 2 men cut 8 cords of wood in 4 days, how long 
will it take 12 men to cut 36 cords ? 

6. If 4 men with a one-horse plow break 28 acres in 
7 days, how many days will it take 3 men with two-horse 
plows (a man with a two-horse plow doing twice as 
much work as a man with a one-horse plow) to break 
42 acres ? 

7. If the eggs laid by 28 hens in 16 weeks are worth 
132.50, what will be the value of the eggs laid by 50 hens 
in 12 weeks ? 

8. If it requires 35 cows giving 77 qts. of milk each, 
per week, to supply 425 customers, how many cows giv- 
ing 270 qts. per month will be required to supply 125 
customers ? 

9. If 30 cows give 462 lbs. of milk in 21 days, how 
many cows are required to give 1200 lbs. in 7 days? 

10. If 4320 lbs. of silage last 30 cows 48 days, how 
much silage is needed for 15 cows for 60 days? 

11. If the contents of a tank of water 2 x 4 x 10 ft. 
weighs 4994 lbs., what will the contents of a tank 7 x 12 
X 19 ft. weigh? 

12. If it takes 2 cu. yds. of concrete to make 40 posts 
6" X 4J" X 7', how many yards will it take to make 678 
posts 4" X 4" X 5'? 

13. If the weight of a volume of water 1 x IJ X 9 ft. 

is (pupil fill blank), what is the weight of a piece 

of ebony | x | x 3 ft., ebony weighing 1.33 times as much 
as water of equal volume? 



POWEES 



In the figure how many units are there on each side of 
tlie square? How many in the whole 
square ? There are 9 square units in a 



square of 3 units on a side, therefore, 9 
is said to be the Square of 3. Simi- 
larl}-, a square witli 4 units on each 
side has a total of 16 square units. 
The Square of a number is the product of a number with 
itself. 

444. In the figure how many units are there on each 
edge? How many cubic units in the cube? There being 
27 cubic units in a cube with 3 units 
on an edge, 27 is said to be the Cube 
of 3. 

The Cube of a number is the prod- 
uct of the number taken 3 times as 
a factor. 



y y / 



y'/ / 



/ 



/ 



/ 



/ 



445. Squares and cubes are called Powers of a number. 
As the square and the cube are the second and third 
powers of numbers, so taking the number 4 times as a 
factor gives the fourth power, 6 times the fifth, etc. 

446. The power of a number to be taken is indicated 
by a small figure written above and to the right of the 

318 



POWERS 319 

number, e.g., 3^ means the square of 3, 4^ means the cube 
of 4, 6^ means the ninth power of 6, etc. 

447. The figure used to indicate the power taken is 
called the Exponent. 

EXERCISE 246. — ORAL 

Find the value of the following : 

1. 62. 4. 13. 7. 19. 10. 122. 

2. 92. 5. 82. 8. 102. 11. 252. 

3. 202. 6. 112. 9. 34_ 12. 303. 

EXERCISE 247. —WRITTEN 

Find the value of : 

1. 843. 3. 1.253. 5. (^|V)2. 7_ (-ll^)3. 

2. 123. 4. .752. 6. (7)3. 8. 12.53. 

448. We have seen that the square of a number is the 
number multiplied by itself, e.g.., the square of 24 is 
24 X 24. We may write this multiplication thus : 

2 tens + 4 units 
2 tens + 4 units 
4 units X 2 tens 4 units^, result of multiplying 

by 4 units. 
2 tens' 4 units X 2 tens, result of multiplying 

by 2 tens. 
2 tens^ + 2(4 units X 2 tens) H- 4 units', sum of partial products. 
Since any number greater than 10 may be regarded as com- 
posed of the sum of two numbers, the square of the sum of any 
two numbers is equal to the square of the first number + 2 X 
(the product of the first x the second) -(- the square of the last. 
The same formula may be arrived at by considering the 
square of 24 as representing an area 24 units on each edge, as 
in the accompanying figure, and cutting the lines of the sides 



320 



PRACTICAL ARITHMETIC 



into 20 units and 4 units to represent 2 tens and 4 units. It is 
then seen that the whole square of 24 consists of ; the large 
square a, which is 20^ and two times 
the rectangle 6, which is 2 x (20 x 4), 
and the small square c, which is 4^ 

Represent the square of the same 
number, 24, in a diagram, similar 
to that just used, but cutting the 
lines into 18 and 6 units instead of 
into 20 and 4. Solve as above. 
Does this change affect the result? 
We may represent the lines by letters n and s, as in the 
figure ; then we have : 

(n + s)2 = w2 + 2(w, X s) + s2. 

By this formula determine the square of 63 : 

63 = 6 tens and 3 units. 

6 tens squared = GO x 60 = 3600 

2 X (6 tens x 3 units) = 2 x 60 X 3 = 360 

3 units squared = 3x3 = 9 

3969 





Si 










a 




o 


6 


«9 












20 


n 




S4 


S 


6 




Tl< 


c 



EXERCISE 248. — "WRITTEN 

Find by the last method given above, the squares of : 



1. 


62. 


8. 


67. 


15. 


199. 


22. 


672. 


2. 


79. 


9. 


98. 


16. 


86. 


23. 


999. 


3. 


24. 


10. 


99. 


17. 


205. 


24. 


897. 


4. 


81. 


11. 


107. 


18. 


640. 


25. 


862. 


5. 


63. 


12. 


129. 


19. 


783. 


26. 


978. 


6. 


72. 


13. 


15. 


20. 


297. 


27. 


209. 


7. 


84. 


14. 


22. 


21. 


248. 


28. 


679, 



EOOTS 

449. "What number multiplied by itself will give 25 ? 
16? 4? 100? What number used three times as a factor 
gives 8? 27? 125? 1000? What number squared equals 
25? What number cubed equals 8? 27? 

450. A number which when squared equals a certain 
number is said to be the Square Root of that number, e.g., 
5 is the square root of 25 ; 4 is the square root of 16. 

451. A number which when cubed equals a certain num- 
ber is said to be the Cube Root of that number, e.g., 2 is the 
cube root of 8 ; 3 is the cube root of 27. 

452. The root of a number is indicated by the sign, V~, 
known as the Radical Sign. V~indicates the cube root, 
V~, the fourth root, etc. 

453. What is the square of 1? Of 10? Of 100? Of 
1000 ? Of 10,000 ? 

How many figures does it take to express the square 
root of a number of 1 or 2 figures? Of 3 or 4 figures? Of 
5 or 6 figures? How many figures in the power equal 1 
figure in the square root ? 

454. If a whole number be divided into groups of 2 
figures each, beginning at units' place, the number of 
groups will equal the number of figures in the root. 

455. Find the square root of 529 : 

321 



322 PRACTICAL ARITHMETIC 

Separating into periods, we see that since there are two peri- 
ods, the root consists of two figures. The square of the tens 
of the root must be contained in the second period, 6. The 
greatest square in 5 is 4, the root of which is 2, which is 
therefore the tens' figure of the root desired. 

5'29^23 Subtracting the square of 2 tens or 400 

^QQ from 529, we have 129. This remainder must 

A.^y[9Q contain, 2 x (tens X units) + units^ (see para- 

— 19C)' graph 448). Two times the 2 tens = 4 tens. 

— — ■ 4 is contained in 12, 3 times. We therefore 

take 3 as the next figure of the root. To find whether the 

remainder exactly contains 2 x (tens x units) + units ^, or 

what is equivalent (twice the tens + the units) x units, add 

the units to twice the tens and multiply by the units, thus : 

(3 + 40) X 3, securing 129. 23 is therefore the square root 

of 529. 

To prove square root, multiply the square root by itself, 

456. Find the square root of 15,713,296 : 

) 15,713,296 )3964 

9_ 

69)671 

nn-i Proceed as in the preceding pro'b- 

_— — ■ lem. In each step consider the part 

. 786)5082 Qf ^j^g j.jjjj^ already found as tens with 

4716 relation to the next figure. 

7924)31696 
31696 

457. Find the square root of 94,864 : 

94864)308 

g Since the divisor 6 is not contained in 4, 

fin8"vd8RJ. ^^ placed in the root as well as in the divisor, 

^ and the next group is brought down. 

4864 ^ 



ROOTS 323 

458. Rule for the extraction of square root. 

1. Separate the number into groups of two figures 
each, beginning at the decimal point. 

2. Find the greatest square in the left period. Its 
root is the first figure of the required root. 

3. Subtract the square of this root from tlie first 
period, and bring down the next period. 

4. Divide the remainder by twice the part of the root, 
already found, considered as tens, as a trial divisor, secur- 
ing the next figure of tlie root. 

5. To the trial divisor add the new figure of the root, 
then multiply by the last figure found, and subtract the 
product from the last remainder. 

6. Bring down the next period, and continue as above. 

459. If the number is not a perfect square, add ciphers 
to the number and continue the division, expressing the 
result as a decimal. 

460. What is the square of .25? Of .75? Of 1.25? 
How many more decimal places are there in the square of 
a decimal than in the decimal? How many decimal places 
are there in the square root of a decimal? 

The square root of a decimal has half as many decimal 
places as the decimal itself. 

Each group of the decimal must contain two figures. 
Annex a cipher, if need be. 

461. What is the square of J? Off? Off? 
What is the square root of ^6? Of |? Of^? 

To obtain the root of a fraction, extract the root of 
both numerator and denominator separately. 



324 



PRACTICAL ARITHMETIC 





] 


3XBRCIS 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 


E 249. -WB] 
V9433_. 

vtiif. 

V3.33. 


TTEN 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 




1. 


V7569. 


V8.7. 


2. 


V743044. 


^■ 


3. 


V6889. 


V987.12. 


4. 


V283024. 


vj. 


5. 


V7921. 


V64289. 

VS. 

V61 


V|. 


6. 


V236089. 


vn. 


7. 


V.9216. 
Vfllf. 


V.0178. 


8. 


V69284.7632 




EXERCISE 250. — 'WRITTEN 

In a right triangle tlie square of the hypotenuse, the 
side opposite the right angle, is equal to the sum of the 

squares of the other two sides. 
1. Two sides of a right tri- 
?%_ angle are 76 and 84 ft. What 

is the length of the hypote- 
nuse? 

1% In ba.se ^s. . __, , - 

; ^^ 2. Ihe hypotenuse oi a tri- 
angle is 82 ft. One side is 79 ft. What is the length of 
the other side? 

3. The base of a ladder is 12 ft. from the house. The 
top touches the eaves 39 ft. high. How long is the 
ladder ? 

4. A pasture shaped as a right triangle is 80 rds. 3 yds. 
4 ft. on its long side, 12 rds. 2 ft. on its short side. How 
long is the other side ? 

5. The area of a circle is 9678 sq. ft. What is its 
radius ? 



ROOTS 



325 



6. What is the diagonal of a rectangle 80 x 40 rds. ? 

7. The base of a 32 ft. ladder is 7 ft. from the house. 
How high on the wall can it touch? 

8. In cutting across the diagonal of a lot twice dailj^ for 
5 days, how much walking is saved if the lot measures 
203' X 98"? 

In carpenter work and other building it is frequently 
necessary to know the hypotenuse of a right triangle. It 
may be found with sufficient 
accuracy for many such 
purposes by use of the 
square and rule. 

9. What length of brace 
is needed from an upright 
post to a horizontal beam, 
the two ends of the brace 



/ 




iil'ill'ii|iiir'iH'ii|M;|'Mji| 
i,i°'i.i^,i?i,Ki,i^i,m,!':i,i':hRi,r,F-a 



to be 5 ft. and 4 ft. from the right angle ? Place the rule 
on the square at 4 and 5 ins., as shown in the figure. 
Read the length of the hypotenuse in inches. Let each 
inch on the square and rule stand for a foot in the prob- 
lem. Solve the same problem by square root, and compaire 
answers. 



CUBE ROOT 

Since the extraction of the cube root may be much more 
easily understood after algebra has been studied, and 
since it is customary to defer its study until then, it will 
not be discussed here. The method of extracting the 
cube root is given in the Appendix for the benefit of any 
who may have occasion for its use. 



326 PRACTICAL ARITHMETIC 

EXERCISE 251 

MiscELLAXEous Review Problems 

1. What is the cost of spraj'ing 6| A. of cucumbers 
6 times with Bordeaux mixture, applying 100 gals, per 
acre each time, using 3 lbs. of bluestoue at 1^ cts. per 
pound, 6 lbs. of lime at 1 ct. per pound in each 50 gals, 
of mixture ? Allow 33 cts. for labor of making each 100 
gals. 

2. Some tall structures are: the Eiffel Tower 984 ft., 
the Washington Monument 555 ft., the Cologne Cathe- 
dral 521 ft., Cheops Pj-ramid 486 ft., Strasburg Cathe- 
dral 474 ft.. Bunker Hill Monument 221 ft. How much 
higher is the Eiffel Tower than each of the other struc- 
tures named? How much higher is the Washington 
Monument than each of the others, except the Eiffel 
Tower ? 

3. Alcohol is .83 as heavy as water. Copper is 8.8 times 
as heavy. How much heavier is 1 cu. ft. of lead than 
1 cu. ft. of alcohol, if 1 cu. ft. of water weighs 62.42 lbs. ? 

4. What is the cost of: 1 smoothing plane, $2.40; 1 
spoke shave, 1.90; 3 chisels at $.42; 1 gauge, 52 cts.; 
1 claw hatchet, $.80; 1 ratchet brace, $1.08; 5 bits, at 
$-19, $.28, $33, $.41, and $.49; 1 screw-driver, $.16; 
1 level, $2.00; 1 square, $1.50 ; 1 rip saw, $1.65; 1 hand 
saw, $1.65? 

5. From a roll of carpet 21|^ yds. long there are cut 
two pieces, one 1\ yds., one 17f yds. How much 
remains ? 

6. Allowing ^ in. per foot for shrinkage, how much 



MISCELLANEOUS REVIEW PROBLEMS 327 

larger and wider than the desired article must be the pat- 
tern for a cast-iron support 9' 11" long x 2' 1.3" wide? 

7. Allowing the same shrinkage for lead, how long 
must be the mould for a casting, to be, when finished, 
2' 4" X 5"? 

8. Allowing -j^g" per foot for shrinkage in brass cast- 
ings, what would be the answer in the last two problems? 

9. In an arithmetic class where term grade was valued 
at 75% and the examination at 25%, one student with a 
term grade of 8-4 made a final mark of 77. What was his 
mark on examination? 

10. On an examination paper of 16 questions one ques- 
tion was three-fourths correct, three were one-half right, 
four were one-third correct, one was eight-ninths correct. 
What was the grade? 

11. If the same errors had occurred on an examination 
paper of 12 questions, what would have been the grade? 
If on a paper of 10 questions? If on a paper of 9 
questions ? 

12. If in feeding pigs, 1 bu. of corn produces 10.9 lbs. 
of gain, what price per bushel is obtained for corn when 
pigs sell for 5.75 cts. per pound? 

13. If .92 A. of rape furnish feed for pigs equal to 
1596 lbs. of corn and 796 lbs. of wheat middlings, what 
is the feeding value of an acre of rape, when corn is 
worth 45 cts. a bushel and wheat middlings 1^18 a ton? 

14. Five pigs at 10 months of age average 243 lbs. in 
weight and sell for 5J cts. per pound. If they consumed 
98 lbs. of wheat bran at $ 18 a ton, 1862 lbs. of corn at 



328 PRACTICAL ARITHMETIC 

50 cts. a bushel, and grazed .25 A. of clover, .25 A. of sor- 
ghum, and .60 A. of peanuts, what was the combined 
value per acre of these grazing crops for pig feeding ? 

15. If 1 A. of peanuts and 37.8 bus. of corn pro- 
duce 1426 lbs. of gain in hogs and they sell for 5 cts. per 
pound, what is the value of an acre of peanuts if corn is 
worth 47 cts. per bushel? 

16. The population of the United States in 1900 was 
76,059,000. It is estimated that the number of births 
exceeds the number of deaths by 15.2 per 1000 of population 
every 10 yrs. Based on these estimates, what may the popu- 
lation of the United States be expected to be in 1910? 

17. The increase in population of the United States 
through immigration in 1903 and 1904 was 800,000 annu- 
ally. In 1905 and 1906 the increase was 1,000,000 annually. 
Taking the average of these four years as the probable 
increase through immigration for the next ten years, to- 
gether with the results of the last problem, what is your 
estimate of the population of the United States in 1910? 

18. Estimated in a similar way, basing each time upon 
the estimated population of the preceding decade, what 
will be the population in 1920? 1930? 1940 ? 1950? 



19. Add each line without writing in columns : 

a. 79, 46, 87, 93, 84, 72, 16. 

I. 857, 965, 847, 964, 876. 

c. 965, 864, 791, 862, 764, 968. 

d. 6482, 9683, 7981, 8472, 6897, 9861. 

e. 64,875, 89,672, 978,459, 679,821. > 



MISCELLANEOUS REVIEW PROBLEMS 329 

20. Estimate the average speed per mile of the trains 
as given in the time-table on page 145. 

21. It requires 151 days for the eggs of the honey bee 
to develop into honey bees that are to become queens: 
■^j of this period is required for the eggs to hatch; || of 
this period is required to mature the larvae and pupse. 
How many days are spent in the egg state? How many 
in the larval and pupal states ? 

22. It requires ^ more days for the eggs to develop 
to become worker bees than to become queen bees : -f of 
this period is required for the eggs to hatch ; ^ to mature 
the larvae and pupee. How many days are spent in the 
egg state? How many in the larval and pupal states? 

23. The plant louse often produces in 12 generations 
in one season, 10,000,000,000,000,000,000,000 ofCspring. 
These are each about -^-^ of an inch long. If all should 
live, how many miles long would such a procession be, ar- 
ranged single file? How many times would this proces- 
sion reach around the earth, considering the circumference 
of the earth as 25,000 miles? 

24. If on an average 1 cattle tick produces 1000 young 
and there are four generations in one year, how many 
ticks may be produced in the fourth generation ? If one- 
half these ticks are females, ^ inch in length, and one-half 
males, ^ of an inch long, arranged single file, how many 
times would this procession encircle the earth ? 

A family of two persons has an income of f 520. Their 
expenses are as follows : 



Eent $120 

Food 210 



Clothing $60 

Fuel 30 



330 



PRACTICAL ARITHMETIC 



Charity . . . 


. $10 


Church . . . 


10 


Eecreation . . 


10 


Incidentals 


10 


Emergencies . 


14 



Light $ 7 

Insurance 24 

Replenishing .... 10 

Car fare 5 

Literature 5 



25. What per cent of the income is spent for rent? 

26. What per cent is spent for food ? 

27. What is the ratio of money spent for rent to that 
spent for food? 



A family of three persons — 
years old — has an income of 
penses are as follows: 

Eent . 
Food . 



man, wife, and one child 6 
f 780. The itemized ex- 



Clothing 
Fuel . 
Light . 
Insurance 
Eeplenishing 



$120 
320 
120 
40 
10 
40 
20 



Car fares . 






$10 


Literature 




. 


10 


Church 




V 


15 


Eecreation 




. 


20 


Charity . . 




. 


10 


Incidentals 






20 


Emergencies 




. 


25 



28. If the food of the child is regarded as J of that of 
the man, and the food of the wife -^ that of the man, 
what is the cost of food for each? 

29. What per cent of the money expended for food by 
the first family is expended for food by the second family? 

30. What is the ratio of the sum of the last six items 
of the first family to the same items of the second family? 

31. The five states of greatest population in 1900 were: 
New York 5,997,853, Pennsylvania 5,258,014, Illinois 

,3,826,351, Ohio 3,672,316, Missouri 2,679,184. How 



MISCELLANEOUS REVIEW PROBLEMS 331 

much does the population of the two latter together 
exceed that of New York? 

32. Five sugar-producing districts are : Cuba 1,664,- 
862,000 lbs., Louisiana 695,101,878 lbs., Hawaiian Islands 
520,138,232 lbs., Philippine Islands 435,000,000 lbs., 
Porto Rico 122,000,000 lbs. How much does the produce 
of the other four together exceed that of Cuba? 

33. The five leading states in wheat production are : 
Minnesota 142,345,672, Kansas $32,469,706, North Da- 
kota 128,383,767, Ohio 127,788,094, Indiana 124,208,- 
398. What per cent of the wheat produced by these five 

.states is grown in each state? 

34. The iron manufactured in five states was : Pennsyl- 
vania $264,571,624, Ohio $65,206,828, Illinois $39,011,- 
051, New York $15,849,531, New Jersey $11,018,575. 
Find the total amount. The production of each state is 
what per cent of the total? 

35. The textile manufactures of five leading states 
were: Massachusetts $184,938,074, Pennsylvania $132,- 
367,499, New York $86,171,293, Rhode Island $67,005,- 
615, New Jersey $52,831,023. The production of each 
state is what per cent of the total of the five states? 

36. The number of miles of railroad for every 100 sq. 
mis. of area in five groups of states was : Middle Atlan- 
tic States 15.8, New England 11.72, Central 10.63, 
Southern 5.31, Western 2.09. What was the average 
mileage per 100 sq. mis. ? The mileage per 100 sq. mis. 
for each section is what per cent of the total? 

The following table shows the value of raw cotton and 



332 



PRACTICAL ARITHMETIC 



its manufactured product for 6 years, with the number 
of wage-earners engaged : 



Materials 


Vat.ub of Pkoduct 


Wage-earners 


Yeak 


1447,546,540 


$759,262,283 


517,237 


1890 


303,709,894 


532,673,488 


384,251 


1880 


353,249,102 


520,386,764 


274,943 


1870 


112,842,111 


214,740,614 


194,083 


1860 


76,715,959 


128,769,971 


146,877 


1850 


11,540,347 


15,454,430 




1840 



37. What was the per cent of increase in value of the 
annual product each decade based upon the preceding 
decade? 

38. What was the per cent of increase in value of manu- 
factured cotton over the crude cotton each decade? 

39. What was the per cent of increase in number of 
wage-earners in each decade since 1850? 

40. At 12 cts. per pound, for how much will a 500-lb. 
bale of cotton sell? 

41. A bale of cotton weighs 500 lbs. and sells for 
i60. The bagging and ties (strap iron) used to wrap 
it weigh 24 lbs., and are included in the total weight of 
the bale. What is the actual cost of the cotton per 
pound? 

42. In making a 450-lb. bale of cotton into thread for 
cotton cloth with a loss of 17 % due to particles of leaf, 
sand and other impurities, how much cotton is actually 
used? 

43. The warp threads in a sheet weigh 10 J ozs., the 
filling threads weigh 8| ozs., 20,160 yds. of warp threads 



MISCELLANEOUS KEVIEW PROBLEMS 333 

weigh 1 lb., and 22,260 yds. of filling weigh 1 lb. 
Find the number of yards of warp and filling used in 
the sheet. 

44. A stripe gingham cloth is made 28" wide, 56 ends 
per inch. The colors arranged in the following order 
form a pattern : 28 ends white, 16 ends blue, 8 ends 
black, 4 ends red. How many times is the pattern re- 
peated in the cloth, and how many ends of each color are 
there ? 

45. A loom weaves 50 yds. of calico cloth in 10-|- hrs. 
How many yards will be woven in 60 hrs. ? 

46. If 1 lb. of cotton-seed meal is equal to 1.75 lbs. 
of corn for cattle feeding, what is the value of a ton of 
cotton-seed meal for cattle feeding when corn is worth 
50 cts. a bushel? 1 bu. = 56 lbs. 

47. If for cattle feeding 3 lbs. of cotton-seed are equal 
to 3.48 lbs. of corn, what is the value of cotton-seed per 
ton for cattle feeding when corn is worth 45 cts. a bushel? 

48. Ten pigs weighing 56 lbs. each bought for f 50, 
after feeding for 120 days weigh 224 lbs. each. They 
then sell for $5,625 a hundred. What was the net profit 
if it cost 4.25 cts. in feed to produce a pound of gain? 

49. If it costs 4.07 cts. to produce a pound of gain 
with hogs fed corn and wheat middlings, and 3.25 cts. to 
produce a pound of gain with hogs fed corn and green 
clover, how much less will it cost to grow 12 hogs from 
50 lbs. up to a weight of 243 lbs. each on corn and clover 
than on corn and wheat middlings, if no charge be made 
for the clover pasture ? 



334 



PRACTICAL ARITHMETIC 



50. A beef animal weighing 986 lbs. is bought for 
3.875 cts. a pound and is fed 30 lbs. of silage worth |3 
a ton, 10 lbs. of clovei- hay worth !^8 a ton, 8 lbs. of 
corn worth 41 cts. a bushel, and 3 lbs. of cotton-seed meal 
worth $32 a ton, per day for 180 days. What is the 
profit on the feeding if the animal gains 1.95 lbs. a day 
and sells for $5.37^ per hundredweight? If the animal 
gains 2.1 lbs. a day and sells for $5.42 per hundred- 
weight ? 

51. How much will it cost to fence each of the lots of 
equal area, a, h, c, as chicken lots, if the figures showing 






l§ 




8 




20 West 


12 


40 


East 


ss 




g 




S 


c 





64 



dimensions in the dia- 
grams be taken to indicate 
feet: posts 8 ft. apart; 
cost of posts 19 cts. each ; 
cost of digging post-holes 
and setting posts 6 cts. 
each ; cost of wire netting 
5 ft. high, 7 cts. a linear 
yard ; estimate exclusive 
of cost of other labor ? 



52. If the figures indicating dimensions in these dia- 
grams be taken to mean yards, what will be the cost of 
fencing each lot with boards : placing posts 8 ft. apart ; 
the posts costing 17 cts, each ; cost of digging post-holes 



MISCELLANEOUS REVIEW PROBLEMS 335 

and setting posts 6 cts. each ; fence to be 5 boards high 
at 11.2 cts. for each board 16 ft. in length. Estimate 
exclusive of cost of nails and labor of construction. 

53. If tlie figures indicate rods, what will be the cost 
of fencing each with barbed wire: posts 16 ft. apart; 
cost of posts Irt cts. cach ; cost of setting posts 1|- cts. 
each; fence 4 wires high costing $2.75 per hundred 
pounds of 1480 ft. Estimate exclusive of cost of staples 
and labor of construction. 

54. Procure at home the prices of the materials used 
in the last three problems and the cost of construction in 
your community, and using such facts solve each of these 
problems. 

55. In plowing, a furrow one foot wide is turned. 
How many times must the field a be crossed to plow 
all of it ? How many turns must be made ? (Figures in- 
dicate rods.) 

56; If each turn consumes 30 sees. , what time is lost in 
turning in field a ? In field 5, plowing lengthwise ? In 
field c, plowing from east to west? (Figures indicate 
rods.) 

57. What is the value of the time lost in turning in 
plowing each field at % 3.50 per day of 10 hrs. ? (Figures 
indicate rods.) 

58. In raking the same fields with an eight-foot raks, 
how many turns are made ? How much time is lost in 
each field ? (Figures indicate rods.) 

59. With a twelve-foot rake, what will be the number 
of turns and the time lost in each field ? (Figures indi- 
cate rods.) 



336 PRACTICAL ARITHMETIC 

60. Two wagon tii-es, one 22 ft. the other 17 ft. in 
circumference, lie upon a floor in contact at one point. 
How far apart are their centres ? 

61. A window of tJie third story of a house is 32 ft. 
from the ground. How long must a ladder be to reach 
it, with the foot of the ladder 10 ft. from the building ? 

62. At i 18 a thousand feet, what will be the value of 
a piece of timber 18 ft. long, 10 ins. wide, and 8 ins. thick ? 

63. How many tons of silage are there in a silo 16 ft. 
in diameter, if the silage is 24 ft. deep in the silo and 1 
cu. ft. weighs 33^ lbs. ? 

64. How many barrels of water will a tank 8 ft. in 
diameter and 8 ft. high hold ? 

65. How many tons of silage will a silo 10 ft. in diame- 
ter and 20 ft. Iiigh hold, filled within 5 ft. of the top, if a 
cubic foot of silage from such a silo weighs 30 lbs. ? 

66. To insure the silage keeping well, a silo should not 
be less than 30 ft. deep. AVhat must be its diameter to 
hold enough silage to feed 25 cows 40 lbs. each a day for 
185 days, if a cubic foot of silage weighs 37 lbs.? 

67. When the temperature is 37.5° Centigrade, what 
will a Fahrenheit thermometer indicate ? 

68. If I pay f 3.50 a cord for wood and $.95 a cord for 
sawing, how much will a pile of wood 29 ft. long, 8 ft. 
wide, and 3 J ft. high cost me ? 

69. If a ring is 18 karats fine, what per cent of it is 
gold ? (1 karat = ^^.) If it is 14 karats fine, what per 
cent of it is gold ? 

70. A haberdasher buys hats at $ 18 a dozen and sells 



MISCELLANEOUS REVIEW rROBLEMS 33T 

them at a profit of 33^%. What is the gain? "What 
is the selling price ? 

71. A man invests $1250 so as to gain 12] %. What 
is his income from his investment ? 

72. If flour costs f 6 a barrel, at what mnst it be sold 
to gain 8^ % ? To gain 16f % ? 

73. A man purchases a hogshead of 12 gross of glass 
articles for $45; 5% was broken in shipping. At what 
price per dozen must the remainder be sold to gain 20 % 
on the whole? 

74> I buy a 30-gal. barrel of vinegar at 25 cts. a gallon. 
Upon examination it is found that 4 gals. 2 qts. have 
leaked out. How must the remainder be sold to gain 
36% on the whole? 

75. A and B are engaged in different lines of business 
with a capital of $4000 each. The first year A gains and 
B loses 20 % of the investment. The second year A loses 
and B gains 20 % on the capital each has then. Which 
is now the better off? 

76. A farmer losing 20 % of his tobacco crop by hail 
received from the insurance company in which the crop 
was insured for 75 % of its value, the sum of $450, cover- 
ing the loss. For what amount was the entire crop 
insured ? 

77. 10% of 5% of a number is |2.88. What is the 
number? 

CROP ROTATION 

Systems of crop rotation prove to be more profitable 
under most conditions tlian the continuous growing of 



338 PRACTICAL ARITHMETIC 

one crop. The conditions in one section of the South are 
illustrated on the opposite page by the record of a 90-acre 
farm continuously cropped and that of a similar farm 
divided into three 30-acre fields and the crops rotated. 

The cost and produce per acre for each field for a series 
of years are given. 

78. Find the profit on each 30-acre field for each year 
and the profit each year on the whole farm under rotation. 

79. Find the profit of the whole farm each year under 
continuous cropping. 

80. Which is the more profitable for the first year? 
How much more profitable than the other method? 

81. Which is the more profitable for the last year? 
How much more profitable than the other method? 

82. How much does the profit of the last 3 years under 
rotation exceed the profit of the last 3 years under con- 
tinuous cropping? 



83. A farmer has land that, with $1.86 worth of fer- 
tilizer per acre and $6.85 per acre for labor and other 
expenses, including taxes, will produce 56 bus. of corn 
per acre. With corn at 50 cts. a bushel the land is draw- 
ing 5% on what capital? 

84. L'nd that, with il.46 worth of fertilizer and 
$12.50 for other expenses, will produce f of a bale of cot- 
ton, worth for the seed f5, for the lint 333 lbs. at 11 cts. 
per pound, is drawing 4 % on what capital ? 

85. Land that will produce 260 bus. of potatoes, 
worth 50 cts. a bushel, with an outlay of $96 for all ex- 
penses, is paying interest at 4 % on what amount ? 



MISCELLANEOUS REVIEW PROBLEMS 



339 



< 


■O OS 

1% 


Corn 37 bus. 
per A. at 50 

Cost §11 per A. 
Profit . . . 




Oats 4 bus. per 

A. at40)« . 

Cost S 9 per A. 

Profit . . . 


■= u 

CO 

oi 

CO 


Cotton 550 lbs. 

per A. at Wf 
Cost $22. 50 per 

A 

Profit . . . 




d 


1 


250 lbs. per A. 

atl0>< . . 

Cost $20 per A. 

Profit . . . 


< 
1 


n 

li 

5" 


O OP-. 


Q 


^ (U 

!= S *3 CC 

o u a( 


-a 

Is 

1 s. 

a 
75 


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S £ P 

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340 PRACTICAL ARITHMETIC 

86. Land near a certain city produces 1300 worth of 
garden truck per acre at a total expense of f 120 per acre. 
Land of similar quality, but so located as to have no 
ma,rket for truck, can raise of its most profitable crop, corn, 
60 bus. per acre at 50 cts. per bu. at a cost of $8.50. 
Disregarding taxes, estimate the capital or value of each 
farm at 4% interest. 

87. What is the increased value of the first farm, due 
to its location? 

88. A field produces 816 lbs. of tobacco averaging 8 cts. 
per pound at a total cost of $47 per acre. The land is 
drawing interest on what capital at 4 % ? Suppose the 
tobacco wilt to take possession of the field and render to- 
bacco raising impossible and that the next most valuable 
crop is corn, 23 bus. per acre, valued at 65 cts. per bushel, 
costing to raise $9.20 an acre. What capital at the same 
rate will the land then represent? 

89. If the yellow yam sweet potato contains 16.64% 
of starch, how many pounds are required to contain 2 tons 
of starch ? 

90. The Red Bermuda contains 2.59 % of sugar, how 
much sugar is there in 3 cwts. ? How many tons are 
required to contain 2.9 T. of sugar? 

91. The average starch content of corn is 65 %, wheat 
58%, rice 75%, Irish potatoes 18%, sweet potatoes about 
21 % . What is the value of the starch in a ton of each of 
these crops at the following prices : corn starch 1.93 cts., 
potato starch 3.57 cts., rice starch 6.53 cts., wheat starch 
4.78 cts. per pound? 

92. If there is 28% of starch in the Red Bermuda 
sweet potato and 9.79 % in the Early Nansmond, how 



MISCELLANEOUS REVIEW PROBLEMS 341 

much more starch is there in 2 T. 3 cwts. of the first 
variety than in 3 T. 7 cwts. of the second? If 58 % of the 
starch present can be separated, how mucli can be had in 
each case? 

93. At 13.50 a day for a man and team, wliat is due 
for 3 wks. 4 days 3 hrs. work? 

94. At 19.00 a day for a man, team, and liarvester, 
what is due for 3 days 7 hrs. work? 

95. Ascertain the local price of such labor in your com- 
munity, and solve the last two problems, using these prices. 

96. Drawing produce on a good road a farmer can haul 
four loads daily, on a poor road only two loads daily. 
How many loads less are hauled in a week because of poor 
roads? In 6 weeks? Counting 4 loads to the day, what 
is the loss in this time to one man with team ? 

97. On poor roads a teamster can draw | of a ton at 
each load, on a good road 1| T. Allowing four loads 
to each daj'' on a good road and two loads a day on a poor 
road, how much lost time is occasioned by the poor road in 
drawing 1600 bus. of potatoes to market (1 bu. = 60 lbs.)? 
How much is the loss at #3.50 a day? 

98. If 3 forty-quart cans of milk containing 3 % of but- 
ter fat bring 6| cts. a quart, for what should 6 sixty-five- 
quart cans of 4 % milk sell ? 

99. Grafting wax is made of: resin 5 ozs., beeswax 
5 ozs., tallow 3 ozs. State the composition in per cents. 

100. If 12 % of the stalks of a corn-field -producing 63 
bus. per acre are barren, how many bushels are lost 
through barren stalks? 



34i 



PRACTICAL ARITHMETIC 



101. What is the weight of a 40 bu. wheat crop on au 
acre if the grain weighs 2400 lbs. and the straw weighs 
3600 lbs. ? What per cent of the total crop is grain? 

102. The following amounts of water expressed as 
inches in depth are required to mature wheat crops of 
the following yields : 15 bus. to the acre require 4.498 
ins. ; 20 bus. require 5.998 ins.; 25 bus., 7.497 ins.; 30 
bus., 8.997 ins. ; 35 bus., 10.495 ins. ; 40 bus., 12 ins. An 
acre of water 1 in. deep weighs 226,584 lbs. How many 
more pounds are -required to raise a 35-bu. crop than a 
15-bu. crop? A 20-bu. crop than a 15-bu. crop? A 40-bu. 
crop than a 15-bu. crop? Make other similar problems 
from the data given. 

A Week's Food foe Two Persons 



Meats 

2 lbs. flank of beef 
1 lb. pickled tongue 
\ lb. salt pork 

\ lb. bacon . . . 

3 lbs. veal cutlet . 
1 lb. fresh fish . . 



Cfroceries and Milk 
qts. milk 



2 lbs. butter .... 
1 doz. eggs .... 
|- lb. of coffee . , . 

^ lb. tea 

6 lbs. flour .... 

lbs. corn meal and 2 

lbs. oatmeal . . 



Cost 

06^ 
08^ 
24^ 
18^ 



40/ 

20/ 
08/ 
08/ 
23/ 

20/ 



Groceries and Milk 

2 lbs. sugar . . 
baking powder . 
seasoning . . 

3 lbs. bananas . 
5 lbs. apples 

Vegetables 
potatoes 1 pk. (15 lbs.) 
cabbage 2 lbs. . . . 
lettuce ^ lb 



Cost 
16/ 
05/ 
10/ 
15/ 
10/ 

15/ 
08/ 
05/ 

peas 1 lb 16/ 

string beans 1 lb. . . . 05/ 

turnips 5 lbs 05/ 

squash 5 lbs 08/ 

2 lbs. dried beans . . . 10/ 
2 lbs. canned tomatoes . 12/ 



MISCELLANEOUS REVIEW PROBL-EMS 348 

103. Find the total cost of supplies for a week. 

104. At the same rate what will the food cost for the 
. year ? 

105. If the food costs ^ of the income, what is the 
income ? 

106. Find the amount of digestible protein in the meat 
and fish consumed. (For data consult tables on pages 
272 and 273.) 

107. Find the amount of digestible protein in the 
vegetables. Find the amount of digestible protein in the 
groceries and milk. 

108. Digestible fats in meat and fish. 

109. Digestible carbohydrates and fats in groceries. 

110. Digestible carbohydrates and fats in vegetables. 

111. If in one day a man requires 100 grams of protein, 
60 grams of fats, and 400 grams of carbohydrates, and a 
woman requires 90 grams of protein, 40 grams of fats, and 
350 grams of carbohydrates, how much does the diet for 
a week exceed or fall short of this standard ? (See 
preceding page.) 

112. The cost of spraying cantaloupes being |4.47 an 
acre per season, what is the cost for 12 A. ? 

113. The net profit from spraying one acre of cucumbers 
on Long Island being 1163.50, what would be the profit 
at the same rate from spraying 14 acres? 

114. The net profit from spraying an average-sized tree 
from 12 to 20 years old throughout one season at a total 
cost of 50 cts. is from 13 to 17. When apples are worth 
11 per bushel, what are the highest and the lowest per 
cents realized upon the investment? 



344 



PRACTICAL ARITHMETIC 



115. Sprayed and iinsprayed apple trees yielding as is 
shown in tlie table below, what is the total yield of the 6 
sprayed and the 3 unsprayed trees, in bushels, in sound 
apples and in diseased apples? 



Date of Spraying and Tree Numher 



Trees sprayed July 10 and 26 and Aug, 9 : 

No. 1 

No. 2 

No. 3 

No. 4 

No. 5 

No. 6 

Trees not sprayed : 

A 

B 

C 



Biixli els 

15.76 
18.26 
18.76 
10.26 
1-3.76 
24.50 

5.875 

9.35 

5.875 



Sound 
Apples 



1278 
1.563 
1526 
749 
1394 
2164 

3 

135 

50 



Diseased 
Apples 



Number 

144 
253 
163 
103 
17 
309 

1276 
1670 
1298 



116. The population of several American and foreign 
cities for two decades is shown in the following table. 
What was the per cent of increase in each city ? Was the 
average increase greater abroad or in the United States ? 





ISTO 


1890 


New York .... 


950,000 


1,51.5,.301 


Berlin . . 










800,000 


1,576,794 


Hamburg . 










348,000 


562,260 


Boston . . 










342,000 


448,000 


Cologne ,. 










144,800 


287,800 


Buffalo . . 










155,000 


2.55,600 


Magdeburg 










97,500 


202,000 


jNIihvaukee 










116,000 


205,000 . 



MISCELLANEOUS REVIEW PROBLEMS 



345 



117. The population of the United States in 1790 was 
3;928,037 ; in 1800, 5,308,937 ; in 1810, 7,239,814 ; in 1820, 
9,638,191; in 1830, 12,860,702; in 1840, 17,017,788; in 
1850, 23,151,876 ; in 1860, 31,335,120 ; in 1870, 38,784,597; 
in 1880, 50,152,866; in 1890, 62,622,260 ; in 1900, 76,059,- 
000. What was the increase in popuhition the first decade 
given? The second? The third? For each succeeding 
decade? 

118. What was the increase from 1800 to 1900? How 
mach greater was the increase during the last decade than 
was the total population of 1790? Than of 1820? 

119. According to the twelfth census the working popu- 
lation of the United States was engaged as follows : 



Pursuit 


Nr.MBER 


Pee cknt of 
Total Population 


Agricultural pursuits 

Professional sei-vine 

Domestic service 

Trade and transportation .... 
Manufacturing and mechanics . . 


10,438,219 
1,264,735 
5,691,746 
4,778,233 

7,112,987 














Total 











What per cent of the total working population was en- 
gaged in each pursuit? 

120. The number of agricultural college students in the 
same year was 5035. What per cent was this of the num- 
ber engaged in agricultural pursuits? 

121. According to the census of 1899, 93 % of the people 
of the United States lived on annual incomes of $400 for 
three persons in a family. According to ■ statistics each 



346 PRACTICAL ARITHMETIC 

member of the average Pennsylvania farmer's family re- 
ceives 1198.26 yearly. What per cent above the average 
income do these farmers receive? 

122. In 1820, of the people engaged in commerce, manu- 
facturing, and agriculture, | were engaged in agriculture. 
In 1900, |- were engaged in agriculture. What fraction 
less was there iia agriculture in 1900 than in 1820? 

123. In 1870 for every 1000 persons engaged in agri- 
culture there were 1112 engaged in other pursuits : in 
1900 for every 1000 in agriculture there were 1806 in 
other pursuits. Show these relations by lines, letting | 
in. represent 100 people. 

124. The average value of farms in the United States 
in 1900 was: total value 13574, buildings 1620, imple- 
ments and machinery $133, live stock $536. What per 
cent of the value of the land is each of the three other 
items given? 

125. For each $1000 of total investment, how many dol- 
lars are invested in each of the other three items given? 

126. For each f 1000 invested in land, how much is in- 
vested in each of the other three items? 

127. If 1200 cu. ins. of air is rendered unfit for breath- 
ing by one person in one minute, what volume of air will 
be required to last 100 persons an hour? 

128. When the air is taken into the lungs (inspired), it 
contains 20.81% oxygen, 79.15% nitrogen, .04% carbon 
dioxide ; when it comes out of the lungs (expired), it has 
16.035% oxygen, 79.557% nitrogen, and the balance is 
carbon dioxide. What per cent of the oxygen is retained 



MISCELLANEOUS REVIEW PROBLEMS 



347 



in the body, and what per cent of carbon dioxide has been 
added ? 

129. If the following be the pulse rate and rate of 
breathing per minute, what per cent is the rate of breath- 
ing of the pulse rate for each animal? 



Man . 
Horse 
Cow . 
Sheep 
Dog . 




Kespiration 

16 
12 
15 
14 
16 



130. Compare the number of heart-beats of a man for 
one day with that of a horse and a cow. Compare horse 
with cow. Cow with sheep. Sheep with dog. 

131. If the pulse (heart-beat) of a horse is 38 per min- 
ute, and that of a mule 46, and both are increased 50 % 
by disease, what will then be the pulse rate of each ? 

132. If the body temperatures of five horses are as fol- 
lows, what is the average body temperature ? 



7 a.m. 



12 m. 



(1) 98.9° 

(2) 99.6° 

(3) 99.4° 

(4) 98.8° 

(5) 100. 1° 

133. If the body temperatures of five cows were taken 
as follows, what was the average temperature ? 

8 a.m. 12 m. 6 p.m. 

(1) 100.5° 100.8° 100.9° 



99.3° 


99.7° 


100° 


100.3° 


99.8° 


100.4° 


99.6° 


100.1° 


100.3° 


100.7° 



318 PEACTICAL AKITHMETIC 



(2) 99.8° 


100.7° 


101.2° 


(3) 101.2° 


101.1° 


101.4° 


(1) 100.8° 


101.2° 


101.8° 


(5) 100.9° 


101.3° 


101.6° 



134. A horse does its best woi'k at 2J mis. per hour, 
pulling 150 lbs. It requires a pull of 8 lbs. to move 2000 
lbs. on a level road on iron rails, 33 lbs. on a good pave- 
ment, 41 lbs. on a plank road, 65 lbs. on a macademized 
road, 150 lbs. on gravel, 237 lbs. on an ordinary road, 
and 457 lbs. on a loose, sandy road. How heavy a load 
should be given a two-horse team on each of the above 
roads to have the team do its best work ? 

135. A horse working 10 hrs. per day, and travelling at 
4 mis. per hour, pulls about 63 lbs. 'How heavy a load 
should it have on each of the above roads at this rate ? 

136. It is estimated that a poor road costs a farmer 
about $15 a year for each horse. What is his loss in this 
way if he keeps 5 horses ? 

137. With hay at $15 per ton, wheat at 75 cts. a bushel, 
pork at 5 cts. a pound, and butter at 25 cts. a pound, what 
is the value of each per ton ? If it costs $ 2.50 a ton to 
market produce, what per cent of the value of each of 
these is consumed by the cost of marketing? 

138. If a man spends f of a day worth 11.60 in market- 
ing |- of a cord of wood worth $2.85 per cord, what is the 
per cent of value consumed in marketing ? 

139. If cotton-seed is 54% as valuable for fertilizer as 
cotton-seed meal, and it costs i 2 a ton to haul the seed to 
market and haul the equivalent in meal back to the farm, 
how much meal should a farmer receive for 5 tons of seed. 



MISCELLANEOUS REVIEW PROBLEMS 349 

when meal is worth $28 a ton, to justify him in exchang- 
ing seed for meal ? 

140. If the fare of 4 people, 96 mis., is 18.64, what will 
be the fare of 12 people, 48 mis.? What will be the fare 
of 8 people, with 4 chiklren Q fare), going 72 mis.? 

141. If a pay-roll for 9 employees for 6 days is 172, 
how much is the pay roll for 15 employees for 9 days ? 

142. If it takes 8 boys, working 8 hrs. a day, 12 days to 
make a tennis court, how long will it take 50 boys work- 
ing 2 hrs. daily ? 

143. If 20 men can do a certain piece of work in 7 days 
of 8 hrs. each, how many men will be required to accom- 
plish the same work in 12 days of 7 hrs. each? 

144. If a grain bin 4-|- x 9 x 4 ft. holds 1262 bus. of 
wheat, how many bushels will a bin 4^ x 15 x 6 ft. hold? 

145. A truck grower ships 18 baskets of beans and 27 
crates of strawberries. The freight is 40 cts. a basket 
on the beans and the refrigerator charges 75 cts. a crate 
on the berries. The beans sell for $1.35 a basket and 
the berries for f 2.87-^- a crate. How much will the grower 
receive for his shipment if a commission of 8| % is charged 
for selling? 

146. If at the Chicago stock-yards the usual charge 
for selling beef cattle is 50 cts. a head, what is the per 
cent of commission on 25 head of cattle weighing 1325 
lbs. each and selling for 5.75 cts. a pound ? 

147. What will two cattle weighing 1225 lbs. each bring 
at i 5| per hundredweight ? 

148. A farmer makes the following exchange with his 



350 PRACTICAL ARITHMETIC 

grocer: he gives 27^ lbs. butter at 221 cts a pound, 
15| doz. eggs at 17-| cts. a dozen, and 3J bus. potatoes at 
45 cts. a bushel, and receives 20 lbs. sugar at 5J cts. a 
pound, 3 lbs. cheese at 13-| cts. a pound, and the balance 
in cash. How much cash does he receive ? 

149. If 10 lbs. of corn and 2 lbs. of cotton-seed meal a 
day for each horse may be substituted for 14 lbs. of corn, 
what will be the saving in a year on a farm where 15 
horses are being fed, if corn is worth 50 cts. a bushel and 
cotton-seed meal 1 28 a ton ? 

150. If a 10-acre field of corn can be cut, shocked, and 
shredded for $4 an acre and" yields 2960 lbs. of stover 
per acre, what is the value of the stover over the cost of 
harvesting the corn, if a ton of stover is worth 1200 lbs. 
of grass hay valued at $10 a ton? 

151. If the following items represent the cost of pro- 
ducing an acre of potatoes, what will be the profit per 
acre on a yield of 235 bus. worth 47 cts. per bushel ? 
Cost of seed $3,939, plowing $1,607, dragging 92 cts., 
planting 60 cts., cultivating $1.709,. hoeing $2,865, 
spraying $3.60, digging $4.35, wear of machinery $21.24, 
and rent of land $5.00. 

152. In Minnesota it costs as follows to cultivate an 
acre of corn : manuring 57,6 cts., seed 21.3 cts., shelling 
seed 2.3 cts., plowing $1,205, dragging 48 cts., planting 
22.5 cts., cultivating $1,619, cutting 66.5 cts., shock- 
ing 52.6 cts., twine 46.7 cts., picking up ears 24.9 cts., 
shredding $3,794, wear of machinery $1,202, rent of land 
$3.50. What is the profit on 40 acres yielding 53 bus. 
per acre at 42 cts. a bushel, and 2964 lbs. of shredded 



MISCELLANEOUS REVIEW PROBLEMS 351 

stover at 13.00 per ton? What is the profit on one 
acre? 

153. If an acre of clay soil 1 ft. deep contains 6.38 
tons of potash and grows a crop of 40 bus. of wheat hav- 
ing a ratio of weight between grain and straw of 2 : 3, 
how many such crops would it take to contain as much 
potash as there is in the soil if 1000 lbs. of wheat contain 
6.3 lbs. of potash and 1000 lbs. wheat straw 5.2 lbs. ? 

154. The average number of marketable potatoes from 
each " seed " piece of several varieties was : variety No. 
1, 3.14 potatoes, No. 2, 3.03 potatoes, No. 3, 3.28 potatoes. 
No. 4, 3.29 potatoes, No. 5, 3.48 potatoes. No. 6, 1.91 po- 
tatoes, No. 7, 1.7 potatoes. What was the average num- 
ber of potatoes per seed piece of all of these varieties ? 
By what per cent did the best exceed the poorest ? By 
what per cent did the best exceed the average ? 

155. In Virginia the Burbank potato yielded 230 bus. 
of marketable potatoes per acre, the Crown Jewel 197 bus. 
What would be the difference in value of yield on 40 
acres of each of these two varieties at 55 cts. per bushel ? 

156. Of 67 hens tested for egg laying ability for two 
years, 10 laid more eggs the second year than the first 
year, and 57 laid fewer eggs the second year. What per 
cent laid more the second year ? What per cent laid fewer 
the second year ? 

157. A 10-acre field continuously in corn yielded 357 
bus. When crimson clover was used in a rotation, the 
yield the year following the clover was 551 bus. What 
was the per cent of increase in value with corn at 48 cts. 
per bushel ? What was the per cent of increase in bushels ? 



352 PRACTICAL ARITHMETIC 

158. I buy a bill of hardware on which the list price 
is $134. The discounts are 25%, 10%, and 5%. How 
much do I have to pay? 

159. If I bu}- a bill of groceries on which there is a 
discount of 15% and 5% for cash, how much must I 
pay? 

160. I am offered a quantity of tile for $390 with dis- 
counts of 20 % and 5 % off for cash. A second firm offers 
me the tile at the same price with a discount of 15 % and 
10% off for cash. From which firm shall I buy? Why? 

161. A farmer sold a team of horses for i| 350 on 1 year's 
time. He refused an offer of §325 cash. Did he gain or 
lose, and how much, by selling on time, money being 
worth 6%? 

162. A feed merchant mixed 62 bus. of oats at 34 cts. a 
bushel, 1200 lbs. of wheat bran at 118 a ton, 35 bus. of 
corn at 43 cts. a bushel, and 700 lbs. of cotton-seed meal at 
§28 a ton. How much must he charge per 100 lbs. in 
order to make a profit of 20 % after giving a toll of 6 % 
by weight for grinding the oats and 5 % for grinding the 
corn ? 

163. If when corn is cut and cured in the shock the 
loss in dry matter is 31%, and when put into the silo 
11 %, what is the total gain in dry matter by putting 
the corn from 10 A., weighing 12 T. per acre, into a 
silo, if, when ready for cutting, corn contains 73.2% of 
water? How much is the dry matter saved worth if silage 
containing 79.1 % water has a feeding value of $3 per ton? 

164. If I buy corn at 42 cts. a bushel on 3 months' time 
at 6 % interest, and the shrinkage in the weight of the corn 



MISCELLANEOUS REVIEW PROBLEMS 353 

is 10 %, at what price must I sell at the end of 3 months 
to make 20 % on the transaction ? 

165. The interest on a mortgage for 1320 at 8% for 
one year is collected by an agent who receives 10 % com- 
mission for collecting. What does he receive? What 
per cent is his commission of the principal? 

166. A farmer has 1350 bus. of corn for which he is 
offered 37 cts. a bushel on December 1. He keeps it until 
March 1 and sells it for 43^ cts. a bushel. Did he make or 
lose by holding the corn if it lost 8 % in weight, and 
money was worth 8 % interest ? 

167. If the farmer makes 12^% profit on his wheat, the 
miller charges 20 % for grinding it into flour, and the 
grocer receives 10 % for selling a barrel of the flour for 
$5.65, what did it cost the farmer to produce the wheat 
required to make a barrel of flour? \ 

168. A man pays 197 taxes on $9682. What is the 
rate ? 

169. What are the taxes on $19,862, the rate being 
.00971? 

170. A town raises $6859 on property assessed at 
$684,936, there being 428 polls at $1.67 each. What 
will be the rate ? 

171. A town having 248 polls, property valuation 
$868,730, raises $6482.94 taxes. What is the rate? 

172. A note for $1575 dated April 9, 1903 was in- 
dorsed as follows: Oct. 15, 1909, $115; July 27, 1904, 
$135; Jan. 21, 1905, $325. What amount was due 
April 9, 1906 at 6% interest? 



354 PRACTICAL ARITHMETIC 

173. What must I pay, Sept. 17, 1907, to take up my 
note for |268 given Jan. 25, 1905, at 8% interest? 

174. A note dated Aug. 24, 1907, secured by a mort- 
gage, is given for 1400 at 8 % interest, but the money is 
not procured until Oct. 9, 1907. What should be the 
amount deducted from the first half-yearly interest be- 
cause of the delay in delivering the money? 

175. What are the taxes on 17682 of real and 12986 
of personal property valued at f, rate .9% ? 

176. A man takes out life insurance for 13500 at 30 
years of age for f 19.06 a year per thousand, and pays for 
20 years. If he lives to 76 years of age and money is 
worth 6%, what has his protection cost over and above 
the $3500 which his estate receives? 

177. If a farmer living 15 miles from market makes a 
trip costing $2.50 in time, to deliver 50 lbs. of butter at 
25 cts. a pound, what per cent of his receipts is consumed 
in cost of marketing ? 

178. If he delivers 650 lbs. instead, at a cost of $3 
for time, what per cent of the receipts is the cost of mar- 
keting? By what per cent is the cost of marketing re- 
duced in the second instance ? 

179. If it costs a strawberry grower living 5 miles 
from market 12 in time to deliver a 32-qt. crate of 
berries at 11^ cts. per quart, what per cent of the value 
of the crate is consumed in marketing? 

180. If he markets 20 crates at a cost of |3 in time, 
what per cent is so consumed ? 

181. If it costs the Vermont farmer $1.93 to haul 



MISCELLANEOUS REVIEW PROBLEMS 355 

2321 lbs. of potatoes 7.1 miles, and the Connecticut farmer 
$2.80 to haul 2500 lbs. of potatoes 6.7 miles, how much 
more will it cost the Connecticut farmer to haul the crop 
on 9 A. yielding 268 bus. per acre 5 mis. to market than 
it would the Vermont farmer to haul a similar crop the 
same distance? How much more per acre? 

182. If it costs $2.11 to haul 3020 lbs. of corn 6.6 miles 
in Pennsylvania and $2.76 to haul 1553 lbs. of corn 11.8 
mis. in Georgia, how much more will it cost the Georgia 
farmer to haul the corn from 25 A., averaging 32 bus. 
per acre, 9 miles to market, than it will a Pennsylvania 
farmer to haul a similar crop the same distance ? 

183. If it costs 6 cts. to haul 100 lbs. of corn 6 miles to 
market in Ohio, and 30 cts. to haul 150 lbs. of corn 13 miles 
to market in Arkansas, the difference being due to better 
roads and larger horses in Ohio, what is the gain per acre, 
from good roads and large horses, to the Ohio farmer living 
7 mis. from market on a crop of 42 bus. per acre ? If this 
gain is taken to represent interest at 6 % on the increased 
value of the land, what is the increase in the value of 
the land per acre? 

184. A dairyman has 2000 lbs. of milk containing 4 % 
of butter fat. From 1000 lbs. of this he skims the cream 
by the gravity settling method, which loses in the skim 
milk 20 % of all the butter fat. The butter fat that he 
does recover in this way he sells for 20 cts. per pound. 
He separates the cream from the other 1000 lbs. of milk 
with the centrifugal cream separator, which loses in the 
skim milk 2 % of all the butter fat. The butter fat he 
obtains in this way, on account of the superior quality. 



356 PRACTICAL ARITHMETIC 

he sells at 25 cts. per pound. How much greater was his 
profit on the 1000 lbs. of milk skimmed by the separator 
than on the 1000 lbs. skimmed by the gravity system? 

185. If 70 gals, of milk containing 5 % of butter fat are 
worth $28, what is the value of 100 gallons of milk con- 
taining 3.5% of butter fat? 

186. If milk containing 5 9^ of butter fat is worth 10 
cts. a quart, what is milk containing 3.5% of butter fat 
worth ? 

187. I have 1000 lbs. of milk containing 3.5 % of butter 
fat. How much cream containing 25 % of butter fat must 
I add to bring it up to a 4 % butter fat standard? If I 
have no cream to add, how much skim milk containing 
no butter fat must I remove to bring it up to the standard 
of 4 % butter fat? 

188. I have 1000 lbs. of 4.5 % milk and wish to reduce 
it to a 4% standard. How much skim milk must I add? 
If I have no skim milk to add, how much 25 % cream 
can I take out of it ? 

189. I wish to mix cream containing 35 % of butter fat 
and milk containing 5 % of butter fat, so as to produce 
140 lbs. of cream containing 25 % of butter fat. How 
many pounds of each must I use in the mixture?- . 

190. I wish to obtain 200 lbs. of milk containing 4% 
of butter fat from two lots of milk, one testing 3.8% of 
butter fat and the other 4.9% of butter fat. How maily 
pounds of each must I use? 

191. If cream containing 20 % of butter fat is worth 60 
cts. per gallon, what is cream worth which contains 25 % 
of butter fat ? 



MISCELLANEOUS REVIEW PROBLEMS 357 

192. What is the price per pound of butter fat if cream 
containing 20 % of butter fat and weiy:liing 8.3 lbs. sells 
for 50 cts. a gallon ? At 32 cts. per pound of butter fat, 
what would be the price per gallon of cream containing 
27 % of butter fat ? Of cream containing 25 % of butter 
fat? 20 % of butter fat? 15 % of butter fat? 

193. If 5 qts. of milk containing 3.5% of butter fat 
have an energy value as food of 3066 calories, and 1 pound 
of rpund beefsteak has an energy value of 841 calories, 
what should round steak sell for per pound Avhen milk 
is worth 8 cts. a quart? 5 cts. per quart? 10 cts. per 
quart? 

194. A dairyman has 1000 lbs. of milk containing 5 "Jo 
of butter fat. 500 lbs. of this he skims with the gravity 
process, and obtains a 20 % cream. He, however, loses 
in the skim milk 25 % of the butter fat. This skim milk 
he sells at 15 cts. per 100 lbs. From the remaining 500 
lbs. of milk he separates the cream with the centrifugal 
separator, making a 50 % cream and losing but 1 % of the 
butter fat in the skim milk. On account of its being 
fresh and pure from the separator he sells this skim milk 
for 25 cts. per 100 lbs. How much more did the dairy- 
man receive from his separator skim milk than from the 
skim milk left from the gravity skimming process? 

195. The maximum amounts of fertilizer removed by 
various forms of farm produce is shown in the following 
table. Placing nitrogen at 18 cts. a pound, phosphoric 
acid at 6 cts., and potash at 5 cts., find the value of each 
of these fertilizers removed in each crop given in the 
table. 



358 



PRACTICAL ARITHMETIC 



Produce 



Pounds op 



Kind 



Nitrogen 



Phosphoric 
Acid 



Potash 



Corn, grain . . . 

Corn stover . . . 

Oats, grain . . . 
Oat straw .... 

AVheat, grain . . 

Wheat, straw . . 

Timothy hay . . . 

Clover seed . . . 

Clover hay . . . 

Cow-pea hay . . . 

Alfalfa hay . . . 

Apples 

Apple leaves . . . 
Apple wood growth 

Potatoes . . . . 
Sugar beets . . . 

Fat cattle . . . . 
Fat hogs . . . . 

Milk 

Butter 

Cotton lint . . . 



100 bus. 

3 T. 
100 bus. 

2^T. 
50 bus. 
2iT. 
3T. 

4 bus. 
4T. 
8T. 
8T. 

600 bus. 

4T. 

^tree 

300 bus. 
20 T. 

1000 lbs. 
1000 lbs. 

10,000 lbs. 
500 lbs. 

500 lbs. 



100 

48 

66 

31 

71 

25 

72 

7 

160 

130 

400 

47 
59 



63 
100 

25 

18 

57 
1 

1.7 



17 
6 

11 

5 

12 

4 

9 

2 

20 

14 

36 

5 
7 
2 

13 
18 

7 
3 

7 
0.2 

.5 



19 
52 
16 
52 
13 
35 
71 
3 

120 
98 

192 

57 

47 

5 

90 
157 

1 
1 

12 
0.1 

2.3 



196. Of 4402 samples of commercial fertilizer analyzed 
in Indiana from 1902 to 1907, 3158 were equal in value to 
that guaranteed, 323 were not within 10 % of such value, 
and 835 were with one or more of the ingredients 20 % 
below the guaranteed value. What per cent was equal 
to the guaranteed value ? 



MISCELLANEOUS REVIEW PROBLEMS 



359 



197. What per cent was not within 10% of value? 
What per cent fell in the last class named ? 

TABLE OF ANALYSIS OF FERTILIZERS IN INDIANA 



Class 



1901 



1904 



1905 



190T 



1. Number of samples collected .... 

2. Number equal to guarantee in every 

particular 

3. Number equal to guarantee in value 

4. Number within 10% of guarantee . . 

5. Number not within 10% of guarantee . 

6. Number with one ingredient or more 

20% below guarantee 

7. Number with one ingredient or more 

30% below guarantee 

8. Number with one ingredient or more 

50% below guarantee 



592 

281 

469 

85 

38 

103 



679 

335 

564 

93 

22 

112 



674 

286 

492 

139 

43 

138 



648 

248 
451 
148 

44 

132 
65 
21 



734 

812 

528 
158 

48 

148 
77 
21 



879 

374 

642 

176 

61 

136 

64 

25 



793 

265 

481 
210 
102 

177 

75 

29 



What per cent of all samples analyzed in each year fell 
in class 2 ? In class 3 ? In class 4 ? In class 5 ? In class 6 ? 
In class 7 ? 

198. The upper 6 ins. of soil weighs per acre 1,370,000 
lbs. If the surface is cultivated thoroughly, it may contain 
14.21% of moisture; if poorly cultivated, only 8.02%. 
What will be the total amount of Avater in the soil under 
poor cultivation? Under good cultivation? Obtain the 
last answer by two different processes. 

199. In Minnesota it was found that during 10 yrs. 
of exclusive grain farming the per cent of nitrogen in a 
soil had decreased from .601 % to .523%. If the soil to 
a depth of 8 ins. per acre weighs 1282 T., how much 
nitrogen was lost from the soil ? 



360 PRACTICAL ARITHMETIC 

200. How much nitrogen will 30 bus. of wheat per acre 
annually take from the soil in 10 yrs., if 1 bu. of wheat 
takes .625 lb. nitrogen from the soil? 

201. What per cent of the total nitrogen lost from the 
soil of problem 199 in the 10 yrs. would be taken out by 
wheat as in the preceding problem? 

202. After 10 yrs. under a system of mixed farming, 
including rotation of crops, the growing of legumes, and 
live-stock husbandry, in another field, the nitrogen in the 
soil had decreased only from .31% to .309%. If the soil 
to a depth of 8 ins. weighs 58.9 lbs. per square foot of sur- 
face, how many pounds less nitrogen did this field contain 
after 10 yrs. ? What was the difference in the loss of 
nitrogen per acre from this field and that of problem 199 
in the 10 yrs. ? 

203. If it costs $29.52 to raise an acre of white pine 
to 40 yrs. of age, and it yields on the stump $4 per cord, 
what is the profit on 40 cords of box-board timber ? 

204. In 1871 a strip of forest land 40 mis. wide and 180 
mis. long was devastated by fire. The loss is estimated at 
4,000,000,000 board feet worth 110,000,000. What was 
the loss per square mile in board feet ? In dollars ? 

205. If one toad destroys in 30 days 720 cutworms, 
600 thousand-legged Avorms, 720 sow-bugs, 1080 ants, 120 
weevils, 120 ground beetles, how ;-^any of each of these 
would 19 toads destroy? How many in a week? In 3 
months ? Many gardeners pay their children for killing 
cutworms at the rate of a penny each. What would 19 
toads earn in a month at this rate ? In 3 months ? 

206. Two boys were known to kill 19 toads. What 



MISCELLANEOUS REVIEW PROBLEMS 



361 



was the loss in 3 mos., even if it required 19 toads to do 
what it was shown one could do in the last problem? 

207. Corn at different stages of growth contains dry 
matter (useful) and water as follows, expressed in tons: 



Fully tasselled 

Fully silked 

Kernels watery to full milk 

Kernels glazed 

Ripe 



Corn 

I'KR ACKR 



9 
12.9 
16.3 
16.1 
14.2 



Watbr 

I' Kit ACKK 



8.2 
11.3 
14 
12.5 
10.2 



Dry Matteu 
PER Acre 



Complete column of dry matter. What per cent of water 
and what per cent of dry matter are there at these different 
periods? 

208. If a good clay soil contains 12,760 lbs. of potash 
per acre one foot deep, and a 40-bu. crop of wheat uses 
35.1 lbs. of potash, how many crops will it take to use 
potash equal to that in the clay soil? 

209. If, with the same field conditions, one variety of 
corn yields 7 bus. per acre more than another variety, 
what will be the gain in planting the better variety on 
96 acres, if the poor seed costs 60 cts. per bushel and the 
seed of the better variety $2.50 per bushel ? Allow 1 bu. 
of seed corn to every eight acres planted and value the 
corn of the crop at 49 cts. per bushel. 

210. Eight bushels of clover seed containing 3 bus. of 
dead seed were bought at I 3.50 per bushel. What was 
the price paid for the live seed? 

211. Fifteen bushels of clover seed containing 1 bu. of 



362 PRACTICAL ARITHMETIC 

dead seed were bought at 15.50 a bushel. What was 
the price paid for the live seed ? 

212. A variety of flax, improved by seed selection, 
yields, on an average, 2.2 bus. per acre better than the 
best common varieties, which yield 15 bus. What is the 
per cent increase due to seed selection ? 

213. If it takes 6|- hrs. to test 9 bus. of seed corn for 
germinating power, how long will it take to test seed 
enough for 600 A., allowing 1 bu. to each 5 A. ? 

214. A pound of cotton can be spun into 168 spools of 
No. 40 sewing thi-ead, 200 yards to the spool. How 
many yards of thread can be spun ? 

215. A much finer thread can be made, of which the 
number of j^ards in the last problem equals -f^. How 
many miles of this fine thread can be made from a pound 
of cotton ? 

216. A still finer thread can be made, of which the 
number of yards in problem 214 equals only ^-J j. How 
many miles of this quality of thread can be made from a 
pound of cotton ? 

217. From one pound of cotton can be made 4 yards 
of bleached muslin worth 8 cts. a yard. What amount 
of lawn can be made from the same amount of cotton if, 
for every yard of bleached muslin, 2\ yards of lawn may 
be made ? The value of the bleached muslin is -^^ of the 
value of the lawn. What is the value of the lawn ? 

218. Four yards of sheeting can be made from a pound 
of cotton with a value equal to | the value of the bleached 
muslin. What is the value of the sheeting ? 



MISCELLANEOUS REVIEW PROBLEMS 363 

219. The number of handkerchiefs that can be made 
from a pound of cotton is ^f- of the number of yards of 
calico that can be made. If the number of yards of calico 
is -J of the number of yards of bleached muslin and the 
price of the calico is ^| of the price of the sheeting, how 
many yards of calico can be made ? What is the value 
per yard ? How many handkerchiefs can be made ? 
What is the value of each, if one handkerchief equals | 
the value of a yard of lawn ? 

220. The value of the denim that can be made from a 
pound of cotton bears the same ratio to the value of 
gingham as the number of yards of lawn to the number 
of handkerchiefs. \ as many yards of denim as gingham 
can be made. With gingham worth 7| cts. a yard, what 
is the denim worth per yard? 

221. Arrange in tabulated form the products of a 
pound of cotton from the smallest quantity of material 
at lowest price to the most valuable product here con- 
sidered, 

222. An untreated loblolly pine fence post, set, costs 
about 14 cts. It lasts about 2 yrs. Compounding the 
interest at 5 per cent, what is the annual cost of such a 
post? If a preservative treatment, which costs 10 cts., in- 
creases the length of use of the post to 18 yrs., what 
is then the total cost of a post, set? What does this 
amount to annually, compounded as above ? What is the 
saving due to treatment per year ? Assuming that there 
are 200 posts to a mile of fence, what is the saving each 
year for a mile ? This is the interest on what amount at 
5 per cent? 



364 



PRACTICAL ARITHMETIC 



223. The accompanying table shows the production in 
thousand feet of the leading kinds of lumber for 3 yrs. 
What was the total production for each year ? What was 
the per cent of increase or decrease of each kind from 
1899 to 1906? What the total per cent of increase or 
decrease ? 



Yellow pine 

Douglas fir 

White and Norway pine 

Hemlock 

Oak 

Spruce 

Western pine .... 

Maple 

Cypress 

Poplar 

Redwood 

Red gum 

Chestnut 

Basswood 

Birch 

Cedar 

Beech 

Cottonwood .... 

Elm 

Ash 

All others 



Mfeet 

9,658,923 

1,736,507 

7,742,391. 

3,420,673 

4,438,027 

1,448,091 

944,185 

633,466 

495,836 

1,115,242 

360,167 

285,417 

206,688 

308,069 

132,601 

232,978 

415,124 
456,731 
269,120 
486,848 



Mfeet 

11,533,070 

2,928,409 

5,332,704 

3,268,787 

2,902,855 

1,303,886 

1,279,237 

587,558 

749,592 

853,554 

519,267 

523,990 

243,537 

228.041 

224,009 

223,035 

321,574 
258,330 
169,178 
684,526 



1906 



Mfeet 

11,661,077 

4,969,843 

4,583,727 

3,537,329 

2,820,393 

1,644,987 

1,386,777 

882,878 

839,276 

683,132 

659,678 

453,678 

407,379 

376,838 

370,432 

357,845 

275,661 

263,996 

224,795 

214,460 

936,555 



224. A tree weighing 10,000 lbs. when dry is 50 per 
cent carbon. How many pounds of carbon are there in 
the tree? 



MISCELLANEOUS KEVIEW PROBLEMS 365 

225. Carbon dioxide being ^\ carbon, and all the carbon 
of the tree being derived from carbon dioxide, how many 
pounds of carbon dioxide are required to furnish the 
carbon in the tree of the last problem ? 

226. Air being .03^ % carbon dioxide, how many pounds 
of air are required to furnish this amount of carbon 
dioxide ? 

227. Air weighing 31.074 grs. per 100 cu. ins., how 
many cubic yards of air are required to furnish the 
amount of carbon used in the growth of the tree men- 
tioned above ? 

228. There are in the atmosphere of the earth about 
6,000 billion pounds of carbon dioxide. How much carbon 
does it contain? For how many trees like that of prob- 
lem 224 would this suffice ? 

229. An adult exhales daily into the air about 245 g. of 
carbon. Estimating the earth's population at 1400 mil- 
lion, how much carbon is thus restored daily to the air ? 

230. Wood, coal, etc., in burning restore their carbon 
to the air. One manufacturing works thus restores from 
the coal burned about 5,100,000 lbs. of carbon. 

A forest consisting of how many trees like the one men- 
tioned in problem 224 would be raised from this carbon? 

231. One square meter of pumpkin or sunflower leaf in 
a summer day of 15 hrs. makes 25 g. of starch which is 
1^ carbon. How many cubic meters of air are required 
to furnish the requisite carbon ? How long a room 3 m. 
wide and 3 m. high would be required to contain it ? 

232. Convert all the measurements of the last problem 
into English measure, and solve. 



366 PRACTICAL ARITHMETIC 

233. If Alfalfa hay contains 10.44 per cent digestible 
protein, 39.6 per cent carbohydrates, and 1.2 per cent fats, 
and red-clover hay contains 6.8 per cent protein, 35.8 per 
cent carbohydrates, and 1.7 per cent fats, — what is the 
difference in the feeding value of a ton of Alfalfa and a 
ton of red clover, estimating digestible protein at 3 cts. 
a pound, carbohydrates at 1 ct. a pound, and fats at 21 cts. 
a pound ? 

234. On land worth $65 an acre Alfalfa is sowed and 
maintained for 4 yrs. at an expense of 130. The cost of 
harvesting the hay is $1.25 a ton ; the crops are : 1st year 
2.78 tons, 2d 3.15 tons, 3d 4.60 tons, 4th 4.28 tons. 
What is the profit on 9 acres, allowing 10 per cent inter- 
est on the value of the land, $12 a ton for hay, and $3 a 
ton for cost of baling and marketing ? 




APPENDIX 



SURFACES OF SOLIDS 

The surface of a solid except its base or bases is called 
the Lateral Surface. The Entire Surface includes its bases. 

A solid, the base of which is a poly- 
gon and the sides of which are triangles 
meeting at a point or vertex, is called a 
Pyramid. 

The distance from the vertex to the 
side of the base is called the Slant Height. 
If the sides and angles of the pyramid 
are respectively equal and the apex is 
directly over the centre of the base, the pyramid is said 
to be regular. 

The surface of a pyramid, as may be seen, is composed 
of a number of triangles with an altitude equal to the 
slant height of the pyramid and the bases 
forming the perimeter of the solid. 

A solid, the base of which is a circle, and 
the surface of which tapers to a point or ver- 
tex, is called a Cone. 

The lateral surface of a cone may be assumed 
to be made up of a number of infinitely small 
triangles. 

Hence, to find the lateral surface of a pyramid or cone, 
multiply the perimeter of the base by ^ the slant height. 

The portion remaining after a part of the top has been 
cut from a pyramid or cone is called a Frustum of a pyra- 
mid or of a cone. 

The lateral surface of a frustum of a pyramid may be 
regarded as composed of a number of trapezoids, the sum 
of the parallel sides of which forms the perimeter of the 

367 




368 



PRACTICAL ARITHMETIC 




bases and the- slant height of which equals the altitude of 
the frustum. 

The lateral surface of a frustum of a cone 
may be considered as made of a number of 
infinitely narrow trapezoids. 

To find the lateral surface of the frustum 

of a pyramid or of 'a cone, multiply half the 

sum of the perimeters of the two bases by 

the slant height. 

A solid having equal polygons parallel to each other 

for its two ends and parallelograms for its sides is a 

Prism. 

From the form of their bases, prisms 
are triangular, quadrangular, etc. 

The lateral surface of a prism may be 
regarded as a series of parallelograms, 
with their combined bases equal to the 
perimeter of the two bases of the prism 
and a height equal to the altitude of the 
prism. 

To find the lateral surface of a prism, multiply the 
perimeter of the base by the altitude. 




VOLUMES OF SOLIDS 



The volume of a solid is the number of solid units it 
contains. 

To find the volume of a prism, multiply the area of 
the base by the altitude. 

A square prism has three times the 
solid contents of a pyramid. In like 
manner, the cylinder has three times the 
solid contents of the cone. 

To find the volume of a pyramid or 

cone, multiply the area of the base by 

one-third the altitude. 

The frustum of a pyramid or cone is equal to three 

pyramids or cones, the common altitude of which is the 

altitude of the frustum and the bases of which are the 




APPENDIX 



369 




upper base, the lower base, and a mean proportional be- 
tween them. 

Hence, to find the volume of a frustum of a pyramid 
ar cone, add to the sum of the areas of the two ends, the 
square root of the product of these areas, 
and multiply the result by one-third of the 
altitude. 

A solid, bounded by a curved surface, 
every point of which is equally distant from 
the point within, called the centre, is a 
Sphere. 

The Diameter of a sphere passes through the centre and 
terminates at the circumference. 

One-half the diameter is the Radius. The circumfer- 
ence of the circle, the radius of which is the radius of the 

sphere, is the Circumference of 
the sphere. 

The surface of a sphere is 
equal to the square of the di- 
ameter of the sphere multiplied 
by 3.1416. 

A sphere may be regarded as composed of pyramids, 
the bases of which form the surface of the sphere and the 
altitudes of which equal the radius of the sphere. 

Hence, to find the volume of a sphere, multiply the 
surface by one-third the radius, or multiply the cube of 
the diameter by .5236. 




THE EXTRACTION OF THE CUBE ROOT 
Rule. 

1. Beginning at units, separate the number into groups 
of three figures each. 

2. Find the greatest cube contained in the left-hand 
group. Write its cube root as the first figure of the re- 
quired root. 

3. Subtract this cube from the first period, and bring 
down the next period. 

4. Divide the number so found by three times the 



370 



PRACTICAL ARITHMETIC 



square of the root already found, considered as tens, as a 
trial divisor, to find the next figure of the root. 

5. To this trial divisor add three times the product of 
the two parts of the root plus the square of the second 
part of the root, to make the complete divisor. 

6. Multiply the complete divisor by the second figure 
of the root ; subtract and bring down the next period. 

7. Continue in a similar way until all periods have 
been used. 

For example, to find the cube root of 242,970,624, pro- 
ceed according to the rule as follows : 

242'970'624(624 required root 
216 cube of 1st figure of root 



1st trial divisor 10800 

3 X (60 X 2) 360 

2^ 4 

1st complete divisor 11164 

2d ti-ial divisor 1153200 

3 X (620 X 4) 7440 

42 16 

2d complete divisor 1160656 



26970 

22328 product of 2d figure 
of root with 1st com- 
plete divisor. 
4642624 

4642624 product of 3d figure 
of root with 2d 
complete divisor. 



1. Separate into periods. 

2. We find by inspection or trial that the cube of 6 is the 
largest cube contained in the first period, 242. 6 is put down 
as the first figure of the root. 

3. Subtracting the cube of 6, 216, from the first period, 242, 
we have 26 ; bringing down the next period, we have 26,970. 

4. The root already found considered as tens is 60. The 
square of this is 3600; three times this is 10,800, the trial 
divisor. This trial divisor, 10,800, is contained in the dividend, 
26,970, two times. 2 is, therefore, set down as the next figure 
of the root. 

5. The two parts of the root already found are 60 and 2. 
The product of 60 x 2 is 120; three times this is 360. The 
square of the last figure found is 4. Adding 360 plus 4 to the 
trial divisor, we have the complete divisor 11,164. 

6. Multiplying the complete divisor by the second figure of 
the required root and subtracting, we have 4642. Bring down 
the next group, 624, giving 4,642,624 for the next dividend. 

7. Proceeding as before : 



APPENDIX 371 

The root already found is 62 or, considered as tens, is 620. The 
square of this is 384,400. This multiplied by 3 is 1,163,200, 
the trial divisor. This trial divisor is contained 4 times in the 
dividend. 4 is, therefore, set down as the next figure of the 
root. 

The two parts of the root already found are 620 and 4. 
Their product is 2480; three time^ this is 7440. Adding thi.s 
together with the square of the last number of the root, whicih 
is 16, to the trial divisor, we have the complete divisor 1,160,656. 

Multiplying this complete divisor by the last figure found, 
we have 4,64/!,624, completing the problem. 

The cube root of 242,970,624 is 624. 

If the number of vt^hich the cube root is to be extracted 
has decimal places, divide the figures at both sides of the 
decimal point into periods of three figures each, annexing 
ciphers to the last period of the decimal, if need be, to 
give three figures. 

There are as many decimal places in the cube root of 
a decimal as there are periods of three figures each in the 
decimal. 

If the number is not a perfect cube, annex ciphers and 
continue the process to as many decimal places as may 
be desired. 

The cube root of a fraction is found by taking the cube 
root of its numerator and of its denominator, or by reduc- 
ing the fraction to a decimal and then extracting the root. 

PROOF OF THE FUNDAMENTAL PROCESSES BY CAST- 
ING OUT NINES 
Addition. 



Add: 71287 7 

67328 8 

79816 4 

42983 8 

54631 1 

316045 1 



Add. 



To test accuracy of the addition, cast out the nines from 
each row and from the sum, setting down the remainders. 
Thus in the first row drop 7 + 2, 8+ 1, set down 7; second 



372 PRACTICAL ARITHMETIC 

row drop 6 + 3 and 7 + 2, set down 8 ; third row drop 9 and 
8 + 1, add 7 + 6 = 13, "drop 9 from 13, leaving 4, set down 4 ; 
fourth line drop 4 + 2 + 3, drop 9, set down 8 ; fifth line drop 
6 + 4 and 6 + 3, set down 1. Prom sum drop 6 + 3, 5 + 4, set 
down 1. Add the iiumbers set down from the first five num- 
bers, cast out 8 + 1, add 4 + 8 + 7 = 19, cast out 2x9, leav- 
ing 1. The number remaining being 1 in both cases, the work 
is presumably correct. 

Subtraction. 

Subtract: 3726813 3l 

2619832 41 Subtract. 
1106981 ^ sj - 

Cast out the nines from both minuend and subtrahend ; sub- 
tract the number remaining from the subtrahend from that re- 
maining from the minuend, restoring one of the nines cast out, 
if need be, in order to subtract. If the work is correct, the 
number so found should equal the number left after casting 
nines from the remainder. 



Multiplication. 

Multiply : 643 4 

249 6 



I Multiply. 



6787 24 
2572 
1286 
160107 6 

Cast nines from multiplier and multiplicand. Find the prod- 
uct of the numbers remaining, and cast nines from it. The 
number then remaining should equal the number left a,fter 
casting nines from the product. 

ARITHMETICAL PROGRESSION 

An Arithmetical Progression is a. series of numbers which 
increase or decrease by a common and constant difference, 
e.g., 4, 8, 12, 16, 20, 24, etc., the common difference here 
being 4. 

The numbers of the series are called its Terms. 



APPENDIX 373 

To find any term of an arithmetical progression, multi- 
ply the common difference by a number one less than the 
required term; add this product to the first term if the 
series is increasing; subtract this product from the first 
term if the series is decreasing. 

Find the 17th term of the series 7, 14, 21 . 

16x7 = 112. 112+7 = 119. 

Find the 12th term of the series 217, 213, 209 . 

11x4 = 44. 217-44 = 173. 

To find the sum of the terms of an arithmetical progres- 
sion, multiply the number of terms by the sum of the first 
and last terms and divide by two. 

What is the sum of the first 10 terms of the series 
2,4,6 ? 

9 X 2 = 18. 18 + 20 = last term. 

(2 + 20) X 10 = 110 = sum of the terms. 
2 

GEOMETRICAL PROGRESSION 

A Geometrical Progression is a series of numbers in 
which any term is equal to the product of the preceding 
term and a constant factor, e.g., 2, 4, 8, 16, 32, 64 — — . 

To find any term of a geometrical progression, raise the 
constant factor to a power one less than the number of 
the required term, and multiply by the first term. 

Find the 6th term, of the series 1, 2, 4, 8 . 

The constant factor 2 to the fifth power = 32. 
32 X 1 = 32. Ans. 

To find the sum of the terms of a geometrical pro- 
gression, multiply the last term by the constant factor ; 
subtract the first term and divide by the constant factor, 
minus 1. 

Find the sum of the series 1, 2, 4, 8 to and in- 
cluding the 6th term. 

The last term = 32. The constant factor = 2. 

32 X 2 = 64. 64 - 1 = Go. 63 -h 1 = 63. Ans. 



374 



PRACTICAL AKITHMETIC 



If the progression is decreasing, subtract the product 
from the first term. 



TABLES OF MEASURES 



LENGTH 



inches (ins.)= 1 foot (ft.) 
feet = 1 yard (yd.) 

1 = 1 rod (rd.) 

= 1 mile (mi.) 



12 

3 

16J feet, or 
5J yards 
820 rods 



rds. 



yds. 



1 = 320 = 1760 = 5280 = 63,360 
1 = 51- =i6i =198 
1 = 3 ' =36 
1 =12 



= 1 inch, used by shoemakers. 

= 1 common cubit. 

= 1 sacred cubit. 

= 1 hand, used to measure the 

height of horses. 
= 1 span. 
= 1 fathom, used to measure depths 

at sea. 

~ ^ P 1 , used in pacing distances. 

= 1 mile. 

= 1 geographical nautical mile or 
knot. 
3 geographical miles = 1 league. 

I of latitude on a meri- 
dian, or of longitude 
on the equator. 



3 barleycorns 
18 inches 
21.888 inches 

4 inches 

9 inches 
6 feet 

3 feet 

5J paces 

8 furlongs 

1.15 statute miles 



60 geographical miles | 
69.16 statute miles 



The length of a degree of latitude is commonly re- 
garded as 69.16 miles, and is that adopted by the United 
States Coast Survey. 



APPENDIX 375 



ANGULAR MEASURE 



60 seconds (") = 1 minute (') 
60 minutes = 1 degree (°) 
360 degrees = 1 circumference 

SURFACE OR SQUARE MEASURE 

144 square inches (sq. ins.) = 1 square foot (sq. ft.) 

9 square feet = 1 square yard (sq. yd.) 

30| square yards = 1 square rod (sq. rd.) 

160 sqiiare rods = 1 acre (A.) 

640 acres = 1 square mile (sq. mi.) 

1 square mile = 1 section 

36 square miles = 1 township 

sq. mis. A. sq. rds. sq. yds. sq. ft. 

1 = 640 = 102,400 = 8,097,600 = 27,878,400 



1 = 1600 = 4840 = 43,560 
1 = 30J = 272J 

100 square feet = 1 square (in roofs, floors, etc.) 

SOLID OR CUBIC MEASURE 

1728 cubic inches (cu. ins.) = 1 cubic foot (cu. ft.) 
27 cubic feet = 1 cubic yard (cu. yd.) 

cu. yd. cu. ft. cu. ins. 

1 = 27 = 46,656 

WOOD MEASURE 

16 cubic feet = 1 cord foot (cd. ft.) 
128 cubic feet] ^ a ^ a \ 
8cordfeetl = l''°^''i(°^-) 

CAPACITY 
Liquid Measure 

4 gills (gi.) = 1 pint (pt.) 
2 pints = 1 quart (qt.) 

4 quarts = 1 gallon (gal.) 



376 PRACTICAL ARITHMETIC 

gal. qts. pts. g-is. 

1 = 4 = 8 = 32 
1 = 2= 8 
1 gallon = 231 cu. ins. 

DRY MEASURE 

2 pints = 1 quart 

8 quarts = 1 peck (pk.) 

4 pecks = 1 bushel (bu.) 

2.5 bushels = 1 barrel (bbl.) 



bbl. 


bus. 


pks. 


qts. 


pts. 


1 = 


2i- 


= 10 = 


80 = 


160 




1 


= 4 = 


32 = 


64 






1 = 


8 = 


16 


1 bushel 




= 2150.42 cu. 


ins. 


1 heaped 


bu. 


= 1^ bus 


s. 






WEIGHT 







AvoiKDUPOis Weight 

16 drams = 1 ounce (oz.) 

16 ounces = 1 pound (lb.) 

100 pounds = 1 hundredweight (cwt.) 

2000 pounds = 1 ton (T.) (short) 

2240 pounds = 1 long ton 

T. cwts. lbs. ozs. 

1 = 20 = 2000 = 32,000 
1 = 100 = 1600 
The following deneminations are used in Avoirdupois 
Weight 



14 lbs. 




= 1 stone 


100 lbs. 


butter 


= 1 firkin 


100 lbs. 


grain or flour 


= 1 cental 


100 lbs. 


dried fish 


= 1 quintal 


100 lbs. 


nails 


= 1 keg 


196 lbs. 


flour 


= 1 barrel 


200 lbs. 


pork or beef 


= 1 barrel 


230 lbs. 


salt at N.Y. works 


= 1 barrel 



APPENDIX 



377 



WEIGHTS OF PRODUCE 

The following are minimum weights per bushel of cer- 
tain articles of produce according to the laws of various 
States : 



Wheat 

Coru in the ear 



Corn shelled 
Rye 

Buckwheat 



Barley 



Oats 



Peas 

White beans 
White potatoes 

Sweet potatoes 

Onions 

Turnips 

Dried peaches 

Dried apples 

Clover seed 

Flax seed 

Millet seed 

Hungarian grass seed 

Timothy seed 



60 lbs. 

70 lbs., except in Miss., 72 lbs.; 
in Ohio, 68 lbs.; in Ind. after 
Dec. 1, and in Ky. after May 1, 
following the time of husking, 
it is 68 lbs. 

56 lbs., except in Cal., 52 lbs. 

56 lbs., except in Cal., 54 lbs.; 
in La., 32 lbs. 

48 lbs., except in Cal., 40 lbs.; 
Ky.,56 1bs.; Ida., N.D., Okl., 
Ore., S.D., Tex., Wash., 42 
lbs.; Kan., Minn., N.C., N.J. , 
Ohio, Tenn., 50 lbs. 

48 lbs., except in Ore., 46 lbs.; 
Ala., Ga., Ky., Pa., 47 lbs.; 
Cal., 50 lbs.; La., 32 lbs. 

32 lbs. except in Ida., and Ore., 
36 lbs.; in Md., 26 lbs.; in 
N.J. and Va., 30 lbs. 

60 lbs. 
60 lbs. 
60 lbs., except in Md., Pa., Va., 

56 lbs. 
65 lbs. 

57 lbs. 

55 lbs. 

33 lbs. 
26 lbs. 

60 lbs., except in N.J., 64 lbs. 

56 lbs. 
50 lbs. 
50 lbs. 

45 lbs., except in Ark., 60 lbs. ; 
N.D., 42 lbs. 



378 PRACTICAL ARITHMETIC 

Blue grass seed 44 lbs. 

Hemp seed 44 lbs. 

Corn meal 50 lbs., except in Ala., Ark., 

Ga., 111., Miss., N.C., Tenn., 

48 lbs. 
Bran 20 lbs. 

TROY WEIGHT 

For Precious Metals, Jewels, etc. 

24 grains = 1 pennyweight (pwt.) 

20 pennyweights = 1 ounce 
12 ounces = 1 pound 



iS7^ grains = 1 ounce I » 
7000 grains = 1 pound J 

480 grains = 1 ounce 1 rp 
5760 grains = 1 pound] •' 

APOTHECARIES' WEIGHT 

20 grains = 1 scruple (sc. or 3) 
3 scruples = 1 dram (dr. or 3) 
8 drams = 1 ounce (oz. or 5 ) 
12 ounces! -, , .,1 ,» . 

5760 grains 1 = 1 P°^"^'l<^l^-°'^^) 

APOTHECARIES' LIQUID MEASURE 

60 minims = 1 fluid dram (f 3) 

8 fluid drams =1 fluid ounce (fS.) 

16 fluid ounces = 1 pint (O.) 
8 pints = 1 gallon (cong.) 

COUNTING 

12 things = 1 dozen (doz.) 

12 dozen = 1 gross (gro.) 

12 gross = 1 great gross (G. gr.) 

20 things = 1 score 



APPENDIX 



379 



24 sheets (paper) = 1 quire 

20 quires, or 480 slieets = 1 ream 



TIME 

60 seconds (sees.) 

60 minutes = 1 

24 hours = 1 

7 days = 1 

2 weeks = 1 
30 (31, 28, 29) days = 1 

3 months, or 13 weeks = 1 
12 months, or 365 days = 1 

365 days 5 hrs. 48 mins. 49.7 sees. = 1 

366 days = 1 
10 years = 1 
100 years = 1 

VALUE 

U. S. Money 

10 mills = 1 ct. (ct., c, or ^) 

10 cents =1 dime (di.) 

100 cents or 10 dimes = 1 dollar (I) 
10 dollars = 1 eagle 

Canadian Monet 
100 cents =1 dollar = 11 



= 1 minute (min.) 
hour (hr.) 
day (da.) 
week (wk.) 
fortnight 
month (mo.) 
quarter 

year (yr.) (common) 
true or solar year 
leap year 
decade 
century (C.) 



English Money 

12 pence (cZ.) = 1 shilling (s.) = *0.243+ 
20 shillings = 1 pound (£) = * 4. 8665 

Ekench Money 
100 centimes = 1 franc (fr.) = $0,193 

German Money 
100 pfennigs = 1 mark (i\I.)= 10.238 



380 



PEACTICAL ARITHMETIC 
Russian Money 

100 copecks = 1 ruble 

AUSTEO-HUNGAKIAN MONET 

100 kreutzer = 1 florin 



VALUE OF FOREIGN COINS IN UNITED STATES MONEY 
(Proclaimed by the Secketaky of the Treasury) 



Country 


Money Unit 


Yalue in United States 


Austria-Hungary . . 

Belgium 

Brazil 

Canada ...... 

Central America . . 

Chile 

China 

Denmark 

Ecuador 

Egypt 

I ranee 

Germany 

Great Britain . . . 

Greece 

Hayti 

India 

Italy 

Japan 

]\lexico 

Netherlands .... 

Norway ■ 

Panama 

Peru 

Portugal 

Russia 

Spain 

Sweden 

Switzerland .... 
Turkey 


Crown 

Franc 

JNlilreis 

Dollar 

Peso 

Peso 

Teal 

Crown 

Sucre 

Pound = 100 piasters 

Franc 

Mark 

Pound 

Drachma 

Gourde 

Pound 

Lira 

Yen 

Peso 

Florin 

Crown 

Balboa 

Libra 

Milreis 

Ruble 

Peseta 

Crown 

Franc 

Piaster 


$ .203 

.193 

.546 
1.00 

.'485 

.365 

.72 to .80 

.268 

.487 
^ 4.943 

.193 

.238 
4.8665 

.193 

.965 
4.8665 

.193 

.498 

.498.- 

.402 

.268 
1.00 
4.8665 
1.08 

.515 

.193 

.268 

.193 

.044 



APPENDIX 
NEGOTIABLE PAPERS 



381 





Interest Laws 


Statutes of Limitation 


States and Terbitokies 




, 












Legal 
Kate 


Muximum 

Contract 

Kate 


Grace 


Judg- 
ments 


Notes 


Open 
Accounts 










Yetrm 


Years 


Years 


Alabama 


8 


's 


G 


20 


6 


3 


Arkansas 


6 


10 


G 


10 


5 


3 


Arizona 


6 


Any 


G 


5 


4 


3 


California 


7 


Any 




5 


4 


2 


Colorado 


8 


Any 




20 


6 


6 


Connecticut . 


6 


fi 








6 


Delaware 


6 


6 






6 


3 


District of Columbia . 


6 


10 




12 


3 


3 


Florida .... 


8 


10 




20 


5 


2 


Georgia .... 


7 


8 


G 


7 


6 


4 


Idaho .... 


7 


12 




6 


5 


4 


Illinois .... 


5 


7 




20 


10 


6 


Indiana .... 





8 


G 


20 


10 


6 


Iowa .... 


6 


8 


G 


20 


10 


5 


Kansas .... 


6 


10 


G 


5 


5 


3 


Kentucky 


6 


6 


6 


15 


15 


5 


I^uisiana ... 


5 


8 


G 


10 


5 


3 


Maine .... 


6 


Any 




20 


6 


6 


Maryland 


6 


6 




12 


3 


3 


Massachusetts 


6 


Any 




20 


6 


6 


Michigan 


5 


7 


G 


10 


6 


6 


Minnesota . 


7 


10 


G 


10 


6 


6 


Mississippi . 


6 


10 


G 


7 


6 


3 


Missouri 


6 


8 


G 


10 


10 


5 


Montana 


■ 8 


Any 




10 


8 


5 


Nebraska 


7 


10 


G 


5 


5 


4 


Nevada .... 


7 


Any 


G 


6 


4 


4 


New Hampshire . 


6 


6 




20 


6 


6 


New Jersey . 


6 







20 


6 


6 


New Mexico . 


6 


12 


G 


7 


6 


4 


New York . . 


.^ 


6 




20 


6 


6 


North Carolina . 


6 


a 


G 


10 


3 


3 


North Dakota 


7 


12 




10 


6 


6 


Ohio . , . 


6 


8 




15 


15 


6 


Oklahoma •. 


7 


12 


G 


5 


5 


3 


Oregon .... 


6 


10 




10 


6 


6 


Pennsylvania 


6 


6 




5 


6 


6 


Rhode Island 


6 


Any 




20 


6 


6 


South Carolina . 


7 


8 


G 


20 


6 


6 


South Dakota 


7 


12 


G 


10 


6 


6 


Tennessee 


6 


(> 




10 


6 


6 


Texas .... 


6 


10 


G 


10 


4 


2 


Utah .... 


8 


Any 




8 


6 


4 


Vermont 


6 


6 




8 


6 


6 


Virginia 


6 


6 




20 


5 


2 
3 


Washington . 


G 


12 




6 


6 


West Virginia 


6 


6 




10 


10 


5 


Wisconsin 


6 


10 




20 


ti 


6 


Wyoming 


8 


12 


G 


21 


5 


8 



382 PEACTICAL AlilTHMETIC 

TABLE OF COMPOUND INTEREST 



Periods 


% Per Cent 


1 Per Cent 


IJ Per Cent 


H Per Cent 


2 Per Cent 


1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 


1.00750000 
1.01505625 
1.02266917 
1.03033919 
1.03806673 

1.04585223 
1.05369612 
1.06159884 
1.06956083 
1.07758254 

1.08566441 
1.09380689 
1.10301044 
1.11027552 
1.11860259 

1.12099211 
1.13544455 
1.14396038 
1.15254009 
1.16118414 


1.01000000 
1.02010000 
1.03030100 
1.04060401 
1.06101U05 

1.06152015 
1.07213535 
1.08285670 
1.09.368527 
1.10462212 

1.115668.34 
1.12682503 
1.13809328 
1.14947421 
1.16096895 

1.17257864 
1.18430443 
1.19614747 
1.20810895 
1.22019003 


1.01250000 
1.02515625 
1.03797070 
1.05094533 
1.06408215 

1.07738318 
1.09085047 
1.10448610 
1.11829217 
1.13227082 

1.14642421 
1.16075451 
1.17526389 
1.18995469 
1.20482913 

1.21988949 
1.23513811 
1.25047734 
1.26610830 
1.28193466 


1.015000 
1.030225 
1.045678 
1.061364 
1.077284 

1.093443 
1.10ti845 
1.126493 
1.143390 
1.160541 

1.177949 
1.195618 
1.213552 
1.231756 
1.250232 

1.268985 
1.288020 
1.307341 
1.326951 
1.346855 


1.020000 
1.040400 
1.061208 
1.082432 
1.104081 

1.126162 
1 .148686 
1.171660 
1.195093 
1.218994 

1.243374 
1.268242 
1.293607 
1.319479 
1.345868 

1.372786 
1.400241 
1 .428246 
1.456811 
1.485947 


Periods 


2^ Per Cent 


8 Per Cent 


8J Per Cent 


4 Per Cent 


5 Per Cent 


6 Per Cent 


1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 


1.025000 
1.050625 
1.076891 
1.103813 
1.131408 

1.159693 
1.188686 
1.218403 
1.248863 
1.280085 

1.312087 
1.344889 
1.378511 
1.412774 
1.448298 

1.484506 
1.521618 
1.559659 
1.598650 
1.638616 


1.030000 
1.060900 
1.092727 
1.125509 
1.159274 

1.194052 
1.229874 
1.266770 
1.304773 
1.343916 

1.384234 
1.425761 
1.4685.34 
1.512590 
1.557967 

1.604706 
1.652848 
1.7024.33 
1.753506 
1.806111 


1.035000 
1.071225 
1.108718 
1.147523 
1.187686 

1.229255 
1.272279 
1.316809 
1.362897 
1.410599 

1.459970 
1.511069 
1.563956 
1.618695 
1.675349 

1.73.3986 
1.794676 
1.857489 
1 .922501 
1.989789 


1.040000 
1.081600 
1.124864 
1.169859 
1.216663 

1.265319 
1.315932 
1.368569 
1.423312 
1.480244 

1.539454 
1.601032 
1.665074 
1.731676 
1.800944 

1.872981 
1.947901 
2.0258-.7 
2.106849 
2.191123 


1.050000 
1.102500 
1.157625 
1.215506 
1.276282 

1.340096 
1.407100 
1.477455 
1.551328 
1.628895 

1.710.339 
1.795856 
1.885649 
1.979932 
2.078928 

2.182875 
2.292018 
2.406619 
2.526950 
2.653298 


1.060000 
1.123600 
1.191016 
1.262477 
1.338226 

1.418519 
1.503630 
1.593848 
1.689479 
1.790848 

1.898299 
2.012197 
2.132928 
2.260904 
2.396558 

2.540352 
2.692773 
2.854339 
3.025600 
3.207136 



APPENDIX 383 

METRIC TABLES 

MEASURES OF LENGTH 

10 millimeters (mm.)= 1 centimeter (cm.) 

10 centimeters = 1 decimeter (dm.) 

10 decimeters = 1 meter (m.) 

10 meters = 1 dekameter (Dm.) 

10 dekameters = 1 hektometer (Hm.) 

10 hektometers = 1 kilometer (Km.) 

20 kilometers = 1 myriameter (Mm.) 

MEASURES OF SURFACE 

100 sq. millimeters (sq. mm.) = 1 sq. centimeter (sq. cm.) 
100 sq. centimeters = 1 sq. decimeter (sq. dm.) 

100 sq. decimeters =1 sq. meter (sq. m.) 

100 sq. meters = 1 sq. dekameter (sq. Dm.) 

100 sq. dekameters = 1 sq. hektometer (sq.Hm.) 

100 sq. hektometers = 1 sq. kilometer (sq. Km.) 



MEASURES OF VOLUME 

1000 cu. millimeters (cu. mm.)= 1 cu. centimeter (cc.) 
1000 cu. centimeters = 1 cu. decimeter (cu. dm.) 

1000 cu. decimeters = 1 cu. meter (cu. m.) 



MEASURES OF CAPACITY 

10 milliliters (ml.) = 1 centiliter (cl.) 

10 centiliters =1 deciliter (dl.) 

10 deciliters = 1 liter (1.) 

10 liters = 1 Dekaliter (Dl.) 

10 dekaliters = 1 Hektoliter (HI.) 

10 hektoliters = 1 Kiloliter (Kl.) 



384 PRACTICAL ARITHMETIC 



MEASURES OF WEIGHT 

10 milligrams (mg.) = 1 centigram (eg.) 

10 centigrams = 1 decigram (dg.) 

10 decigrams = 1 gram (g.) 

10 grams , = 1 dekagram (Dg.) 

10 dekagrams = 1 liektogram (Hg.) 

10 hektograms = 1 kilogram ( K.) 

10 kilograms = 1 myriagram (Mg.) 

10 myriagrams = 1 quintal (q.) 

10 quintals = 1 tonneau (T.) 



METRIC EQUIVALENTS OF ENGLISH MEASURES 

1 acre= .4047 hectare. 

1 bushel = 35.24 liters. 

1 cubic foot = 28.316 liters. 

1 cubic inch = 16.39 cubic centimeters. 

1 cubic yard = .7645 cubic meter. 

1 foot = 30.48 centimeters. 

1 gallon = 3.785 liters. 

1 grain = .0648 gram. 

1 inch = 25.4 millimeters. 

1 mile = 1.609 kilometers. 

1 ounce (avoirdupois) = 28.35 grams. 

1 ounce (Troy) = 31.1 grams. 

1 peck = 8.809 liters. 

1 pint =.4732 liter. • 

1 pound = .4536 kilo. 

1 quart (dry) = 1.101 liters. 

1 quart (liquid) = .9464 liter. 

1 square foot = .0929 square meter. 

1 square inch = 6.452 square centimeterSc 

1 square yard = .8361 square meter. 

1 ton (2000 lbs.) = .9072 metric ton. 

1 ton (2240 lbs.) = 1.017 metric tons. 

1 yard = .9144 meter. 



APPENDIX 



385 



ENGLISH EQUIVALENTS OF METRIC MEASURES 

1 centimeter = .3937 inch. 

1 cubic centimeter = .061 cubic inch. 

1 cubic meter = 35.31 cubic feet, or 1.308 cubic yards. 

1 gram = 15.43 grains. 

1 hectare = 2.471 acres. 

1 kilo = 2. 205 pounds. 

1 kilometer = .6214 mile. 

1 liter = .9081 dry quart, or 1.051 liquid quarts. 

1 meter = 3.281 feet. 

1 millimeter = .0394 inch. 

1 square centimeter = .155 square inch. 

1 square meter = 1.196 square yards, or 10.76 square 

feet. 
1 metric ton = 1.102 short tons, or .9842 long ton. 



CATTLEMEN'S NOTATION 
Explanation of the Valuk of the Various Notches. 



A notch in bottom of the 
animal's left ear equals 1, 
two notches equal 2. 

A notch in top of left ear 
equals 3, two notches equal 
6, three notches equal 9. 

A notch in bottom of 
right ear equals 10, two 
notches equal 20. 

A notch in top of right 
ear equals 30, two notches 
equal 60, three notches equal 
90. 

A notch in end of left ear 
equals 100. 

A notch in end of right 
ear equals 200. 

A hole in end of left ear 
equals 400. 

A hole in end of right ear 
equals 500. 

A hole in bottom of left 
ear equals 1000. 

Numhers can thus he made from 1 to 1999. 




200 



SOOi 




386 PRACTICAL ARITHMETIC 

LUMBERMEN'S NOTATION 
In marking lumber the following characters are used ^ 

A Al All Alii X X XI XII XIII yn 

S 6 7 8 9 10 11 1« 13 14 

X\ Al All Alll XIX X' /I X'll XIII 

15 16 17 18 19 2(} 21 22 23 



Xf X\ X\l XMI XXIil XMIII )f I 

2t 25 26 



25 26 27 28 29 30 40 



50 60 70 80 90 100 200