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EFFICI ENCY
ARITHMETIC
ADVANCED
BY
CHARLES E. CHADSEY, Ph. D.
SUPERINTENDEl^r' OF SCHOOLS
DETROIT. MICH. •
AND
JAMES H. SMITH, A. M.
INSTRUCTOR IN MATHEMATICS
AND MANUAL TRAINING. SCHOOL
OF EDUCATION. UNIVERSITY OF
CHICAGO
ATKINSON, MENTZER & COMPANY
CHICAGO NEW YORK BOSTON ATLANTA DALLAS
/
615124
C
COPYRIGHT, 1917, BY'
ATKINSON, MENTZER & COMPANY
All rights reserved
PREFACE
This book has been prepared in the belief that work in
Arithmetic in the seventh and eighth grades should emphasize
drill upon fundamentals and their application to living, vital
problems that the average child is almost sure to encounter in
his individual experiences. At the same time, it is recognized
that for the great majorit3;^^ing the l>ooks of this series certain
topics will never receive %bf&ideration in the school training
unless presented in this volume. Great care has been taken to
present these topics in a simple, clear manner which ought to
make their meaning and significance intelligible even to the
younger pupils.
The problems of the book, almost without exception, are
actual problems taken from the various lines of business
represented. Business men from all sections of the country
have contributed problems, furnished definite and accurate
information upon which to base problems, and have criticized
the work from the standpoint of practical efficiency and
reliability. Acknowledgment is hereby made to these gentle-
men for their invaluable assistance.
The methods of presentation and explanation of topics new
to the child have been carefully tested in the school room and
their effectiveness is thereby assured. Simplicity, clearness,
and the avoidance of unnecessary repetition we believe to be
characteristic of this series, especially in the applications of
percentage and practical measurements which so often unneces-
sarily confuse the pupil.
Many school systems are modifying their courses in mathe-
mathics in order to permit elementary algebra to be commenced
in the eighth grade. This volume permits, through its arrange-
ment, a very simple omission of topics in Part I which will
III
IV PREFACE
enable any teacher to cover the essential topics in less than
the customary two years. The arrangement also enables those
who prefer to postpone some of the topics found in Part I to
combine the seventh- and eighth-grade topics in such a way
as to give a more extended discussion of closely related subjects.
The fact that there are in reality only a few mathematical
principles involved in ordinary arithmetic is kept clearly in
mind. Too often the pupil has been led to believe that each
new topic has little in common with preceding topics and
therefore fails to learn the greatest educational lesson that
can be taught — ^the application of a known principle to a new
condition. The effort in this book is to keep the relationship
between mathematical facts constantly before the pupil.
Teachers of arithmetic must never forget that accuracy and
reasonable rapidity in manipulation of niunbers are one of the
chief aims in this study. Pupils of the seventh and eighth
grades need continued practice of this kind. Ample oppor-
tunity for this drill is furnished, and from the beginning to the
end of the course there should be recurrence to these exercises.
While it is not possible, in the limited space, to make personal
acknowledgment to the large number of educators who have
rendered assistance of great value in the preparation of this
volume, the authors desire to express their indebtedness
especially to Miss Katherine L. McLaughlin of the Elementary
School of the School of Education, University of Chicago, to
Mr. Warren E. Hicks, Assistant for Industrial Education,
Department of Public Instruction, Madison, Wisconsin, to Mr.
Lewis A. Bennert, Principal of School No. 3, Patterson, New
Jersey, and to Mr. James C. Thomas of the publishers'
editorial department, for their invaluable criticisms and
suggestions.
CONTENTS
PART I— SEVENTH YEAR
CHAPTER I. REVIEW OF THE FUNDAMENTALS— 1-22
Training for Speed and Accuract.
CHAPTER II. REVIEW OF FRACTIONS— 23-44
Three Meanings op Fractions, 23; Reduction op Fractions, 23,
Addition and Substraction of Frachons, 25; Multiplication and
Division op Fracteons, 29; Review op Decimals, 34; Appued Rbtiew
Problems in Fractions, 41.
CHAPTER III. PERCENTAGE— 46-76
•
Explaining Per Cent, 45; The Decimal Point and Percentage, 45;
Common Fractions and Their Equivalent Per Cents, 46; Equations
Applied to Percentage, 48; Drill Problems in Percentage, 51;
Problems Collected bt Pupils, 61; Applied PiiOBLBBis in Per-
centage, 63.
CHAPTER IV. APPLICATIONS OF PERCENTAGE— 77-112
Business Transactions, 77; Discounts, 79; Interest, 83; Partial
Payments, 89; Commission, 92; Taxes, 95; Special Assessments, 98;
Custom Duties, 100; Internal Revenue, 103; Income Taxes, 104;
Insurance, 106.
CHAPTER V BUSINESS FORMS AND ACCOUNTS— 113-132
Sales Sups, 113; Invoices, 115; Monthly Statements, 117; Receipts,
118; Cash Accounts, 119; Daybook or Journal, 121; Personal
Accounts, 122; Inventories, 124; Pay Rolls, 125; Cashier's Memo-
randum, 126; Agencies for Shipping Merchandise, 127.
CHAPTER VI. PRACTICAL MEASUREMENTS— 133-154
Lines and Angles, 135; Rectangles, 137; Boy Scouts — Appued
Problems, 140; Parallelograms, 142; Trapezoids, 144; Triangles, 145;
Area of Triangles, 146; Appued Problems, 149.
CONTENTS
PART II— EIGHTH YEAR
CHAPTER I. REVIEW EXERCISES— 155-178
Training for Efficibnct, 155; Chbcking Up, 155; Speed Tests in
Multiplication, 159; Short Methods in Multiplication, 160; Speed
Tests in Division, 164; Short Methods in Division, 164; Review of
Fractions, 167; Review of Decimals, 169; Review of Percentage, 170.
CHAPTER II. BANKS AND BANKING— 179-206
National and State Banks, 179; Federal Reserve Banks, 181;
Savings Accounts, 186; Bank Discount, 188; Exchange, 190; Stocks
AND Bonds, 194; Signatures and Seals, 199; Investbientb, 203.
CHAPTER III. REMITTING MONEY— 207-218
Postal Money Orders, 207; Express Monet Orders, 208; Bank
Drafts, 209; Checks, 210; Emergency Remittances, 212; Telegraph-
ing Money, 212; Cabling Money, 213; Money by Wireless, 14.
CHAPTER IV. PRACTICAL MEASUREMENTS— 219-254
•
QUADRILATERAU3, 219; TRIANGLES, 220; SQUARES AND SqUARB RoOTS
221; Right Triangles, 226; Equilateral Triangles, 231; Circles,
233; Shop Problems, 235; Hexagons, 240; Solids, 241; Prisms, 242;
Cylinders, 246; Silos, 247; Irrigation, 248; Good Roads, 250.
CHAPTER V. GRAPHS— 255-261
Pictorial Graphs, 255; Line Graphs, 256; Bar Graphs, 258; Dis-
tribution Graphs, 260; Circle Graphs, 261.
CHAPTER VI. MEASURING INSTRUMENTS-262-279
Thermometer, 262; Barometer, 264; Hygrobceter, 265; Weather
Reports, 266; Electric Meter, 270; Gas Meter, 272; Steam Gauge,
274; Surveyor's Chain, 275; Measurement of Time, 276; Standard
Time, 277; International Date Line, 279.
CHAPTER VII. THE METRIC SYSTEM— 280-287
Weights and Measures, 280; Lengths, 281; Square Measure, 282;
Volume, 283; Capacity, 284; Weight, 285.
CHAPTER VIII. EFFICIENCY IN THE HOME— 288-299
Building a HoifE, 289; Furnishing a HoiiE, 290; Expenses of a
Home, 292; Camppire Girls, 293; The Family Budget, 294; Efficiency
IN Business, 296; Supplement, 300; Index, 313.
ADVANCED ARITHMETIC
PART I
Ttaining for Speed and Accurate
Several weeks before the opening of the regular baseball
season, the players of the big leagues go soutli for a spring
training trip. The players, with their lack of exercise during
the winter's vacation, would not be in proper condition to go
into the opening game of the season without this sort of
preparation.
You are just returning from a sunmier's vacation, during
which you have lost some of your speed and accuracy in the
various processes of arithmetic. It is therefore wise for you
to take a preliminary trainii^ trip by reviewing the f uudamentfd
When asked what the new workers in his firm needed most
in arithmetic, the head of the school for training workers in
one of the largest mercantile firms in the country replied:
"Teach them to add, subtract, multiply and divide." He
emphasized what all business men want — speed and accuracy
in those four fundamental processes.
CHAPTER I
REVIEW EXERCISES
Exercise 1. Reading Numbers
In your studies and in reading the magazines and daily
papers you are frequently called upon to read numbers. For
convenience in reading, large numbers are pointed off into
periods as in the following illustration:
. g
- (=3 5 »
goo ts
3 -3 3 § g i 2 •
g -3 § I •§ I i -a
» & c ■*» M o ^ a
6,069,000,000,000,000,000,000.
The number above represents the estimated weight of the
earth in tons. Read it.
In the following table the diameter and average distance
from the sun is given for each of the planets in our solar system.
Read these distances.
Naiue of
planet
Diameter
in miles
Average distance from
the sun in miles
1. Mercury
2,962
35,392,638
2. Venus
7,510
66,131,478
3. Earth
7,925
91,430,220
4. Mars
4,920
139,312,226
6. Jupiter
88,390
475,693,149
6. Saturn
77,904
872,134,583
7. Uranus
33,024
1,753,851,052
8. Neptune
36,620
2,746,271,232
A rapid review of this chapter should be given, followed by a systematic
use of one or more of the standardized drill exercises at the beginning of
each recitation period.
REVIEW EXERCISES
Exercise 2. Writing Numbers
Occasionally one is called upon to write difficult numbers,
and he should be able to do so when the need arises.
Write the following numbers:
1. Ten thousand ten.
2. One hundred fifty thousand fifteen.
3. Two million two hundred thousand.
4. Sixteen million sixteen thousand sixteen.
6. Twenty-eight million four hundred fifteen thousand.
6. Two billion one million two hundred thousand seventy.
7. Four trillion four hundred billion two million.
8. Sixteen billion sixty million fifteen thousand.
9. Twenty-four billion sixty million sixty thousand.
10. Seventy million seventeen thousand six.
11. Twenty-nine billion six million twenty thousand.
12. Fifty million one hundred fifty thousand thirteen*
13. Forty billion one hundred seventy million.
14. Eight hundred thousand nine hundred sixty-four.
16. Twenty-four million twenty-six thousand two hundred.
Exercise 3. Roman Notation
It is customary to express chapters of books and often dates
on important buildings in Roman numerals. Read the following
numbers:
1. IV
6. XIX
11. XLIV
16. D
2. VI
7. XX
12. LXVI
17. M
3. XIV
8. XXII
18. XC
18. MDC
4. XVI
». XXXIV
14. XCVII
19. MDCCCXCVII
6. XVIII
10. XL
16. C
20. MDCCCCXVII
Express in Romaii numerals:
1. 9
S. 29
6. 47
7. 72
9. 1492
2. 14
4. 33
«. 58
8. 96
10. 1918
4 SEVENTH YEAR
EXERCISES FOR SPEED AliD ACCURACY
Addition! Subtractioni Multiplication and Division^
To THE Teacher: The following exercises have been ar-
ranged to assist pupils to develop accuracy and speed in the
fundamental operations. The exercises have been organized
so that the same time should be given for each exercise. For
the seventh grade allow two minutes for each exercise. If the
teacher finds that the previous preparation of the class makes
this standard too high, or too low, she should adjust the time
limit to suit her class.
The best results can be secured if it is possible to have these
exercises hektographed or mimeographed for drill purposes.
Some of the exercises can be conveniently done by placing a
sheet of paper under the examples in the book and writing
the answers on this sheet of loose paper.
Every exercise should be jsiccurately timed with a watch.
These exercises may be used in two ways:
(1) All pupils may practice on each exercise together.
After time is called, the pupils should exchange papers and
correct them as the teacher reads the answers. Keep individual
records of the number of examples right for each exercise.
(2) Start all of the pupils on Exercise 4. As soon as the
pupil has finished correctly all the examples in one exercise
within the time allowed, have him try the next exercise. Under
this plan a pupil can progress at his own pace. Individual
differences in pupils are thus recognized and provided for by
this method. The papers of those who have finished should
be collected and corrected before the next drill period. Some
reliable pupil may be appointed by the teacher to help in this
work.
^These exercises were arranged by Charles L. Spain, Assistant Supt. of
Schools, Detroit, Michigan.
EXERCISES FOR SPEED AND ACCURACY
]
Sxercis
ie 4.
Addition
6
9
7
6
2
3
6 1
4
9
6
6
7
1
2
3
1
7
9
7
4
4
6
7
7
3
3
8
7
2 4
9
2
9
2
6
9
6
7
2
1
6
1
6
3
3
8
7
6
7
8
4
4
9
6
2
6
6
6
9
7
8
7
6
9
2
6
4
8
8
9
6
1
1
4
9
4
9
2
4
4
4
6
1
6
8
3
3
1
7
7
6
3
3
7
2
4
1
6
3
6
2
Exercise 6. Subtraction
17 66 98 77 19 34 76 68 49 46 49 66
647674683463
66
76
97
88 49 83 66 99 89 67
28
36
3
4
6
6 7 2 6 16 6
4
3
23
76
83
72 66 67 43 69 66
66
69
J
2
1
2 6 7 3 9 6
_6
4
Exercise 6. Addition
4
7
4
1
2
2
6
7
6
3
2
4
9
1
4
1
4
9
1
3
3
3
8
6
1
3
6
3
2
6
2
1
1
2
1
8
6
6
8
3
2
6
7
8
1
8
9
2
6
6
7
8
1
3
1
1
6
1
9
8
7
6
1
9
6
4
4
8
6
2
8
7
4
8
9
6
7
2
3
1
1
6
6
9
6
6
9
3
8
6 SEVENTH YEAR
Exercise 7. Addition
56 31 47 24 14 24 32 70
32 48 61 62 15 33 36 18
17
43
20
20
26
81
42
22
72
21
13
50
73
13
27
16
48
33
52
75
32
17
12
26
31
33
41
21
23
62
26
61
Exercise 8. Multiplication
26
46
68
94
87
53
85
67
26
49
2
3
7
5
6
7
4
8
9
5
24
19
28
91
87
39
83
16
54
57
4
2
6
3
7
4
9
7
6
3
Exercise 9. Addition .
32 24 31 25 70 42 50 36
16 13 22 33 17 31 30 20
31 62 11 10 11 16 19 32
20
42
25
62
17
10
23
60
19
13
20
16
51
55
61
16
30
22
4^
12
20
32
14
12
Exercise 10. Subtraction
68 57 79 32 61 89 76 78 39 48 59 36
27 34 26 21 20 65 60 18 22 36 54 16
44
62
76
63
67
31
44
89
74
42
80
33
31
41
74
33
20
11
22
67
63
32
60
21
The order of the examples in each of these exercises should be fre-
quently changed to prevent memorizing of answers.
EXERCISES FOR SPEED AND ACCURACY
Exercise 11. Division
8)48
7)66
9)81
6)46
7)84
4)36
7)63
6)64
6)66
8)66
9)63
7)36
6)60
9)90
4)36
9)46
4)20
7)42
7)70
9)36
8)40
6)36
6)36
6)48
9)99
8)64
9)64
9)27
3)24
6)42
6)66
8)80
7)77
6)72
6)60
3)21
7)28
4)40
s
6)40
6)26
4)24
3)27
8)98
4)48
3)33
3)30
6)24
8)32
6)16
6)18
7)28
3)36
4)44
2)22
4)16
Exercise 12.
Addition
36
17
63 48
27 13
1 37
> 16
67
26
38
32
69
26
62 67
18 26
42
29
49
42
17 36
66 IE
1 27
; 64
36
26
64
26
34
48
39 66
22 18
24
28
Exercise 13.
Addition
6
3
6
1
6
7
7
7
6
4
7
6
8
3
6
1
3
4
9
6
4
•
9
4
8
6
6
9
1
9
6
7
9
6
1
7
7
7
4
9
3
7
1
1
1
7
8
9
4
4
1
1
6
6
7
6
4
2
9
7
6
2
9
6
4
8
2
6
7
6
4
7
8
8
6
9
6
7
9
7
7
6
4
4
6
1
8
6
7
8
8 SEVENTH YEAR
Exercise 14. Subtraction
66 39 61 46 76 31 92 99
48 28 43 32 64 17 67 76
76
92
29
68
67
44
87
46
26
68
16
49
16
36
68
23
21
74
46
88
62
63
77
66
19
36
12
69
22
34
24
61
Exercise 16. Addition
2 6 6 4 13 2 6
3 4 4 12 7 5 1
24763239
11379757
44337816
14228447
22 6 6 6 2 2 5
66342633
32243361
Exercise 16. Multiplication
168 672 327 689 216 379
4 7 9 3 8 6
427 626 917 669 637 329
3 _6 _* _2 _8 8
Exercise 17. Addition
76 77 86 96 66 89 66 47
38 36 39 34 79 46 64 95
37 46 26 36 32 68 96 34
86 68 76 77 99 47 46 77
EXERCISES FOR SPEED AND ACCURACY 9
Exercise IB. Division
23)698
•
17)306
72)864
38)466
36)736
27)729
Exercise 19.
Addition
68
16
18
22
16
12
S2
19
13
47
29
11
26
29
20
32
•
20
20
66
37
14
28
60
40
26
26
13
14
22
29
37
17
34
22
28
27
17
14
36
14
36
^
Exercise 20. Subtraction
63
41
74
p
63
81
70
84
27
26
36
19
17
29
46
30
43
78
66
42
63
67
22
39
49
37
17
44
48
48
41
64
47
40
22
63
39
33
66
38
39
16
44
Exercise 21.
Addition
22
69
36
61
76
37
29
41
36
64
37
64
70
60
67
37
22
71
67
27
63
37
90
31
43
22
76
26
79
67
61
96
27
87
88
68
10 SEVENTH YEAR
Exercise 22. Mttltiplication
48 67 72 86 92 83 60 76
30 40 60 20 60 70 80 40
84
36
48
63
71
38
93
90
60
40
80
90
20
30
Exercise 23.
Addition
38
67
32
21
36
30
74
72
64
67
64
43
29
63
44
78
34
43
76
97
60
76
61
61
78
86
89
66
83
27
20
66
96
96
64
10
40
81
67
36
These exercises axe continued on page 14.
Exercise 24
Not only does one need to know how to work examples
rapidly in addition, subtraction, multiplication and division,
but he also needs to know how to apply these processes rapidly
and accurately in solving problems.
The time limit set for the abstract drill exercises is not to be used for
this exercise. The teacher may have the pupils complete the solutions
of these exercises for seat work.
In the following exercise merely indicate the processes used
in solving each problem:
1. A real estate dealer owns a farm of 142 acres worth
$125 an acre; 6 city lots worth $1500 each and a store valued
at $8750. Find the value of all of his property.
Suggestions for solution: 142 acres are worth 142 times as much as 1
acre, hence multipHcation is the process necessary for finding the value
of the farm. The next statement says: "5 city lots worth $1500 each.**
The word each is the key word in that statement. 6 lots are worth 5 times
as much as 1 lot, hence multiplication is used to find the value of the 5 lots.
To find the value of the farm, the five city lots and the store, we must
find the sum of all their values, hence addition is the last process.
PRACTICE PROBLEMS 11
Indicating the soMion:^ (142 X $125) + (5 X $1500) +$8750 =
value of all of his property.
2. A farmer sold 6 jars of butter containing respectively
24 lb., 26 lb., 29 lb., 28 lb., and 31 lb. Find the total num-
ber of pounds that he sold.
Indicating the sohdion: 24+26+29+28+31 =no. of lb. sold.
8. A boy bought a pony for $55. His expenses for the month
amounted to $6. He sold the pony for $58. Did he gain or
lose and how much?
4. The cost of drilling a well was 40|4 per foot for drilling
and 80^ per foot for the iron tubing. If the well was drilled
150 ft. and 100 ft. of tubing was used, how much did it cost?
5. The distance from Chicago to St. Louis is 282 miles.
What will a round-trip ticket cost at 2^ per mile?
6. A man bought a lot for $1250. He built a house on it
that cost $5275 and then sold the property for $7000. How
much did he gain?
7. In 1917, the House of Representatives had a membership
of 435. If the population of the United States was approxi-
mately 100,000,000 at that time, what was the number of people
to one representative?
8. A farmer exchanges 36 bushels of apples at $1 per bushel
for coal at $8 per ton. How many tons does he receive?
9. Mr. Brown bought a house for $8000. He paid $2000
down and agreed to pay the balance in 8 equal yearly payments.
How large was each payment?
10. A real estate man trades 40 front feet of city ground at
$240 a front foot for a Western farm of 80 acres. How much
is the farm worth per acre?
^Parentheses should be used to separate the various steps in the problem
in order to eliminate the necessity for teaching the law of signs.
12 SEVENTH YEAR
11. K, as computed, the water area of the earth is approxi-
mately 144,500,000 square miles and the total surface of the
earth is approximately 196,907,000 square miles, how much
more water surface than land is there?
12. If the flow of water through the Chicago Drainage
Canal is 360,000 cubic feet per minute, how much water passes
through it in 24 hours?
18. A building worth $400,000 was damaged to the. amount
of $75,000 by fire. The owners received from an insurance
company $60,000 damages. What was the net loss to the
owners of the building?
14. A falling body drops 144 feet in three seconds and 256
feet in four seconds. How far does it drop in the fourth second?
16. The product of four numbers is 10,920; three of the num-
bers are 7, 8 and 15. What is the fourth number?
16. A gallon contains 231 cubic inches. How many gallons
are there in a cubic foot (1728 cubic in.)? •
17. A man had $1275.45 on deposit in a bank. He gave
checks for the following amounts: $110.00; $25.00; $222.50;
$8.75 and $76.25. What was his balance in the bank after
those checks had been cashed?
18. 15 acres of potatoes yielded 4125 bushels. What was
the average yield per acre?
19. Mr. Jones bought 79 acres of land for $5530. How much
did he pay per acre?
20. A speculator bought wheat in the fall of 1916 for $1.59
per bushel and sold it for $1.73 per bushel. How much did he
make if he handled 600,000 bushels in the deal?
21. A man earns $1200 a year. His expenses per year are
$975. In how many years can he save $1800 under those
conditions?
' PRACTICE PROBLEMS 13
22. Mrs. Klein bought 2 dozen eggs at 28 cents per dozen,
2 pounds of butter at 38 cents per pound and 10 pounds of
sugar for 63 cents. How much change should she receive
from a ten-dollar bill?
23. A grocer bought 300 sacks of flour at 75^ per sack and
paid $12.00 freight on the whole amount. He is selling the
flour at $1.00 per sack. How much profit does he make on
each sack?
24. A man bought three houses. He paid $5500 for the
first; $4565 for the second and $7750 for the third. He sold
the three houses for $18,500. How much did he gain?
25. A farmer sold 1600 bushels of rutabagas at 35^ per 100
pounds (1 bu. of rutabagas weighs 52 lb.). How much did he
receive for them?
26. A dealer bought 3726 bushels of wheat at $1.03 per
bushel and sold it at $1.07 per bushel. How much did he make
on the transaction?
27. A grocer bought a box containing 100 apples for $2.00.
Ten of them spoiled. He sold the remainder at 6 cents each.
How much did he gain on the box of apples?
28. John has 45 marbles. Harry and James each have
9 times as many as John. How many marbles do they all have?
29. If the daily pay of a railroad conductor is $4.80 for
an 8-hour day, what is his salary for a year of 330 working days
if his overtime amounts to 320 hours and is paid at the regular
daily rate?
30. A man's estate amounted to $15,630. His wife received
$6000 and the rest was divided equally among his three children.
How much did each receive?
31. 11,161,000 bales (500 pounds each) of cotton were raised
in the U. S. in 1916. Find the production in pounds.
14
SEVENTH YEAR
Exercise 26. Division
2)430
6)896
3)171
2)642
6)474
9)766
4)372
2)198
3)622
9)468
7)269
3)147
6 )326
8 )472
6)888
111
222
362
426
631
226
621
420
Exercise 26. Addition
636 326 784
340 362 216
441
236
726
262
673
316
160
228
796
203
436
323
666
132
438
361
726
262
869
120
262
626
661
326
622
176
Exercise 27. Subtraction
746
473
763
394
223
48
61
86
62
68
624
260
416
432
848
66
30
97
21
69
421
666
•
317
690
600
38
36
68
60
73
Exercise 28.
Addition
127
423
377
266
188
177
609
346
369
208
127
606
718
306
223
361
746
462
119
227
148
647
329
136
228
239
136
226
EXERCISES FOR SPEED AND ACCURACY 15
427
12
Exercise 29. Multiplication
342 872
27 36
961
27
Exercise 30. Subtraction
678
364
466
123
646
124
388
236
394
181
189
146
867
640
311
200
386
362
618
303
621
611
786
463
157
133
141
120
•
383
202
468
367
124
114
•
Exercise 31.
Addition
34
73
29
19
22
26
23
29
28
•
77
43
Y2
26
93
36
81
46
84
11
68
16
62
24
20
63
64
93
61
70
12
17
13
20
30
83
64
56
16
47
48
21
27
Exercise 32.
Division
20)600
30)900
40)120
60)660
70)490
60)300
80)240
20)800
40)280
70)630
60)420
80)400
30)270
80)480
80)640
60)260
20)140
90)810
70)360
20)120
50)700
70)280
60)300
60)660
80)800
90)630
50)760
16
SEVENTH YEAR
679
446
227
106
449
228
34
17
91
63
49
30
62
74
83
Exercise 33. Subtxaction
856 634 756
687 312 667
472
186
883
360
696
244
200
326
186
222
Exercise 34.
42
86
88
24
89
66
28
67
29
96
44
70
20
85
88
60
92
37
Addition
791
693
69
83
14
22
47
98
73
26
40
384
272
786
665
327
207
86
36
43
33
66
67
36
20
46
Exercise 36. Addition
764
843
697
634
488
886
668
488
397
636
927
848
368
456
543
384
163
646
844
567
Exercise 36
t. Multiplicati
on .
462
672
147
121
251
362
EXERCISES FOR SPEED AND ACCURACY 17
Exercise 37. Addition
288
le?
472
144
263
321
326
221
149
186
176
490
281
482
201
214
199
129
161
266
221
186
246
178
127
Exercise
106
38. Diviidon
102
89)8722 84)7644 37)2442
21)2626 84)6804
Exercise 39.
Addition
624
249
190
462
309
318
676
607
166
346
234
169
646
266
192
488
262
413
Exercise 40. Subtraction
763 228 374
386 169 186
823 912 973
337 864 699
433 741
277 666
249
626
462
267
318
«
199
607
496
346
606
169
619
ction
783
831
299
664
211
243
186
178
266
666
167
478
18 SEVENTH YEAR
Exercise 41. Addition
971
466
998
878
246
761
783
326
876
717
202
344
HI
411
602
616
116
661
888
600
761
136
494
228
438
812
209
802
787
794
Exercise 42. Multiplication
2344
688
3271
689
75
422
Exercise 43.
Addition
422
492 '
666
862
667
836
122
646
896
976
263
636
361
624
962
•
262
227
327
166
213
426
831
447
991
772
991
887
.104
•
Exercise 44.
Divii
sdon
33)792
72)16992
21)378
Exercise 46.
Addition
467
717
617
913
308
297
124
890
434
718
383
466
323
262
913
'
444
999
363
422
363
424
802
660
232
282
791
78i9
666
416
346
671
EXERCISES FOR SPEED AND ACCURACY 19
Exercise 46. Subtntctton
11 723697 683121 896762
33 83701 76243 69863
400271
38106
31)868
Exercise 47. Division
Exercise 48. Subtractioa
976432186
78523321
934106626
66687810
773642
6&666
Exercise 49
Most stores now have cashiers
to make change for their customers.
This ia much more economical be-
cause the cashier by constant prac-
tice becomes much more efficient
than would be possible for the many
clerks whose attention is mainly
devoted to selling goods.
The modem method of making chai^ for a purchase is by
addition. For example, if you seli goods to the amount of $1,73
and recrave a five-dollar bill from the purchaser, instead of
subtractii^ $1.73 from $5.00 you start with the amount $1.73
and take 2^, 25(i and 3 one-dollar bills from the change drawer
and say to the purchaser $1.73, $1.75, $2.00, $3.00, $4.00,
$5.00. This method is not only quicker, but saves the purchaser
20 SEVENTH YEAR
the trouble of counting his change. Practice making change
in this way for the following purchases.
Amount of money
Amount of purchase presented to the cashier
1. $ 0.12 A dollar bill
2. $ 3.48 Ten-dollar bill
3. $ 1.06 Two dollar bills
4. $ 5.28 Two five-dollar bills
6. $ .08 A dollar bill
6. $11.27 A ten- and a five-dollar bill
7. $12.39 Three five-dollar bills
8. $ 7.33 Ten-dollar bill
9. $ .65 Five-dollar bill
10. $ 2.48 Three dollar bills
11. $ .42 A half-dollar
SUPPLEMENTARY EXERCISES
These exercises are provided for pupils who finish the regular
practice exercises. They are purposely made more difficult
in order to offer a special incentive to rapid workers. The
same time limits should be used for these exercises that are
used in the preceding exercises.
1
i
Exercise 60.
Addition
2
6
2
1
7
8
8
7
3
3
2
3
6
8
9
6
4
4
6
8
1
2
6
6
9
2
4
6
7
3
6
9
3
1
2
8
6
2
1
2
4
4
1
7
9
3
3
3
8
9
6
1
3
6
7
8
7
6
4
1
7
9
9
6
3
7
7
6
4
6
6
7
9
4
1
7
2
3
2
8
6
6
9
8
4
3
1
1
SUPPLEMENTARY EXERCISES 21
Exercise 61.
Subtraction
8346
4206
9378
6600
6237
2973
6763
1828
2176
4266
»
8836
7000
1642
1961
4996
6284
5803
•
6082
3734
8312
2768
4766
1887
3123
Exercise 62.
Multiplication
6328
1976
5836
8219
2
9
7
3
6786
3628
9163
7668
8
5
6
4
3784
2178
6639
6689
9
3
8
7
Exercise 63. Addition
667
913
422
308
457
717
637
416
492
836
124
383
232
286
772
991
896
976
718
890
363
408
426
831
661
624
323
262
927
873
4%
999
807
673
768
926
Exercise 64.
Multiplication
6293
3829
4673
8166
27
64
38
96
22
SEVENTH YEAR
Exercise 66.
Division
2)7662
9)82603
7)26992
8)46288
6)31416
6)36834
3)3834
2)4906
9)46324
Exercise 66.
Subtraction
937462
483692
267634
362183
217926
108926
871039
668372
783219
714826
219387
Exercise 67.
438478
Division
3)8673
4)24728
7)4893
632000
371483
693042
217662
72)30816
44)1684
68)36366
Exercise 68. Addition
8073
3468
7604
2936
3884
6846
6921
2836
6846
1649
1279
8706
9648
1906
6331
6331
2499
6342
2783
6276
7628
6674
7807
6619
9746
CHAPTER II
REVIEW OF COMMON FRACTIONS
Exercise 1. Three Meanings of a Fraction
The fraction f may have any one of three meanings. (1) It
may mean 3 of the 4 equal parts of a thing; (2) ^ of 3 equal
things; or (3) 3 divided by 4.
For example: an inch is divided into fourths, f of an inch
may mean 3 of the 4 equal parts of an inch; J of 3 inches;
or the quotient of 3 inches divided by 4.
3 of the 4 equal parts of an inch.
H I I J of 3 inches.
1 '- 1 13 inchest- 4.
The above diagram shows the three meanings of the fraction
f . Work these three meanings out on your ruler.
Exercise 2. Reduction to Lowest Terms
The denominator 4 of the fraction indicates the size of the
equal parts by showing into how many equal parts the whole
has been divided. The numerator 3 shows the number of these
equal parts which form the fraction.
1. Show the three meanings that the fraction -3^ may have.
2. In the fraction ^ what is the denominator? What is
the numerator?
3. This fraction shows that the whole has been divided
into how many equal parts?
4. How many of these parts have been taken to form the
fraction?
23
24 SEVENTH YEAR
6. Answer the same questions for the following fractions
T^> "g"' 6> 3> 8> li"'
6. Divide both the numerator and the denominator of the
fraction -^ by 4. What is the result?
7. Compare the fraction f with the fraction -j^, using
the above diagram. Show that the two fractions are equal
by using your ruler.
8. Divide both terms of the fraction ^ by 3. Use your
ruler to compare the result with ^.
9. Divide both terms of the fraction ^ by 2. Compare the
result with ^.
10. Multiply both terms of the fraction f by 3. Use your
ruler to compare the result with f .
11. Multiply both terms of the fraction ^ by 2. Compare
the result with -J.
Use other examples, if necessary, to make clear the following:
PRINCIPLE: When the numerator and denominator of a frac-
tion are both multiplied by or both divided by the same
ntmiber, the value of the fraction is not changed.
When the numerator and denominator of a fraction are
both divided by the same number, the fraction is said to be
reduced to lower terms.
When both terms are multiplied by the same number, the
fraction is said to be reduced to higher terms.
EEVIEW OF FRACTIONS
25
12. Change ^ to higher terms by multiplymg both terms by 2 ;
by 3; by 5. Reduction to higher terms is used in reducing
fractions to a common denominator.
13. Which is shorter: To divide both terms of ^ by 5, and
then both terms of the result by 3, or to reduce to lowest terms
by dividing both terms of ^ by 15?
Reduce to lowest terms:
1.
f
7.
M
13.
if
19.
u
S6.
U
2.
T^
8.
U
14.
ft
20.
u
26.
U
8.
t
9.
if
16.
if
21.
u
27.
u
4.
A
10.
U
16.
U
22.
?2
3d
28.
M
6.
H
11.
H
17.
if
23.
If
29.
m
6.
n
12.
M
18.
U
24.
u
30.
m
Exercise 3. Addition and Subtraction of Similar Fractions
Similar fractions are fractions having the same denominator.
1. $3 +$4 are how many dollars?
2. 3 books+4 books are how many books?
8. 3 fourths+4 fourths are how many fourths?
The form f +^ means the same as 3 fourths+4 fourths.
Which is more quickly written? Which form occupies the
least space?
If we use the more convenient form f for 3 fourths, we must
not forget that the denominator merely indicates the name
or size of the equal parts. The numerator shows how many of
these equal parts compose the fraction. In adding the frac-
tions l+f, we are merely adding two numbers of fourths,
making -J. How shall we proceed, then, in subtraction of
similar fractions?
26
SEVENTH YEAR
Add or subtract the foUowii^:
1.
i + f
2.
^ + f
3.
7 3
1 1 1 1
4.
i + f
6.
l + i
6.
l-t
7.
f-f
8
9
10
11
12
13
14
5 I 2 _
T -h T -
it T3 —
5 2. ~~
6 "" 6 ""
1 I 2 _
3 T^ 3 —
4
5
9
TT I 11
3 _
5 ""
4 _
16.
2 I 5
-f =
ri 1 —
16.
A+A-A
17.
f-f + i
18.
3 1 2 _ 1
5 T^ 5 5
19.
l-f-f
20.
H+A-A
21.
l + l + l
Exercise 4. Addition and Subtraction of Dissimilar Fractions
Dissimilar fractions are fractions not having the same denom-
inators.
Can you add $3 and 4 books together? You can not unless
you say 3 things and 4 things are 7 things; or 3 articles+4
articles are 7 articles. Only like numbers can be added or
subtracted. The term thing or article might be called the
common denominator of the two numbers.
Can we add f+f? What must be done before we can add
them? What is the least common denominator of these two
fractions?
The following form will be found very convenient for adding
dissimilar fractions:
2 I 3_8+9_17«l 5.
3"r4 — j2 — 12 "■•^1^
The advantages of writing the denominator once as ir '^* .
form above are (1) it is shorter; (2) it indicates the commit
denominator more clearly and (3) shows that only the numer-
ators are to be added. The expression ^^^ should be read
REVIEW OF FRACTIONS
27
Add or subtract as indicated:
1.
f + i =
7.
t+A =
13.
A+l =
19.
f-! =
2.
ii-l =
8.
7 3 _
5 - 5 =
14.
l + f =
20.
i + l-
3.
l + f =
9.
T^+t =
16.
f-l =
21.
i-f =
4.
il-f =
10.
f-A=
16.
^-4 =
22.
i+A=
6.
ii+f =
11.
1 3 _
4 14
17.
4 + 1 =
23.
H-^ =
6.
f-A=
12.
|-f =
18.
f + f =
24.
n-^=
After the pupils understand these problems, put the work on a time
basis and give a drill exercise. 8 minutes is suggested as a suitable time
limit for the average class.
Exercise 6. Addition and Subtraction of Mixed Numbers
In addition and subtraction of mixed numbers the form
shown below is one of the most convenient:
Example; Add 3|, 12f , 7^, 15^.
As shown in the illustration, the least common
denominator is found and written below the
line. The numerators are then placed to the
right of the vertical line, the sum being -|t
or Iff. This sum is then added to the integers,
making 38ff .
q3
^8
9
12f
18
7A
•3
8
15|
12
38ff
M
Add:
1. 13f
8f
27|
431
2.
25|
H
38f
3.
48|
62f
95|
86f
4.
Subtract:
6. 9 8 o-g
7. 25^—85
8. 16|- 9i
9. 17|-10|
5f
S.
21^
7f
36^
H
48i
6|
9f
.0. 7-}-
-4|
.1. 12 -
-81
28 SEVENTH YEAR
12. A box of scouring brick weighed 60f lb. The box itself
weighed 4^ lb. How much did the scouring brick weigh ?
13. The sum of two numbers is 28 J. One of the numbers is
17f. What is the other?
14. In two bins of potatoes there are 128^ bu. In one
there are 62 J bu. How many are there in the other?
16. A flagstaff 62^ ft. high was made of two poles spliced
together. The lower pole was 28 f ft. tall. How mtich did
the upper pole add to its height?
16. A kite string 286^ ft. long broke at a distance of 127^
ft. from the lower end. What length of string went with the kite?
17. A clerk earned $90 per month. His expense for board,
for this period, was $30 i; for laundering, $5 J; for articles
of clothing, $14 J; for life insurance, $3^; for incidentals,
$14 f. What was the surplus for the month?
18. A boy sawed a piece of board exactly 20 inches long
from a board 26^ inches long. Allowing -^ of an inch for the
cut of the saw, find the length of the piece that was left.
19. Four boards were glued together for a table top. When
planed for the glue joints, they measured 6f in., 7§ in., 7 J in.
and 6^ in. respectively. Find the width of the table top.
How much would have to be planed off this top to make it
27 in. in width.
20. A school room is 12 ft. high. The picture molding is
3f ft. from the ceiling. How far is the molding from the floor?
21. How wide must a strip of goods be cut to make a ruffle
3 in. wide when finished if ^ in. is turned under for the heading
and f in. is used for the lower hem?
22. A room is 12^ ft. long and 11 f ft. wide. How many
feet of base board are required to go around the room, deducting
3§ ft. for the door?
REVIEW OF FRACTIONS
29
Ezerdse 6. Multiplicatioii of Fracti<ni8
Example:
4X3 = ?
Take a foot ruler. What is ^ of a foot in inches? What is ^ of f of
a foot in inches? Show, then, that ^ of ^ of a foot ^-^ of a foot, i of f
of a foot =YS ^^ ^ foot? j- of f of a foot --j^ of a foot? In multiplication
of fractions the word of may be replaced by the sign X.
Therefore: f Xf = A-
Ck>mpare the product of the numerators of the fractions with the num-
erator of the result, -f^.
Ck>mpare the product of the denominators of the fractions with the
denominator of Uie result, ■^.
Reduce -^ to its lowest terms.
Cancellation is the process of reducing to lower terms before multiplying
by dividing any numefator and any denominator of the fractions by the
same number:
1 1
^X^=^
< 3 2
2 1
We see, then, that in the multiplication of fractions the product of
the numerators of the fractions becomes the numerator of the result and
the product of the denominators the denominator of the result, cancellation
being used to shorten the process.
Multiply the following fractions: Use cancellation.
1- l^X f = 9. i^X I = 17. i X I X A=
18. "§■ X "5 X"5^=
19« "2 X 3X7*^
ao. fxfxii=
ai. MxM xH=
aa. MxMx i =
28. MxMx I =
84. MxHxU^
2. ixf =
10. HxA=
8. f X^-
11. |xM=
4. T«WX f = :
18. if Xt%=
6. Jxi= 3
18. 1 X 1 -
6. ^Xf= :
I*. Mx||=
V |xf =
18. fxf =
8. ixi-
16. ixi =
30 SEVENTH YEAR
26. A boy glued 5 maple strips and 4 walnut strips together
to make a pen tray. If each of the strips was -^ in. wide,
how wide was the piece for the tray?
26. A teacher asked a boy to make him a book case for a
set of encyclopedias consisting of 30 volumes. How long must
the boy make each of the two shelves if the books average
2| in. in thickness?
27. How many yards of ruf9ing must be made to put 5
ruffles around a dress skirt three yards in girth if ^ extra is
allowed for the gathering?
28. How much will f of a yard of ribbon cost at 22 cents
per yard?
29. A piece of goods containing 6 quarter-inch tucks and a
1-in. hem is 20 in. when finished. How wide was it before
being tucked and hemmed?
30. How wide must a piece of goods be, to be 24 in. wide
when complete, if we allow for 6 "one-eighth'' inch tucks;
6 "one-fourth" inch tucks and a 2-in. hem?
Exercise 7. Division of Fractions
In division of fractions we may use two methods: (1) reduce
to a conunon denominator and divide the numerators; (2) invert
the divisor and multiply.
(1) Example: |-.f =g^l2=^=^or if
Note that you are dividing 12 fifteenths by 10 fifteenths, giving as a
result \% times — the denominator being eliminated in the division.
(2) Example: |4-§ = ?
Take a sheet of paper and fold it
into thirds as in the illustration.
How many times will the shaded
portion representing f be contained in the whole sheet?
_-_J_ , J. ^_ ..,I.T..— —
.
■ . ' ' .
, . , . ■
'•-' \ ■ '
■^■l : ■'. \ ■'.
^
. • !•■ J
,_\
REVIEW OF FRACTIONS
31
Since a whole sheet contains f of a sheet 1^ or ^ times,
f of a sheet contains f of a sheet ^ of -f times.
2
Therefore: 4 2^36 1
-+-«-X-=-or 1-
5 3 5 2 5 5
1
■| is the divisor. We see that the f- has heen inoerted, beooming -f when
we multiply. By using the above method with other examples you wiU
find that the divisor is always inverted before you multiply.
«
PRINCIPLE: To divide one fraction by another, invert the
divisor and multiply.
This method is preferred to reducing to a oonomon denominator because
the division example is converted into a multiplication example, which
is the easiest of all the processes in fractions.
Divide the following fractions:
1.
8. f + f-
10. J -5- i =
1.
8.
f
3 J. 5 ^
1
7
16. f -i- i
17. M
8. H- I =
A=
18. f
18. H
20. f
22 __
Ezerdse 8. Multiplication and Division of Mixed Numbers
How do you change a mixed number to an improper fraction?
Which is easier: to divide 2f by if or to divide |- by |-? In
multiplication ai^d division of mixed nmnbers, then, it is easier
first to reduce the mixed numbers to improper fractions and
then perform the operation of multiplying or dividing.
Multiply or divide:
1. 3fX2f
2. 6§Xlf
8. 12f ^2|
4. 5f4-3^
6. 3iX8f
6. 2-3-5-3-j-
7. 2|xlf
8'7X • o3.
• • 3 "^"^4
9. lfX2| =
10. 6iX6| =
11. 6|-J^3^ =
12* V7g"~r"03"=^
32 SEVENTH YEAR
13.
4iX2| =
17. 6|X1VV=
21. lfX3i =
14.
9fxiH=
18. 4jX3| =
22. 8|-5-li =
16.
19. ll-i-lf =
28. 2fX2j =
16.
3i-Mi =
20. 4f-5-3i =
24. 2|-f-3j =
26. How many times can 1 J gallons of oil be drawn from a
barrel holding 31^ gallons?
26. How many bushels of apples at Slf can be bought
for $7i?
27. If nine hogsheads would hold 50f bu., what would
1 hogshead hold?
28. How many pounds of bacon at $J per pound can be
bought for $i?
29. At $lf per crate, how many crates of peaches can be
bought for $17^?
30. A railway section of 8^ miles cost for construction
$246,504 J. What did it cost per mile?
31. A banker bought a tract of timber for $7490, at $53^
per acre. How many acres did he buy?
32. If I pay $5f for books at $f per volume, how many
volumes do I buy?
33. At $f per basket, how many baskets of fruit can be
bought for $27?
34. At 3^ miles an hour, how long does it take a person
to walk 8f miles?
36. A teacher has a desk book rack 21 in. long. How many
text books averaging ^ in. thick will it hold?
36. A class bought two strips of ribbon of diflferent colors
for class colors. They divided the strips, which were 2lJ
yards in length, into 32 equal parts. How long was each piece?
REVIEW OF FRACTIONS 33
87. A girl making a base for a letter rack wished to locate
the central line. If the base board is 3^ in. wide, how far will
the center line lie from each edge?
38. When sugar is selling at 7§ cents per pound, how many
pounds are sold for a dollar at that rate?
Exercise 9. Drill on the Four Processes in Fractions
Solve the following:
10. |xt=
12. t+l-
13. f Xf =
i-4. 3 '2
15. J -1 =
16. |+f =
26. Find the cost of a lOf -lb. turkey at 28 cents a pound.
26. How much will a 4^-lb. chicken cost at 24§ cents a
pound?
27. A roast weighing 4§ lb. costs 81 cents. How much was
the cost per pound?
28. A barrel of flour weighs 196 lb. How many pounds are
there in a J-bbl. sack? In a |-bbL sack?
29. Obtain local prices at a butcher shop and find the cost
of 2f lb. of round steak; 5^ lb. of rib roast; and 1^ lb. of
pork chops.
30. A man owned f of a mill and sold f of his share. What
part of the total value of the mill did he sell? What part of
the mill did he still own?
1.
fxf =
2.
5 8
6 IT-
3.
1 + 1 =
4.
1-^1 =
6.
A-f-
6.
Hxn=
7.
i^f=
8.
1 + 1 =
17.
ixj=
18.
i+i =
19.
f -i=
20.
f^i=
21.
1+1=
22.
ix^=
38.
1-^1=
24.
UH=
34
SEVENTH YEAR
Exercise 10. Review of Decimal Fractions
A fraction, whose denominator is ten or some product of
tens, is called a decimal. The value of a figure in a decimal
is shown by its position with regard to the decimal point.
o
a
I I I
® 8 £
S S S
s
1
•a
JS
d
^ n & §
u 'i s s § 5
45 p 'o ^ ua ■*»
s S
s -*? ■
O 0) a
rS -5? o
a s
1
1 1 1,1 1 1 . 1 1 1,1 1 1
In the above number how does the 1 in tenths place compare
in value to the 1 in units place? How does the 1 in units
place compare in value to the 1 in hundreds place? How does
the 1 in units place compare in value with the 1 in tenths place?
How does the 1 in units place compare in value with the 1
in thousandths place? Start at the 1 in hundred thousands
place and go to the right. How do the values of the I's change?
Start at the 1 in millionths place and go to the left. How do
the values of the I's change?
The number above is read one hundred eleven thousand,
one hundred eleven, and one hundred eleven thousand one
hundred eleven millionths.
Read the following decimals:
1. .001
2. 19.02
3. .0005
4. 50.001
5. .00125
6. .375
7. 3.1416
8. 1.4142
9. 2150.42
10. .866
11. .7584
12. .5236
13. 1.732
14. 8.75
16. .875
16. .0875
17. .00875
18. .000875
19. .005
20. .000005
REVIEW OF DECIMALS 35
How many decimal places are needed to write tenths;
thousandths; hundredths; ten-thousandths; millionths; hun-
dred-thousandths? Practice on this question until you can
give the answers instantly, because it will help you in writing
decimals.
Write in figures:^
!• One hundredth.
2. Two hundred and five ten-thousandths.
3. Sixty-three thousandths.
4. Twenty-five hundredths.
6. Seven hundred fifteen thousandths.
6. Eighty-seven thousandths.
7. Nine hundred forty thousandths.
8. Sixty-three hundredths.
9. Sixty-seven thousandths.
10. Eight thousandths.
11. Five ten-thousandths.
12. One hundred twenty-five hundred-thousandths
13. Twenty-five millionths.
14. Twenty-five and five ten-thousandths.
16. One hundred and forty-three thousandths.
16. One hundred forty-three thousandths.
17. Four hundred one and four hundred one thousandths.
18. Three and twenty-five ten-thousandths.
19. Eight hundred and s6ven millionths.
^In writing decimals, it is a good plan to have no erasers at the black-
board and require the pupils to be sure of the number of places before
they be|^ writing each decimal that you read to them.
36 SEVENTH YEAR
Exercise 11. Addition and Subtraction of Decimals
Decimals are added and subtracted in the same manner
as whole numbers. The decimal points must be kept in a
vertical line and the other figures in their proper columns.
Add:
1. 2.7; .3; 37.1; 2.04; .0033;. 16.125; 105.06.
2. 15.03; 325.075; 18.0025; 15.005; 87.08.
8. .0025; .009; .00125; .875; .05.
4. .425; 3.1416; 1.4142; 15.375; 8.8736; 5.75.
5. 45.375; 37.525; 29.65; 86.245; 18.0005; 57.075.
6. .0075; 5.0035; .2508; .025; 2.1754; .7856.
7. 3.006; 61.375; 25.025; 7.75; .0725; 15.7.
8. 25.5; 5.78; .375; 2.14; 37.45; 4.806; 8.6.
9. .625; .375; .875; .125; .75; .25; .075.
10. 4.5; 67.34; 8.054; .4862; 325.8; .755.
Subtract: .
1. 4.312 from 7.505. 6. 87.45 from 148.1.
2. 1.4142 from 3.1416. 7. 29.802 from 32.
3. 23.075 from 28.008. 8. .25 from 25.1.
4. 1.387 from 2.025. 9. 2.62 from 4.875.
6. 6.76 from 11.025. 10. 27.51 from 30.
Note: Practice should be rriven in reading decimals as follows:
1.4142 — read: one, point, four, one, four, two.
Exercise 12. Multiplication of Decimals
Express the decimal .05 as a common fraction.
Also the decimal .5 as a common fraction.
REVIEW OF DECIMALS
37
If we multiply TDirXtV without cancelling, what is the
product?
How do we express yMu ^ * decimal?
Therefore: If we multiply .05 by .5, the product is .025.
How does the number of decimal places in the product
compare with the number of decimal places in both the multi-
plicand and multiplier?
PRINCIPLE: In multiplication of decimals as many places
are pointed off in the product as there are decimal places
in both multiplicand and multiplier.
Multiply:
1. 25.5X4.025
2. .005 X. 25
8. 3.75X3.78
4. 4.002 X. 32
6. .866X1.4
6. 273.5X1.64
7. 352.x. 0175
8. .0002 X. 0021
9. 62.5X7.05
10. .21 X. 3
11. $145.50X.375
12. $257.75 X. 06
18. $1250. X. 055
14. 2.72 X. 08
16. .0385 X. 55
16. 6.45X3.83
17. $250. X. 055
18. 275.5 X. 039
19. $272.75X.0275
20. 7.5X3.1416
21. 2.54X2.54
22. .5326X175.65
28. .0375 X. 0025
24. 855.x 0075
26. A cubic foot of water weighs approximately 62.5 pounds.
Copper is 8.93 times as heavy as the same volume of water.
How much will a cubic foot of copper weigh?
26. Gold is 19.3 times as heavy as the same volume of water.
Find the weight of a cubic foot of gold.
27. How much heavier is a cubic foot of gold than a cubic
foot of copper?
28. A gallon of water weighs 8.34 pounds. Kerosene is .8 as
heavy as the same volume of water. What is the weight of a
gallon of kerosene?
38 SEVENTH YEAR
Exercise 13. Applied Problems
XT. S. Army Daily (Garrison) Ration per Man
Beef, fresh 20. oz. Milk, evap. unsweetened . 0.5 oz.
Flour 18. oz. Vinegar^ 0.64 oz.
Baking powder 0.08 oz. Salt 0.64 oz.
Beans 2.4 oz. Pepper, black 0.04 oz.
Potatoes 20. oz. Cinnamon 0.014 oz.
Primes 1.28 oz. Lard 0.64 oz.
Coffee,roasted and ground 1.12 oz. Butter 0.5 oz.
Sugar 3.2 oz. Syrup 1.28 oz.
Flavoring extract, lemon . .0.014 oz.
1. Copy in column form and find the total weight, in
pounds and ounces, of the seventeen items given in this table.
2. Find the total required for one week. For thirty days.
3. Find the daily amount required for a company of 95
men. For two companies of 85 men each.
4. Find the daily amount that would be needed for a regi-
ment of 972 men.
6. Five Signal Corps men were stationed 21 days at Mt.
View. Find the total amount of rations they required.
6. It took 47 Army engineers 14 days to build a certain
bridge. What amount of rations did they require?
7. A batallion of three companies aggregating 270 men
was stationed at a certain point for two weeks. What amount
of beef, flour and potatoes was required for that period?
8. What amount of beans, prunes, coffee and sugar was
needed during that time?
9. Find the amount required of the other ten items for the
same period for these 270 men.
10. Find from local prices what the daily ration would
amount to for 100 men for 30 days for beef, beans and coffee.
'Approximate reduction to ounces. The government standard gives
vinegar 0.16 gill and syrup 0.32 gill.
REVIEW OF DECIMALS 39
Exercise 14. Division of Dedmals
1. Divide .025 by .05.
Express as common fractions and divide. What is the
quotient? Express this quotient as a decimal.
Divide the following decimals by using common fractions:
2. .626 -^ 12.5.
3. .625-^.125.
Check your results secured by dividing with common frac-
tions with the quotients expressed in the decimal form as
shown below:
.5. .05 5
.05) .02 5 12. 5). 6 25 .125). 625
25 6 25 625
Answer the following questions for each of the above prob-
lems:
4. How many decimal places are there in the divisor?
6. How many decimal places is the decimal point in the
quotient to the right of the decimal point in the dividend?
6, Can you tell from the above problems how the quotient
should be pointed oflf in the division of decimals?
PRIKCIPLE: In division of decimals, as many decimal places
are pointed off in the quotient to the right of the decimal
point in the dividend as there are decimal places in the
divisor.
Caviion: Be sure that you place the figures of the quotient
exactly where they belong or you will introduce an error in
the result when you point oflf the decimal places in the quotient.
Divide the following (carry out three decimal places if they
do not come out even) :
40 SEVENTH YEAR
1. 30. by 7.5 6. 31.042 by 8.3 11. 26.52 by 3.4
2. 1.2 by .6 7. 8.2 by .0041 12. 20.5 by 8.2
3. 36. by 2.4 8. 46.875 by .375 18. 8.5 by 3.4
4. 61.165 by 37.9 9. .0003 by .5 14. 6.3 by .18
6. .008 by .04 10. .4 by .002 16. 3. by 8
Exercise 15. Changing a Common Fraction to a Decimal
On page 23 it was shown that one meaning of a fraction is:
the numerator divided by the denominator. This is the simplest
method to use in reducing a common fraction to a decimal.
Reduce f to a decimal. Divide 3 by 8.
.375
8)3.000
Therefore
: | = .375
Reduce the following fractions to decimals:
•
1. i
6. f
11. i
16. ^
^•i
7.1
". 1
17. i
O. 3
8.1
13. f
18. f
*.i
A £
14. 1
19. tV
R 1
0. 8
10. i
16. f •
20.^
Exercise 16. Ch
andne a Decii
nal to a Common Fr
Express the decimal .375 as a common fraction. Reduce
this fraction to its lowest terms. Example : 1^7^ = ^^ = f .
Reduce to common fractions:
1. .50
6. .6
11. .125
16. .05
2. .626
7. .875
12. .2
17. .075
8. .75'
8. .03125
13. .33§
18. .025
4. .8
9. .0125
14. .66f
19. .02
6. .25
10. .0375
16. .16|
20. .35
APPLIED PROBLEMS IN FRACTIONS
Applied Problems Involving Fractions
The following problems were supplied by one of the largest
stores in the United States. They are practical problems,
representing selections from admd sales slips, involving frac-
tions. Many of the great commercial bouses find it necessary
to tnun their applicants in such problems as these in order to
make them proficient in fractions.
One young man graduated from a school for training em-
ployees in a half-day. Why? Simply because he had mastered
his arithmetic before applying for a position and so did not
need the course of trmning.
Exercise 17
Find the amount of the purchases in each of the following
problems:
1. Mrs. H. A. Marshall purchased 9| yards broadcloth at
$2.75 per yard.
3. Mrs. S. A. Thompson bought 1§ yards tulle at Jp.75
per yard.
3. Miss Myrtle Hanlon purchased if yards net at 55^;
ij yards lace at 30fi; 1^ yards veiling at {1.75.
42 SEVENTH YEAR
4. Mrs. Harry Smith bought 2f yards lace at 65ff ; 2f yards
edging at 3ff; 8f yards edging at 3ff; 1^ yards edging at 15^.
6. Mrs. C. P. Murray purchased 1 J yards velour at $2.50;
1^ yards velvet at $3.50.
6. Mrs. M. M. Spaulding bought 5^ yards dress goods at
$2.65; 4f yards dress goods at $3.55; 2^ yards dress goods at
$6.00; 3^ yards dress goods at $5.35.
•
7. Mrs. E. F. Chatfield ordered 6^ yards lace at 45^;
Ij yards veiling at 95ff; 1 J yards fillet at 55 ff; ^ yard net at
8. Mrs. R. F. Arnold purchased 5^ yards edging at 12ff;
2^ yards silk at 85ff ; 1^ yards cretonne at $1.50; ^ yard damask
at 15ff.
9. Mr. C. P. Chase purchased the following: 31 J yards
linoleum at $1.40; 81^ feet wood strips, laid, at 5§ff; 6f yards
cork carpet at $1.25; 2f dozen f-inch Daisy pads at 80ff.
10. Mrs. R. H. Byron purchased ^ dozen tassels at $9.00
per dozen; 1^ yards braid at 60ff; 1 J yards guimpe at $1.75;
1^ yards trimming at 45ff.
11. Mr. S. E. Brown bought 1^ dozen stair pads at $2.00;
21^ yards china matting at 40ff; 6f yards Armstrong linoleum
at $1.75.
12. Mr. H. H. Howard purchased 1^ yards linoleum at 80^;
1 Duchess rug at $7.50; 1 Bokhara rug at $35.00; 1 Smyrna
rug at $7.00; 11^ yards velvet stair carpet at $1.35.
13. Mrs. F. A. Cornell made the following purchases: 6 J
yards guimpe at 45(5; f dozen tassels at $2.25; 4f yards fringe
at $1.75.
•
14. Mrs. M. H. Gardner bought j dozen tassels at 75«f;
3 J yards trimming at $1.05; 5| yards braid at 50^; 1 J yards
braid at $1.25.
APPLIED PROBLEMS IN FRACTIONS 43
16. Mrs. J. C. Gibson gave the following order: 1^ yards
fringe at lOff ; 2§ yards trimming at 25ff; 3^ yards braid at 50ff.
16. Mrs. E. S. Harding purchased 15^ yards cretonne at
60ff; f yard taffeta at $2.50; 1 velour remnant at $1.50.
17. Mrs. F. L. Black bought ^ yard braid at 75ff; 2| yards
swansdown at $1.75; 1^ yards trimming at 18ff.
18. Mr. Frank Adams purchased J dozen rolls paper at
12ff ; f yards oil cloth at 30ff ; if yards art paper at 25^; ^ dozen
Dutch Klenzer at 90ff.
19. Mrs. Chas. Madison made the following purchases:
f yards oil cloth at 65 ff; 17^ yards lace at 5ff; ^ dozen bars
Ivory Soap at 84ff; J dozen cans Kitchen Klenzer at 50ff.
20. Mrs. M. C. Nelson bought 2^ yards net at $2.50; 1§
yards muslin at $2.50; 16 f yards net at 35ff; if yards Sunfast
at $2.25; f pair portieres at $21.50.
21. Mrs. Harry Newell bought the following items: 7|
yards Sundour at $2.50; 4f yards edging at 10^; 12^ yards
muslin at 40ff.
22. Mrs. D. D. Penfield gave the following order: f dozen
towels at $3.00; f yards damask at $1.50; f dozen wash cloths
at $1.00; § dozen dusters at $1.75.
23. Mrs. C. H. Van Buren bought the following: f yards
sheeting at 75ff; f dozen towels at $6.00; f yard linen at 65ff;
§ yard linen at $1.25.
24. Mrs. C. P. Warren purchased as follows: f dozen
broom bags at $2.40; 3f yards crash at 30^; 2\ yards huck
at 65ff ; 3^ yards linen at 65ff.
26. Mrs. Harry S. Perry purchased the following: ^ pound
candy at 40ff ; 2^ yards embroidery at 15ff ; 4f yards embroidery
at 15ff; if yards embroidery at 18^.
44 SEVENTH YEAR
26. Mrs. Wm. Penn bought the following: ij yards silk
at $2.00; 1 J yards silk crepe at $2.00; 1 J yards silk at $1.00;
f yards silk net at $1.10.
27. Mrs. O. O. Morrison gave the following order: f yards
silk at $1.75; 9 yards silk poplin at 50ff; 1^ yards silk at $1.75;
f yards crepe at $1.50; 1 J yards silk at 75ff.
28. Mrs. S. S. Melrose bought as follows: 2 J yards ribbon
at 28^; 2§ yards ribbon at 29fi; if yards ribbon at 7ff ; 4f yards
ribbon at 14ff.
29. Mrs. Charles Mason purchased the following: 2 J yards
ribbon at 25ff ; 3 J yards ribbon at 18ff; 1^ yards ribbon at 38ff;
§ yard ribbon at 38ff.
30. Mrs. Chas. P. Hulce ordered 2j yards trimming at 85ff;
f yards trinmiing at $3.00; 2j yards braid at50ff;4^ yards
braid at 7ff; 1^ yards cord at 8^4.
81. Miss T. E. Bennett made the following purchases: ij
yards edging at 7^; 2§ yards lace at 4^; if yards lace at 60fi;
1 J yards lace at 25^.
82. Mrs. Harold P. Piatt bought the following: J yard dress
goods at $3.10; f yards dress goods at 65ff ; J yard dress goods
at $3.25; ^ yard dress goods at $3.50.
33. Mrs. C. F. Prince ordered the following: 1 J yards silver
lace at $4.65; lOf yards lace at $2.95; 2f| yards lace at $3.50;
12 J yards lace at $1.50; | yards veiling at 50ff.
84. Miss S. A. Roberts bought 1§ yards braid at $1.65; 4^
yards braid at 15^; 4§ yards braid at 3^4; 8^ yards braid at lOji;
1 J yards braid at $1.50.
86. Mrs. C. F. Sheldon purchased 16 J yards net at 50ff;
3f yards muslin at 55^; 44f yards net at $1.00; 2§ yards net
at $1.25; 2^ yards Sundour at $1.25.
CHAPTER III
PERCENTAGE
Exercise 1
The expression per cent means hundredths. To say that
4 per cent of a certain cow's milk is butter fat means that
xcir of the milk is butter fat. The sign % is usually used in
place of the words per cent.
The fraction twenty-five hundredths may be expressed in
three ways: (1) as a common fraction, -^(p^; (2) as a decimal,
.25; (3) as a per cent, 25%. The name hundredths is expressed
in the first case by the denominator 100; in the second case
by means of the decimal point and the two decimal places;
and in the third case by the sign %.
It is customary to omit the decimal point after whole numbers. The
decimal point is placed in the expression 25.% to make clear the process
of changing from decimals to per cent.
How has the decimal point been moved in changing from
the decimal 0.25 to the expression 25.%?
A decimal, then, may be changed to a per cent by moving
the decimal point two places to the right and attaching the
% sign.
Change the following decimals to per cents:
1. .25 6. .125 11. .75 16. .3
2. .35 7. .875 12. .005 17. .025
8. .01 8. .5 18. .00125 18. .0075
4. .2 9. .625 14. 2.5 19. .85
6. .16f 10. .375 16. 3.75 20. .20
45
46
SEVENTH YEAR
We have already shown that 25.% = .25. In changing
from % to a decimal^ how is the decimal point moved?
Change the following per cents to decimals:
1. 20%
6. 25%
11. 250%
16. 50%
2. 33i%
7. .25%
18. 625%
17. 37i%
8. 376%
8. 75%
18. 10%
18. i%
*. 12i%
9. 62|%
14. 66|%
1». lf%
5. .12^%
10. 40%
16. 60%
20. 3.9%
Exercise 2
How do you change a common fraction to a decimal? Change
the following fractions to decimals and then to per cents as
follows : -^=-05 =
1.
2.
3.
4.
6.
1
2
1
3
1
4
1
5
1
6
0'
8. i
10. f
11.
12.
13.
14.
16.
1
8
3
J
2
5
3
5
4
5
16.
17.
18.
19.
20.
3.
4
2
3
5.
6
1
TF
1
From the results that you have secured in the above exercise,
fill out a table similar to the form shown below. Leam all the
% equivalents of the conmion fractions, for you will need this
information in the following exercise.
Common Fractions and Their Equivalent Per Cents
^=?% .
i=?%
!=?%
i=?%
i=?%
1- = ?%
!=?%
!=?%
Have the teacher check this table before you leam it so that you will
not leam any incorrect equivalents.
PERCENTAGE 47
Exercise 3
Find 12^% of 64. 12 1% = what common fraction?
If we know that 12^% = 5, which is easier, to take .12^X64
or i of 64?
Find the following per cents by using fractional equivalents:
1. 33^% of 120 18. 76% of 320
2. 87^% of 160 14. 66f % of 300
8. 26% of 60 16. 16§% of 96
4. 20% of 45 16. 83|% of 36
5. 37i% of 200 17. 2% of 160
6. 50% of 1640 18. 80% of 60
7. 12 §% of 400 l«. 60% of 450
8. lli% of 81 20. 26% of 820
9. 62^% of 72 21. 14f % of 70
10. 40% of 75 22. 37 J% of 16
11. 10% of 160 " 28. 33^% of 63
12. 6|% of 32 24. 50% of 84
Since per cents may be expressed in equivalent decimals, it
is often convenient to multiply by a decimal if the fractional
equivalent is large.
Find the following per cents, using decimal multipliers:
25. 17% of 153 81. 6% of 43
26. 23% of 90 82. 7% of 65
27. 52% of 83 88. 11% of 85
28. 37% of 135 84. 15% of 124
29. 29% of 105 85. 21% of 34
80. 16% of 38 86. .6% of 96
87. Find 5§% of $2000.
38. Which is larger, 17% of $35 or 15% of $39?
48 SEVENTH YEAR
Exercise 4
Choose the most convenient equivalent and find the following
per cents:
1. 25% of 1240 16. 21% of 825
2. 8% of 412 17. 40% of 150
8. 12% of 217 18. 60% of 842
4. 20% of 315 19. 16% of 124
6. 12§% of 720 20. 87^% of 128
6. 16f % of 96 21. 2% of 600
7. 22% of 121 22. 7% of 125
.8. 5% of 132 23. 60% of $80
9. 5% of 120 24. 33^% of $360
10. 80% of 250 26. 11^% of $450
11. 13% of 138 26. 75% of $480
12. 37^% of 88 27. 17% of $312
13. 66f % of 75 28. 6% of $450
14. 15% of 200 29. 5i% of $110
16. 62^% of 160 30. if % of $50
EQUATIONS
Exercise 6
1. What is the product of 9X15? 9 and 15 are called the
factors of the product, 135.
2. If the two factors are given, what process is used in
finding the product?
3. If 8 times a certain number =128, what is the number?
4. If 5 times a certain number =55, what is the number?
6. If the product of two factors =48 and one of the factors
is 6j what is the other factor?
PERCENTAGE-THE EQUATION 49
6. If the product of two factors is 91 and one of the factors
is 13, what is the other factor?
7. If the product of two factors and one of the factors are
given, what process is used to find the other factor?
Show how the preceding problems illustrate the principles:
1. Factor X factor = product.
2. Product -^ one factor ~ the other factor.
The letter X is often used to stand for the unknown product ^
or the unknown factor. It is shorter and is not confusing if
you remember that it always stands for the unknown number.
Such expressions as 9X15 = X and 8XX=128 are called
equations because the expressions on the left and right sides
of the equality sign are equal.
Any equaiion can be represented by a balance as shown in the
illustration above, putting the expressions on the scale pans and
thus showing their equality. The value of X in the equation
9 X 15 = X can be found by multiplying the two factors 9 and 15.
The value X in the equation 8XX=128 is found by dividing
the product 128 by the factor 8, giving the other factor X= 16.
Find the values of X in the following equations:
1. 7XX=35 8. .06X300=X
2. X=9X25 4. .25XX=50
50 SEVENTH YEAR
6. XX15 = 75 9. 40 = XX500
6. X= 12X20 10. 6%X$150=X
7. 12XX = 240 11. 25%XX = $40
8. 240 = XX20 12. $16 = X%X$200
Exercise 6
Percentage problems may be easily solved by stating them
in the form of an equation and then solving by the principles:
1. Factor X factor = product.
2. Product -^ one factor = the other factor.
Remember that, in multiplying or dividing, per cents must be expressed
either as decimals or as common fractions.
1. What is 6% of $200?
This problem may easily be changed into an equation. X may stand
for what, which merely stands for the unknown number. Is may be
replaced by the equality sign ( = ) and the word of may be replaced by
the sign X. The equation is:
X=6%X$200.
6% and $200 are both factors of the unknown product X.
The principle Factor Xf actor = prodiLct applies to this equation. Before
we multiply, it will be necessary to change 6% to a decimal or a common
fraction because the multiplier must be an abstract number.
6% = .06. Therefore: 6%XS200 = .06XS200=S12.00.
2. What is 25% of $80?
Equation: X=25%XI80.
25% = i Then 25% X|80 =i X$80 =$20.
State the equations for the following problems and then
solve them:
3. What is 5% of $300? 8. What is 15% of $25?
4. What is 10% of $120? 9. What is 60% of $350?
6. What is 33^% of $90? 10. What is 8% of $110?
6. What is 50% of 22 pounds? 11. What is 16f % of 48 hogs?
7. What is 20% of 84 miles? 12. What is 12^% of 24 cents?
PERCENTAGR-THE EQUATION 61
Exercise 7
1. A boy bought a motorcycle for $70 and sold it at a gain
of 20%. How much did he gain?
This problem can be changed into the simple form of the preceding exer-
cise. The question is: How much did he gain? The problem states
that he gained 20%. Since gain is alivaya figured on the cost, he gained
20% of $70. In short form the problem really means:
What is 20% of $70?
Equation: X=20%X$70.
X = .20 X $70 = $14.00, the gain.
Remember that the number of per cent must be changed to a decimal
or a common fraction before multiplying, because the multiplier must be
an abstract nimiber.
8. A merchant sold a suit costing $15 at a profit of 40%.
What was his profit on the suit?
By studying this problem as we did problem 1, we see that it can be
put in the shortened form:
What is 40% of $15?
Equation: X =40% X$15.
40%=f . Then X=fX$15 =$6.00, the profit.
3. A firm recently announced an increase of 15% in the
salaries of all of its employees. How much increase would a
man receive whose salary had been $100 per month?
4. On a loan of $250 for a year, I receive 6% of that sum
for the use of the money. How much do I receive for the use
of the money?
6. A real estate dealer sold a lot costing $1500 at a gain of
33|%. What was his gain?
Exercises 6 to 13 have been arranged according to the three t3rpes of
percentage problems for the convenience of the teacher who prefers to use
a different method from the one developed in the text.
52 SEVENTH YEAR
6. A fanner planted 40% of his farm of 240 acres in com.
How many acres did he plant in com?
7. A ranch owner had 648 cattle and marketed 12 J% of
them. How many cattle did he market?
8. An agent sold an automobile costing him $1200 at a
profit of 33^%. Find the amount of his profit.
9. My neighbor sold a cow costing him $75 at a gain of
20%. Find the amount of his profit.
10. I have a balance of $150 on deposit in the bank. If I
give Ja tailor a check for 20% of this amount to pay for a suit of
clothes, how much does my suit cost me?
11. A grocer sells eggs costing 24 cents per dozen at a profit
of 25%. How much profit does he make on each dozen of
eggs?
12. A farmer takes a can containing 100 pounds of milk to
4
a creamery. A test is made of the milk and it shows that the
milk contains 3.9% of butter fat. How many pounds of butter
fat are there in the can of milk?
13. A family pays 30% of their income of $1200 for rent.
How much do they pay for rent?
14. At what price must a horse costing $125 be sold to gain
for its owner 20%?
16. If a suit marked at $25 is reduced 20% in price, what is
the reduced price mark?
16. A man bought 4 suburban lots for $700 each. On two
of them he made a gain of 25% when he sold them and on the
others he lost 10%. What was his loss or gain on the four lots?
The last three problems in this exercise may be more conveniently
solved by using the method shown in the next exercise.
PERCENTAGE— THE EQUATION 53
Exercise 8
1. What will be the result if 200 is increased 12% of itself?
200 is already 100% of itself. If it is increased 12%, the result will
be 112% of 200.
Equation: X«112%X200.
X = 1.12 X200 =224.00, the new result.
2. What will be the result if $125 is decreased 20%?
$125 « 100% of itself. 100% -20% (decrease) =80%.
The new result will be only 80% of $125.
X=80%X$125.
X=iX$125=$100.
What will be the result if
3. 300 is increased 30%? 13. $30 is decreased 33 J%?
4. $500 is increased 6%? 14. $250 is decreased 20%?
6. 180 lb. is increased 10%? 16. 360 is decreased 10%?
6. $240 is increased 16f %? 16. $75 is decreased 20%?
7. 80 is increased 20%? 17. 40 is decreased 40%?
8. 36 is increased 33 J%? 18. 240 bu. is decreased 12§%?
9. 1601b. is increased 12 1%? 19. 140 lb. is decreased 10%?
10. 20 bu. is increased 25%? 20. $120 is decreased 16f %?
11. $500 is increased 8%? 21. $80 is decreased 37|%?
12. 32 is increased 25%? 22. 8 bu. is decreased 50%?
23. K a suit of clothes marked at $30 is reduced 16f % in
price, what is the reduced price mark?
24. A certain brand of shoes, retailing at $5 per pair, advanced
20% in price in a year. What was the increased price of a pair
of these shoes?
26. A man paying a rental of $408 per year finds that his
rent is to be increased 12% on account of improvements on the
property. What is his new rent per year?
54 SEVENTH YEAR
26. K $1640 worth of groceries have advanced 25% in price
since they were purchased, what is their new valuation?
27. A man has $14,000 invested in a lumber business and !
$26,000 in an artificial stone enterprise. In the lumber business,
he loses 8% of his investment. What amount must he gain on
the other investment to yield him a profit of 10% on both
investments?
Exercise 9
!• 24 is what % of 30?
This type of problem may easily be changed into the equation form:
24=X%X30.
In this equation we have the product (24) given and also one of the
factors (30). The other factor is unknown. This equation involves the
principle:
Product-:- one factor = the other factor.
.S or 80%
30)24.0
240
Therefore: 24=80% of 30.
2. 16 is what % of 24?
Equation : 16 = X% X24.
The unknown factor X% =the product 16-^the factor 24.
Since a fraction may stand for an indicated division, we may indicate
this division in the form of the fraction, -J^.
Then X%=M = 1^661%.
Therefore : 16 is 66f % of 24.
8. 6 is ?% of 18? 9. $80 is ?% of $120?
4. 20 is ?% of 25? 10. 24 bu. is ?% of 40 bu.?
6. 15 is ?% of 18? 11. 48 is ?% of 64?
6. 25 is ?% of 40? 12. $120 is ?% of $2400?
7. 48 is ?% of 80? 18. $16 is ?% of $200?
8. 27 is ?% of 36? 14. 20 bu. is ?% of 24 bu.?
PERCENTAGE— PRACTICE PROBLEMS 55
16. 80 is ?% of 160? 22. $400 is ?% of J1200?
16. 81 is ?% of 90? 28. $63 is ?% of $1260?
17. 21 is ?% of 63? 24. $7 is ?% of $140?
18. 24 is ?% of 240? 26. $15 is ?% of $300?
19. 16 is ?% of 96? 26. $12 is ?% of $240?
20. 75 is ?% of 125? 27. 320 acres is ?% of 480 acres?
21. $60 is ?% of $75? 28. 10 gaUons is ?% of 80 gallons?
Work of this type is valuable in giving experience in solving equations
before attempting to solve concrete problems in which such equations
are involved.
Exercise 10
1. A newsboy bought 50 Sunday papers and sold 48 of thena.
What per cent of his papers did he sell?
Since he sold 48 out of 50, the question is:
48 is what % of 50?
Equation: 48=X%X50.
PRINCIPLE : Product -^ one factor = the other factor.
Then X% =48^50 = .96 or 96%.
2. A farmer bought a carloaxi of steers averaging 930 lb.
When the farmer sold them, they averaged 1240 lb. What
was the per cent of increase in their weight?
1240 lb. -930 lb. =310 lb., the increase.
310 lb. is what % of 930 lb.?
3. If the farmer bought the steers for $7.00 per hundred
and sold them for $9.45 per hundred, what was his per cent of
gain in the selling price per hundred over the buying price?
4. If a grocer buys eggs at 24 cents per dozen and sells
them at 28 cents per dozen, what is his per cent of profit?
6. During the season of 1916, the Boston American League
ball team won 91 games out of a total of 154. What per cent
of its games did Boston win?
56 SEVENTH YEAR
6. During the same season, Brooklyn in the National
League won 94 games out of 154. Find the per cent of games
won by Brooklyn.
7. In the Worid's Series between Boston and Brooklyn,
Boston won 4 out of the 5 games played. What per cent of
games did Boston win in this series?
8. A lumber firm increased its capital from $30,000 to
$45,000. What was the per cent of increase in its capital?
9. A laboratory test showed that a white potato, weighing
16 oz., contained 10 oz. of water. What is the per cent of water
in potatoes as shown by this test?
10. The same kind of a test on a sweet potato, weighing
15 oz., showed that it contained 8.25 oz. of water. What per
cent of water is there in a sweet potato?
11. If the per cent of refuse is the same in both white and
sweet potatoes, which of these vegetables contains the more
nutritive material?
12. If sweet potatoes are selling at 4 cents per pound and
white potatoes at 2 cents per pound, which is more economical,
considering the amount of nutritive material in each?
13. What per cent of profit must be made on the sale of
goods costing $50,000 to cover an expense of $7500 and a net
gain of the same amount?
14. A certain grade of canned peas advanced in price from
12 cents to 15 cents per can. Find the per cent of increase.
16. An owner of a bungalow costing $3000 rents it for $25
per month. His expenses are $60 for repairs, taxes and insur-
ance. Find the per cent of profit each year on his investment.
16. A farmer applied fertilizer to a field yielding an average
of 48 bushels of corn per acre and secured 66 bushels per acre.
Find the per cent of increase due to the fertilizer.
PERCENTAGE— FRACTIONAL EQUIVALENTS 57
Exercise 11
1. 24 is 75% of what number?
Equation: 24=75%XX.
X, the unknown f actor , =24 -5- .75 =32.
Care must be taken in this type of problem to reduce the per cent to
a decimal or a conmion fraction before dividing.
2. 16 is 25% of what number?
Equation: 16=25%XX.
In this problem, we see that 16 =25% or ^ of the number. The number
—A times 16, or 64.
Fractional equivalents are much shorter in solving some equations thaii
decimals. Practice using both in solving equations and then choose the
more convenient method for each equation.
8. 18 is \2\% of ? 12. $15 is 6% of ?
4. 21 is 75% of ? 18. $21 is 6% of ?
6. 48 is 80% of ? 14. $14 is 4% of ?
6. 40 is 62|% of ? 16. $12.80 is 8% of ?
7. 8 is 16f % of 7 16. 11 lb. is 4% of ?
8. 64 is 50% of ? 17. 9 is 2^% of ?
9. 12 is 25% of ? 18. 12 is 3% of ?
10. 63 is 87 f% of ? 19. 245 is 20% of ?
11. 9 is 16f % of ? 20. 81 is 37|% of ?
Exercise 12
1. If a man sells a house for $2760, which is 92% of what
he paid for it, what was the original purchase price?
In short form this problem means: $2760 is 92% of ? (cost).
Equation: $2760 =92% XX.
Find the value of X.
58 SEVENTH YEAR
2. I wrote a check for an insurance premium for $52.24
and found that it would take out 42% of the money I had on
deposit in the bank. How much money did I have on deposit?
3. After losing 18% of his investment in a gold mine, a
man has $6192.60 left. How much did he have invested in
the mine?
4. A farmer sold a cow for $84, thereby gaining 20%.
How much did the cow cost?
Suggestions: The cost of the cow = 100% of the .cost.
If the farmer gained 20%, he sold the cow for how many % of
the cost?
5. The present enrollment of a school of 486 pupils is 20%
more than its last year's enrollment. What was the last year's
enrollment?
6. The circulation of a certain newspaper is now 39,875.
This is an increase of 10% over that of last year. What was
last year's circulation?
7. If a railway line has been extended 18% of its original
length and is now 554.6 miles long, what was its original length?
8. If I add to my bank deposit $120, which is 60% of
what I already have on deposit, what was my balance before
making the deposit?
9. I paid $5 for a pair of shoes. This was 16f % of what I
paid for a suit. How much did I pay for the suit?
10. A bank distributes dividends amounting to $4800.
This sum is 12% of its capital stock. Find its capital stock.
11. A banker gained 8% on an investment. If his profits
were $202, what was the amount of his investment?
«
12. A boy gained 6 lb. during his summer vacation. This
was 6 J% of his weight at the beginning of the vacation. How
much did he weigh at the close of the vacation?
PERCENTAGE— REVIEW PROBLEMS 59
REVIEW PROBLEMS IN PERCENTAGE^
Exercise 13
1. Mr. Brown lost 15% on an investment of $1800. What
was his loss?
2. A boy who weighs 77 lb. has gained 10% since his last
birthday. What was his weight then?
3. An owner of a farm worth $175 an acre wishes to get
a return of 4^% on his investment. What rent must he charge?
4. If you have 12 problems to solve for home work and work
10 correctly, what should your grade be, considering the prob-
lems of equal value in grading?
6. 23 pupils in a class of 25 were promoted. What per cent
of pupils failed?
6. A man has an annual income of $1500 and pays $420
a year for rent. What per cent of his income does he pay for
rent?
7. A liveryman bought a team of horses for $350. After
using them for two years, he sold them at a- loss of 40%. What
did he receive for the team?
8. A contractor figured a house to cost $4375 and secured
the contract for $5500. What was his per cent of profit if his
estimate was correct?
9. An abandoned beach hotel which cost $80,000 is sold for
$48,000 at what per cent of loss? The purchaser reopens it
for a new class of patronage and sells it to a company for the
original cost. What was his per cent of profit?
10. A boy gave his playmates 75% of his apples and had
4 left. How many had he at first?
^This list of problems is designed to give practice in stating equations
for the three types of percentage problems.
60 SEVENTH YEAR
11. A teamster paid $100 each for 2 horses, $60 for a wagon,
anci $20 for a second-hand set of harness! At what price must
he sell the outfit to gain 10%?
12. The sales of a certain store were $72,000 for the year and
the profit made was $8000. What was the per cent of profit?
13. A mill is sold for $856,000 at an advance of 14^% on
its cost price. How much did it cost?
14. A man's expenses in a year are $1200. His salary is
133f % of that amount. How much money can he save in a
year out of his salary?
15. A grocer buys eggs at wholesale for 24f!^ and sells them
for 32f! per dozen. What is his per cent of profit?
16. I paid my rent with a check for $37.50, which was 5%
of my deposits in the bank. What was the balance remaining
in the bank?
17. A collector charged $60 for collecting a debt of $1200.
What per cent did he charge for collecting?
18. The engine in my automobile is 40 H. P. My neighbor's
engine is 60 H. P. His engine is how many per cent as powerful
as mine?
19. A factory employing 40 equally paid operators of
machines, reduces its force by 25% and increases by 25% the
wages of those that remain. Does it pay more or less in wages
than before?
20. Helen spent 35% of her Christmas money on one shop-
ping trip and 28% on the next trip. What per cent of her money
was left? If she had $7.40 left, how much money had she at
first?
21. A merchant sold goods for which he paid $30,000 at an
average of 30% higher price, but lost 5% from the failure of
certain debtors. What was the amount of his profit?
PERCENTAGE— PUPILS' OWN PROBLEMS 61
22. If one cow yields 15 quarts of milk each day, the milk
containing 3.6% of butter fat, and another cow yields 12
quarts of milk per day, containing 4.5% of butter fat, which
cow is the more profitable for butter making?
23. A house and lot were purchased for $4000. The house
was moved and sold for S2000 and the cost of moving. At what
price must the lot be sold to realize a total gain of 25% on the
investment?
24. The sales in a store were $960 for one day, which would
have meant a profit of 20% but for the unfortunate acceptance
of a counterfeit 20-dollar bill which could not be traced to the
payer. What was the net per cent of gain?
25. Standard milk is 87% water, 4% fat, .7% ash, 3.3%
protein and the remainder is made up of carbohydrates. What
per cent of standard milk is carbohydrates?
26. A merchant marks a suit of clothes costing $20 at an
increase of 60%. Later he discounts the marked price 20%.
What was the cost to the purchaser? What was the merchant's
per cent of profit on his cost?
27. After grooving, a 4-inch floor board is only 3 J inches
on its face. If you figure the number of board feet for a floor,
what per cent must you add to allow for the grooving?
Exercise 14
PROBLEMS COLLECTED BY PUPILS
The following problems were gathered by a seventh grade
class from their experiences and consultations with their
parents. See how many of these problems you can solve.
1. I have done 8 of the 50 arithmetic drill cards. What
per cent have I yet to do?
2. My father received an order from the army for $85,900
worth of goods. He receives 4% commission. How much
does he receive?
62 SEVENTH YEAR
3. I bought a share of stock last year for $114. I have just
sold it for $181. What was my per cent of gain?
4. Last year flour was $6.75 per bbl. and this year (1916)
it is $10.00 per bbl. What is the per cent of increase?
6. A bill of lumber was sold, the price being $864, but an
allowance of 10% was made for poor grade. There was also
a discount of 2% for prompt payment. Find the net amount
of the bill.
6. A manufacturer makes and sells an article for $24.00 per
dozen. His overhead charges^ are 20% of this and he allows
a cash discount of 7%. What is the net amount of his profit
per dozen, after deducting $15.00 for materials and cost of
manufacturing?
a
7. A wholesale dealer buys a boiler from the manufacturer
at the list price of $24.00 less 40% discount. He sells it to his
retail customer at 30% discount from the list price. How
much profit does he make on the sale?
8. A corporation is capitalized at $50,000. How much busi-
ness will they have to do yearly to pay a dividend of 10% on
their capital stock, provided their profit is 5% of their total
sales?
9. During 1915 a manufacturer employed 206 men at
$2.00 per day. In 1916 he employed 175 men and his total
daily wage bill was $395.00. By what per cent had the daily
per capita wage increased?
10. In 1900, $100 would buy a certain number of articles
of goods. In 1910, it took $120 to buy the same articles and
in 1916 it took $160 to buy the same goods. By what per cent
should wages have increased between 1910 and 1916 to have
enabled the laborer to purchase the same quantity of goods in
1916 as he had been able to purchase in 1910?
^Overhead charges cover all expenses of a factory except cost of material
and cost of labor.
PERCENTAGE— DAIRY PRODUCTS
63
16
Prepare a list of percentage problems based on the business
conditions in your community. Each pupil should bring in
at least two problems from which the teacher can select a list
for review work in percentage. Try to get actual transactions
to use in your problems.
Exercise 16
MILK AND CREAM
Efficient dairymen are now testing
the milk of each cow to see which are
the most productive. Those which are
not profitable are sold and others secured
in their places which produce a higher
per cent of butter fat. The amount
of butter fat is ascertained by means
of the Babcock test.
1. Some pupil in the class should make a careful study of
the Babcock test and make a full report to the class.
2. Standard milk is 87% water, 4% fat, 3.3% protein,
.7% ash, and the remainder is made up of carbohydrates.
What per cent of standard milk is carbohydrates?
3. Cream is 74% water, 2.5% protein, 4.5% carbohydrates,
.5% ash and the remainder fat. What per cent of the cream is
fat?
The test for butter fat is made in bottles similar
to the one shown in the illustration. The butter fat
accumulates in^ the neck of the bottle and can be
measured on the scale with a pair of dividers. The
bottle in the illustration shows a test yielding 4%
of butter fat.
64 SEVENTH YEAR
4. A farmer took a can of milk weighing 275 lb. to the
creamery. The test for this milk showed 3.8% of butter fat.
How much did he receive for this butter fat at 26 cents per
pound?
5. A certain recorded Jersey cow yielded 17,557 pounds
of milk in one year. From this amount of milk, 998 pounds
of butter fat were obtained. What per cent of the milk was
butter fat?
6. A certain recorded Guernsey cow yielded in one year
910 pounds of butter fat in 17,285 pounds of milk. What was
the per cent of butter fat in her milk?
7. A Shorthorn cow yielded 18,075 pounds of milk in a year.
The milk of this cow contained 735 pounds of butter fat.
What was the per cent of butter fat in her milk?
8. A cow's milk was tested by a dairyman with a view to
purchasing the cow. He found her milk to test 3.2% butter
fat. If the price was satisfactory, would you buy the cow to
add to a dairy herd?
9. A certain Holstein cow yielded an average of 14,134
pounds of milk per year for five years. If her milk tested
3.7% butter fat, how many pounds of butter fat did this cow
produce in the five years?
10. How much was this butter fat worth at 28 cents per
pound?
11. If one cow yields 30 lb. of milk per day testing 3.4%
of butter fat and another cow yields 25 lb. of milk testing
4.4% of butter fat, which cow is the more profitable and how
much per week?
If whole milk is sold for city consumption, the quantity of milk is a
more important consideration than the per cent of butter fat, providing
that the percentage of butter fat does not fall below a minimum of about
3.4%.
PERCENTAGE— DAIRY PRODUCTS 65
12. A dairymaD tested ten cows for butter fat with the
following resulte :
Pounds of milk Per cent of
Cow per day butter f&t
1 30 3.9
2 28 3.4
3 24 4.0
4 35 4.1
6 26 3.3
6 32 3.9
7 22 3.8
8 29 4.2
9 21 3.5
10 28 4.0
Which cows would you recommend that he keep and which
ones would you recommend that he sell and buy others to take
their places? Give ■ easoos for your decisions.
Duchess Skylark Ormsby,
a Holstein-Friesian cow, has
the record of being the
world's champion butter
producer. She produced
27,761 lb. of milk in a
year, yielding 1205 lb. of
butter fat.
15. Find the per cent
of butter fat in the milk of
the champion cow.
14. At 35 cents a pound, how much was that amount of
butter fat worth?
16. How much would the whole milk from this cow have
brought at $2.00 per hundred pounds?
Counuy of Uw iDtenutioDal HsrvegCer Co.
66 SEVENTH YEAR
THE MEAT ZHDUSTRY
{Applied percentage problems)
The meat industry is one
of the moat important enter-
prises in our country. In a
recent year the production of
beef, veal, mutton and pork
amounted to 22,378,000,000
lb., an average of about 220
lb. for each person in the
United States. Not all of
this immense production of meat was consumed in tbb country,
however, for a large portion of it was exported to foreign
countries.
Exercise 17
1, A farmer sold a carload of 20 steers avera^ng 1250 lb.
in weight for Sll.OO per hundred pounds. How much did he
receive for them?
3. If one of these steers loses 40% in being dressed, what
is the weight of the dressed beef in a steer weighing 1250 lb.7
3. If a steer weighing 1093 pounds alive weighs 632 pounds
when dressed, what per cent did this steer lose in being slaugh-
tered?
4. The two loins of a hog weigh about 10% of the weight of
a live hog. How much would each of the loins from a 220-
Ib. hog weigh?
6. A farmer ships a carload of 95 hogs aver^ng 225 pounds
in weight, receiving $12.35 per hundred. How much did he
receive for the carload of hogs?
6. Find the broker's commission at $10.00 per carload of
19,000 lb. and 5 cents [>er hundred in excess of that weight.
PERCENTAGE— THE MEAT INDUSTRY
67
J Bound 24.00%
ZJLoin JC.60'
3%FIatat 2^3 ■
4Jtib 9.64 -
A'MwBi 9.46-
OBridM e.oo
7'Chadt 22.05
SSJfkin/t 0,ZS
9^uei
In slaughtering a beef, the waste materials are all used.
From these waste materials or by-products are made leather,
glue, oleo oil, soap and fertilizers.
The carcass of a beef is divided
into 8 different cuts as shown in
the illustration at the left. The
percentage of the dressed weight
included in each cut of the beef is
also shown.
7. A dressed carcass of a steer
weighs 670 lb. Find the weight
included in each of the different
cuts for one-half of the carcass,
using the percentages in the illus-
tration.
8. If the by-products of a steer costing $132 were estimated
as worth $36, what per cent of the original cost of the steer
was obtained from the by-products?
9. A hog loses 25% to 35% of its weight in being dressed.
How much will a 200-lb. hog lose in weight if the loss is 33%?
10- How much will the 200-lb. hog weigh when dressed?
11. How much will a 175-lb. hog weigh, dressed; shrinking
35%?
12. The two short cut hams of a hog are about 13f % of
the live weight of a hog. How much do the two short cut
hams of a 230-lb. hog weigh?
Oleomargarine is one of the most important products made
by the packing industry. It is made from a mixture of oleo
oil, neutral, vegetable oil, milk and cream, and butter. The
oleo oil is made from the fat of cattle. Neutral is made from
the finest leaf fat of hogs. The vegetable oils include such oils
as cottonseed oil and peanut oil.
68 SEVENTH YEAR
15. The wholesale price on a certain brand of oleomargarine
was 24ff per pound in December of a recent year. The cheapest
brand made by the same firm was selling at only 75% of that
price. What was the price of the cheaper grade?
14. The retail price of the best brand of oleomargarine
mentioned in problem 11 was 28f!S at a certain grocery store.
The retail price was how many per cent greater than the whole-
sale price?
16. A certain meat packing firm states that 80% of their
sales go for the purchase of live stock, 8% for labor, 5% fo^-
freight and 4f % for other expenses. What per cent of their
sales is left for dividends for the stockholders?
16. If their total sales amounted to $500,000,000 per year^
compute the amount paid for live stock, the amount paid for
labor and the amount left for dividends. .
The receipts at the nine principal live stock markets in the
United States for the years ending October 1 are as follows:
Cattle Sheep Hogs
1911 9,416,374 13,530,833 19,217,506
1912 8,861,404 14,148,096 21,035,035
1913 9,188,500 14,146,284 19,997,656
1914 8,193,856 14,702,889 19,366,263
1915 8,464,185 11,994,851 21,366,263
17. What has been the percent of decrease in the number
of cattle from 1911 to 1915?
18. What has been the per cent of decrease in the number
of sheep received from 1914 to 1915?
19. What was the per cent of increase in the supply of hogs
from 1911 to 1915?
20. The average wholesale price of dressed beef in New York
in 1911 was $8.77 and in 1915 it was $11.64. What has been
the per cent of increase in the wholesale price of beef in that
period?
PEECENTAGE— THE COTTON INDUSTRY 69
COTTON
When picked, cotton is
first pnned,' and then
packed into bales weighing
approximately 500 pounds.
To economiae space in ship-
ping long distances these
bales usually are com-
pressed by powerful mar
chines into the smallest
possible compass. The
illustration shows one of Hi«h 0.0,1*1- Cotton C«np«>a.
these machines compressing a bale of cotton.
The following table gives the number of bales produced in
the leading cotton-producing states.
No. of bales No. of bales No. of bales
1913 1914 1915
Toms 3,945,000 4,692,000 3,175,000 .
Georgia 2,317,000 2,718,000 1,900,000
South Carolina 1,378,000 1.634,000 1,190,000
Alabama 1,495,000 1,751,000 1,050,000
Miesisaippi 1,311,000 1,246,000 940,000
Arkansas 1,073,000 1,016,000 786,000
North Carolina 793,000 931,000 708,000
Oklahoma 840,000 1,292,000 630,000
Louisiana 444,000 449,000 360,000
Tennessee 379,000 384,000 296,000
Missouri 67,000 82,000 52,000
Florida 59,000 81,000 B0,000
Vii^inia 23,000 25,000 16,000
All other states 32,000 64,000 40,000
United States 14,156,000 16,136,000 11,161,000
Total Value of Crop. $885,350,000 1591,030,000 $602,393,000
■Qinning is the process of removing the seeds from the cotton-
70 SEVENTH YEAR
Exercise 18
1. What was the per cent of increase in the number of bales
of cotton from 1913 to 1914? (See preceding page.)
2. Find the price per pound for cotton in 1913; for 1914 and
for 1915. The large crop and the outbreak of the great European
War in 1914 were responsible for the low price in 1914. Com-
pute the prices per bale.
3. Note the decreased production in 1915. What was the
per cent of decrease from the jrield for 1914?
4. What per cent of the total production of the United
States was the production of Texas in 1914; in 1915?
6. The production of Oklahoma in 1915 was what per cent
of its production in 1914?
6. The total production of the United States for 19 14. was
what per cent greater than the total production for 1915?
7. The total exports of cotton for 1913 was 4,562,295,675
lb. What was the value of our cotton exports in 1913 at 12.2
cents per pound?
8. Cotton constitutes about 53% of our total agricultural
exports. From the data given in problem 7, compute the value
of our total agricultural exports for 1913.
9. It is estimated that cotton forms 63% of the total crop
production in Texas. From the data in the table and the cost
per pound in problem 2, find the value of the total crop pro-
duction of Texas in 1915.
This offers a valuable type of work — getting information from a table
of statistics. Additional exercises of this type may be made from tables
of statistics such as those found in the Statesman's Year Book or other
similar pubhcations.
PERCENTAGE— FOOD PRICES
71
FOOD PiaCES
Exercise 19
The following table, originally published in a large daily
newspaper, shows the advances in the wholesale prices of
certain food supplies
during a recent year.
1. Find the per cent
of increase for each food
product given in the
table.
Food Products. 1915.
Hams, fresh $0.16
Bacon 24
Beef, No. 1, ribs 17
Sbeep, whole 00^
Leg of muttoD 12
Chickens, broilers 20^
Turkeys 20
Eggs, No. 1 24%
Butter 27
Potatoes .* 48
Onions, green 07
Cabbage (barrel) 86
Lettuce, leaf (box) .35
Celery (bunch) 26
Com, small cans (dozen) 78
Tomatoes, fresh 90
Nayy beans (bushel) 3.15
Peas, 2-lb. cans (dozen) 85
Apples, green (barrel) 3.25
Raspberries (No. lO's) 5.50
Peaches 2.86
Lemons, crate 3.00
Tea 36
Flour (barrel) 6.25
Sugar, granulated (100 lb.) 5.50
Cornstarch 03
Rolled oats 03
Spaghetti 06
Sardines 07%
Soap, kitchen 02%
1916.
$0.20
.26%
.19
.14%
.16
.24%
.30
.33
.34%
1.60
.10
1.90
.55
.30
.90
1.25
6.65
1.05
4.76
6.25
3.75
7.25
.40
7.95
6.40
.03%
.04
.07%
.12
.03%
2. Find the average
per cent of increase in
all these food products.
8. Ascertain if pos-
sible the present whole-
sale prices on the food
products listed and de-
termine the per cents of
increase or decrease since the last year shown in the table.
4. If you can get the prices, prepare a list of prices on
farm products and determine the per cents of increase or
decrease for two recent years. Compare com, oats, hay, cotton,
cattle, hogs, rice, sheep, horses, tobacco, and other such
farm products.
Local Prices
Secure at a local grocery store the retail prices on a list of
at least 10 articles for this year and also the prices for last year
on the same quality of goods.
6. Find the per cent of increase or decrease on each of the
articles that you have listed. Ask the grocer to tell you the
causes for the increases or decreases on the various articles.
73 SEVENTH YEAR
FOOD VALUES
There are four principd food
substances in the foods that we eat :
(1) protein (pro'-te-in) (2) corbo-
% hydrate; (3) fat; (4) mirieral Tnatter.
R Water is also an important con-
stituent of food products. Differ-
^ ent food products contain different
ij- proportions of these food substances.
Eggs, as shown in the illustration,
are composed of 73.7% water,
14.8% protein, 10.5% fat and 1% ash or mineral matter.
The protein compounds not only build up the tissues of the
body but they also furnish enei^ to enable us to do our work.
The carbohydrates and fats supply enei^ for the body.
Exercise 20
1. Usii^ the percentages given in the illustration above,
find the number of ounces of each of the constituents in a pound
of eggs.
2. The average composition of 1 pound of beef is as follows:
water 10.72 oz.; protein 3.04 oz.; fat 2.08 oz.; and mineral
matter .16 oz. Find the per cent of each substance in the
average pound of beef.
8, A white potato is composed of 1.8% prot«in, .1% fat,
14.7% carbohydrates, .8% ash, 62.6% water and 20% refuse.
Find the number of ounces of each constituent in 1 lb. of pota-
toes. (Refer to page 312 for additional data for problems.)
4. White bread is composed of 9.2% protein, 1.3% fat,
53.1% carbohydrates, 1.1% ash, 35.3% water. How many
ounces ore there of each food substance in a pound loaf of bread?
5, Compare amounts of various food substances in bread
and potatoes.
PERCENTAGE PROBLEMS— FOOD VALUES 73
6. If cereals and their products supply 62% of the carbo-
hydrates, and vegetables and fruits together 16% of the
carbohydrates, what per cent of the total carbohydrates do
both of these classes supply?
7. If meat and poultry supply 16% of the total food material
in the average American home, and dairy products 18%,
cereals and their products 31%, vegetables and fruits, together,
25%, how much of the total food materials do these items
constitute?
8. If meat and poultry supply 30% of the protein, the
dairy products 10% of it, cereals and their products 43% of it,
and vegetables and fruits together 9% of it, how much of the
protein is supplied by these four kinds of food?
9. If meat and poultry supply 59% of the fat, dairy prod-
ucts 26% of the fat, cereals and their products 9% of the
fat, and fruits and vegetables together 2% of the fat, what
per cent of the total fat do these four kinds of food supply?
Domestic science courses not only teach how to cook foods
but also what kinds of foods to prepare in order to secure a
proper proportion of the various food substances. When coal
is burned, it supplies heat which may be converted into the
energy of steam and run a steam engine. In a similar manner
the food which we eat is consumed by our bodies, supplying
heat and energy to do our work. Experiments have been made
to show the amount of energy which each food product yields.
These amounts of energy are expressed in terms of calories
(kal'-o-ries).
A calorie is used in this connection to mean the amount of
heat required to raise 1 pound of water 4° Fahrenheit.
The number of calories per day needed by any person varies
with his weight and the amount of work which he does. A
man at hard work or an active growing boy may require as
74 SEVENTH YEAR
much as 5000 calories of food energy per day. An average man
requires about 2500 calories when engaged in an occupation
where he is sitting most of the day.
The problem of the scientific cook is to serve foods which
will contain the proper food substances and at the same time
supply a sufficient number of calories each day.
The following table^ shows the amount of each food product
which will yield 100 calories:
Milk f cup, whole; 1^ cups, skim
^ream J cup, thin; 1 J tablespoons, very thick
Butter 1 tablespoon
Bread 2 slices S^xS^^xJ'
Fresh fruit 1 large orange or apple
Eggs 1 large, 1^ medium
Meat (beef, mutton, chicken, etc.) About 2 oz. lean
Bacon (cooked crisp) About ^ oz. (very variable)
Potatoes 1 medium
Sugar 1 tablespoon
Cocoa, made with milk -f of a cup
Cooked or flaked breakfast foods f to 1 J cups
Dried fruit 4 or 5 prunes or dates
Exercise 21
1. A man requiring 25(X) calories per day eats the following
breakfast: 1 cup of breakfast food with J cup of thin cream,
1 cup of cocoa made with milk, 2 slices of bread, 1 tablespoon
of butter, 2 small slices of bacon and 1 egg (large). Find the*
nmnber of calories supplied by this breakfast.
2. What per cent of the total requirement for a day is
furnished by that breakfast?
3. It is desirable that a family of five consume 3 quarts
of milk per day. If they consume 17 quarts per week, what
per cent of the desirable quantity have they used?
^See Rose, Feeding the Family.
PERCENTAGE PROBLEMS— FOOD VALUES 75
4. From the preceding table, prepare a menu for breakfast
that will furnish between 700 and 900 calories.
6. Prepare a menu for lunch to furnish approximately
1000 calories.
6. Which will furnish the largest number of calories, a
large orange or a medium sized egg? (See table, page 74.)
7. How many calories will a dozen medium sized eggs
supply?
8. How many calories are there in a quart of milk? (2 cups
make a pint.)
9. How many calories are there in a pound of prunes (40
to the pound)?
10. A man requiring 3000 calories per day eats a breakfast
furnishing 700 calories, a lunch furnishing about 900 calories
and a dinner furnishing about 1400 calories. Find the per
cent of the total furnished by each meal.
11. If the meals for a family for a week cost $5.60 and the
meat costs $1.40, the vegetables 70 cents and the butter 48
cents, what per cent of the total was spent for each group?
12. What per cent of the weekly expense was left for other
materials?
IS. If it takes 1 hour to prepare an entire meal and 20 min-
utes to make the dessert, what per cent of the whole time is
given to the dessert?
The following table shows the number of calories supplied
by a pound of each food product:
Beef, fresh lean 709 Beans 1564
Beef, fat 1357 Oatmeal 1810
Bacon (average) 2836 Lettuce 87
Butter 3488 Cabbage 143
Apples 285 Sugar 1814
Potatoes, white 378 Bread - 1174
Milk, whole 314 Eggs 672
76 SEVENTH YEAR
Exercise 22
1. The food value of a pound of fresh lean beef is what per
cent of the food value of a pound of butter?
2. A pound of white potatoes furnishes what per cent as
many calories as a pound of butter?
3. How does the food value of a pound of lettuce compare
with the food value of a pound of white potatoes? (Express in
per cent.)
4. In the same way compare the food values of fat beef
and bacon.
5. Which is cheaper, sugar at 7 cents per pound or beans
at 10 cents per pound, considering the food values of each?
6. Which is cheaper, apples at 6 cents per pound or bacon
at 28 cents per pound?
7. Which is cheaper, oatmeal at 5 cents per pound or eggs
at 26 cents per dozen? (Figure eggs at 1§ lb. per doz.)
8. From the cost of milk and butter in your community,
compute the cost of the amount of each necessary to supply
100 calories.
9. Find the cost of 100 calorie portions of cabbage, potatoes,
lean beef, beans, sugar, bread, eggs and bacon in your commu-
nity.
10. Prepare a menu for a lunch from the items listed on page
75, providing 900 calories for each of 4 persons. From local
prices in your community, estimate the cost of this lunch for
each person.
11. Prepare and present a problem on food values to the
class for solution.
12. If you have a school lunch room, estimate the cost to
the students of 100 calorie portions of as many of the dishes
as you can find the data to compute.
CHAPTER IV
APPLICATIONS OF PERCENTAGE
The subjects treated in this chapter do not involve any new
principles of percentage but merely an application of the prin-
ciples already mastered to new business situations. New
terms and new business forms will have to be mastered in
making the application of the principles already learned.
The discussion, then, at the beginning of each list of problems
should be thoroughly mastered in order to get a good knowledge
of business terms and organization.
BUSINESS TRANSACTIONS
Exercise 1
The gross profit in any business transaction is the difference
between the cost price and the selling price. The net profit
is the gross profit less the expenses of the transaction.
1. A notion store sold 100 pairs of wooden knitting needles
at 10 cents per pair, at a profit of 33^%. What was the cost
of each pair of needles?
2. If the selling price of an article is 4 times the cost, what
is the per cent of gain?
3. A fancy vest is sold for $7 at a profit of 40%. What
was its cost price?
4. A village lot was purchased for $1000, but because of a
decline in real estate values was sold for $750. What was the
per cent of loss?
6. A man sold a horse for $120 at a loss of 25%. What
did the horse cost him?
77
78 SEVENTH YEAR
6. A merchant bought goods listed at $1200 at a reduction
of 40%. He sold them at a profit of 25%. What was the total
selling price of the goods?
7. A merchant having goods worth $10,000 increased his
stock 25% and sold the entire stock at an averagje profit of
20%. For what sum did he sell it?
8. When an article that cost $24 is sold at a profit of 10%
and the purchaser sells it again at a loss of 20%, what is its
last selling price?
9. A liveryman sold a horse for $175 at a profit of 25%.
What was the cost of the horse?
10. A man sold two farms for $7500 each. On one he gained
20% and on the other he lost 20%. Did he gain or lose on the
entire transaction and how much?
11. A farmer bought a herd of 20 steers, averaging 1100
lb. each, at $7.50 per hundred. He fed them 700 bu. of corn
worth 65ji per bu., 15 tons of hay worth $12 per ton and
roughage worth $60. If his pasture of 20 acres was worth $6
per acre, what was his profit on the herd of cattle if they weighed
1476 lb. and brought $10.50 per hundred when he sold them?
12. A farmer sold his neighbor a cow at an advance of 10%
of what she cost him. His neighbor sold her to a dairyman at
an advance of 25%, receiving $110 for the cow. Find the
amount of profit made by each.
13. A manufacturer sold a hardware dealer a stove at a
profit of 10% on the cost of manufacturing. The hardware
dealer sold the stove to a customer for $61.60 at a profit of
40%. Find the cost to the manufacturer.
14. A dair3nnan sold two cows for $90 each. On one he
gained 20% and on the other he lost 10%. Find his per cent
of gain or loss on the entire transaction.
APPLICATIONS OF PERCENTAGE— DISCOUNTS 79
DISCOUNTS
Exercise 2
A discount is a sum deducted from the price of an article.
Discounts are usually computed by per cents. To state that
you will sell an article at a discount of 25% means that you
will sell it for j off or 25% off the regular list price.
Many firms give discounts for cash purchases. It is profitable
for these firms to give small discounts for cash purchases
because they can re-invest the money and be making additional
profits.
1* A music dealer sold a piano which he had listed for $400
at a discount of 20%. How much did he receive for it?
list price of the piano ==$400
20% of $400=i of $400= 80=the discount.
He received $320
The amount that is left after the discount is subtracted from
the list price is called the net proceeds. In problem 1, $400 is
the list price, $80 is the discount and $320 is the net proceeds.
Find the discounts and net proceeds of the following list
prices at the stated discounts:
2. $100, 25%. 6. $1.00, 30%. 10. $20, 15%.
3. $ 25, 10%. 7. $1.50, 33j%. 11. $40, 25%.
4. $250, 20%. 8. $500, 2%. 12. $5.00, 10%.
5. $ 30, 40%. 9. $125, 20%. 13. $452.75, 2%.
14. After using a motorcycle, costing $150, for a month,
a boy offered it for sale at a discount of 15% of the cost price*
How much did he want for the motorcycle?
16. A merchant bought a bill of goods amounting to $1240
and received a cash discount of 2% for prompt payment. What
was the net proceeds of his bill?
80 SEVENTH YEAR
CLEARANCE SALES
Exercise 3
Retail stores iiave clearance sales in order to dispose of old
goods on hand and make room for new styles and up-to-date
patterns. They often give reductions of 10%, 20%, 33 J%, or
even as high as 50%. In order to dispose of goods left on
hand in which the styles are likely to change, the merchant
may offer the goods at cost in order to prevent a loss at a later
date when the goods are out of style.
1. A merchant advertised a 20% discount sale on shirtSo
How much was the price on a shirt listed regularly at $2.50?
2.. A clothier oiffers a discount of 15% on all suits and over-
coats in his store. What is his sale price on suits listed at $25?
3. A furniture store advertised a closing out sale, offering
a discount of 33f % on the regular prices. Find the cost of
the following articles listed regularly as' follows: 1 library
table — $30.00; 2 rocking chairs at $15.00 each; 1 davenport —
$42.00; 1 brass bed— $24.00; 1 mattress— $12.00; 1 set of
springs — $9.00; and 1 dresser— $24.00.
4. In a clearance sale, a merchant gave a discount of
40% on novelty dress goods and 20% on the staple weaves.
Why could he afford to give a larger discount on the novelty
goods?
6. One shoe store advertised a ceitain shoe that retails
regularly at $4.00 for $3.45; another store advertised the same
shoe at a discount of 15%. Which was the better offer and how
much?
*
6. A merchant advertised $2.00 silks at a discount of 20%.
What was his sale pric6 on those silks?
7. Straw hats worth $3.00 early in the season were sold
late in the season at $1.50. What was the per cent of discount?
APPLICATIONS OF PERCENTAGE— DISCOUNTS 81
COMMERCIAL DISCOUNTS
Exercise 4
*
Wholesale dealers and manufacturers often offer two or
more discounts off the list price. These discounts are called
Irade or commercial discounts.
There are several advantages in using this system of com-
mercial discounts. In the first place, catalogues are expensive
to issue. By making the list prices of the articles high, fluctua-
tions in the cost of materials will not make it necessary to issue
a new catalogue. Instead, the firm can merely send out a
new discount sheet which gives the discounts allowed on the
various classes of articles. This discount sheet costs very
little compared with the original cost of the catalogue. Further-
more a retail dealer can show his customer the catalogue and
give him a discount on the list price without the customer
knowing the extent of his profit. Can you think of any other
advantages of commercial discounts?
If a firm is selling goods at a certain discount, a decrease in the cost of
production may enable them to add a second discount. A discount is
also usually allowed for prompt payment. Consequently, we occasionally
see goods listed subject to a series of three successive discounts.
Commercial discoimts are computed in sucession. The
first discount is taken from the list price and the second dis-
count is then computed on the remainder and so on.
1. A bed room suite was listed at $80 less discounts of 20%
and 10%. What was the net price?
20%X$80 =$16, the first discount.
$80 —$16 =$64/the remainder.
10%X$64 =$6.40, the second discount.
$64 -$6.40 =$57.60, the net price.
The net price is the list price less the conmiercial discounts.
82 SEVENTH YEAR
2. A piano listed at $500 has discounts of 30% and 5%.
Find the net price.
3. A hardware firm .quotes a certain grade of hammers at
$12 a dozen, less discounts of 33j% and 25%. What is the
cost of each hammer to a local dealer? What must he mark
a hammer to make a profit of 50%?
4. A merchant buys sweaters from a factory at $24
per dozen at discounts of 20% and 5%. What must he sell
them at in order to make a profit of 60%?
5. Stoves are quoted by a manufacturer at $40 each, subject
to discounts of 25%, 10% and 5%. What is the net price to
the retail dealer if he is allowed a further discount of 2% for
cash?
6. Find the net price on a dining table and set of six chairs
listed at $80 if discounts of 20% and 15% are allowed.
7. A music cabinet is listed at $65 with discounts of 25%,
10% and 5%. Find the net price.
List price Discount Net price
8. $175 20%, 10% and 5% ?
9. $150 25% and 5% ?
10. $400 30%, 10% and 5% ?
11. $40 20% and 3% ?
12. $75 25% and 2% ?
In order to save computation, firms have tables showii^
a single discount which is equivalent to the series of successive
discounts.
13. What single discount is equivalent to successive discounts
of 20% and 10%?
20% X 100% =20% 10% X 80% =8%
100%- 20% =80% 80%- 8% = 72%, net price.
APPLICATIONS OF PERCENTAGE— DISCOUNTS 83
100% -72% = 28%.
Therefore, 28% is equivalent to successive discounts of 20%
and 10%.
14. What single discount is equivalent to successive discounts
of 30% and 20%?
16. Find the single discount equivalent to commercial dis-
counts of 25%, 10% and 5%.
16. Which is better, a single discount of 40% or successive
discounts of 25% and 20%? How much better?
17. Find the net price of a bill of goods amounting to $280
with discoimts of 25% and 10% with an additional discount
of 2% for cash.
18. Find the net price on a set of harness listed at $60,
subject to discoimts of 20% and 10%.
Note: Bank DiscqurU will be treated under the topic Banks.
INTEREST
Exercise 6
Much of the business of the world is carried on with borrowed
money. Men of ability and industry often do not have enough
money of their own to supply the capital necessary for estab-
lishing or conducting their business enterprises. On the
other hand there are men who prefer to loan their money rather
than attempt to run a business of their own.
Thus money is loaned, in the business world, not as a matter
of personal favor or accommodation, but as a matter of busi-
ness based on benefits to both lender and borrower. The
person who lends the money receives pay for the use of it from
the borrower. Money paid for the use of money is called
inte/^esL
84 SEVENTH YEAR
The borrower in receiving money loaned to him, gives a
dated and signed promise to return the money loaned (or the
principal) with a certain interest at a stated date. Such a
paper is called a note. Here is a note of simple form:
„ afterdate ^ Cf. promise to pay to
..-.i§?^fw.f^56:. •r orrierQnf^Ji/n^^
with interest at .^ ^-^/.— /or value received,
^^^cAa/^
In a new conmiunity, where capital is greatly needed, money
would often command a much, higher rate of interest than the
law would allow. Most states provide penalties for charging
a higher rate of interest than the legal rate fixed by law. The
laws of the different states are not uniform as to the rate of
interest that will be permitted. Interest that is unlawful in
rate is called usury. Find what is the legal rate of interest in
your state by inquiring at the bank.
In ordinary transactions involving interest any month is
considered one-twelfth of the year and thirty days constitute
a month. In the case of large amounts of money, where
exactness as to time is very important, the time of the loan is
often stated in days and is reckoned according to agreement or
custom. In exact interest 365 days are considered a year.
Since banks consider 360 days a year in computing bank
discount, it is customary to figure interest on that basis. The
following form is very convenient for computing simple interest
because it allows one to use cancellation:
APPLICATIONS OF PERCENTAGE— INTEREST 85
Find the interest on $300 for 1 year, 3 months and 15 days at
6%.
3 93
Z00 300 4
00
20
4
In the above problem, the rate is used as a common fraction
Y^'y the time 1 year (360 days) +3 months (90 days) +15 days
=465 days which is |^ of a year. The interest for 1 year
($300 Xt^) must therefore be multiplied by |^ to find the
interest for the given time.
When the time is expressed in years and months, the form
can be shortened by expressing the years and months as twelfths
of a year.
Find the interest on $200 for 1 year, 6 months at 6%.
6 18
«00Xj-^X^ = $18.
i
Find the interest on:
1, $500 for 6 months at 6%.
2. $350 for 1 year at 7%.
8. $1000 for 2 years at 6%.
4. $2000 for 2 years at 5|%.
5. $250 for 2 years, 6 months at 7%.
6. $6500 for 5 years, 6 months at 5%.
7. $325 for 2 years, 9 months at 6%.
8. $480 for 1 year, 8 months, 15 days at 6%.
86 SEVENTH YEAR
9. $2000 for 2 years, 8 months, 20 days at 5%.
10. $500 for 1 year, 5 months, 18 days at 6%.
11. $425.50 for 1 year, 3 months, 21 days at 6%.
12. $218.50 for 2 years, 10 months, 12 days at 6%.
18. $350.75 for 2 years, 8 months, 19 days at 6%.
14. $875.25 for 1 year, 3 months, 27 days at 6%.
16. $5000 for 4 years, 7 months, 18 days at 5%.
16. $150 for 1 year, 3 months, 20 days at 7%.
17. $200 for 6 months at 3%.
18. $175 for 1 year, 2 months, 15 days at 6%.
19. $300 for 2 years, 4 months at 6%.
20. $2500 for 1 year, 9 months, 18 days at 5%.
Some teachers prefer to use the Six Per Cent Method in finding interest
instead of the Cancellation Method used in the preceding explanation.
The Six Per Cent Method may be used by teachers who prefer it or whose
course of study requires it. This method uses the following data:
The interest on $1 for 1 year =$.06
The interest on $1 for 1 month = .005
The interest on $1 for 1 day = .000^
Find the interest on $250 for 3 years, 3 months, 18 days at 6%.
Interest on $1 for 3 years = 3X.06 =$.18
Interest on $1 for 3 months = 3X.005 = .015
Interest on $1 for 18 days = 18 X .OOOj = .003
Interest on $1 for the entire time —$.198
Interest on $250 for 3 years, 3 months, 18 days = 250 X$. 198 » $49.50.
The interest at any other rate than 6% can. be found by taking -^ of
the interest at 6% and multiplying by the given rate.
When the times are stated for the beginning and end of the
interest-bearing period, the following form is used in determining
the time for computing the interest:
APPLICATIONS OF PERCENTAGE— INTEREST 87
21. What is the interest on a note for $300 dated April 1,
1906, and paid May 15, 1908, at 6%?
Year Month Day
1908— 6 —15
1906— 4 — 1
2— 1 —14
Therefore, the time is 2 years, 1 month and 14 days. Com-
pute the interest.
22. Find the interest on $200 from Sept. 26, 1915, to Jan. 24,
1917, at 6%.
Year Month Day ^e can not subtract 26 days from 24
1916 — 12 — 64 days, so we reduce 1 month, taken from
X9n — I 2^ the months column to days, making 30 days;
1915— 9 — 2 6 add the 30 days to the 24 days, making
1 — 3 — 28 54 days. 26 days from 54 days leaves 28
days. We have already used the 1 month
in the months column, so we must take a year from the year
column (leaving 1916) and reduce it to 12 months. 12
months— 9 mo. leaves 3 months. 1916—1915 = 1 year.
Therefore, the time is 1 year, 3 months, 28 days. Compute
the interest.
Find the interest on:
23. $750 from April 7, 1915, to July 14, 1917, at 6%.
24. $350.75 frcxn Dec. 18, 1912, to March 16, 1915, at 6%.
25. $2000 from Nov. 1, 1916, to Jan. 1, 1918, at 5%.
26. $150 fix)m July 25, 1910, to March 15, 1912, at 7%.
27. $275 from Oct. 9, 1913, to March 3, 1915, at 6%.
28. $5000 from Aug. 16, 1916, to August 16, 1921, at 5%.
29. $500 from May 22, 1914, to Sept. 22, 1917, at 6%.
88
se\:enth year
80. $850 from Mar. 1, 1915, to Oct. 5, 1916, at 6%.
81. $425 from Feb. 10, 1917, to Mar. 13, 1918, at 6%,
82. $1500 from Jan. 12, 1916, to July 3, 1917, at 5%.
83. $236.25 from Dec. 6, 1916, to Oct. 12, 1917, at 6%.
84. I borrowed $300 on July 18, 1916, at 6%, promising to
pay the note on demand. The owner presented the note for
pajrment on April 21, 1917. How much interest was there on
the not^ at that time? What was the total sum due the lender?
Bankers and other firms who have a great deal of interest to
compute use tables in order to save time and insure greater
accuracy. The following interest table was computed on the
basis of 360 days to the year. Some tables are computed on
the basis of 365 days to the year if the exact interest is wanted.
INTEREST ON $1.00
Montlis Days
Time
5%
6%
7%
1
2
3
4
5
6
7
8
9
10
20
$.000139
.000278
.000417
.000556
.000694
.000833
.000972
.001111
.001250
.001389
.002778
$.000167
.000333
.000500
.000667
.000833
.001000
.001167
.001333
.001500
.001667
.003333 .
$.000194
.000389
.000583
.000778
.000972
.001167
.001361
.001556
.001750
.001944
.003889
1
2
3
. 4
5
6
.004167
.008333
.012500
.016666
.020833
.025000
.005000
.010000
.015000
.020000
.025000
.030000
.005833
.018667
.017500
.023333
.029167
.035000
1 Year
.050000
.060000
.070000
APPLICATIONS OF PERCENTAGE— INTEREST 89
Exercise 6
1. Find the interest on $200 for 2 years, 3 months, 13 days
at 6%, using the above table:
Interest on $1.00 for 2 years ■»$ . 12
Interest on $1.00 for 3 months » .015
Interest on $1.00 for 10 days « .001667
Interest on $1.00 for 3 days = .0005
Interest on $1.00 for total time =$.137167
Interest on $200 for the given time, 200 X$. 137167 » $27.43+.
Using the interest table, find the interest on:
2. $300 for 1 year, 6 months at 6%.
3. $250 for 1 year, 4 months, 20 days at 7%.
4. $500 for 2 years, 7 months, 9 days at 5%.
5. $75 for 1 year, 6 months, 5 days at 7%.
6. $2000 for 3 years, 6 months at 5%.
7. $700 for 8 months, 25 days at 6%.
8. $100 for 2 years, 9 months, 24 dajrs at 7%.
9. $500 for 1 year, 2 months, 23 days at 6%.
10. $375 for 3 years, 6 months at
PARTIAL PAYMENTS
When a note is given for a long period, the interest is usually
to be paid periodically, and not to be deferred until the principal
becomes due. A part of the principal may likewise be paid
from time to time. Such a payment is called a partial payment.
The amount paid should be stated on the back of the note,
together with the date on which it is received.
The subject of Partial Payments in Arithmetics is one
in which there has been much confusion, owing to the diverse
90
SEVENTH YEAR
laws of (ii£Ferent states. The tendency is towards unity of
practice in partial payments, since nearly all of the states have
adopted this rule sustained by the Supreme Court of the
United States in cases that have come before it. This is
known as the United States Rule, and is in substance as follows:
When a partial payment or the sum of two or m^e
partial payments is equal to, or more than, the interest
due, it is to he subtracted from the amount (principal
^interest du£) at the time; and the remainder is to be
considered a new principal, from that time to the
next payment.
The following form shows the method of recording partial
payments on a note:^
^^^ow
Ic^Vi aj
thi
JQif^tiMi^LQ??^u
jfierdate fel__— ^pnmise to pay to
order of .^..hft/^
with interest at S2.-W-. — -— .- for value received.
l^jOcfu2/y^
f^jkju/ucd/ orut/iw/notb:
QuUini^^SO. QofmjJOoO
fQmltm^75. ihhrvlDot
^Payments on a note are usually made at interest-bearing dates. If the
interest is payable on Jan. 1 and July 1 of each year, it is often specified
that partial payments may be made on those dates.
APPLICATIONS OF PERCENTAGE 91
Exercise 7
1. Find the amount of the note on p. 90^ due on settlement
at maturity.
Solution:
$400.00 1st principal
24.00 interest from July 1, 1915, to July 1, 1916.
424.00 amount due July 1, 1916.
50.00 payment July 1, 1916.
374.00 new principaL
11.2 2 interest from July 1, 1916, to Jan. 1, 1917.
385.22 amount due Jan. 1, 1917.
75.00 payment Jan. 1, 1917.
310.22 new principal.
18.61 interest from Jan. 1, 1917, to Jan. 1, 1918.
328.83 amount due Jan. 1, 1918.
100.00 payment Jan. 1, 1918.
228.83 new principal.
6.86 interest from Jan. 1, 1918, to July 1, 1918.
$235.69 amount due on note at date of maturity.
2. Find the amount due at maturity Jan. 15^ 1918, on
a note drawn at Indianapolis, Ind., Jan. 15, 1916, for $1000
with interest at 6%, having the following credits indorsed
upon it:
July 15, 1916, $80. Jan. 15, 1917, $107. July 15, 1917, $29.
3. What was due at maturity, Aug. 10, 1917, on a note
drawn at San Francisco, Cal., Feb. 10, 1915, for $650 with
interest at 6%, having the following partial payments indorsed
upon it?
Aug. 10, 1915, $109.50. Aug. 10, 1916, $219.50.
Feb. 10, 1916, $116.50. Feb. 10, 1917, $50.00
4. What amount was due at maturity Jujy 15, 1917,
on a note drawn at St. Louis, Mo., July 15, 1915, for $800
with interest at 5%, having these credits indorsed upon it?
Jan. 15, 1916, $210. July 15, 1916, $215. Jan. 15, 1917, $50.
92 SEVENTH YEAR
COMMISSION
If a fruit grower or farmer wishes
to sell his produce in a distant city,
he can not usually afford to leave
his work and go to the city to attempt
to find a buyer. It is more profitable
for him to have some firm in the city
sell the produce for him. Refrigerator
cars now make it possible to ship
fruits and vegetables thousands of miles to distant cities
where higher prices can be secured for them.
There are two ways in which the grower can dispose of his
products: (1) he can sell directly to some wholesale firm or
(2) he can consign it to a commission firm to sell for him at .
a certain per cent of the sale.
If the grower sells directly to a firm, he usually sends a sight
draft attached to a bill of lading, making it necessary for the
firm to pay the draft before they can secure the bill of lading
and get possession of the goods from the railroad company.
This sight draft can be deposited by the grower with the
local bank for collection. The local bank then sends this
draft to a bank in the city, where the debtor does business,
for collection. It is customary for the local bank to allow the
grower to check against the amount of the draft, but he must
replace the money if the draft is refused by the firm to which
he sent the- goods.
If a grower asks a commission firm to sell the goods for
him, he consigns the shipment to them and they dispose of
it to the best advantage, charging a certain commission for
their work. After deducting commission, freight, cartage,
storage or any other necessary expenses, the commission firm
Bends the proceeds to the shipper.
APPLICATIONS OF PERCENTAGE— COMMISSIONS 93
Wheat, com and other grains ore bought and sold m large
cities in boards of trade where the members, called brokers, are
required to pay for the privilege of buying and selling produce.
Exercise 8
1. A fruit grower in Michigan consigned to a commission
firm in Chicago 240 barrels of apples to be sold to the best
advantage. The freight charges were 12f5 per 100 lb. and the
apple barrels were considered as weighing 160 lb. each. Find
the amoimt of the freight charges.
2. The cartage (or drayage) on these apples amounted to 6^
per barrel. Find the cartage charges.
3. 128 barrels were placed in cold storage at the rate of ISjif
for the first month and 12f5 for each month thereafter. 80
barrels were sold out of cold storage during the first month and
the remainder during the second month. Find the storage
charges.^
4. The following sales were made: 60 bbl. of Wolf Rivers
at an average of $4.25 per bbl.; 35 bbl. of Baldwins at $3.75
per bbl.; 52 bbl. of Northern Spys at $5.00 per bbl.; 93 bbl.
of Greenings at $3.50 per bbl. What was the commission on
the total sales at 7%?
5. After deducting the commission, storage, cartage and
freight, find the proceeds which the commission firm sent to
the shipper.
6. A potato grower sold a carload of potatoes consisting
of 240 even-weight sacks of 150 lb. each at 80 cents a bushel.
What did he receive for the carload? (1 bu. potatoes =60 lb.)
7. The buyer paid freight at the rate of 27 cents per hundred
pounds. What was the freight bill?
^Any fraction of a month counts as a whole month in computing storage.
94 SEVENTH YEAR
8. James Condon of New Jersey had 186 bbl. of sweet
potatoes which he wished to sell. He wired his broker in Detroit,
Mich., to sell them to the best advantage. The broker was
offered $3.25 per bbL F. O. B. loading point. This, Condon
accepted. How much did Condon receive for the carload of
potatoes?
9. How much must he send his broker at 15^ per bbl.
brokerage?
10. What were Condon's net proceeds on the sale?
11. A woman canvasser sells an improved kitchen utensil
on a commission of 15%. What must be the amount of the
sales to pay her $30.00?
12. An administrator for an estate of $750,000 gave a bond
for double that amount. . The premium of the bond was $1185.
The agent securing the bond received a conmiission of 15%
of the premium. What was his commission?
13. A firm bought 42,070 lb. of onions in 111. at 75ji per bu.
of 57 lb. and sold them in Michigan at 95|i per bu. of 54 lb.
They paid freight at the rate of 7^5 per 100 lb. How much was
the firm's actual gain on the onions?
14. If a travelling salesman receives a commission of 10%
on his sales, what will be the amount of his commission if his
yearly sales amount to $25,000?
15. A real estate agent sells a building for $15,500, receiving
a commission of 3%. What does he receive for his services?
16. A collector remits to his customer $114 after deducting
a commission of 5%. How much did he collect?
17. A produce broker received $309 to invest in potatoes
at 60^ per bushel, on a commission of 3%. How many bushels
<ilid he buy?^
^First find the cost of each bu. of potatoes, including tha nnmraimiion.
APPLICATIONS OF PERCENTAGE— TAXES 95
18. A fanner placed 2000 bu. of new com in crib in Novem-
ber, 1915, to be sold by a commission firm when the price
reached 85^ per bu. This com was sold at that price in June,
1916. The shrinkage on the com was 12%. The commission
was 6%. Find the amount of the commission.
19. A real estate agent sold a farm for $20,000, receiving
for his services, from the owner,, a commission of 2%. What
was the amount of his conmiission?
20. A real estate agent purchased a farm for a customer,
and added to the price 5% commission. His bill was what per
cent of the price he paid? The bill was for $10,500. What was
the price paid?
21. Having deducted $5.00 for expenses, and $45.50 for
commission at 5%, a conmiission merchant forwarded to his
principal the remainder of the cash received for a consignment
of farm products. What amount was remitted to the con-
signor?
22. A broker receives $4010 t^o be invested in wheat at
$1.00 per bushel, his commission being j% for making the
purchase. What will his customer pay for each bushel so
purchased? How many bushels can be purchased for the
amount stated?
TAXES
The state, the county, the city and the school district must
have funds to pay the expenses of the officers and laborers who
render services to those divisions of government.
1. What are some of the services that the officers of the
€ity perform for the people in that city?
2. What benefits do the inhabitants of a school district
get from the funds spent for school purposes?
8. How do the state and county governments serve the
people?
96
SEVENTH YEAR
The funds necessary for carrying on the government of the
state and various local divisions are usually raised by taxing
the people on the amount of property which they own.
Property is divided into two classes: (1) real estate, includ-
ing lands and buildings; and (2) personal property, consisting
of movable possessions such as clothing and jewelry, household
furnishings, domestic animals,- and farm products, the merchan-
dise and productions of stores and shops, machines and engines,
vehicles, mortgages and notes, stocks and bonds, money, etc.
Officers, generally called assessors, determine the value of
the property. Then the proper officers of each local division
of government estimate the amount of money that they will
need to carry an the government of their division for the next
year. This levy is turned in to some county or state officer
who divides the levy by the assessed valuation of the property
to find the rate of taxation for each local division. Collectors
then collect the proper amount from each person according
to the amount of his property. The following table gives an
illustration of the manner in which the various rates of taxation
are computed:
HOW THE TAX RATES ARE COMPUTED
Division of
Government
Levy
Assessed Valua-
tion of
Property*
Rate of Taxa-
tion = Levy -r-
Assessed Val.
State
$19,994,495.11
198,703.42
1,500.00
4,000.00
14,259.27
$2,499,311,888
42,277,324
1,228,410
295,443
534,055
.0080
.0047
.0012+
.0135-f
.0267+
Countv
Town
Citv
School District
Tntal Rate of Ti
axfttion , . .
.0641 +
^Assessed valuation of the property in this state is taken as | of the
bual value. Systems of taxation vary in different states.
APPLICATIONS OF PERCENTAGE— TAXES 97
Exercise 9
1. What would be a man's taxes who lived in all these
divisions if his property was assessed for $15^350?
Compute the amount of tax in each local division and then find the
total. Why must a ooUector compute these yarioua amounts separately?
2. What is the rate of taxation in your county for county
purposes? In your state for state purposes? In your school
district for school purposes?
Appoint some one in the class to get this information from the collector,
the county derk, or consult a tax receipt.
8. If property is taxed at the rate of 15.50 per $1000,
what is the per cent of taxation? How many mills is that on
the dollar?
4. In a certain village the assessed valuation of the property
is, in round numbers, $300,000. The amount of tax needed
for canying on the government is $5000. What will be the rate
of taxation for village purposes?
5. A school board estimates that the expenses of running
their school will be $4500 and make a levy for that amount.
If the assessed valuation of the property in the district is
$350,000, what will be the rate of the school tax?
6. The assessed valuation of a tract of land adjoining a
city is valued at $15,000 and the present rate of taxation is
1.5%. If the land is annexed to the city in which the rate of
taxation is 2.5%, what will be the increase in the taxes of the
owner of the land? What benefits will he receive for the extra
taxes that he pays?
7. If 'the assessed value of the property in a certain county
is $18,596,482 and the total taxes levied upon it for state and
local piuposes is $650,876.87, what is the total rate of taxation?
B. In a certain township (town) a tax of $20,000 is to be
98 SEVENTH YEAR
raised. If there are 500 citizens to pay a poll tax of $1 each,
how much of the tax must be laid on property?
A poU tax is a small tax levied on males without regard to
their property. "Poll" means head; that is, the tax is so much
a head. Poll taxes are being abolished in many places. Find
whether your community still has a poll tax.
9. A man has $1200 loaned out at 6% interest. He is
assessed on ^ the amount of his loan and the rate of taxation
is 4 J%. How much will be his net returns each year on the
loan after he pays his taxes?
10. In a village containing propeity assessed at $200,000,
the rate of taxation is 3%. If a poll tax of $2 can be collected
from 800 citizens, how much can the assessed rate of taxation
be reduced?
11. A village levied $4800 in taxes on property valued at
$600,000. Find the rate of taxation.
SPECIAL ASSESSMENTS
If a city wishes to pave a street, it assesses the cost upon the
owners of the adjoining property because the pavement will
add to the value of the property. The city usually pays for
the pavement of the intersections of the street. Such assess-
ments are called special assessments.
Drainage ditches are also paid for in special assessments, the amount
of the tax depending upon the distance from the ditch. The owners of
land adjoining the ditch are benefited most and hence must pay the highest
tax.
If the object of the special assessment is equally beneficial to all the
inhabitants of the city, such as parks and libraries, the special taxes are
levied upon all the property in the city.
Find an example of a special assessment that has been levied
in your community. How was the tax assessed? Make five
problems out of the information you secure on this special
assessment.
APPLICATIONS OF PERCENTAGE— ASSESSMENTS 99
PROBLEMS
1. If the assessment valuation for a certain city is $1,800,000
and there is to be raised for a special purpose $48,000, what will
be the rate of taxation required for this purpose?
2. What will this add to the tax of a resident who owns
property assessed at 16000?
3. A drainage district was formed for reclaiming some of
the low land along the Illinois River. The area drained was
1280 acres. The cost of the work was $25,600. What was the
assessment on each acre if the amount was equally distributed?
4. The streets of a city are being paved at a cost of $1.20
per sq. yd. The width of the paving is 30 feet. The cost of
the curbing is 60^ per running foot. How much will be the
tax on a man with a frontage of 50 feet if he is required to
pay for the pavement to the middle of the street?
6. What will be the assessment on the owner of a comer
lot in the same city if his lot is 150 ft. long an^d 45 feet wide?
The city pays for the intersections of the streets.
EXPENSES OF THE NATIONAL GOVERNMENT
The principal items in the yearly expenses of the national
government in a recent year were as follows:
EXPENSES
Post Office $311,728,452.70
Army 164,635,576.67
Navy 155,029,425.78
Pensions 159,302,351.20
Miscellaneous 198,538,737.91
Money must be raised by our national government to meet
these expenses. The main sources from which the national
government derives its income are:
100 SEVENTH YEAR
INCOME
Post Office $312,057,688.83
Customs Duties 213,185,845.63
Internal Revenue 387,764,776.17
Income Tax. 132,937,252.61
Miscellaneous 51,889,016.28 '
The postal revenues practically balance the postal expenses.
The sums above show a profit of $329,236.07 in that depart-
ment for the year 1916.
CUSTOMS DUTIES
«
Congress has the authority to fix duties on imports. They
pass a law enumerating various schedules or classes of articles
and give the duty on each item in a schedule. Such a law is
called a tariff.
Since tarififs are frequently discussed in political campaigns,
you, as future voters, should understand how a duty is levied
and its efifect upon prices in this country.
Suppose that it costs $1.00 per yard to make a certain grade
of cloth in Europe. If the duty on this kind of goods is 35%
of the value of the cloth, the duty will amount to 35 cents per
yard. Since the importer can not afiford to lose this duty of
35 cents, he must sell his cloth in the United States for at least
$1.35 per yard.
1. Suppose on the other hand that it costs $1.35 to manu-
facture the same grade of cloth in the United States. Caii
our factories compete with the European goods after the
importers pay the tax of 35%?
2. Could our factories compete with the European mahu-
facturer of that grade of cloth if he only had to pay a duty of
20%?
3. Could the importer compete with our factories if he had
to pay a duty of 60% on the cloth?
APPLICATIONS OF PERCENTAGE— REVENUE 101
Since a duty of 36% in the above illustration protects our
factories against the lower prices of imported goods from Europe,
it is said to be a protective duty. The principal discussions in
political campaigns have been over raising, lowering or main-
taining the tariff duties then in force.
In 1916, Congress passed a law creating a tariff commission
to consist of representatives from the leading political parties
of our country. This commission is to determine accurately
the costs of production of various articles in the United States
and in foreign countries and to report this information to Con-
gress. This should enable Congress to form a much better list
of tariff schedules than it has done in the past.
Not all imports are taxed. There are some necessities that
we want to encourage people to ship to this country and we
allow them to come in free. Among the articles on the /r66 list
are agricultural implements, bibles, coffee, com, cotton, hides,
meats, potatoes, salt, wool, milk and cream.
Tariff duties are of two kinds, ad valorem, and specific. Ad
yalorem duties are those levied against the valiie of the goods
imported. Specific duties are duties based upon the number,
weight, etc.
For example, if a duty on dress goods is 30% of the value of
the goods, such a duty is said to be an od valorem duty. If the
duty is 5 cents per pound, the duty is said to be specific.
Ad valorem duties are more difficult to levy than specific duties because
the goverment must keep experts who can accurately judge the quality of
the various kinds of goods. Specific ciuties on the other hand are easily
levied because the quantity expressed in yards, pounds, gallons, etc., has
merely to be measured. Specific duties, however, have the disadvantage
of putting the heaviest burden on the cheaper grades of goods.
K the duties are too high, foreign goods will not be imported
and there will be a decrease in the amount of revenue obtained
from customs duties.
102
SEVENTH YEAR
Among the many duties of the Tariff Act of 1913 are the
following:
Article
Schedule
Duty
Ink Powders
A
15% ad valorem.
Window Glass
B
Ic per lb. between 154 and 384 sq. in.
Automobiles
C
Over $2000—45% ad valorem. Less
than $2000—30% ad valorem.
Mahogany Lumber
D
10% ad valorem in rough boards.
Horses
G
10% ad valorem.
Beans
G
25c per bu. of 60 lb.
Cotton Stockings . .
I
Value up to 70c per doz., 30% ad
valorem. More than $1.20 per doz.,
50% ad valorem.
Wool Clothing
K
35% ad valorem.
Silk Clothing
L
50% ad valorem.
Writing Paper
M
25% ad valorem.
Firecrackers
N
6c per lb.
Roman Candles —
N
10c per lb.
Cut Diamonds ....
N
20% ad valorem.
Typewriters
Free List
No duty.
Potatoes
Free List
No duty.
Tell which of the above duties are ad valorem and which are
specific.
Goods are classed under different schedules. For instance.
Schedule A includes chemicals, oils, and paints; Schedule G
includes agricultural products and provisions, etc. Similar
articles are grouped together in the same schedule. The letters
of the alphabet A to N are used to designate the different
schedules.
Exercise 10
Use the preceding table to find the corresponding duties.
1. Find the duty on a French automobile costing $2500.
APPLICATIONS OF PERCENTAGE— REVENUE 103
2* Find the duty on an imported automobile costing $1500.
8. I buy a team of work horses in Canada for $300. How
much duty must I pay to bring them into this country?
4, A firm in New York buys from a firm in London the
following goods: 20 reams of writing paper @ 50^ per ream;
100 lb. of firecrackers; 100 lb. of Roman Candles; 3 typewriters
@ $60 each. Find the total amount of the duties on these goods.
«
6. If I buy 2000 ft. of mahogany lumber in Central America
at $60 per M and import it into this country, how much duty
shall I have to pay?
6. A firm imports the following bill of goods: 3 dozen silk
handkerchiefs @ $3.95 per dozen; 50 ready-made woUen dresses
at $12 each; 6 dozen cotton stockings at $1.80 per dozen.
Find the total duties on this bill of goods.
7. A jeweler imported cut diamonds to the value of $50,000.
How much import duties did he pay?
8. A firm imported 10 bags of beans weighing 120 lb.
each and 20 sacks of potatoes weighing 150 lb. each. Find the
amount of his duty.
9. A school supply firm imported ink powder invoiced at
$2500 in Liverpool, England. How much duty did they pay
on this bill of goods?
10. A glass firm imports window glass in sizes from 154 sq.
in. to 384 sq. in. If the glass weighed 1000 lb., how much
duty did they pay on the shipment?
INTERNAL REVENUE
Another important source of revenue for the government is
the income from internal duties or excises which are levied on
certain kinds of manufactured products in this country, such
as distilled liquors, tobacco goods and substitutes for butter.
104 SEVENTH YEAR
When extra revenue is needed, special stamp taxes are often
levied upon certain drugs, notes, bills of lading, telegrams and
certain legal papers.
Internal duties as well as import duties are usually added to
the cost of the article and the consumer really pays the tax.
Since the consumer does not pay these duties directly to the
government, excises and import duties are often called indirect
taxes.
1. In 1908 the receipts of the national government from
internal revenue amounted to $251,711,126.70. The expense
of collecting this sum was $4,650,049.89. What per cent of
the receipts was paid for the collection of the internal revenue?
INCOME TAXES
The income tax which the national government collects upon
net inarmed over a certain amount is a direct tax.^ Single persons
whose net incomes exceed $3000 and married persons whose
incomes exceed $4000 are required to make out a schedule for
the national government showing the amqunts of their respective
incomes. In computing the net income a person is allowed to
deduct from the gross income the expenses of conducting the
business. Living expenses can not be deducted in computing
a person's net income. If a person returns a false amount for
his net income, heavy penalties are imposed upon him if he is
detected.
1. Why should incomes of less than $3000 (or $4000 for
married persons) be exempt (or excused) from the income tax?
2. Why should a married man have a larger sum for exemp-
tion than a single man?
Since a man with an extremely large income is regarded as
^The sixteenth amendment to the Constitution of the United States
adopted in 1913 gave Congress the authority to levy an income tax.
APPLICATIONS OF PERCENTAGE— INCOME TAX 105 *
better able to pay toward the support of the government than
one with a small income, the large incomes are taxed at a
higher rate. This extra amount is called a surtax. The following
table shows the amounts and rates of the graduated income
tax in force Jan. 1, 1917:
AMOUNTS AND RATES OF THE INCOME TAX
Amount of Net Income
Rate of Tax
All of Net Income less $3000 or $4000
2%
1% additional
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
$20,000 to $40,000
$40,000 to $60,000
$60,000 to $80,000
$80,000 to $100,000
$100,000 to $150,000
$150,000 to $200,000
$200,000 to $250,000
$250,000 to $300,000
$300,000 to $500,000
$500,000 to $1,000,000
$1,000,000 to $1,500,000
$1,500,000 to $2,000,000
Excess over $2.000.000
Exercise 11
1. A married man has an income of $100,000 per year.
Find the amount of his income tax.
$100,000 - $4000 = $96,000.
2% of $96,000, the normal tax $1920
1% on income from $20,000 to $40,000 200
2% on income from $40,000 to $60,000 400
3% on income from $60,000 to $80,000 600
4% on income from $80,000 to $96,000 640
Total amount of Income Tax $3760
106 SEVENTH YEAR
2. The net income of a certain married man is $10,000 per
year. Find his income tax.
3. The yeariy income of a single woman is reported in her
tax schedule as $9327. How much will be her tax?
4. What will be the income tax of an unmarried man who
has an income of $22,500?
6. Find the income tax on an income of $8000 if the ex-
emption is $4000.
6. The income of a certain wealthy financier is $8,753,200.
Find his income tax. (Married man^s exemption.)
7. Find the income tax on a single woman's income amount-
ing to $276,450 per year.
8. Find a married man's income tax on a net yearly income
of $72,350.
9. A certain wealthy man's net income amounts to
$1,150,000 per year. He is married. Find his income tax.
10. Find the income tax for a single person whose net yearly
income is scheduled at $23,480.
11. Why should a person with a large income pay a higher
rate on the amounts above a certain sum?
INSURANCE
Insurance is a contract whereby, for a certain payment
called a premium, a company guarantees an individual or firm
against loss from certain perils. The contract is stated in a
document called a policy.
Instead of one person carrying all the risk on his life or
property, insurance distributes the risk over a large number of
persons so that no one person has to bear an extremely heavy
loss.
The most common forms of insurance are:
APPLICATIONS OF PERCENTAGE— INSURANCE 107
Fire Insurance insures against loss from injury to property,
or destruction of it, by fire.
Life Insurance insures a person against loss through the
death of another.
Accident Insurance insures a person against disability caused
by an accidental injury to him; and in case of his death from
the injury received, it insures an indemnity to a specified
beneficiary.
CasuaUy Insurance, of various kinds, insures against loss
resulting from accidental injury to property, such as live
stock, plate glass, etc.
Fidelity Insurance insures against loss arising from the
default or dishonesty of public officers, or of clerks or agents
in the employ of the insured.
Marine Insurance insures against loss by injury to, or dis-
appearance of, ships, cargoes, or freight, by perils of the sea.
FIRE INSURANCE
In order to prevent insurance from having the nature of a
betting or gambling contract, an agent is not supposed to
insure property for its full value against loss by fire. The
person whose property is insured must bear a portion of the
risk himself.
•
The rate of the premium is generally stated at so much per
hundred dollars and varies according to conditions such as
the kind of fire department, nearness to other buildings, con-
struction of the building, etc. Most firms insure property
for three years at two and a half times the yearly rate.
Insurance on furniture is strictly construed in accordance
with the exact terms of the policy. If the furniture is removed
at all without express permission from the building in which
it is insured, the insurance fails.
108 SEVENTH YEAR
Exercise 12
1. If I deem my house worth $5000, and desire to insure
it for one year for three-fifths of its value, what must I pay
for the policy when it costs $7.50 for each $1000 of insurance
taken?
2. A farmhouse and bam and other buildings pertaining
to them, valued at $15,000, are insured for one year for two-
thirds of their value, at 75 cents for each hundred dollars of
•
insurance. What is the cost of the policy?
3. If the furniture in my cottage is worth $1000, and
I wish to insure it for 60% of its value, having to pay $1.66f
for each hundred dollars of insurance, what will the policy cost,
me?
4. A church pays, in all, $180 yearly, for insurance to the
amount of $10,000, in each of three separate companies,
the rate of insurance being the same in each company. What
is the rate of insurance?
If my house, insured for $4000, is destroyed and I am unable to prove
that it was really worth over $2000, I can recover from the insurance
company no more than the latter amount.
6. If when insured against fire for $5000 it was destroyed,
and I can prove its value only to the amount of 60% of this
sum, what amount of compensation do I receive?
To insure a house for three years at a time, one has to pay two and
one half times the rate for a single year.
6. My insurance for a three-year period is $31.25. What
would have been my insurance for a single year?
By insuring a house for five years at a time, one has to pay four
times the rate for a single year.
7. If a man pays $200 for the five-year period, what would
the insurance cost him for a single year? For a period of
three years? For five separate periods of one year each?
APPLICATIONS OF PERCENTAGE— INSURANCE 109
8. If I have furniture insured for $1200, temporarily stored
in an outbuilding which is not mentioned in my policy, and the
outbuilding and furniture are destroyed by fire, what amount
can I recover on my loss ot furniture?
9. A rug worth $150 is hung out in the yard to air, uid
is ruined by sparks from a passii^ fire engine. If it formed a
part of the household furniture that is insured for $1000,
can the owner recover its value from the insurance company?
10. What could be recovered if it had been thus destroyed
while hui^ on a line on a porch of the residence?
11. A dozen books supposed to be rare and valuable are
insured for $1200. They are destroyed by fire, and it is then
proved that they were recently manufactured, and of no greater
possible value than $3 apiece. What is the limit of indemnity
that the company should pay for them?
Insurance Applied
Mr. Manning owned a
suburban lot on which he
contracted with a house
construction company to
build a home at a total
cost of $4500. On the
completion of the new
home, Mr. Manning, rec-
ognizing the importance
of proper protection to his family, took out an insurance
policy on the house.
Exercise 13
1. An insurance company insured the house for 80% of
its cost. Find the amount of his policy.
110 SEVENTH YEAR
2. Why will an insurance company not insure a house at
its full value?
3. The rate of insurance on this house was 72 cents per
$100 for a "three-year period." What was the cost of the
insurance per year?
4. Mr. Manning made out an inventory of his household
goods and estimated them to be worth $950. He decided to
take out $800 on his household goods. Why was it a good
plan to make out an inventory of the goods before insuring?
What should be done with this inventory?
6. The rate of insurance on his household goods was 79
cents per $100 for three years. Find the amount of the premium
on the household goods.
LIFE INSURANCE
There are two principal kinds of life insurance companies:
the "oW Ztne" companies and the mutual companies. The old
line companies have worked out definite rates for diflferent ages
and the premium for each year is definitely stated in the
policy. The mutual companies usually levy an assessment at
certain intervals, generally each month, to pay the death claims.
The '^oZd Zt'ne" companies usually have several kinds of policies
such as 15-payment life; 20-payment life; endowment policies;
ordinary life policies. In the 15-payment life policy, the person
insured makes fifteen yearly payments at the end of which
his insurance is paid for the rest of his life. The 20-payinent
life, as the title indicates, is paid for at the end of 20 yearly
payments. An endowment policy usually requires a larger
premium and if the insured person lives to the end of the period
named in the policy he can draw out the amount of the policy.
In an ordinary life policy a definite yearly payment is required
each year until the person dies. All of these forms usually
APPLICATIONS OF PERCENTAGE— INSURANCE 111
have a cash surrender value which will be paid the insured
person upon the surrender of the policy. Most policies also
have a table showing the amount of money which the company
will loan on a policy.
Since the risk of the death of a person increases with age,
the premium increases each year. It is therefore an advantage
to take out insurance as early as possible. The age nearest
the birthday of the person insured is the age considered. A
medical examination is aiso required to protect the company
from undesirable risks.
Premiums per $1000
Age
Ordinary Life
•
20-Payment Life
20- Year Endowment
20
$19.21
$29.39
$48.48
21
19.62
29.84
48.63
23
20.51
30.80
48.96
25
21.49
31.83
49.33
27
22.56
32.94
49.73
30
24.38
34.76
50.43
35
28.11
38.34
51.91
40
33.01
42.79
54.06
45
39.55
48.52
57.34
50
48.48
56.17
62.55
Exercise 14
1. At the age of 21, a man insured his life for $2000 on
what is called the ordinary life plan, for an annual payment of
$39.24. What does he pay in fifteen years?
2. Had he deferred the insurance for five years, it would
have cost him $44.10 for each year. How much more would
this have been than the amount the insurance actually did cost
him for the same period of ten years?
8. A man took out a IS-payment life policy for $1000 at
the age of 30 at $40.25 for each annual payment. What was
112 SEVENTH YEAR
the total amount of his fifteen payments? How can the com-
pany afford to insure him at an amoimt which will yield less
than the face of the policy?
4. A man insured his life on the endowment plan for SIOOO
at the age of 21, paying $48.63 annually for a 20-year period,
and lived beyond the time and received the amount of the
policy. What was the total amount of his payments?
5. What did the insurance company receive to pay them
for taking the risk of his death during that period?
6. A .man took out a 20-payment life participating policy
for $2000 at the age of 24, with a premium stated at $62.16
per year. If his dividends on the policy amounted on an
average to $10 per year for 19 years, how much did the insurance
cost him?
A participating policy pays dividends to the holder after the first year
according to the profits of the company. These dividends are usually
deducted from the premium, the insured person paying the balance due
the company.
7. At the end of the period, the policy had a cash surrender
value of $994. If he surrendered his policy at the end of the
period, how much will his insurance cost him besides the interest
on his payments?
ACCIDENT INSURANCE
1. A man has paid $18 for 4 years for an accident insurance
policy. Owing to an accident, he is disabled for a period of
6 weeks, during which time he receives $25 a week. What
has been the net financial value of the insurance to him?
What has been the net loss to the insurance company?
2. A horse insured for $300 is choked to death, being ignor«
antly tied with a running noose of rope for a halter about its
neck. Is the owner entitled to the insurance? If by a com«
promise 40% of the policy is paid, what sum does the owner
receive?
CHAPTER V
BUSINESS FORMS AND ACCOUNTS
The Memorandum or Salesman's Slip
<Browri ^ Duj^dR
/7/6 J9maI2
* 0.6H
sold by &
Drygood5
£»uf faio, KT
purchase
Change
2
I
I
P/u.Ho^ 25
Ha/ruUw\AkjULb
I
00
3b
20
15
bH
In buying goods at a
retail store, a salesman's
slip or memorandum of
the purchase is usually
made by the salesman or
clerk.
By means of carbon
paper placed under the
sheet on which the clerk
is writing, a duplicate of
the slip is made. The
firm keeps one copy and
gives the other copy to
the customer for refer-
ence.
The form indicated above shows one form of such a
memorandum. It shows the items of the purchase, the amount
received by the clerk and the change given to the customer.
This memorandum should be kept by the purchaser until he
is sure that he does not wish to exchange any of the goods.
If the purchase is charged, it is so indicated upon a similar
memorandum containing the customer's name and address.
This memorandum should be kept by the customer to check the
account when the monthly statement is rendered.
If printed forms of salesman's slips can be secured from local stores,
it will save much time in the ruling of these forms by the pupils.
113
114 SEVENTH YEAR
Exercise 1
1. I bought the following items at a grocery store; 15 lb.
of potatoes for 30 cents; 2 cans of com @ 7 cents per lb. ; and
1 doz. oranges @ 40 cents. Make out the salesman's slip for
the customer.
2. How much change should I receive if I tendered the clerk
a two-dollar bill?
8. Mrs. Jones bought the following articles at a dry-goods :
store; 6 yd. ribbon @ 18^ per yd.; 2 spools of No. 50 white
thread @ 5^ per spool; 10 yards of pique (pe ka') @ 30^ per J
yd.; 3 yd. of flannel @ 80^ per yd. Make out the clerk's
memorandum of the sale.
4. How much change should Mrs. Jones receive from a ,
ten-dollar bill?
6. I bought the following household supplies at a hardware
store: 1 ironing board @ $1.75; 1 pair of waffle irons @ 90^;
2 aluminum kettles @ 65^ each. Make out a salesman's slip
for the sale.
6. How much change did I receive from the clerk if I ten-
dered him a five-dollar bill to pay for the purchases?
Make out salesman's slips for the following orders:
7. Mrs. Stevenson bought ^ doz. plates No. 4 @ $1.25;
§ doz. plates No. 8 @ $3.00; ^ doz. tea cups and saucers @
$3.00 and ^ doz. sauce dishes at $1.90.
8. Miss Dillon purchased the following articles: 1 whisk
broom @ 35 cents; 1 vanity case @ 50 cents; 1 set of cups @
$2.00; and 1 shoe horn @ 50 cents.
9. What are some of the advantages of using the memoran-
dum or salesman's slip?
10. Make out a sales slip with prices of articles which you
purchased at a store.
BUSINESS FORMS AND ACCOUNTS
115
The Invoice or Bill
An invoice or bill is a more formal accomit of a transaction
than a salesman's memorandum. Invoices are sent to a cus-
tomer by a firm with each shipment of goods. The following
is a modification of a form used by a large wholesale firm:
This sale made subject to conditions on bacK. of invoice
OMer ■ 83s;6 j^j^ ^ Company, vuat,
Kansas City^ Mo.
Soid by AJ«.Grlgg9
QulBCY. 111. Tem\S 2% - 10 days
Invoiced J M. 3, ChecKed j.c.t.
<Soht to ij^i^jiat
J«B.
L
11
4 Pet. Hnt HAMI*
4 ** Bacon A/6§
(uBvrpd)
4 ** Cook«d Hau
5 ** Jtaliaa Stylt Haaw
54
15
48
35
^7
.23
.23
.24
■ «■ • •••
*The abbreviation 12/1 4# means from 12 to 14 pounds.
In the above invoice, the number in the first colmim at the
right of the descriptions of the articles shows the number of
pounds. The corresponding numbers in the next column
give the cost per pound. Multiply the cost per pound by the
number of pounds and enter the result in the next column
which contains the totals for each article.
Exercise 2
1. Extend the invoice shown above, filling in the sums as
shown by the dots.
2. Find the net amount of the bill if it is paid within 10
days. (Terms 2% — 10 days, means that 2% discoimt will
be allowed if the bill is paid within 10 dayo.)
116 SEVENTH YEAR
Extend the following invoices. You may omit the headings
but make a drawing for the rest of the invoice form:
8. 2 10# Carton Regular Frankforts
2 Pieces CJooked Pork Loin
10 Pieces Fresh Ox Tails
2 Pieces Bacon 5 to 8#
4. 1 Piece Fresh Beef Round
3 Pieces Fresh Pork Loins
10 Pieces Fresh Spare Ribs
15 Pieces Fresh Pigs Feet
1 Piece Cooked Ham
6. 1 Piece Fresh Beef Ribs
20 Pieces Fresh Spare Rib
1 Piece Fresh Pork Loin
2 Pieces Cooked Hams
l-26# Plain Fresh Pork Sausage
6. 1 Fresh Side Beef
8 Fresh Beef Shanks
2 Jelly L. Tongue
2 Boxes Frankforts
2(^ Polish Sausage .
Make out bills for the following goods, using fictitious names
for the firm and the purchaser:
7. 1 parlor lamp @ $2.95; 3 glass candlesticks @ 29f&;
1 chafing dishy $7.50; 2 brass jardinieres at $1.75; 2 vases at
$3.00; 2 cut glass salt cellars at 95ff.
8. 2 granite stew pans @ 39^; 2 muffin pans @ 27i] 1 can
opener @ 10^; 2 aluminum measuring cups @ lOfi; 2 pair
scissors @ 75ff ; 2 butcher knives @ 50fi; 1 electric iron @ $3.79.
9. 1 pair slippers @ $2.00; 1 pah- rubbers @ $1.25; 2 bottles
gilt-edge polish @ 2bi\ 3 pairs shoe strings @ lOfi; 1 pair ladies'
shoes $5.50.
20
13*
8
31
10
8
11
25
93
14^
19
16
10
12^
15
5
13
29
86
13|
10
12^
14
15§
27
28
25
15
179
8
11
7
11
27i
20
12*
20
11
BUSINESS FORMS AND ACCOUNTS
117
The Monthly Statement
When salesman's slips oi bills are rendered with orders,
the customer is supposed to keep these forms with the various
items shown on them in order to check the monthly statement
which is sent at the end of each month. The following is one
form of a monthly statement that is used:
When the customer so
desu-es, an itemized
statement will be ren-
dered, but this makes a
great deal of extra work
for the firm and is un-
necessary if the customer
keeps his slips or bills to
check the totals listed
under the various dates of the monthly statement.
Statement '•»»». i. im.
In AccomtrWrn
tIS.CLAKKE
Mfm^mciijWis.
Mr*. R»rY«y Buchuian
Aug.
1
4
5
14
19
U
30
OroMri**
1
2
3
2
1
3
37
69
46
76
95
30
25
19
42
Exercise 3
1. Make out a monthly statement to Mrs. F. R. Fitzgerald
from Adams Bros., Grocers, for the following grocery orders,
showing only the totals for each day:
Aug. 1 — 2 loaves of bread @ lOff; 2 pounds prunes @ 20^5;
10 pounds sugar @ Ti.
Aug. 3 — 1 pound cheese @ 36j!f; § dozen lemons @ 30ji5;
1 peck potatoes Zbi.
Aug. 4 — 2 cans com @ 18ff; 1 basket tomatoes @ 25ff.
Aug. 9 — Celery lOff; 1 head lettuce lOff; 1 package rolled
oats @ lOi.
Aug. 12 — 10 bars of soap for 42^5; 1 basket tomatoes 19^;
1 sack flour 95f(.
Aug. 17 — 10 pounds sugar @ 7^i; 2 dozen eggs @ 33ff; 2
pounds butter @ 36ff.
118 SEVENTH YEAR
Aug. 20 — 1 peck potatoes SQ^; 2 packages crackers @ 10<5;
1 sack salt 10)i(.
Aug. 23 — 3 quarts peas for 25f!!; 1 package puffed rice 16^;
10 pounds apples @ 5^,
Aug. 30 — 1 jar olives 35^; 2 pounds navy beans @ 12|!f; 5
pounds rice for 39^5.
2. Make out an itemized statement of the same account,
showing each of the items and the total for each day.
3, Make out a series of purchases from a dry-goods store
during some month and render a monthly statement for them.
Receipts
When a sum of money is paid on an account, the customer
should receive a receipt, showing the date and amount paid
as in the following form:
GALVESTON, TEXAS, J[jJiU5^9\ 7
ofj^/nj amd/ ^ , ^^ Dollars
If the full amount of the account is paid instead of a portion
of it, the words "in /uK o/ account to daie^' would be used in
place of the expression "on account.'^
If an account is paid by a check, the check stands as a suffi-
cient receipt for the payment. For this reason, many persons
pay all their accounts by checks.
This saves the firm the trouble of making out extra receipts
or returning the receipted bill to the customer, because the
cancelled checks are returned by the bank with their monthly
statement.
BUSINESS FORMS AND ACCOUNTS 119
Exercise 4
1. R. A. Milton owes Schneider & Co. S30.25 for hardware
supplies. He pays them $25.00 to apply on his account.
Write a proper receipt for this payment.
2. J. R. Kennedy pays Dr. L. J. Hammers, $15.75 as
payment in full for his professional services. Write a receipt
for the settlement of this account.
3. Write a receipt for Hogan Bros, to Mrs. J. C. Veeder
for a settlement in full of her account of $11.75.
4. Write a receipt for Adams Bros, to Mrs. F. R. Fitzgerald
for a settlement in full of the account shown on page 117.
5. Write a receipt for some actual payment in which you
have been the receiver of the money or have paid a sum of
money to some other person.
6. I ordered a suit from a tailor. He required a deposit of
$10.00 and gave me a receipt for this amount, in part payment
for the suit. Write such a receipt for a tailor.
7. Write a receipt to a plumber from his employer for
$15.00 in payment for 20 hours' work at 75 cents per hour.
The Cash Account
Most methodical people, whether engaged in active business
or not, keep a cash account of their receipts and expenditures.
The cashbook represents the owner's pocketbook or cash
drawer. "Cash'' is treated as a real person. It is debited, or
charged with all money received; and is credited with all moneys
paid out. Two pages are usually used for a cash account, the
left hand page being used for the debits and the right hand page
being used for the credits.
The '^Balance^' or difference between the amounts of the two
pages will be the cash on hand. The first entry on each debtor
page is the amount of cash on hand.
120
SEVENTH YEAR
Debit Side of a Boy's Cash Accoont
Nov.
1
Balance on haxsd
M
3
Errand
M
4
Assisting in Groeary stora
N
U
m n H N
M
18
•t N M M
1
I
1
90
25
50
50
50
10
65
Credit Side of the Same Boy's Cash Account
NOT,
M
n
N
M
6
10
17
21
30
School Supplies
Sweater Vast
School JSntertainment
Book
To£a/dnce
2
6
45
50
25
50
95
•
10
65
At the end of each month a cash account is "balanced'' as
shown in the above account. This account shows the boy to
have a balance on hand of $6.95 on Nov. 30, because it takes
that amount to make the credit side of the account "balance'*
the debit side.
Exercise 6.
Prepare a cash account for this boy during December,
starting with the cash on hand as shown in the preceding
account and entering the following items on the proper side
of the account.
1. Dec. 2, Bought a necktie 60^; Dec. 2, Received $1.50
for working in the grocery store; Dec. 5, Received from sale
of old books $1.15; Dec. 9, Received from the grocery store
$1.50 for services; Dec. 14, Bought Christmas present for
mother $2.50; Dec. 15, Received for assistance at opera house
$1.25; Dec. 16, Wages from store $1.50; Dec. 19, For Christmas
presents bought $3.85; Dec. 23, Wages from store $1.50;
Dec. 25, Received as present from mother and father $10.00
in cash; Dec. 30, Wages from store $1.60.
BUSINESS FORMS AND ACCOUNTS 121
2. Balance the account on Dec. 31 and enter the proper
amount under ''To balance" on the credit side of the account.
8. What would be the first item of this boy's account for
January, 1917?
The Daybook or Journal
When goods are sold on credit, the merchant enters the sales,
as they occur, in an account book called the Daybook, or
Journal, stating the separate items and the price of each. A
single page of such an account book may contain business
transactions with various persons.
Where memorandum slips are kept, many firms do not keep
a day book but keep these slips as a record of the daily transac-
tions. These memorandum slips are filed in some systematic
way, each customer's slips being kept together.
The following illustration shows a typical page of the journal
of a men's clothing store:
135.
1916.
Nov. 7
William Smith, Dr.
To 3 pairs socks @ .25
75
To 1 shirt
1 50
To 1 necktie
50
To 4 collars @ .15
60
To 1 pair suspenders
1 00
Nov. 7
R. P. Jones, Dr.
To 3 handkerchiefs @ .20
60
To 2 union suits @ 1.50
3 00
To 2 collar buttons @ .10
20
Nov. 7
John F. Brown, Cr.
By cash
Nov. 7
L. B. Strayer
To 1 hat
4 35
3 80
7 50
4 60
122 SEVENTH YEAR
It will be seen that the preposition to is used with debits and
by with credits. The abbreviation Dr. is used for debtor and
means that Wm. Smith and R. P. Jones are debtors to the
firm for the goods which they have purchased. The abbre-
viation Cr. is used for creditor and means that John F. Brown
is to be given credit on his account for the cash which he has
paid.
Exercise 6
Prepare a page of a day book containing the following
transactions for Nov. 2:
1. Sold J. R. Stock 1 pair of shoes at $5.00; 1 box of Hole-
proof hose at $1.50; 2 collars at 15 cents each; and a shirt for
$2.00.
2. Received a cash payment from Wm. Smith for $7.50
to apply on his account.
3. Sold Mrs. J. F. Doan 1 pair shoes at $6.00; 1 box of
Shinola at 10 cents; and 2 handkerchiefs at 35 cents each.
4. Add other accounts that a general dry-goods and shoe
store would have. Fill out the page in this way.
Personal Accounts
In a book called a ledger a page or portion of a page is devoted
to transactions with a single person. These accounts then are
called personal accounts and it is from these accounts that the
monthly statements are prepared.
These accounts are "posted" by a bookkeeper from the
memorandum slips or daybook. The account may be itemized
or the totals only may be entered for each day^s purchase.
A page of a ledger containing a personal account is divided^
into two parts. A person^s indebtedness to the firm is shown
on the left or debtor side of the page; and his payments are
BUSINESS PX)RMS AND ACCOUNTS
123
shown on the right or creditor side. This account is usually
balanced once a month. Here is an account on the page of
a ledger
•
•
Dr,
lilliam anith
Or.
1916
1916
NOT. 1
Balanec tram Oct.
7
SO NOT. 2
Caih
7
50
» 7
lldi«.
4
35 "30
^afdnce
16
10
* 15
M
3
50
•• 29
M
Sdlsnce
8
25
^•f^r
23
60
23
60
16
10
The above personal account of William Smith shows a
balance of $7.50 from his Oct. account still due the firm.
He was sent a monthly statement and promptly responds on
Nov. 2 with a cash payment. The account shown in the
illustration of the daybook on page 121 is shown here entered
on the Dr. side of Wm. Smith's account as indicated in the
daybook. On Dec. 1, Wm. Smith will be sent a statement
of his account, showing a balance due of $16.10.
Exercise 7
1. Prepare a similar personal account for December for
Wm. Smith using imaginary amounts ajid balancing his account
on Dec. 31.
2. Prepare a personal account for R. P. Jones, including
as one of the items, the account shown in the daybook on page
121. Use imaginary accounts for the rest of his account.
8. Prepare a personal account for F. W. Trowbridge from
the following items found in the daybook: Balance due
Nov. 1, as shown in ledger, $8.75; Nov. 3 paid cash, $8.75;
Nov. 5 bought a hat at $4.00 and a tie for 76 cents; Nov. 9
bought 1 box of hose at $1.50; Nov. 15 bought a suit for $27.50;
Nov. 26 bought a pair of shoes for $6.00; Nov. 29 paid cash,
$30 00.
124 SEVENTH YEAR
4. Prepare a personal account of a farmer with a hardware
and implement company, inserting items that a farmer buys
at such a store.
5. Prepare a personal account of a woman at a druggist's,
showing purchases of various medicines, spices, and other
supplies which a drug store in your community keeps.
The Inventory
An inventory consists of a list of articles on hand at the time
the inventory is taken together with a statement of the value
of the various articles. An inventory is a necessity for a firm
in estimating the amount of gain or loss in their business.
Inventory of a School Recitation Room
Furniture:
1 teacher's desk $15. 00
25 single desks at 3.50 87.50
2 chairs at 2.00 4.00
1 filing cabinet 20.00
1 desk book rack 1 . 25
Supplies:
2 sets practice exercises in arithmetic $19.20
1 ream white practice paper 48
1 hektograph (2 faces) 2 . 50
3 arithmetic texts (Chadsey-Smith) 1 . 35
2 boxes crayon at 20 cents .40
Pictures and Flowers:
2 window boxes of ferns at 5.00 $10. 00
1 picture 10. 00
Total value,
BUSINESS FORMS AND ACCOUNTS 125
When there has been a loss of household goods by fire,
msurance companies usually demand that an inventory be
made of the goods destroyed by fire. It is therefore a good
policy to make out an inventory of your household goods at
the cost price and keep it in a safe place for reference in case
of the destruction of your goods by fire.
Exercise 8
1. With the help of the teacher and a supply catalogue,
make out an inventory of the supplies and furniture in your
school room. This may be presented to the school board for
reference in case of fire.
2.. Make an inventory of the furniture and furnishings in
your home, estimating the goods at cost and give this to your
parents to deposit in the safety deposit box in the bank for
reference if it were needed in making out an inventory in case
of fire.
3. If your father is on a farm or in a business in the city,
assist him in making out an inventory for his supplies that he
has on hand.
4. Make an inventory of your own school supplies.
The Pay Roll
In factories, stores, and offices where the employees are
paid by the hour, there must be some system for keeping a
record of then- tune. Some firms employ a card system on
which each employee has his time checked when he begins
and leaves. Others use a system of checks, the worker taking
out his check When he begins and returning it when he leaves.
Some employers have an electric clock with various numbers,
each laborer punching his number on entering and also on leav-
ing. The record is made on a revolving sheet of paper on the
proper time space.
126
SEVENTH YEAR
The following form is a simple arrangement for making out
the pay roll:
No.
N»
l!en.
Tues.
Wed.
Thur*.
Tri,
Snt.
Total
Tina
Rata
pap hp.
ilpount
DM
1.
A. Bro«B
8
8
10
49
85#
n2.2s
2.
R. Jor.«ii
8
8
9
51
25^
12.75
3.
J . Schridt
8
9
9
35^
4.
F. J«in»«n
9
8
9
35^
5.
P. Gregory
8
8
10
40^
«.
R. DorB«y
8
9
8
40^
•».
S. Stodd»rd
9
9
10
32^
8.
V. Strlpri
9
8
9
36^
9.
N. Costal :e
8
8
8
8
30^
The amount of time is multiplied by the proper rate per hour
for each employee and the various sums placed in the last
column showing the amount due. From this pay roll the
cashier makes out a memorandum showing the number of
each kind of bills and each kind of coin in order to put the
exact amount in each employee's envelope, to be handed to
him at the close of the week. The following form gives one
plan for the cashier's memorandum:
Cashier's Memorandum
No.
Wdges
*20
^
^
*2
■jfj-
50*
25*
10*
5*
1*
1
U-:iS
/
/
/
2
17.. 7 5
/
/
/
/
3
4
5
6
7
8
9
TOIAL
•
•
?
•
•
•?
a
?
•
?
?
a
BUSINESS FORMS AND ACCOUNTS 127
Ezerdse 9
1. Complete the rest of the pay roll as indicated in the
portions already filled out.
2. Fill out the rest of the cashier's memorandum in the
manner shown m the first two lines.
8. Fmd the total number of each denomination of bills
and coins.
4. What is the total amount of wages due the employees?
5. From the number of bills and coins in each column, see
if the cashier's memorandum checks with the total amount in
wages.
AGENCIES FOR SHIPPING MERCHANDISE
When goods are ordered, there are three ways of shipping
them to the customer: parcel post, express and freight. The
customer should state, when ordering the goods, what method
of shipping to use, unless he leaves that to the judgment of the
firm. Parcel Post is generally cheaper for small articles. Perish-
able goods such as strawberries are generally shipped by
express. When the goods are bulky and immediate delivery is
not essential, freight is the cheapest means of transporting
them. Express and parcel post packages are generally delivered
free, but freight is not. We should be informed on the relative
cost and convenience of these agencies for shipping goods in
order to know how to order supplies of various kinds.
Parcel Post
Merchandise is shipped by the post office department under
a system of parcel post rates. All parcels weighing 4 ounces
or less are carried at 1 cent per oimce, regardless of the distance.
The rates on parcels heavier than 4 ounces vary according to
the weight and the distance of the place to which the goods
128
SEVENTH YEAR
are shipped. For convenience in handling the matter of dis-
tance, the government has estabhshed a system of zones.
Each post office has a book which classes 3ach city in our
coimtry in its appropriate zone with regard to that office. The
following table gives only a portion of the weights and zones
under the parcel post system:
HrUl
Loeia
ZOBM 1*2
Z«M S
ZeM4
Zoo* 5
■or* than 150
■llM disiaat
CitlM 151
to 300 BilM
diataai.
Cltl»a 301
to 600 BilM
dletMrt.
CiilM 601
tolOOOaUes
dUtwi.
Over 4 OS. up to 1 lb.
5#
50
60
70
80
* 1 lb. " * 2 lb.
6^
60
80
110
140
" 2 lb. * * 3 lb.
6^
70
100
150
200
" 3 lb. • * 4 lb.
7^
60
120
190
260
• 4 lb. • "5 lb.
1^
90
140
230
320
• 10 lb. * "11 lb.
1<¥
150
260
470
680
" 15 lb. •« "16 lb.
13^
200
360
670
980
* 19 lb. •• "20 lb.
150
240
440
830
1.22
» 25 lb. •• ••26 lb.
180
300
50 pounds 18 the limit in wei<;ht
for parcels in the local lone and
zones 1 and 2.
20 pounds is the limit in weight
for the other lones.
•• 30 lb. •• "31 lb.
200
350
» 40 lb. * "41 lb.
250
450
• 49 lb. " "90 lb.
900
540
ziones o, / and o
eluded in this table on
lack of space.
»re ooii la-
I account of
Exercise 10
1. A farmer 101 miles from Chicago wishes to ship a package
of butter weighing 4^ pounds to a customer in that city.
Find the parcel post charges on the shipment.
2. The distance from Pittsburgh to Chicago is 492 miles.
How much will it cost to send a 4-pound package from Chicago
to Pittsburgh by parcel post?
3. The distance from St. Louis to New Orleans is 748 miles.
How much will it cost to ship a 10^-pound package by parcel
post from New Orleans to St. Louis?
BUSINESS FORMS AND ACCOUNTS 129
4. The distance from Detroit to New York is 595 miles.
How much will a parcel post shipment of 15 f pounds cost
between those cities?
5. I wish to ship a package of merchandise weighing 4^
pounds to a city in the third zone. How much postage must
1 put on the package?
6. A man in southern Wisconsin advertised a 12-pound
case of fancy comb honey for $2.60 per case, charges prepaid.
How much more would it cost him to ship to a customer in
the third zone than to one in the second zone?
7. A farmer agreed to supply a city customer with 2 pounds
of butter per week at 32 cents per pound, the customer paying
the parcel post charges. The city was in the first zone. How
much will the customer save in a year if he has his butter
shipped in 4§-pound packages every two weeks instead of
2 J-pound packages every week?
Find the parcel post charges on
the following parcel post
packages:
•
Weight
Zone
Charges
8. 8 ounces
Fourth
?
9. 3 pounds
Fifth
?
10. 15^ pounds
Third
?
11. 50 pounds
Second
?
12. 20 pounds
Fourth
?
13. lOf pounds
Third
?
14. 5 pounds
Fifth
?
16. 3^ pounds
Fourth
?
16. 2 pounds
Fifth
?
17. 11 pounds
Third
?
18. 31 pounds
Second
19. 40 pounds
First
?
20. 19 f pounds
Fourth
?
130
SEVENTH YEAR
Express
Express rates vary with the weight of the shipment and the
distance between the shipping points. In computing express
rates, the 'rate per hundred pounds is indicated and a scale
based upon this rate is indicated. A portion of such a system
of rates is shown in the table below.
Rat* ptr ICO lb.
n.oo
«1.25
$1.40
n.so
•1.70
n.-'s
12.00
«3.40
C3.85
$4.20
It»t« for 1 lb.
as
.26
.26
.26
.26
.26
.27
.28
.29
.29
. • 2 «
.26
.27
.27
.27
.28
.28
.28
.31
.32
.33
. • 5 •
.29
.30
.31
.31
.32
.32
.34
.41
.43
A5
• • 10 *
.32
.35
.36
.37
.39
.40
.42
.56
.61
.64
• - 15 *
.3«
.40
.42
.44
.47
.47
.51
.72
.79
.84
. •• ao "
.40
.45
.48
.50
.54
.55
.60
.88
.97
1.04
• - 30 •
.47
.55
.59
.62
.68
.70
.77
1.19
1.3?
1.43
. - 40 *
.55
.65
.71
.75
.83
.85
.95
1.51
1.69
1.83
• • 45 *
.59
.70
.77
.81
.90
.92
1^
1.67
1.87
2.03
The express rates per 100 pounds from Chicago to the cities
mentioned in the following table are:
St. Louis $1.40
Minneapolis 2. 00
Fort Worth 3.85
Pittsburgh 1.70
Charleston, S. C 3.40
Denver $4.20
Indianapolis 1 . 00
Columbus, Ohio 1 . 50
Nashville 1.75
Detroit 1.25
Exercise 11
1. Find the cost of an express package weighing 20 pounds
from Chicago to Fort Worth, Texas.
2. How much will it cost to ship a box weighing 100 pounds
by express from Chicago to Detroit?
8. What will be the express charges on a 1 0-pound package
from Chicago to Denver?
BUSINESS FORMS AND ACCOUNTS 131
Find the express charges on a
4. 10-poimd package from Chicago to Charleston, S. C.
6. 30 pounds from Chicago to Minneapolis.
6. 15 pounds from Chicago to Pittsburgh.
7. 45 pounds from Chicago to St. Louis.
8. 2 pounds from Chicago to Nashville.
9. 5 poimds from Chicago to Columbus, Ohio.
10* 40 pounds from Chicago to Indianapolis.
11. 30 pounds from Chicago to Fort Worth.
12. 15 pounds from Chicago to Denver.
13. Find the cost of an express package weighing 45 pounds
from Chicago to Charleston, S. C.
Freight Rates
Railroad companies figure freight rates to the large cities
and make practically the same rates to the smaller cities in
the vicinity of each large city. Merchandise is divided for
freight shipments into four classes. Among the various articles
listed in each class are:
(1) First class — ^Books, clocks, dry goods, fire arms, lamps,
rugs, toys, etc.
(2) Second class — Bedsteads, cream separators, extension
tables, linoleum, refrigerators, wheelbarrows, etc.
(3) Third class — Iron kettles, iron safes, stoves and ranges,
etc.
(4) Fourth class — ^Anvils, poultry food, steel roofing, stock
food, plain or barbed wire, etc.
The following table shows the rates per 100 pounds on the
four classes of freight from Chicago to the cities mentioned:
132
SEVENTH YEAR
ciir
Pirtt
ClM«
8«e«ad
ClM»
9liT«
ClM*
Tmurtk
ClMV
St. Uuis
1.46
1.37
♦ .«•
I.3S
Detroit
.39
.34
.23
.17
Nashville
.82
.68
.33
.43
ladianapoll*
.33
.28
.23
.15
r»rt l»rth
1.67
1.41
1.16
1.06
DraT»r
l.fK)
1.45
1.10
.85
'Pittsburg '
.47
.41
.32
.22
Exercise 12
1. How much would a
stove weighing 675
pounds cost to ship by
freight from Chicago to
Indianapolis?
Suggestion: Look at
the description of the
classes of freight to find
in which class stoves are
listed and then compute by the rate per 100 pounds as shown
in the table.
2. A rowboat weighing 150 pounds is shipped from Chicago
to St. Louis. If rowboats are classed at a rate 4 times first
class, what is the freight on the rowboat?
3. A farmer living near Nashville wishes to order some
barbed wire from Chicago. Find the freight which he will
have to pay on a shipment of four 80-rod spools weighing
90 pounds each.
4. Find the difference in the charges by freight and express
for a box of dry goods weighing 150 pounds from Chicago to
Pittsburgh. When would a merchant be likely to order the
goods by express rather than by freight?
6. A merchant in Detroit ordered a rug weighing 35 pounds
when packed for shipment in Chicago. Find the cost of the
freight on this rug.
Find the freight rate per 100 pounds on the following articles
from Chicago to the city named:
6. Bpoks to Denver. 8. Stock food to St. Louis.
7. Iron safes to Nashville. 9, Refrigerators to Fort Worth.
10. Clocks to Detroit.
CHAPTER VI
PRACTICAL MEASUREMENTS
As a proper preparation for the problems in practical measure-
ments a review of the following facts is essential.
Refer to the tables in the back of the book to recall facts
that you have forgotten. You will need these facts in solving
problems in daily Ufe.
Exercise 1
1. 1 yard = ? feet.
2. 1 pound = ? ounces.
8. 1 minute =? seconds.
4. 1 foot=? inches.
5. 1 square yard^? sq. ft.
6. 1 dozen =? things.
7. 1 square foot=? sq. in.
8. lton=?lb.
9. 1 long ton = ? lb.
10. 1 gallon =? cu. in.
11. 1 cubic yard = ? cu. ft.
12. 1 week=? days.
18. 1 yard =? inches.
14. 1 quire =? sheets.
15. 1 hour=? minutes.
16. 1 cubic foot=? cu. in.
17. 1 ream =? sheets.
18. 1 quart = ? pints.
19. 1 day = ? hours.
20. :
lrod=?feet.
21. :
I common year=? days.
22. :
I leap year=? days.
28. :
I mile =? feet.
24. :
I peck=? quarts.
25. :
I bushel =? cu. in.
26.
1 gross =? dozen.
27.
1 cord = ? cu. ft.
28.
1 gallon = ? quarts.
29.
1 bushel = ? pecks.
80.
1 niile=?rods.
81.
1 gross =? things.
82.
1 bushel = ? quarts.
38.
1 acre = ? sq. rd.
34.
1 niile = ? yards.
85.
1 cu. foot==? gal. (approx.)
36.
1 square mile = ? acres.
37.
1 square rod = ? sq. yd
88.
1 barrel = ? gallons.
133
134 SEVENTH YEAR
Exercise 2. Miscellaneous Problems
1. How many dozen eggs are there in a standard crate
containing 360 eggs?
2. How many square feet are there in an acre?
3. How many cubic inches are there in a quart, liquid
measure?
4. How many cubic inches are there in a quart, dry measure?
5. How many inches are there in a mile?
6. The capacity of a coal car is 70,000 pounds. How many
long tons of coal will it hold?
7. A pile of cord wood is 20 feet long and 6 feet high. If
the sticks are 4 feet long, how many cords does the pile contain?
8. If round steak is selling at 24^ a pound, how much
should a butcher charge you if the scale reads 1 lb, 12 oz.?
9. A lot is 165 feet long and 65 feet wide. Express the
dimensions of the lot in rods. How many feet of fence will it
take to enclose the lot?
10. A horse is 16 hands high. (A hand is 4 in.) How high
is the horse? (Express height in feet and inches.)
Exercise 3
Tell what the following numbers stand for:
Example: 1. 36 in. =the number of inches in a yard.
2. 231 sq. in. 7. 27 cu. ft. 12. 24 sheets 17. 1728 cu. in.
3. 160 sq. rd. 8. 144 sq.m. 13. 2000 lb. 18. 7 days
4.5280 ft. 9- 16^ ft. 14. 30|sq.yd. 19. 128 cu. ft.
5. 4 qt. 10. 12 in. 16. 5^ yd. 20. 365 days
6. 2150.42 cu. in. 11. 320 rd. 16. 9 sq. ft. 21. 1760 yd.
PRACTICAL MEASUREMENTS— ANGLES 135
The following figures and definitions are very important
because they are used in describing the various kinds of figures
in measurements, both in this book and in their applications in
daily life.
A Straight Line
•B
A straight line is a line which does not change its direction
at any point. Two letters, one at each end of the line, are
generally used to name a line — as the line A B.
Parallel Lines
Figure 1
Figure 2
Figure 3
If two straight lines on a flat surface are always the same
distance apart and therefore can not meet, no matter how
far they are extended, they are said to be parallel. (See Figures
1, 2 and 3.)
The rails on a straight stretch of a railroad track are parallel
because they are the same distance apart. Give another
example of parallel lines.
Figure 4
Figure 5
136
SEVENTH YEAR
When two lines meet, they form an angle. The size of the
angle depends upon the difference in direction of the lines and
not upon the length of the lines forming the angle. For example,
the angles in Figures 4 and 5 are equal.
The point A where the two lines meet is called the vertex of
the ajigle.
The angle in Figure 4 may be read angle A or angle B A C or
angle 1. For shortness Ihe sign < is used for the word angle.
Angle A is the same as < A.
D
1
C
Figure 6
N
•B
If a straight line is drawn to meet another straight line, so
that* the angles thuQ formed (as angles 1 and 2 in Figure 6)
are equal, the lines are perpendicular to each other.^
Perpendicular lines form right angles.
An angle smaller than a right angle is an a^ute angle.
An angle larger than a right angle is an obtuse angle.
Angles 1 and 2 in Figure 6 are right angles. Angle 2 in
Figure 7 is an acute angle and Angle 1 in Figure 7 is an obtuse
angle.
iRight angles may be formed by paper folding. Take a sheet of paper
and fold an edge over on itself. Then crease with the edges held together.
The crease will be perpendicular to the edge of the paper. Show how to
fold the paper to make acute and obtuse angles.
PRACTICAL MEASUREMENTS— RECTANGLES 137
Rectangles
A figure of four sides is a quadrilateral.
How many sides has the rectangle
AB CD?
How are the two pairs of opposite sides
drawn?
How many angles has a rectangle?
What kind of angles are they?
A rectangle is a quadrilateral whose
opposite sides are parallel and whose angles are right angles.
Exercise 4
1. How many small squares are there in one row along the
base AB?
S. How many rows are there in the width or altitude, B C ?
8. How many small squares are there in the area of the
rectangle A B C D?
We see, then, that the area of a rectai^le may be found by
multiplying 1 square unit of area by the number of units in
length by the number of the same kind of units in the width.
We can state this more briefly in the :
PRINCIPLE: Tbe area of a rectangle is equal to the product
of tbe base and altitude.
4. Let A stand for the area, b for the base and a for the
altitude. The above principle can be stated in a much shorter
form, called a, formula:^ A=bXa.
5. If b and a are f^ven, how do you Snfi the area, A7
6. If the area, A, and the base, b, are f^ven, how do you
find the altitude, a?
'Show that the letters are used in a formula t« stand for a word in order
that time may be saved when the principle needs to be stated in writing.
138 SEVENTH YEAR
7. If the area, A, and the altitude, a, are given, how do you
find the base, b?
The perimeter of a rectangle is equal to the sum of its four sides.
Exercise 6
1. If the base A B is 15 inches and the altitude B C is 8
inches, what is the perimeter of the rectangle A B C D ?
2. What is the area in square feet of the floor of your
recitation room?^
3. What is the perimeter in feet of this room?
4. How much would it cost to put a baseboard around the
sides of the room at 10 cents per running foot? Make allow-
ances for the doors.
5. How many board feet of lumber were used in covering
this floor if an allowance of j of the area is added to cover
loss from cutting and the amount used in tongue and groove
work on the boards?
6. What did this lumber cost at $80 per M?
7. In a certain park there is a rectangular wading pool
40 feet long, 28 feet wide and 2 feet deep. How much did it
cost to cement the bottom and sides of this pool at 15 cents
per square foot?
8. Around the outside of the pool there is a concrete walk
3 feet wide. Find the area of the concrete walk.
9. What is the perimeter of the pool? What is the perimeter
of the walk?
10. A rectangular field is 80 rods long and 40 rods wide.
How many acres are there in the field?
Problems using local data should be prepared by the pupils and presented
to the class for solution.
PRACTICAL MEASUREMENTS— PROBLEMS 139
11. What must be the dimensions of a rug for a room 18
feet in length and 14 feet in width, if a yard of uncovered floor
space is left on each end of the room and 2§ feet is left on each
side?
12. How many square feet of floor space will be left uncovered
in the room? Show two ways of solving this problem.
13. A rectangular lot contains 9570 square feet. It is 130
feet long. How wide is it?
14. Find the cost of covering the blackboard space in your
school room with slate at 15^ a square foot.
15. How much will it cost to cover the floor of a kitchen
9'xl5' with linoleum at 85 j5 per square yard?
16. For a room to be properly lighted, the area of the glass
surface should be at least ^ of the area of the floor space. Is
your school room properly lighted?
17. A field is 80 rods long. How many rows of com will it
take to make an acre if the rows are 3 feet 8 inches apart?
18. A rectangular field contains 60 acres. It is 120 rods
long. How wide is it?
19. How long is a tennis court? How wide is it for doubles?
How many square feet does it contain?
20. A township is 6 miles long and 6 miles wide. How many
acres are there in a township?
21. A mile of a certain city street is to be paved with brick
at a cost of $1.20 per square yard. If the pavement is to be
30 feet wide, what will be the cost per mile?
22. The property owners are required to pay for half of the
width of the pavement extending in front of their lots.^ How
much would the pavement cost in front of a lot 50 feet wide?
*The city usually pays for the cost of the pavement at the intersections
of the street.
140
SEVENTH YEAR
Boy Scouts' Tents
Boy Scouts are taught to make tents out of square and
rectangular pieces of canvas. The figures below show how to
make a tent out of square sheets of canvas. A square 7 feet
by 7 feet will provide a shelter for 1 man and a square 9 feet
by 9 feet a shelter for two men.
The following figures show how to make a tent from a
rectangular piece of canvas twice as long as it is wide. See if
you can hang and stake such a tent properly.
Camping
Among the various requirements necessary to obtain a merit
badge for Camping, a scout must:
1. Have slept fifty nights in the open or under canvas at
different times.
2. Demonstrate how to put up a tent and ditch it.
(From the Handbook for Boys — The Boy Scouts of America.)
PRACTICAL MEASUREMENTS— BOY SCOUTS 141
Exercise 6
1. How many square feet of canvas are needed in a one-man
shelter that is made from a sheet 7'x7'?
2. How many square feet of canvas are there in a two-man
shelter?
3. Two Boy Scouts found that they could buy 7'x7' sheets
of ducking for $1.75 each or a 9'x9' sheet for $2.50. Which
would provide the cheaper shelter for them, the single or the
double tents?
4. Four Boy Scouts found that they could buy a canvas
9'xl8' for $4.75. How much would they save by buying this
sheet and making a four-man shelter, rather than buying
individual sheets costing $1.75 each?
Gardening
Among the viarious things that a scout may do to obtain a
merit badge for gardening is:
(a) To operate a garden plot of not less than 20 feet square
and show a net profit of not less than $5 on the season's
work. Keep an accurate crop report.
Exercise 7
1. If the garden plot must be at least 20 feet square, how
many square feet does this minimum sized plot contain?
2. Express the area of the minimum plot in square rods.
8. What part of an acre is this minimum plot?
4. A certain boy raised beans on a garden plot 33 feet wide
and 132 feet long. His profit was $110.75. Find his profit per
square rod. Would he have been able to secure the merit
badge for gardening on a minimum sized plot at that rate?
5. What would have been his profit per acre at that rate?
142 SEVENTH YEAR
Parallelograms
A parallelogram is a
quadrilateral with its oppo-
site sides parallel. The
figure on the left is a
parallelogram.
A rectangle is a parallelogram with its angles all right angles.
A parallelogram with angles not right angles is called a rhomboid.
The figure above is likewise a rhomboid.
? $ The line AB is called
the ba^e of the parallelo-
gram. The line D E, which
I is the perpendicular dis-
A E B o tance between the base
D C and the base A B, is called the aUitvde of the parallelogram.
Cut out of a sheet of paper a parallelogram similar to
A B C D. Fold over the edge A E on the base A B and crease
along the line D E. Cut or tear off the part A E D and fit
it in the position B O C. What shape is the figure D E O C?
Show that the rectangle D E O C has the same base and
altitude as the parallelogram A B C D.
Cut out a parallelogram with a base of 6 inches and an
altitude of 3 inches. Change into a rectangle with the same
base and altitude. What is the area of this rectangle? Since
the same amount of paper forms the parallelogram, what is
the area of the parallelogram?
Then show how we obtain the principle: The area of a
parallelogram is equal to the product of its base times its
altitude.
This principle may also be expressed by the formula:
A = b X a.
In this formula what is the product and what are the factors?
PRACTICAL MEASUREMENTS— PROBLEMS 143
Exercise 8
1. If the base and altitude of a parallelogram are given, how
do you find the area, A?^
2. If the area, A, and the base, b, of a parallelogram are
given, how do you find the altitude, a?
3. If the area. A, and the altitude, a, of a parallelogram are
given, how do you find the base, b?
4. The base of a parallelogram is 4 feet and the altitude is
3 feet. What is its area?
6. The area of a parallelogram is 24 square feet. The
altitude of the parallelogram is 4 feet. Find the base.
6. Find the area of a parallelogram with a base of 7 feet
and an altitude of 2 yards.
7. A flower bed is shaped in the form of a parallelogram
with each side equal to 6 feet. By measuring I find the per-
pendicular distance between the sides to be 3^ feet. What
is the area of the flower bed?
8. What is the perimeter of the flower bed described in
the preceding problem?
9. How many bricks 8 inches long would it take to build a
border one brick thick around this flower bed?
10. The area of a field in the form of a parallelogram is 20
acres. The base is 80 rods. What is the perpendicular distance
between the bases (the altitude)?
Fill in the missing dimensions:
Aba
11. 400 sq. ft. 25 ft. ?
12. ? 5 yd. 12 ft.
13. 36sq. yd. 9 yd. ?
^Such problems as 1 to 3 of this exercise give practice in reviewing the
principles relating to product 'and factors. Have pupils state the answers
in formulae if possible.
144 SEVENTH YEAR
c r Trapezoids
\^/ A trapezoid is a quadrilateral
Yo with only one pair of opposite
A sides parallel.
^ /^\ ThefigureABCDisatrape-
^ ^ ' zoid.
1. By measuring find the middle point O of the line C B.
Draw E F parallel to the line A D. By cutting oflf part E B O
and placing it in the position O F C, what shaped figure is
formed?
2. K A B = 16 inches and D C = 12 inches, what is the
length of A E?
By using other numbers and remembering that E B is the
same length as C F, you can show that the base of the parallelo-
gram into which the trapezoid has been changed is ^ the sum
of the two bases of the trapezoid. The altitude of the parallelo-
gram is the same as the altitude of the trapezoid. With this
information show that:
PRINCIPLE: The area of a trapezoid is equal to half the sum
of the two bases times the altitude.
Exercise 9
1. Find the area of a trapezoid whose bases are 12 inches
and 18 inches and whose altitude is 11 inches.
Solution: § of (12+18) = 16, number of inches in § the
simi of the bases.
11X16=166.
Therefore: The area of the trapezoid is 165 square inches.
2. Find the area of a trapezoid of which the upper base is
10 feet, and the lower base 18 feet and the altitude 9 feet.
3. A board is 10 inches wide at one end and 14 inches wide
at the other end. If it is 10 feet long,, how many square feet
are there on the surface of the board?
PRACTICAL MEASUREMENTS— TRIANGLES 145
zo leDS.
tORI>5.
4. A man once gave me this problem to
solve. A railroad cut off a small piece
of his land in the form shown at the left.
He had threshed oats off of the tract and
wished to compute the yield per acre,
but he did not know how many acres
there were in the piece. Find the number
of acres in the field.
5. If the field yielded 210 bushels of
oats, what was the average yield per acre?
Triangles
A triangle is a figure bounded by three straight lines, called
its sides. As the name indicates, a ^rt-angle has three angles.
Triangles may be grouped according to sides or angles.
{Scalene — ^no two sides being equal.
Isosceles — having only two sides equal.
Equilaleral — shaving all three sides equal.
iAcute Angled — Shaving all the angles acute.
2. Angles<06iit5e Angled — having one angle obtuse.
[Right Angled — having one angle a right angle.
Scalene
Isosceles
Equilateral
Acute Angled
Obtuse Angled
Right Angled
146 SEVENTH YEAR
Areas of Triangles
The altitude of any triangle
k;"" 7 is the perpendicular from the
/jy^Sv / vertex to the base, as the line
/!§ \^ / CE.
/ :< ^s^ / Draw any shaped triangle as
L\ :^^ ABC.
From C draw a line C D
parallel to the base of the triangle, A B.
From B draw a line parallel to the side A C.
What kind of figure is A B D C? How does its base and
altitude compare with the base and altitude of the triangle
ABC?
Cut out your parallelogram and cut it along the diagonal
line B C. How do triangles ABC and B D C compare in size?
The triangle A B C is what part of the parallelogram A B D C?
The area of the parallelogram = the product of base X altitude.
The area of the triangle = ^ the area of the parallelogram.
Show that the areas of the other forms of triangles equal
\ the area of the parallelograms constructed as shown in the
scalene triangle above.
PRINCIPLE : The area of any triangle is one-half of the product
of the base times the altitude.
Draw a triangle on a sheet of paper. Cut it out carefully
and number the angles 1, 2 and 3. Cut the triangle into three
parts so that you can arrange the angles about a point on one
side of a straight line. Show that the sum of the three angles of a
triangle is equal to two right angles (or 180°). Draw other
shaped triangles to show that this principle holds true for any
shaped triangle.
PRACTICAL MEASUREMENTS— TRIANGLES 147
Exercise 10
1. The base of a triangle is 16 inches and the altitude is
11 inches. Find the area.
Solution:
The product of the base times the altitude = 16X11 = 176.
^ of the product 176=88.
Therefore: The area of the triangle is 88 square inches.
In finding the product, be sure that both base and altitude
are expressed in the same linear units. Only the final area,
then, will need to be labeled.
Find the area of the following triangles:
Altitude X
Base =
Area.
2.
10
ft.
15 ft.
?
3.
8
in.
12 in.
?
4.
20
rd.
35 rd.
?
6.
11
in.
19 in.
?
6.
f
ft.
If ft.
?
7.
6f
in.
12 in.
?
8.
1.65 ft.
2.3 ft.
?
9.
.3
yd.
.5 yd.
?
10.
4
ft.
2^ ft.
?
11. A field in the shape of a right triangle has a base of
20 rods and an altitude of 16 rods. Find its area in square
rods. How many acres in this triangular field?
12. A diamond (also called a rhombus) may
be divided into 2 equal triangles. If the short
diagonal is 6 inches and the long diagonal 8
inches, find the area of the diamond.
(Hint — The two diagonals are perpendicular to each other and bisect
each other.)
148
SEVENTH YEAR
13. If the bam, of which the end is shown
in the illustration, is 36 feet long, find the
total number of square feet in the sides and
ends of the bam?
14. How much would it cost to paint the
above bam at 10^ per square yard?
16. A tract of ground 40 feet square is divided into 4 equal
triangles by diagonal lines. What is the area of each triangle?
16. The area of a triangle is 35 square feet and the altitude
is 10 feet. What is the length of the base?
Solution: Since the area of a triangle is ^ of the product
of the base X altitude, the product of the base times the altitude
must be 2X35 square feet = 70 square feet. If the product
of the baseXaltitude is 70 and the altitude 10, the base must
be 70^10 or 7.
Therefore: The base of the triangle = 7 feet.
Find the missing term in the following problems:
Altitude of triangle Base of triangle Area of triangle
17.
•
5 ft.
?
25 sq. ft.
18.
?
9 in.
54 sq. in.
19.
7 in.
•
28 sq. in.
20.
f ft.
?
f sq. ft.
21.
?
•
.32 rd.
.384 sq. rd.
22.
5 yd.
7|yd.
?
•
23.
20 rd.
15 rd.
?
24.
7 ft.
?
•
21 sq. ft.
26.
f ft.
1| ft.
?
26.
16 in.
?
96 sq. in.
^ 27. Find illustrations of triangles in your neighborhood
and prepare problems for the class to solve.
PAPER, PRINTING AND BOOKBINDING 149
APPLIED REVIEW PROBLEMS
Print Paper
A Modem Paper Mill
Next to food, clothing and shelter, paper is probably the
moet important necessity in modern civilization. Make a list
of the various ways in which paper is used. See which member
of the class can make the largest list.
Print paper, used in our daily newspapers, is made from wood
pulp. The spruce tree furnishes the best wood for making
print paper. These trees are sawed into blocks of proper
length and ground by stone rollers, on which water is dripping,
into a very fine pulp. Chemicals are mixed with some of the
wood in order to toughen the fibers so that the paper will not
tear easily. The wood pulp is collected on a wire form and run
through a series of rollers, being dried during the process.
Exercise 1
1. It takes 113.92 cubic feet of timber to make 1 ton of
print paper. This is what part of a cord, expressed decimally?
2. A spruce tree 2 feet in diameter will produce approxi-
■ mately 1.8 tons of print paper. How many cubic feet of wood
are there in such a tree?
3. How many cords of wood are there in a tree of that size?
How much would this wood be worth at $3.50 per cord?
150 SEVENTH GRADE
4. Allowing for waste, and counting 8^ board feet for each
cubic foot, what would be the value of the lumber in such a
tree at $28.60 per M7
5. Find the value at 3 J cents per pound of the print paper
that may be manufactured from a tree of that size. Compare
the values of the paper, lumber and wood from such a tree.
Print paper is slupped from a
certain paper mill in rolls having an
average weight of 1700 pounds. The
width of the paper in these rolls is
752 inches.
6. A strip of this paper 1 foot in
length and the width of the roll
weighs 1^^ ounces. What is the length of one of these 1700
pound rolls in feet?
7. How many miles long is one of these rolls?
A daily paper, on
a certain day, issued
an edition of 100,000
32-p^e papers, the
size of each page being
18^' X 23^'. Each
print paper roll
weighed 1650 pounds.
The width of the
paper was 73 inches
and its average weight per foot in length was Ig ounces.
8. What was the length of a roU of this paper in feet?
6. What was the length of a roll in miles?
10. How many sheets were there in each 32-page paper?
11. How many times is the width of a sheet of the paper
contained in the width of the roll?
PAPER, PRINTING AND BOOKBINDING 151
12. How many inches in length would be used to print one
32-page paper?
13. Each roll will print how many papers? (See Prob. 11.)
14. How many rolls of this paper were required for the
edition of 100,000 papers? How many tons would these rolls
weigh?
15. How many trees of the size stated in Problem 2 were
required to produce the wood pulp used in manufacturing the
paper for this edition?
Type
Look at this page and see how many kinds of type and other
characters are used. The type in this line is designated as
*'10 point." The type in the lines at the bottom of this page
is known as "8 point." The type in the line at top of the
illustration is "6 point."
Type sizes are classified by "points"
and for this purpose the inch is divided
into 72 parts or "points." "12 point,"
which is a standard of measurement
(conmionly called pica)j is ^ of an
inch high, and "6 point" is ^ of
an inch high.
In printing; the term "em" applies to the exact square
space occupied by a single letter counted as wide as it is high.^
The "em" is the unit of measure of the quantity of type on a
page.
The number of lines on a page varies with the size of the
type and the amount of space separating the Unes.
*As a matter of fact, the type letter is so made as to require less space
sideways than up and down. On this account, letters and figures are
measured by their depth and not their width.
Comparison of Type
a
6 Point
D
8 Point
n
10 Point
12 Point
152 SEVENTH YEAR
Exercise 2
1. "6 point" type is what part of an inch high?
2. "8 point" type is what part of an inch high?
S. "10 point" type is what part of an inch high?
4. "12 point" type is what part of an inch high?
5. Measure very accurately one of the lines on this page.
How many picas wide is it?
6. Counting 70 letters to an 8 point line and 38 lines to a
page^ how many "ems" would a page contain? (An "em"
is equivalent to an average of two characters — ^letters, figures,
or punctuation marks.)
7. Counting 58 letters to a line and 33 lines to a page, how
many "ems" would a "10 point" page contain?
8. Counting 48 letters to a line and 28 lines to a page, how
many "ems" would a "12 point" page contain?
Book Making
The paper used for school books is necessarily of a much
better quality . than the print paper used by newspapers.
With wood pulp must be combined a certain percentage of
"rags" (cotton or linen) to make this higher grade of paper.
Instead of this kmd of paper being shipped in roUs it is
marketed flat and sold by the ream, 500 sheets to the ream.
By a close inspection of the top of this book, it will be seen
that it is bound in sections of 32 pages (16 leaves) each, called
forms.
Exercise 3
1. Divide the total number of pages in this book, including
the 6 introductory pages in the front of the book, by 32 and see
how many '^forms^' are required.
PAPER, PRINTING AND BOOKBINDING 153
2. Take a sheet of paper 31* by 21* and fold it successively
4 times. Open it up suflSciently to enable you to number the
pages in regular order (as they would open if the edges were
cut) from 1 to 32. Then spread the sheet out flat and see how
the plates are arranged in printing a form.
3. Counting both sides of the sheet, how many printing
impressions are required in printing one book of this size?
4. How many sheets of the size stated are used in making
one book?
5. How many books will 1 ream of paper make?
6. How many reams of paper are needed for an edition of
25,000 copies of this book?
7. Assuming that each ream of this paper weighs 75 pounds,
what weight of paper is required for an edition of 25,000 books?
Book Binding
A very important step in book making is the binding. This
may be of paper, of cloth, of leather, or of some combination of
these materials. School books are usually full cloth bound.
The printed forms, which are folded by machinery as they
come from the press, are ordinarily of 32 pages, although in
larger books they may be of 64 pages.
Exercise 4
1. If the glueing and re-enforcing of the "back bone"
of each book, before the cover is put on, requires an average of
^ minute per book, how many working days of 8 hours would it
require for one person to care for that part of an edition of
25,000 books?
2. The cloth required for the outside of this book is cut
approximately 8^*^ by 12*. How many yards of binding cloth
36 inches wide are needed for 25,000 copies?
164
SEVENTH YEAR
3. If the "binders' board" which is used inside of the cloth
cover is cut 7f 'x5 J*, how many sheets of board, size 22'x28"'
would be required for an edition of 25,000 books?
Exercise 5
The announced circulation of a metropolitan daily newspaper
for a certain date was 681,562 papers of 80 pages each. The
following facts were included in this newspaper's statement
explaining the issue. This illustrates the extensive use of
timber in the production of print paper alone.
It required the usable timber from
84 acres to produce the amount of
paper needed for this one issue.
It required 425 tons of paper for this
one issue.
It required the labor of 510 men 4
days to make the output. of paper for
this one issue.
It required a train of 15 cars, each
carrying 28 tons, to transport this
paper from the mills to the city.
It required 60 truckloads, each
weighing 7 tons, to deliver this paper
from the railroad.
It would make a paper path 18
inches wide and 10,843 miles in length
if the sheets required for this one issue
were spread out end to end. This
would be sufficient to stretch from
Bering Strait to Cape Horn.
It would paper an expanse of 85,-
876,560 square feet if spread out in
single sheets over a flat surface.
1. 80 pages means how
many single sheets, or
leaves?
2. The size of the news-
paper here referred to is
18 J inches by 23 ^ inches.
What is the length, in
inches, of one paper of this
issue, the sheets laid end
to end? The length in
feet?
3. Multiply this num-
ber of feet by 681,562
papers, and reduce to
miles.
4. How many square inches in one single sheet of this
paper? In the 40 sheets (80 pages) of this paper?
6. How many square feet are there in one full paper of
this issue? An acre contains how many square feet?
6. Reduce 85,876,560 square feet to acres. How many
160-acre farms would this amount of paper cover?
PART II
Training for Efficiency. ChecUng Up
It ia considered good business practice to check all bills and
accounta to be sure that they are accurate. In order to do this
checking rapidly and accurately, practice on the different com-
putations that are used.
Since no business man wishes his work delayed by slow
cheeking, it is important that short methods be used whenever
it is possible. The following pages not only give examples
for rapid work, but also show some of the short methods that
are commonly used.
In striving for efficiency in rapid computations, use a i>encil
just aa little as possible. Pencil and paper are not always at
hand and it is therefore necessary to make mental computations
to check the work. It is often sufficient to estimate a result
roughly and then check more accurately at one's leisure.
Practice in this type of checking can be secured by estimating
results approximately in order to check solutions of problems.
155
156 EIGHTH YEAR
CHAPTER I
Exercise 1
Practice on the first ten examples in this exercise until yoH
can do all of them correctly in 5 minutes.
1. 2. 3. 4. 5.
2496 8765 2340 5426 1982
1983 4312 5864 3798 4651
7218 9736 3217 4125 3928
4520 1326 8629 7864 5416
6924 5298 . 4837 3907 7718
6.
7,
8.
9.
10.
3178
3927
7856
4455
3792
4056
8220
9742
6872
4891
2792
4065
6319
9987
7726
4695
3918
2390
2436
3555
9781
4639
2945
2856
4930
11. The areas of the six New England States are as follows:
Maine, 33,040 square miles; N. H., 9341 ; Vt., 9504; Mass., 8266;
R. I., 1248; Conn., 4965. What is the total area of the New
England States?
12. The six leading dairy states had the following number of
dairy cows in 1910: N. Y., 1,509,594; Wis., 1,473,505; la.,
1,406,792; Minn., 1,085,388; 111., 1,050,223; Tex., 1,013,867.
Find the total number of dairy cows in these six leading states.
IS. The total wheat production in the different continents
in 1915 was as follows: North America, 1,351,763,000 bushels;
South America, 200,640,000 bushels; Europe, 2,080,819,000
bushels; Asia, 460,245,000 bushels; Africa, 90,859,000 bushels;
Australia and New Zealand, 32,480,000 bushels. Find the total
production of the world for that year.
REVIEW EXERCISES
157
Exercise 2
We should be able to add horizontally (or across a page)
as well as vertically (up or down). By adding both ways you
get a "cross check" on the correctness of your additions.
Work on the following problems until your results "crosscheck."
1.
87+43+26-|r29=
16 23 58 94=
63 05 41 89 =
27 96 38 42 =
81 27 96 54 =
2.
57+36+29+14
76 12 45 38
67 84 15 29
47 36 91 28
56 18 72 39
8.
43+65+81+71
21 58 64 37
83 41 92 65
61 23 59 84
95 64 32 81
4.
32+56+98+41
72 65 41 89
68 24 15 97
41 36 89 27
19 72 43 86
5.
61+57+84+93
68 54 71 29
80 95 43 16
29 85 47 13
37 68 95 82
6.
14+50+97+83
26 81 43 93
80 36 12 75
41 67 83 25
59 88 64 97
7.
73+96+81+24
63 75 98 26
25 76 31 48
58 19 86 57
76 84 39 46
8.
25+83+17+94
52 78 61 27
76 19 94 53
15 64 82 23
82 93 47 90
158 EIGHTH YEAR
Exercise 3
Subtract the first 10 examples as a speed test. Keep a record
of your time. You should be able to do them in 2 minutes.
1. 2. 3. 4. 5.
2,164
1,907
3,986
2,497
4,000
3,179
2,869
1,964 .
10,100
2,786
6.
10,724
9,847
7.
29,847
18,868
8.
32,809 '
14,987
9.
40,400
3,976
10.
21,610
19,143
11. The area of Texas is 265,896 square miles. How much
larger in area is Texas than Rhode Island, which has an area
of 1248 square miles?
12. The population of the United States in 1910, exclusive
of the detached possessions, was 92,228,531. Including the
detached possessions, it was 101,102,677. What was the
population of the detached possessions?
13. If, as computed, the water area of the earth is approxi-
mately 144,500,000 square miles, and the total surface of the
earth is approximately 196,907,000 square niiles, how much
more water surface than land is there?
14. The ancients believed one-seventh of the earth's surface
to be water. This would be approximately 20,642,857 square
miles. How great was their error as to the amount?
16. The distance from New York to San Francisco by sea,
by way of Cape Horn, is reckoned at 13,000 miles. By way of
the Panama Canal it is reckoned at 5278 miles. How much
shorter is the Panama route?
16. A bushel contains 2150.42 cubic inches and a cubic foot
1728 cubic inches. How much does the bushel exceed the
cubic foot in size?
REVIEW EXERCISES— SPEED TESTS 150
Exercise 4
Since the subtrahend and the difference together equal the
minuendy in subtraction, any one of the three can be easily
supplied if the others are given. Supply the subtrahends:
1. 2,837 2. 20,000 8. 240,000
1,956
18,276
20,700
4. 3,500
5. 401,286
6 546,280
3,080
297,497
397,149
7. 5,962
8. 954,362
9. 717,400
3,000
100,000
200,099
10. 75,160
11. 400,000
12. 100,000
42,839
286,934
66,752
18. 19,763
14. 79,080
16. 327,861
11,274 16,111 100,000
SPEED TESTS IN MULTIPLICATION
Exercise 6. Time: 3 minutes
Multiply:
9389
5
2459
2
6382
7
6195
3
2574
8
3429
9
9837
4
5289
6
4562
5
3768
2
a
6497
7
3869
8
8576
9
6542
4
6347
6
160 EIGHTH YEAR
Exercise 6. Time: 6 minutes
Multiply:
2459 6382 9837 3429
82 75 46 39
3768 5497 6542 8576
28 57 64 93
SHORT METHODS IN MXJLTIPLICATION
1. 345X10 = 3450
3.45X10 = 34.5
To multiply an integer by 10, add a zero to the number.
To multiply a decimal by 10, move the decimal point one
place to the right.
Read the products without using a pencil:
2. 68 X 10= 6. 120X10= 10. 45.6X10 =
3. 231X10= 7. 5.03X10= 11. 9.74X10 =
4. 4.63X10= 8. 23.4X10= 12. 860 X10 =
5. 938X10= 9. .48X10= IS. 10.35X10 =
14, John has $2.75 and his brother has 10 times as much in
the bank. How much has his brother in the bank?
16. The lumber in a book rack costs 15 cents. The lumber in
a medicine chest costs 10 times as much. Find the cost of the
lumber in the medicine chest.
Exercise 7
1. 42 X 100 =4200.
.427X100=42.7
To multiply an integer by 100, add two zeros to the number.
To multiply a decimal by 100, move the decimal point two
places to the right.
REVIEW EXERCISES 161
Give products without using a pencil:
2. .625 X100= 7. .7854X100= 12. 83 X100 =
S. 68 X100= 8. 471 X100= 13. 62.5 X100 =
4. .5236 X100= 9. 32.5 X100= 14. 45 X100 =
5. 527 X100= 10. 628 X100= 16. .0625X100 =
6. 3.1416X100= 11. 52.3 X100= 16. 42.85X100 =
17. Show a short method of multiplying a number by 200;
by 300; by 400; by 500.
18. Show a short method of multiplying a number by 1000;
by 2000; by 3000; by 4000.
19. A school bought 100 pamphlets on soil fertility at $.06
each. How much did the 100 cost?
20. A man bought a farm of 157 acres at $100 per acre.
How much did the farm cost?
Exercise 8
1. 344X 25 = 34,400 =8600.
4
2. 344X125 = 344,000= 43,000.
8
To multiply a number by 25, multiply the number by 100
and divide by 4. •
To multiply a number by 125, multiply the number by 1000
and divide by 8.
Without pencil:
3. 44X 25= 7. 15X 25 = 11. 64X125 =
4. 24X125= 8. 12 X$ .25= 12. 128 X 25 =
6. 32 X 25= 9. 18 X $1.25= 13. 32X125 =
6. 72X125= 10. 244X 25 = 14. 88X 25 =
162 EIGHTH YEAR
16. My father bought a farm of 80 acres at $125 per acre.
How much did the farm cost him?
16. A farmer sold a herd of 12 calves at $25 each. How much
did he receive for the herd?
17. Give a short method of multiplying a number by 50.
18. Give a short method of multiplying a number by 75.
FRACTIONAL PARTS USED IN SHORT METHODS
Exercise 9
33i = 1 of 100. 12| = J of 100.
16f = 1 of 100. 66f = ^ of 200.
1. Show that multiplying a number by 100 and dividing by
8 is the same as multiplying the number by 33^.
2. Show a short method of multiplying a number by 16f .
3. State a short method of multiplying a number by 12 1.
4. State a short method of multiplying a number by 66f .
Without pencil give the following products:
5. 45X33| 13. 16X12^ =
6. 36Xl6f 14. 72X33j =
7. 128X12|= 16. 63X66f =
8. 6X66f = 16. 42Xl6f =
9. 32X12^= 17. 40X12 J =
10. 216X33^= 18. 12X66f =
11. 252X66|= 19. 84X16f =
12. 246Xl6f = 20. 96X12| =
21. A merchant bought a bolt of dress goods containing 40
yards at 12^ cents a yard. How much did the bolt cost?
22. A banker bought a tract of timber containing 33^ acres
at $60 per acre. How much did he pay for the tract?
REVIEW EXERCISES 168
Exercise 10
1. Multiply 45 by 99.
100X45=4500
Subtracting: 1X45= 45
99X45=4455
To multiply a number by 99, multiply the number by 100
and subtract the number from that product.
2. 84X99= 4. 246X99= 6. 420X99 =
8. 37X99= 6. 854X99= 7. 575X99 =
8. By comparison with the above method show how to
multiply a number by 9.
9. State a short method for multiplying a number by 999.
10. Show how to multiply a number by 49 by a short method.
11. A ^-barrel sack of flour contains 49 pounds. How many
pounds are there in 44 such sacks?
12. Show short methods of multiplying by 19, 29, 39, 69, etc.
Exercise 11
1. Multiply 5i by 5|.
^7 In multiplying these two mixed numbers,
5? we have the products 6X5; 6 X^; iX5; and
25 §X|. But (5xi) and (iX5) is the same
2j as 1X5. We then have (5X5) + (1X5) or
2^ 6X5. To this quotient we add the product
i of i X|, or i.
30j 5iX5^ = (6X5) + (ixi)=30i.
2. Multiply 8 J X8§. The product=(9X8) + (|x|)=72f
8. 4§X4| = ? 6. 7^X 7^ = ?
4. 6|X6^ = ? 6. 12|X12| = ?
164
EIGHTH YEAR
7. What is the cost of 8§ yards of cloth at 8 J cents per yard?
8. What is the cost of 5 J pounds of apples at 5 J cents
per pound?
9. Show that 8^X8f = (9X8) + (Jxf).
10. Show that 9|x9f = (10X9) + (|xf).
SPEED TESTS IN DIVISION
Exercise 12. Time: 3 minutes
6)1890
9)6273 4)1584
6)5244
3)2919
8)4768 2)1810
7)6475
9)4365
6)5778 7)6118
Exercise 13. Time: 6 minutes
8)3880
'92)29440
39)15093
61)53192
65)46155
83)58764
47)17578
Exercise 14. Time: 8 minutes
67)17152
82)29602
231)106953
347)227979
945)574560
927)377289
SHORT METHODS IN DIVISION
Exercise 16
To divide a number by 10, 100, or 1000, move the decimal
point to the left one, two, or three places, respectively, prefixing
zeros if necessary.
1. 32-^ 10=3.2 2. 32-^100 = .32 8. 32 -r- 1000 = .032
REVIEW EXERCISES
165
4. 67 -^ 10=
5. 3.9-i-100=
6. 62,5^ 10 =»
7. 42.5 -^1000=
8. 4.5 -i- 100=
». 2.37 -i- 10=
10. 3475-5-1000=
11. 675-5-1000 =
1«. 43.5-5- 100 =
18. I bought 2450 board feet of lumber at $80 per thousand.
How much did I pay for the lumber?
14. A man shipped 50 sacks of potatoes weighing 4995
pounds. How many hundredweight did he ship?
16. How much was his freight at 20 cents per cwt.?
Exercise 16
1. Divide 4225 by 25.
4X4225 = 16,900.
16,900-^100 = 169.
To divide a number by 25, multiply the number by 4 and
divide the product by 100.
2. 1570-r25= 5. 1225-^25= 8. 475-5-25 =
8. 345-5-25= 6. 1850-^25= 9. 875-5-25=
4. 625-5-25= 7. 2315-5-25= 10. 72-^-25 =
11. A merchant bought some wash ties at 25 cents each.
How many would he get for $26.75?
12. Show a short method similar to the above for dividing
a number by 125.
13. A farmer paid $20,000 for a farm. If he paid $125 per
acre, how many acres did he buy?
14. A real estate dealer sold a tract of 25 acres of rough
pasture land for $1125. What was the selling price per acre?
16. My neighbor bought a tract of unimproved land for
$6175 at $25 per acre. How many acres did he buy?
Pupils should be encouraged to use these short methods in every prob-
lem where they apply.
166 EIGHTH YEAR
■
Exercise 17
To divide a number by 33f , multiply the number by 3 and
divide by 100. Show that this method is correct by using
fractions.
1. Divide 400 by 33^
3X400=1200. 1200^100 = 12.
4004-33^ = 12.
2. 750-J-33f = 6. 75-^33f =
8. 900^33^= 6. 125-^33^ =
4. 660^33^= 7. 480-^33| =
8. Show a short method of dividing a number by 12^^.
9. Show a short method of dividing a number by 16f .
10. Show a short method of dividing a number by 66f .
Exercise 18
One may often save time by dividing a number by two
factors of the divisor.
1. Divide 774 by 18.
3)774
6)2^ 774^18=43.
43
Perform the following divisions by using factors of the divisor:
2. 555-^-15= 6. 2720^32= 8. 1176^56 =
3. 1674^27= 6. 28354-45= 9. 2765-4-35 =
4. 688-4-16= 7. 2706-f-33= 10. 1148-^28 =
11. A farmer raised 2860 bushels of corn on 44 acres of
ground. Find the yield per acre.
12. A load of shelled corn weighed 1596 pounds. A bushel of
shelled com weighs 56 pounds. How many bushels were there
in the load?
REVIEW EXERCISES 167
REVIEW OF FRACTIONS
The diflferent processes in fractions should become just
as familiar to us as the four fundamental operations in whole
numbers. Practice on the following exercises until you can
do each of them in 2 minutes.
Exercise 19
f+t =
i + i =
1^+1 =
f+ii=
T^+f =
Exercise 20
H-f =
7 3 _
¥ - I =
f-| =
1--^ =
Exercise 21
|x| =
4 V ^ -
¥ ^ 4 -
fxf =
8 v/ 3 _
r2X 4 -
5 vx 3 _
6 A 4 —
l^Xf =.
|xf =
3 y 1 _
3X2 —
AxA=
Exercise 22
•
l-A=
5 . 3 _
8 ~ 4 =
2 . 7 _
3 "^ ^ —
8 "=" 2 =
5 ^ 4 _
6 • 9 —
Exercise 23
f-f=
1 + 1 =
4 . 2 _
5 ~ 3 —
f+t=
|x^ =
2 1 _
3 - 4 -
7 . 5 _
12 • 8 —
Refer to pages
26 to 32 in Part I for
explanations of these
processes if they are not clear.
168 EIGHTH YEAR
MIXED NUMBERS
Exercise 24
Add the following:
1. 23f , 45|, 82f , 35f . 7. From 23| subtract ISf .
2. 9j, 13|, 16f , 8|, llj. 8. From 9^ subtract 7|.
3. 7f , 4|, 9|, 12|, 3|. 9. From 32| subtract 19f .
4. 17 J, 25f , 43f , 32f , 57|. 10. From 20f subtract 14f .
5- 6§, 8|, 6|, 9f , 7^. 11. From 5 J subtract 3f .
6. 6|j 2f, 6f, 4|, l|. 12. From 60^ subtract lOf.
Exercise 26
Find the following products and quotients:
1. 3|xlf 4.12 Xlf. T.Divide 8|by2j.
2. 8|X3f. 6. 3|x2f. S.Divide 3§by2.
3. lOfxif 6. 22§X2f . 9. Divide 12f by 2f
10. In a track meet the winner of the running broad jump
leaped 16 J feet. His nearest competitor jumped 16 J feet.
How much farther was the first jump than the second?
11. A square rod is 16j feet by 16^ feet. How many
square feet are there in a square rod?
12. Find the cost of 7 J yards of gingham at 12^ cents a
yard.
13. In the spring of 1917 a 24^-pound sack of flour sold
for 5^ cents a pound. What was the price per sack?
14. How many guest towels f of a yard long can be made
from a strip of linen toweling 4§ yards long?
15. Find the cost of if pounds of steak at 28 cents a
pound.
REVIEW OF DECIMALS 169
MISCELLANEOUS PROBUBMS
Exerdse 26
DECIMALS
• 1. Add: 8.25; .072; 7.055; .0075; 13.5; .068.
8. Add: .0054; 3.125; 11.2347; 3.1416; .7854; .866.
S. 2150.42-1728 = ? 6. 425.68-98.375 = ?
4. 6.5-1.4142 = ? 6. $2-$1.37 = ?
7. Multiply 324.5 by .035.
8. What is the principle of pointing off decimal places in
the product?
9. .032X2.8 = ? 12. 4.05 X. 62 = ?
10. 3.1416X25 = ? IS. 63.3X25.7 = ?
11. .0025X.03 = ? 14. .008 X. 0016 = ?
15. Divide 8.575 by 3.43.
16. What is the principle for pointing off decimal places in
the quotient?
17. .287 -^ 3.5=? 20. 32.5 -^ 260 = ?
18. .02145-^.007 = ? 21. 82.254-25 = ?
19. 25.5^425 = ? 22. .0025 -h .05 = ?
23. Find the cost of 7725 bricks at $16.25 per thousand}
24. What are the freight charges on a barrel of apples
weighing 160 pounds, at $0.22 per hundred pounds?
25. A chicken weighing 4.25 pounds cost $1.02. Find the
cost per pound.
26. Find the cost of 225 feet of lumber at $67.50 per 1000
feet.
*Use the short method of dividing by 1000 to find the number of thovr
sands of brick.
170 EIGHTH YEAR
REVIEW OF PERCENTAGE
Exercise 27
1. 80% of 520 eggs placed in an incubator hatched. How
many of the eggs hatched? How many did not hatch?
•
2. The leaves of an alfalfa plant constitute 45% of its
weight. How many pounds of leaves are there in a ton of
.alfalfa hay? How many pounds of stems in a ton?
3. A girl's spelling paper was marked 96% correct. How
many words did she spell correctly out of 50?
4. A hog shrinks about 33^% on being dressed. What is
the dressed weight of a 210-pound hog?
6. Which would you rather have— 20% of $864 or 25% of
$725?
6. There are 525,000,000 acres of improved land in the
United States. About 20% of that amount is planted each
year in com. Find the number of acres devoted to raising corn.
7. A farmer took four 100-pound cans of milk to the cream-
ery. The milk tested 3.8% of butter fat. How many pounds of
butter fat were there in the four cans?
8. 85% of butter is butter fat. How many pounds of butter
fat are there in a 5-pound jar of butter?
9. Ice is 91.7% as heavy as water. A cubic foot of water
weighs 62 § pounds. How much does a cubic foot of ice weigh?
10. Sandstone is 235% as heavy as water. Find the weight
of a cubic foot of sandstone.
11. A manufacturer makes a stove at a cost of $18.00.
He sells it to a retail customer at a gain of 20%. The retail
dealer pays $1.60 freight and sells it to a farmer at a profit of
25%. Find the price paid by the farmer.
REVIEW OF PERCENTAGE 171
Exercise 28
U A pint is what per cent of a quart?
2. A foot is what per cent of a yard?
3. A peck is what per cent of a bushel?
4. A farmer planted 45 acres of com on a farm of 160 acres.
What per cent of his farm is in com?
6. A certain prize cow yielded 21,944 pounds of milk in a
year. Her milk contained 944 pounds of butter fat. What
per cent of butter fat did her milk contain?
6. A farmer tested 180 kernels from one lot of seed com,
and 14 kernels failed to grow. What per cent failed to grow?
7. The same farmer tested 160 kernels from another lot of
seed com and found 26 kernels that failed to sprout. What
per cent of this lot failed to grow? Which lot would be best
for planting?
8. There are 135 boys in a school of 250 pupils. What per
cent of the pupils are boys? What per cent are girls?
9. Fred played in 10 ball games during the smnmer. He
was at the bat 50 times and made 16 base hits. What was his
per cent of base hits? Compare his percentage of base hits
with your favorite player in the big leagues.
10. A grammar school basket ball team won 9 out of the 12
games that they played. What per cent of games did they
win?
11. A girl earned $45.00 during her summer vacation and
put $28.80 of that amount in her savings account. What per
cent of her earnings did she put in her savings account?
12. A merchant sold eggs which cost him 24 cents a dozen at
27 cents a dozen. What was his per cent of profit? What
would have been his per cent of profit at 26 cents per dozen?
172 EIGHTH YEAR
13. An agent bought an automobile for $800 and sold it for
$1120. What was his per cent of profit?
14. A cubic foot of wrought iron weighs 489 pounds. A
cubic foot of water weighs 62.5 pounds. Water is what per cent
as heavy as wrought iron?
Exercise 29
1. Sea water contains approximately 3% of salt. How much
sea water must be evaporated to obtain 12 pounds of salt?
2. A farmer sold 45 hogs, which were 62^% of his total
number of hogs. How many hogs did he have left?
3. Butter fat constitutes 85% of the weight of butter.
How many pounds of butter can be made from 6.8 pounds of
butter fat which is contained in a can of cream?
4. A horse buyer sold a horse for $161 at a profit of 15%.
Find the cost of the horse.
6. A dressed steer weighed 877.5 pounds. This was only
65% of its Uve weight. What was the live weight of the steer?
6. The weight of a cubic foot of water (62.5 pounds) is
5.18% of the weight of a cubic foot of gold. Find the weight
of a cubic foot of gold.
7. A merchant sold a suit of clothes for $28 at a gain of
40%. Find how much the merchant paid for the suit.
8. A firm increased the wages of its employees 10%. What
was the previous salary of a man who is receiving $132 under
the new schedule?
9. The number of girls in a class is 21. If the girls comprise
60% of the membership of the class, find the total number in
the class.
10. A basket ball team won 80% of its games during a certain
year. If it won 12 games, how many games did it play?
REVIEW EXERCISES— INTEREST 173
INTEREST
Exercise 30
1. Find the interest dh $750 for 1 year 3 months and 18
days at 6%.
2. Find the interest on $5000 for 10 months and 12 days at
5%.
3. A milliner has a certificate of deposit from a bank for
$350. The bank pays her 3% interest on that amount if she
leaves it in the bank more than 3 months. What was her
interest for 6 months?
4. A merchant borrowed $2500 from a loan company for
3 years at 6%. What was his yearly interest payment?
6. A farmer bought a farm for $12,500. He made a cash
payment of $4500. He borrowed $6000 from an insurance
company at 5^% and gave the owner his note for the remainder
at 6% interest. What was the total of his interest payments
per year?
6. A school district issued twenty $1000 (one-thousand-
dollar) bonds bearing 5% interest, one of the bonds being paid
oflf at the end of each year. What was the interest on these
bonds the first year?
7. How much was the interest decreased each year by paying
oflf one of the bonds?
8. Find the total interest paid on the twenty bonds before
they were all paid off?
9. The interest from a certain note for one year at 6%
amounted to $72. Find the face of the note.
10. The interest on a note for $400 for 6 months was $14.
Find the rate of the interest.
11. Find the interest on $250 for 3 years 6 months at 6%.
174 EIGHTH YEAR
COMMISSION
Exercise 31
1. A lawyer charged 5% for collecting debts for a grocer,
amounting to $1375. What was his fee?
2. A salesman received a salary of $1200 per year and a
commission of 2% on his sales. What was his total income for
the year if his sales amounted to $40,000?
3. A eonmiission firm sold a carload of 196 barrels of
Black Twig apples at $3.50 per barrel. What was their com-
mission at 7% on the sales?
4. A eonmiission firm bought $36,500 worth of cotton for
* m
a factory. What was the amount of their commission at 2%?
Find the total cost of the cotton to the firm.
6. A commission firm sold 300 baskets of Concord grapes
at 18 cents each and remitted $50.22 to the owner. Find the
rate of their commission.
6. A real estate dealer sold a farm of 160 acres at $125 per
acre on a commission of 2%. What was the amount of his
commission on the transaction?
?• A collector charged 5% commission for collecting a
debt of $1500. Hew much should he remit to the creditor?
8. A real estate dealer sold 5 city lots at $2500 each, charg-
ing 3% commission. Find his commission on the 5 lots.
9. What was a broker's commission for selling 1600 bushels
of wheat at f j4 per bushel?
10. An agent received $2.50 commission on an article which
he sold at $9.60. Find his rate of commission*
11. A real estate agent sold a farm at a commission of 5%.
If he received $500 for his commission, what was the selling
price of the farm? How much did he remit to the owner?
REVIEW EXERCISES— DISCOUNTS 175
DISCOUNTS
Exercise 32
1, A certain ice company sells a 1250-pound ice ticket for
$4.00. A discount of 25 cents is allowed from this price if it
is paid for within 10 days. What is the per cent allowed for
prompt payment?
2. My gas bill for the month of January, 1917, was $1.98.
A discount of 22 cents is allowed if the bill is paid within 10
days. Find the per cent of discount for prompt payment.
8. A school bought a dozen jack planes listed at $36.00
per dozen. It was allowed the regular discount of 20% and
an extra discount of 2% for cash. What as the net cost of
the dozen planes?
4. A fmniture store advertised a discount of 20% on all
fmniture during the month of July. What was the sale price
on a library table formerly listed at $24.00?
6. A retail dealer bought a piano listed at $500 with dis-
counts of 20% and 15%. What was the net price of the piano?
6. Which is better for a retail dealer, discounts of 20%
and 15% or a single discount of 33f %?
7. A merchant marked dress goods costing $1.20 per yard
to sell at a profit of 50%. During a clearance sale he discounted
the marked price 25%. Find his sale price per yard on the
dress goods.
8. A hardware firm bought a bill of goods amounting to
$1345.40. They were allowed a discount of 2% for prompt
payment. What was their net bill?
9. A dealer sold straw hats of a certain grade for $3.00
early in the season. Late in the season he sold them at a
clearance sale for $1.80. Find the per cent of discount which
he gave on this sale.
176 EIGHTH YEAR
TAXES
Exercise 33
1. The tax rate for a rural school district was $.79 per $100
of valuation. $.79 is what decimal fraction of $100?
2. What was the total amount raised in taxes for this dis-
trict if the total valuation of the district was $84,643?
3. In a certain state the assessed valuation of property is
taken as ^ of the full value. If I own a house and lot valued
at $3600, what will be my assessed valuation on the place?
4. If the total tax rate is $4.35 per $100, what will be the
taxes on this house and lot?
6. The state tax on this property amounted to 80 cents per
$100. Find the amount of state tax on the house and lot.
6. The school tax on this property was $1.95 per $100.
Find the amount of the school tax.
7. The valuation in a certain county was $32,450,000 and
the amount levied for taxes in a certain year was $120,000.
Find the approximate rate per $100 of taxable property.
8. A single woman schedules her income as follows: Divi-
dends from stock, $2500; rent from farm, $1020; rent on city
residence, $360; miscellaneous sources, $500. What was her
income tax? (See page 105.)
9. A town having property valued at $350,000 made a
special assessment of 3 mills on the dollar^ for library purposes.
What was the amount raised for library purposes?
10. A county made a special assessment of 2 mills on the
dollar for good roads. How much taxes were raised if the
valuation of the county was $28,372,480?
lA rate of 3 mills on the dollar reduced to a decimal = .003 of the assessed
valuation.
REVIEW EXERCISES— INSURANCE 177
INSURANCE
Exercise 34
1. How much must I pay to insure my household goods val-
ued at J500 at a rate of 42 cents per $100?
2. The premium on a house worth $3000, insured at 80%
of its value, was $15.60. Find the rate of insurance per $100.
3. A grocer insured his stock of goods valued at $2000 at
80% of their value at a premium of 1% for 3 years. What was
the amount of his premium?
4. A school house cost $40,000. It was insured at 80% of
its value at a premium of 1 J% for 3 years. Find the amount
of the premium.
6. A lawyer took out an ordinary life insurance policy for
$5000 at the age of 30. The rate in his company at that age
was $19.74 per thousand. What was his annual premium?
6. The agent securing the policy received a commission of
50% of the first premium. What was the agent's commission
on the $5000 policy?
7. Why should an inventory of household goods be made out
before they are insured?
8. A man carried insurance on his household goods for
$1000 at the rate of 40 cents per $100. He paid this rate for
10 years. How much did his insurance cost him?
9. During the tenth year his house was burned and his
household goods were a total loss. The inventory of his goods
showed that their value was really only $700 and he received
that amount in the adjustment with the insurance company.
Since he had paid insurance, on $1000, how much insurance did
he pay from which he received no returns?
10. If I pay a premium of $37.50 on a house insured at
$3000, what is the rate per $100?
178 EIGHTH YEAR
APPROXIMATION PROBLEMS
Exercise 36
Many problems actually arising in life are not solved at
once with exactness, but only approximately. The habit of
inspecting a problem and roughly estimating the answer
(in advance) is of value in preventing the danger of being
satisfied with an absurdly incorrect result.
1. A man owes the following amounts: $173.57, $54.55,
$46.10 and $198.28. Does he owe more or less than $500?
2. I can save from my wages $3.50 per day. Working 26
days per month, about how long will it take me to save $1000?
3. A fruit ranch yields 2600 boxes of peaches which sell
at 48 cents the box. Will the receipts exceed $1300?
4. 4000 boxes of apples bring $1.14 per box. Will the
proceeds exceed or be less than $5000?
6. I have borrowed $1385 for one year at 8%. Shall I
pay more or less than $100 interest?
6. A man purchased a house for $6100, and sold it later
for $6800. Did he gain more or less than 10%?
7. Give the approximate cost of 16 dozen eggs at 24 cents.
8. Give the interest for one year on $990 at 6%.
9. Give the income from $22,240 at 6%; 7%; 11%.
10. What is 9% of 6,500,000? Is it 58,500 or 585,000?
Give the approximate results of the following:
11. 50X49? 1100^50.4? 18,527+1460? 527+110+92?
12. Is 6,521,865 divided by 276 about 2000 or 20,000?
13. What is the distance covered by an automobile in 21
hours when averaging 18 f miles per hour?
14. The assessed valuation of a school district is $21,945,865.
The expenses of conducting the schools are $112,000. What
is the approximate rate of taxation for school purposes?
CHAPTER II
BA»ES AND BANKING
interior of a Metropolitan Bank
A bank receives money on deposit. A bank also cashes checks,
lends and transmits money, and discounts promissory notes.
Nalional banka are authorized by the national government
and are inspected by national officers to see that the business
is conducted in compliance with the provisions of the National
Banking Act.
State banks are organized under state laws and are inspected
by state officers.
Trust companies, organized under state laws, not only do a
banking business, but also settle estates, take care of the
property of minors, and perform other services in the nature
of trust.
179
180 EIGHTH YEAR
In some states certain individuals or partnerships call their
offices "private bankSj'^ although they possess no bank charters
and are not subject to any official inspection.
In order to organize a National bank, shares of $100 each
are sold to a group of stockholders. National banks must
have a capital of at least one hundred thousand dollars, ^'except
that banks with a capital of not less than fifty thousand dollars
may, with the approval of the Secretary of the Treasury, be
organized in any place the population of which does not exceed
six thousand inhabitants."
National banks are required to keep on deposit with the
government, United States bonds equal to one-fourth of their
capital stock, as security for their circulating notes which they
may issue to that amount.
If a National bank fails, the government pays the bank notes
that the bank has in circulation from the sale of the government
bonds deposited to secure them. The bank notes, then, are
accepted by people as readily as the government paper money
or "greenbacks."
Notice different bills to see if you can find: (1) silver certifi-
cates; (2) gold certificates; (3) government notes or "green-
backs;" (4) national bank notes.
Hundreds of years ago men who made a business of borrowing and
lending money had benches in the market places of the principal cities
and drove bargains with borrowers and lenders. The Italian word **banca''
meant bench and from it we derive our word hank. When one of the old-
time bankers failed, his bench was broken. "BanJcrupt" meaning broken
bendi, came to mean a debtor who could not pay.
For the protection of their depositors, National banks are
required to keep on reserve at least 12% of their deposits.
Experience has shown that this is sufficient to meet the daily
withdrawals by depositors. Part of this reserve may be de-
posited in certain city reserve banks.
BANKS AND BANKING— FEDERAL RESERVE 181
Federal Reserve Banks
In order to furnish an elastic currency, to afiford means of
rediscounting commercial paper, and to establish a more
eflfective supervision of banking in the United States, the
government of the United States established in 1914 a system
of Federal Reserve banks.^
Federal Reserve Banks are to be found only in the twelve
specified Federal Reserve cities, viz.: New York, Chicago,
Philadelphia, Boston, St. Louis, Cleveland, San Francisco,
Minneapolis, Kansas City, Atlanta, Richmond and Dallas.
No Federal Reserve bank is permitted to begin business with
a capital of less than $4,000,000. ^ny one may own shares in
a Federal Reserve bank, but only a member bank of its district
is permitted to own at any one time more than $25,000 of the
capital stock of one of these banks.
Exercise 1
1. If a capitalist owns the maximum amount permitted
in a Federal Reserve bank in each of the cities named, what is
the par value of his investment?
2. What was the minimum capital required for the be-
ginning of business by eight Federal Reserve banks?
8. The shares of stock of a Federal Reserve bank are of
the par value of $100 each. How many shares are required
to be taken, to amount to the minimum sum required for
beginnmg the busmess of the bank?
4. Three State banks and two business houses each purchase
the maximum peirmitted amount of stock in a Federal Reserve
bank. What is the amount of their stock in it?
*A Federal Reserve bank is essentially "a banker's bank." It sus-
tains with its members much the same relation that ordinary banks
sustain with their depositors.
182
EIGHTH YEAR
6. If a certain Federal Reserve bank has a capital of
$20,000,000 and yields a dividend of 6% annually on the
capital stocky what will be the amount of the dividends dis-
tributed in one year?
Checking Accounts
FARMERS' NATIONAL BANK
DEPOSITED TO THE CREDIT OF
/
tcAf. sormiXfu y" Co<
Fort Dkarborn. i. . UMXaM/<gtoi7
(CHKCKS ARK RKCKIVEO FOR COLLECTION)
QjouJ,(o
All kinds of banks
receive money on
deposit for safe
keeping. Some
banks make a small
charge for their care
of money deposited
in small amounts,
and some pay a low
rate of interest for
large deposits left
with them on check-
ing account. Gen-
erally, however, the
depositor neither
receives interest
upon, nor pays for
the care of, money
deposited on check-
ing account.
With the money to be deposited, at any time, the depositor
hands to the receiving teller of the bank a deposit slip filled
out with his name, the date and the items of amount deposited
and the nature of the deposit, whether it consists of bills, coin
or checks on banks.
What are the three headings on the deposit slip shown above
under which the various amounts are listed?
DRAFTS ...
G8
20
CHECKS ....
H3
GS
CURRENCY . . . ,
Q>
HO
■
TOTAL
118
.25
BANKS AND BANKING— CHECKS
183
1. Make a deposit slip similar to the form given and fill
out the deposit slip for John Smith for the following items:
a draft for $50.00; three checks for $7.50, $3.75 and $14.25;
and the following amount of money: 2 ten-dollar bills; 7 five-
dollar bills; 13 one-dollar bills; 11 half-dollars; 17 quarters;
22 dimes; 31 nickels; 48 pennies.
2. Write a deposit slip for Richard Roe on a deposit slip
secured from one of the local banks. Turn in a list of the kinds
of money, etc., as shown in Problem 1. (It will be more con-
venient for the teacher to secure the blank forms from a bank
for class use.)
Check Books
Check books with blanks which can be easily and rapidly
filled out are supplied by the banks. They contain stubs from
which the checks may be torn oflf, and which are prepared to
retain a memorandum of each check drawn, so that when
all the blank checks have been used, the stubs will show a
record of all the moneys withdrawn from the bank by means
of them.
•hli ^ . flot^tA^ ^
^ovSaM ^I
•^
iL
iio.3^s:
'W.i ^.'7l wu 4 /
'Tn^Y^s, wlz-%^
Mt
'^j^Mve^ntu^ cfjutty y ^mo ^
e. f./focMjU
When the depositor wishes to withdraw from the bank
a,ny of the money deposited to his credit, he fills out a check,
which is an order for the amount to be withdrawn. The check
may be made payable to himself or to some other person to
whom he wishes to make a payment.
184
EIGHTH YEAR
The person who presents the check to the paying teller,
to be "cashed," must indorse it. This is done by writing
his name on the back of the check, as shown below :^
If the depositor makes a check payable to himself and indorses
it, any one may present it for payment. If he makes it payable
to some particular person, that person (called the payee)
must indorse it, whether he transfers it to any one else or pre-
sents it for payment at the bank.
Checks should be presented promptly for payment. When
checks are received by a bank for deposit, they are credited
as cash, for they are immediately collected from the banks
on which they are drawn.
8. If you receive a check made payable to yourself and
you lose it before you have indorsed it, can the finder cash it
at the bank without forging your name?
4. If you receive a check made payable to yourself and
you indorse it and then lose it, can the finder cash it at the
bank?
6. If you receive a check made payable to "bearer," can
any one cash it at the bank without your indorsement of it?
Is it best to make checks in this way?
6. If in sending a check you indorse it with an order to pay
a certain person (giving his name), can any other person who
finds it cash it?
*An indorsement should be on the back of the left end of the check
at least one inch from the end.
BANKS AND BANKING— CHECKS
185
A check so indorsed is said to be ^'indorsed in full."
An Indorsement in Full
7- If you receive a check made payable to yourself, and if^
instead of presenting it personally at the bank, you send it to
another person with the mere indorsement of your name
(which is called an indorsement in blank), and it is lost in
transit, can any finder of it cash it?
8. Write a check for a fictitious amount to be paid to John
Doe,^ and sign the name Richard Roe.
9. Write a check for a fictitious amount to be paid to
Richard Roe, and sign the name John Doe.
10. Indorse in blank the check written in Problem 8 above.
11. Indorse in full the check in Problem 9, using any other
fictitious name.
12. On a check made by John Doe to himself, write an
indorsement in full, authorizing payment to Richard Roe.
The use of checks renders it easy to pay bills by mail, and
in various ways it lessens the risk of loss in the transmission
of money.
At stated periods, usually at. the close of each month, the
paid checks are returned by banks to the persons who issued
them; and they thus serve as receipts, since they show that
the moneys have been paid.
*"John Doe" and "Richard Roe" have been for centuries legal desig-
nations for supposititious or unknown personages.
186
EIGHTH YEAR
Savings Accounts
State banks usually have savings departments in which
they pay a small rate of interest (usually 3% or 4%) on savings
deposits. One dollar is usually required for opening a savings
account.
When the interest is due, it is added to the depositor's account
and draws interest the same as the original deposits. The
following quotation from a savings account book shows their
method of computing interest:
"Interest will be allowed from the first day of the month following the
deposit, except that deposits made up to the 5th of any month shall be
considered as being made upon the first day of the month, and will draw
interest accordingly. Interest will be computed on the first da3rs of Janu-
ary and July of each year on all sums then on deposit, at the rate of three
per cent per annum on all savings deposits which have remained on deposit
for one month or more, but interest will not be allowed upon fractional
parts of a dollar, nor for fractional parts of a month, nor on any sum with-
drawn between interest days, for any of the periods which may have
elapsed since the preceding interest day. All withdrawals between interest
days will be deducted from the first deposit." — ^Woodlawn Trust and
Savings Bank.
Form of a Savings Accoimt
Date
Teller
Withdrawals
Deposits
Balance
7/ 2/16
W
$100
$100
8/15/16
W
50
150
10/ 1/16
W
30
180
10/30/16
W
$20
160
11/26/16
W
10
170
Exercise 3
1. Compute the interest on the above savings account for
the interest-paying date Jan. 1, 1917> according to the rules
given in the quotation from the Woodlawn Trust and Savings
Bank.
BANKS AND BANKING— INTEREST
187
2. If there were no deposits or withdrawals between Jan. 1,
1917, and July 1, 1917, what would be the balance on the
latter date?
Compound Interest
If, when due, the simple interest is added to the principal
to form a new principal for the next interest period and this
process is repeated during all the interest periods of the loan,
the difference between the final amount and the original prin-
cipal is called compound inter^t.
From the preceding exercise it is seen that savings banks
make use of compound interest. The calculation of compound
interest for any considerable length of time involves so many
steps that it is generally avoided by the use of a Compound
Interest Table. The following table shows the amount of one
dollar for twenty annual interest periods:
Tabub bkowino amount or $1.00 at compound xntsbbbt, bxtindbd to nvB
DBCXMAL8 FOB BACH OT TWBNTT PBBIOD8 VBOM 1 TO 7 PBB CBNT.
1
2
3
4
5
6
7
Tbab
PbbCbmt
PbbCbnt
PbbCbnt
PbbCbnt
PbbCbnt
PbbCbnt
Pbb Cbnt
1
1.01000^
1.020109
1.03030
^1.02000
1.03000
1.04000
1.06000
1.06000
1.07000
2
1.04040
1.06090
1.08160
1.10250
1.12360
1.14490
8
1.06121
1.09273
1.12486
1.16763
1.19102
1.22604
4
1.04060
1.08243
1.12551
1.16986
1.21561
1.26248
1.31080
6
1.05101
1.10408
1.15927
1.21665
1.27628
1.33823
1.40255
6
1.06162
1.12616
1.19405
1.26532
1.34010
1.41852
1.60073
7
1.07213
1.14869
1.22987
1.31593
1.40710
1.50363
1.60578
8
1.08286
1.17166
1.26677
1.36857
1.47746
1.59385
1.71819
1.00368
1.19509
1.30477
1.42331
1.55133
1.68948
1.83846
10
1.10462
1.21899
1.34392
1.48024
1.62889
1.79085
1.96715
11
1.11567
1.24337
1.38423
1.63945
1.71034
1.89830
2.10485
12
1.12682
1.26824
1.42576
1.60103
1.79686
2.01220
2.26219
13
1.13809
1.29361
1.46853
1.66507
1.88565
2.13293
2.40985
14
1.14947
1.31948
1.51259
1.73168
1,97993
2.26090
2.57853
15
1.16097
1.34587
1.55797
1.80094
2.07898
2.39666
2.75903
16
1.17258
1.87279
1.60471
1.87298
2.18287
2.64035
2.05316
17
1.18430
1.40024
1.65285
1.94790
2.29202
2.69277
8 ! 37993
18
1.19615
1.42825
1.70243
2.02682
2.40662
2.86434
19
1.20811
1.45681
1.76361
2.10685
2.62696
3.02660
S. 61663
20
1.22019
1.48595
1.80611
2.19112
2.65330
3.20714
3.86968
188 EIGHTH YEAR
The preceding table is made out for annual payments. For semi-
annual periods take half the rate for double the number of years. For
example: to find the compound amount on $1 at 6% for 10 years
compounded semi-annually find the amount in the table for 3% for
20 years. The compound interest is the difference between the com-
pound amount and the original principal.
Exercise 4
1. Find by the table the compound amount of $1000
at 6% for ten years, payable annually.
2. Find the compound interest of the same.
8. How much greater is this than the simple interest would
be?
4. Find by the table the compoimd amount of $1000
at 6% for ten years, payable semi-annually?
5. How much greater is this than the compoimd amoimt
of the same principal at the same rate per cent, the interest
being paid annually?
6. What is the nearest full year at which the original
principal will double itself at compound interest at 6%, payable
annually?
7. What is the nearest full year at which the original
principal will treble itself at compound interest at 6%, payable
annually?
Bank Discount
PromissoryNotes, which may be transferred from one person to
another by being properly endorsed, are called Negotiable Notes.
In lending money on notes or discoimting notes payable to
another party, banks require the interest to be paid in advance.
That is, they deduct it from the face of the note and the borrower
receives the remainder. 6% is the rate usually used in bank
discount.
BANKS AND BANKING— DISCOUNTS 189
The money which a borrower actually receives is called
the proceeds of the note. The interest deducted in advance
is called bank discount. The note given to the bank to secure
the loan does not promise to pay interest, since this is paid
at. the time when the note is received. Only the face of such
a note is to be paid.
^smoq iM^^^^^fh^
... afterdate C/ _ promise to pay to the
- . QdOdi . /j9P. . ^.OUl^^d^.. for value received,
lh^,S^.
Exercise 6
1. What is the hartk discount on the above note?
2. What are the proceeds of the above note?
8. Find the bank discoimt on a note for $450 for 60 days
at 6%. Find the proceeds.
4. What is the bank discount on $180 for 30 days at 6%?
6. If you give a bank your note for $2360 for 90 dajrs
at 6% discoimt, what will be the proceeds?
6. If I wish to borrow $250 from a bank for 1 year at 6%,
for what amoimt must the note be drawn?
Explanation: 6% of $1 = $.06. $1.00 - $.06 = $.94, proceeds
of $1. The note then must be drawn for as many dollars as
$.94 is contained times in $250. Find the amount
190 EIGHTH YEAR
7. In order that the proceeds of a note discounted at a
bank for 60 days at 6% may be S160, what must be the face
of the note?
8. In order that the proceeds of a note discoimted at a
bank for 30 days at 6% may be $850, what must be the face
of the note?
9. John Doe has a note from Richard Roe for $300 for 1
year at 6% interest.^ How much would he receive for it at
a bank if the discount was 6%?
10. In order to secure the sum of $248 as proceeds of a note
at bank; discount of 6%, for what sum must a 60-day note
be written?
Exchange
One of the most important functions of a bank is the pa3nnent
of debts without the actual transfer of money through the
interchange of checks and drafts.
To collect a debt from a debtor in another town or city,
the creditor may "draw" on him for the amount due. This is
done by sending to a bank in the debtor's home town or city
an order to pay the amount. This order is called a draft.
Generally the draft is sent to a bank with which the debtor
does business. The draft may be made payable to the creditor
himself, and sent to the bank for collection, or it may be made
payable to the bank itself. The order is addressed directly
to the debtor drawn upon, the address being written generally
in the lower left comer of the paper.
If the debtor is ordered to pay the draft "at sight," the
paper is called a sight draft. . If the order calls for payment
at a stated later time, it is called a time draft.
. ^In discounting a note bearing interest, the amount of the note at
maturity is cUscoimted.
BANKS AND BANKING— DRAFTS
191
Sight Draft
^t50.00
j4i sight pay to the order of ^A^f^.
,P/]^M^yi(!(}^k^
for value received ^nd charge the same to the account of
.^.^lS?!^i?^-/Kfc. .&Q£m,£)QO.,
,.Cfuf^gJi^
Time Draft
.^di^Ma^frrw, sight, pay to the order of ^ddsmeiT-Ss^^^m:...
^MJO'<MM/ncl/ucOamd)^^tlk'£}xla^i4^ %o)i fir vaiut
rtceived and charge to
wY« » a^B •• «S •^■MWWBBW ^«i «««•••■
If a draft is a time draft, the bank receiving it immediately
presents it to the party addressed and if it is satisfactory that
party writes his acceptance and the date across the face as
shown in the above illustration.
A check drawn by one bank upon another is called a "bank
draft." It is used largely to avoid the needless transmission
of actual money from one city to another. The cashier signs
for the bank making the draft and the name of his institution
appears at the top of the paper, as on a letterhead, while the
name of the bank drawn upon appears below.
192 EIGHTH YEAR
A Bank Draft
ItPMOO %ru^^
Pay to the order of .^Smmi^OU
£){t^,SJio^^
in current fu fids.
!^^.^^^i^!^^ .Jy^fi:^^
...^J^iJ^m^JtQ^t/rUj.JMi ^oA^UJf/U
The banks in large cities have a cUaring hxmse where each
bank presents checks and drafts which they have cashed for
the other banks in the city and only the balances due are paid
in actual currency. Clearing houses in central banking cities
provide for the exchange of checks and drafts of banks in
di£ferent cities. Balances are paid in clearing house certificates
or in actual currency.
Where the obligations of the business houses (including
banks) of one city to those of another city are pretty evenly
balanced by obligations of the latter to the former, there will
be no occasion for the transmission of cash from one city to
the other for the settlement of the obligations; the obligations
of the business houses of the one city will largely cancel those
of the other, and this is effected by the use of drafts.
If the business houses of St. Louis owe to those of New York
a large surplus over the indebtedness of New York to St. Louis,
there must be a shipment of money to settle the balance. Be-
cause of the desire to avoid the actual shipment of money,
bank drafts on New York will be sold in St. Louis at a slight
premium;^ while drafts on St. Louis will be sold in New York
at a slight discoimt.
^A premium is an extra amount over the face value. The premiimi or
discoimt is calculated on the face of the draft.
BANKS AND BANKING— DRAFTS 193
According to the condition of the money market, drafts
may be "at par*' or they may "appreciate" or "decline."
Exercise 6
1. Write a sight draft, using fictitious names.
2. Write a time draft, using fictitious firms' names.
8. Find the cost of a sight draft for $500 where there is
in the money market a premium of f %.
4. Where exchange is at a discount of f %, what will be
the cost of a sight draft for $500?
6. What is the cost of a sight draft for $1200 where
exchange is at a premium of f %?
6. What will be the cost of a sight draft for $625 where
exchange is at a discoimt of ^%?
Time Drafts
In the case of time drafts, the element of time has to be
taken into account. The bank discount for the time specified
is deducted from the face of the draft, and the premium, or
discount, is then calculated on the face of the draft and added
to or subtracted from the remainder.
Exercise 7
1. A sixty-day time draft for $300 must be bought where
exchange is at premium of ^%. What is the bank discount?
2. What can be obtained for a draft for $400 payable in
90 days from sight, and discounted at the time of its acceptance?
What was its cost at a discount of f %?
8. What must I pay for a 60-day sight draft for $600,
the premium being i%, discount 6%?
4. What will be the cost of a draft for $1000 payable
60 day^ after sight, at a premium of j%, discount 6%?
194 EIGHTH YEAR
STOCKS AND BONDS
Stocks
To a very great extent the business of the country is now
conducted by corporate companies, called corporations. A
corporation is regarded in law as an artificial person created
by law for specified purposes and having specified powers.
The capital stock of a corporation is divided into shares
generally having a face or par value of $100 each and are
usually spoken of as stocks.
A corporation with a capital stock of $50,000 has 500 shares
of $100 each which have been sold to different individuals.
All who own any of the stock of a corporation are members
of it and have votes in it in proportion to the number of shares
of stock which they possess.
If the corporation is large and its members widely scattered,
the members elect a Board of Directors to manage the affairs
of the corporation.
The advantages of corporations are: (1) They enable a large
amoimt of money to be collected from small investors who
would not be able to invest this money profitably in small '
amounts. (2) The stockholders of a corporation are subject
to a limited liability (usually the money invested in the stock)
in the case of failure in the business of the corporation.
In a partnership or an unincorporated company each person
must stand responsible for the debts of the firm and even his
private property can be taken to pay the debts of the firm.
The certifixxAes of stock issued to the members of a corporation
state the numbers of shares held, the face value of each and
how the stock may be transferred.
The following reproduction illustrates the form of a stock
certificate:
STOCKS AND BOND&-STOCKS
Stock oerlificateB vary somewhat in statement, but the Comnton Stock
Certificates are usually in the general form here illustrated.
Exercise 8
1. What is the par value of each share of stock?
S. How many shares of stock are there in this company?
8. In what state was this company incorporated?
i. How may the stocks in this company be transferred?
A dividend is a sum received for each share when all or a
portion of the profits of a corporation are distributed to the
shareholders.
8. If the dividends of the Regal Hat Company were $5000,
how much of a dividend would be paid on each of the 500
shares?
196 EIGHTH YEAR
6. The dividend of $10 on each share would be what per
cent of the par value of each share?
7. Will investors be anxious to buy stock that is paying
10% dividends when money usually only yields 6% interest?
In order to secure stock which pays a high dividend, investors
will pay more than the par value of the stock. They may pay
$150 for a share of stock whose par value is only $100. Such
stock would be quoted as worth 150 in the newspaper report
of the stock exchange.
The following were among the items in the report of a daily
paper on the New York Stock Exchange for Nov. 11, 1916:
Sales High Low Close Net Change
1. Am. B. Sugar 2900 102j 101 J lOlf - ^
2. Am. Exp 200 139i 136 139| 3i
3. Am. Wool 1000 53 52f 53 -f
4. do.ipf 100 98 98 98
5. Beth. Steel 200 670 665 665 '-10
6. do. pf 600 152 149 152
We see from the above sales that stocks in items 1, 2, 5 and 6
are selling above par. Hence those companies must be paying
good dividends to the investors. Items 3 and 4 show those
stocks were sold below par. What are the net changes in each
kind of stock since the preceding day?
8. Bring to the class for study extracts of the stock quo-
tations in the daily paper showing a table similar to the above
table.
Large corporations sometimes issue stock of two kinds or
classes, common and preferred stock. The preferred stock
guarantees that all dividends up to a certain per cent of the
par value must first be divided among the holders of the pre-
ferred stock. If there are any profits left, they are distributed
among the holders of the common stock.
*The expression do. in the above table means the same as the preceding
item and thus is a short way of expressing Am. Wool again.
STOCKS AND BONDS— STOCKS 197
The stock quotations given in the preceding table show that
the preferred stock in Item 4 is more valuable than the common
stock in Item 3. That corporation then is not doing a profitable
enough business to enable sufficient dividends to be paid
regularly to the common stock holders. In Item 6 of the table,
the common stock is selling at $670 per share. This extremely
high price was caused by unusually large profits coming from
the manufacture of munitions for i^e in the European War.
The excess profits were divided as shown above among the
common stock holders, thus making their stock much more
valuable than the preferred stock in that company.
The amount a broker receives for buying and selling stock is
called brokerage. .
In buying and selling stocks the brokerage is generally \%
of the par value of the stocks. When stocks are bought, the
brokerage is added to the market price to find the total cost.
When stocks are sold, the brokerage is taken from the selling
price to find the proceeds due the owner of the stock.
If the class can secure data from some local corporation,
a study of the organization of this local company will prove a
valuable exercise.
.Exercise 9
1. If a gas and electric company, incorporated, pays
quarterly dividends, two of them being 3% and two of them
2%, what income is derived annually from 10 shares, of $100
each?
2. What will be the cost of 100 shares of stock of a certain
railway (par value $100) if you buy them at 125% and pay
\% brokerage?
Solution: 125%+|% = 125|%.
125|%X$100 = $125.125, cost of 1 share.
100 X $125. 125 =$12,512.50, cost of 100 shares.
198 EIGHTH YEAR
8. A broker sells 200 shares ot American Express stock at
139 J%, brokerage J%. Find the amount of the proceeds
which he sends the previous owner of the stocks.
Solution: 139j%-i% = 139|%, proceeds from 1 share.
139i%X $100 =$139,125, proceeds from 1 share.
200X139.126 =$27,826.00, proceeds from 200
shares.
4. A broker sells 500 shares of American Wool preferred at
98, brokerage f %. What is the amount of the proceeds which
he sends his principal?
6. If money is worth 5%, what must be the dividends from
one share of the Bethlehem Common Steel in order for it to
sell for 670? What per cent of the par value is this?
Solution:
5% X $670 = $33.50, amount of dividends on one share.
$33.50 =X%X $100.
X% = ^i^= .335 or 33.5%, per cent of par value.
6. If money is worth 5%, what will be the market quotation
for stocks of good security pajdng an annual dividend of $9.00
per share? $9.00 is 5% of what value?
7. If the common stock of a great steel manufacturing
corporation is sold at 72% (par value $100 per share), what
will be the cost of 300 shares, including brokerage at f %?
8. If the preferred stock (par value $100 per share) of a
certain coal mining corporation sells at 115%, what will be
the cost of 10 shares of it, including the brokerage of J%?
9. What profit is made by purchasing 100 shares ($100
each) of stock of a certain railway at 97% and selling them at
107%, paying f % brokerage for each transaction?
10. How much stock of a certain street car company, incor-
porated, must be purchased to insure an income of $600 from
it if the stock pays semi-annual dividends of 4%?
STOCKS AND BONDS— BONDS
While corporate companies usually provide the necessary
capital for the conduct of their business, through the sale of
stock certificaies, they may also provide for additional capital
by the sale of bonds, which are generally secured by the tangible
property of the corporation, and the bonds become the first
lien on the business.
In case of default in the payment when due, either of the
accrued interest or of the principal, the holders of the bonds
are in most instances legally empowered to sell the property
of the corporation issuing the bonds, and to re-imburse them-
selves from the proceeds.
Bonds bear a fixed rate of interest, while the stock proceeds
are governed by the earning power of the business.
Bonds issued by the Federal government, by a state or
by a county must be previously authorized by legislation, or
by a direct vote of the people, who become the guarantors.
On page 206 is ^ven an illustration of a typical city
bond.
In addition to the ugnatiu^ of the proper executive officers,
all stocks and bonds must have affixed to them the seal of the
government, the state, the county or the business corporation
issuii^ them.
(rest Seal FacrimUe ol the Seal used
3tat<^s. re- by a buaiaess corporatiOD,
>i o( the reduced to about Hot Ota
EIGHTH YEAR
STOCKS AND BONDS— BONDS 201
Detachable interest coupons, or small dated certificates,
are generally issued with and as a part of each bond. These
are to be separated from the bonds and presented for payment
on the dates named upon them.*
Bonds, like stock oertificatea, necessarily vary more or lees in st&tement.
The illustration on the preceding page showe the general form of
a corporation bona, and the illustrations on this page
tne general form of the detachable coupons.
These coupons are usually transferable, beit^ deemed
equivalent to cash, and are collectible by any person holding
them.
Bonds without coupons are called regist^ed bonds, and
their transfer from one holder to another must be recorded
upon the books of the corporation issuing them.
What are the advantages of registered bonds in case of theft?
Exercise 10
1. A village issues corporation bonds to the amount of
$40,000 to build a school house. The bonds bear 5^% interest.
What is the amount of interest paid to the bondholders in one
year?
S. If a man receives £480 for the coupons of his bonds,
bearii^ 6%, what amount of the bonds does he hold?
The coupons attached to a bond are numbered from right to left, or from
the bottom up. In this way they may be detached in the order of number
and dat«. For the bond here illustrated thirty-nine coupons are required —
one for each semi-annual interest payment from January, 1915, to January,
1934 — covering a period of 20 years.
202 EIGHTH YEAR
8. In order to secure an income of $1200 annually, how
many bonds of the denomination of $100, bearing 6% interest,
must I buy?
4. A bank buys 50 U. S. bonds of the denomination of
$1000, pajdng for them a premium of 3 J% and a brokerage
fee of f %. What do the bonds cost the bank?
5. How much must be paid for the Gas and Electric Com-
pany bonds of a certain city, at a premium of 3%, the brokerage
being M%?
6. If I paid $3200 for bonds of the face value of $4000
and receive 6% interest on the face of the bonds, what do I
receive in a year, and what per cent do I receive on my invest-
ment?
7. Which is the better investment, a 6% bond bought
at $92 for $100 face value, or a 6% bond bought at par?
Suggestion: $6 is what per cent of $92?
8. What must be paid for 6% bonds in order to receive
an income of 6% on my investment?
Suggestion: $5 is 6% of what amount?
9. An American business corporation operating a rubber
plantation in Mexico issues bonds for $60,000, payable in
15 years. If they are sold at $93 for $100 of par value, what is
realized from them when 80% of the issue is "taken," or sold?
10. Find out what bonds have been issued in your commu-
nity. For what amounts were they issued? What rates of
interest do they bear?
11. If a conmiercial corporation issues bonds to the amount
of $60,000 to run eight years at 7%, and after paying interest
for five years fails, and after a year of delay pays only 78%
of the face of the bonds, what does the holder of each $100 bond
receive in all?
INVESTMENTS 203
12. What would he have received on a 6% bond for the full
period?
18. To secure an income of 8%, how much below par must
I buy bonds bearing 6%?
The organization of an imaginary corporation or a study of
some local corporation by the class would prove an excellent
means of understanding stocks and bonds. If the time permits,
the class should undertake such a problem.
INVESTMENTS
The supply or amount of money on hand, together with the
demand for loans, determines, to a large extent, the rate of
interest which must be paid to secure a loan.
If the supply of ready money is large and the demand for
loans is weak, the rate of interest will be low.
On the other hand, if the supply of ready money is small
and there is a large demand for loans, the rate of interest will
be high.
The risk involved in a loan is also an important factor in
determining diflferences in the rates of loans. If the risk of
loss is great, a high rate must be paid to secure a loan. If there
is very slight chance of any loss, the rate of interest is low.
Many new enterprises are started in the United States every
year. Some of these enterprises are successful and yield large
dividends. On the other hand, a large per cent of these enter-
prises fail and the investors suffer either a partial or a total loss.
One should never take only the agent's word as to the safety
of an investment, but should consult some reliable disinterested
party who is well posted in the field of investments, such as a
reliable banker or broker.
The policy of "Safety First'' is a very good one to follow
in the field of investments.
204 EIGHTH YEAR
Exercise 11
1. U. S. Government bonds usually sell at or above par
value v/hen the rate of interest is as low as 2%. Government
bonds are non-taxable. What other reason is there for the rate
of interest on government bonds being so low?
2. Municipal bonds usually bear from 4% to 5% interest.
Why is the rate higher on these bonds than on U. S. Government
bonds? Are these bonds taxable?
3. What is the usual rate that is paid on certificates of
deposit or safety deposits in a bank?
4. Why are careful investments in real estate considered
good investments? What are some disadvantages of such
investments?
5. A certain company advertised that they would give
2 shares of common stock free with each share of preferred
stock purchased before a certain date and claimed that both
kinds of stock should soon be worth more than par. Would
you invest in this stock? Why?
6. Another company advertises a certain sugar stock that
will pay 10% on the investment. How would the risk on this
investment compare with a good municipal bond yielding
5% interest?
7. The following advertisement appeared in a daily paper:
"Absolutely safe, exceptionally profitable, long-time invest-
ment;^ as good security as municipal bonds, with five times the
returns." As an investor, how would that advertisement appeal
to you?
•
8. An agent for a certain mining company was selling stock
at about f of the par value. He stated to a prospective buyer
that he would guarantee that the value of the stock would
^Teachers should show that the investment could not yield five times
the returns if the security was as good as municipal bonds.
INVESTMENTS 205
double in less than 6 months. Would you have bought this
stock on the strength of the agent's statement?
9. An insurance company loaned a farmer $3000, taking
a first mortgage^ on his farm valued at $5800. Was this a safe
investment for the insurance company?
10. If you had $20,000 to invest, would you invest it in one
place or divide it among several forms of investment? Discuss
the advantages and disadvantages of both of these methods.
Exercise 12
1. A girl deposited $75 in a State bank, deceiving a certifi-
cate of deposit, bearing 3% interest. How much interest
should she receive at the end of 6 months?
2. How much interest would she have received in a Postal
Savings bank for 6 months at 2%? Was her risk of losing her
money any greater in the State bank than it would have been
in the postal savings bank?
8. If I buy a'^municipal bond bearing 4^% interest for
$106.50, including brokerage, what is the rate of income on
my investment?
Suggestion: $4.50 is what % of $106.50?
4. What is the rate of income on stock costing $138.50,
including brokerage, if the yearly dividend amounts to $6.50
per share?
5. In deciding which is the better investment, a municipal
bond bearing 4^% interest, quoted at 106f , or a stock quoted
at 138| and known at that time to be yielding yearly dividends
of $6.50 per share, what other factors must be considered
besides the present rate of income?
*A mortgage is a contract by which the owner of the property agrees
to let the party loaning the money sell his property to secure payment
for a loan if he fails to meet the terms stated in the contract.
206 EIGHTH YEAR
6. A man wishes to buy a city residence. It rents for $60
per month, and he estimates that his expenses for this property
would amount to $240 a year. How much can he ofifer for the
property if he wishes to secure an income of 6% on his invest-
ment?
7. A carpenter in a certain village bought a house for $1875.
After spending $400 on improvements, he sold the property
for $2850. Find his per cent of gain on the money invested.
8. An 80-acre farm sold for $4000 in 1900. In 1903 the
same farm was sold for $4800. In 1915 it was sold for $9000.
Find the per cent of increase in its value between 1900 and
1903 ; between 1903 and 1916. What other returns were secured
by the owners beside the increase in the value of the land?
9. Mr. Bentley inherited $5000 from his father. He has
an opportunity to loan it to a farmer at 5% on a first mortgage
on a farm valued at $12,000 or invest it in a pecan grove which
an agent assures him will yield 10%. His banker tells him the
latter investment is very risky. Which shoyld he take?
10. An agent of a mining company canvassed the citizens
of a small village to sell mining stock. He told them that the
company wanted to keep the stock from getting into the hands
of rich capitalists. Would this statement have induced you to
buy or deterred you from investing in the stock?
11. A company invests $12,000 in "stump lands,'' from which
the pine timber has been removed, and $3000 in machinery
to uproot and pulverize the stumps, for the extraction of
turpentine. The annual profit is 15% on the investment, for
four years, at the end of which time the land has doubled in
value, and the machinery is sold for half the cost price. What
is the real per cent of annual profit?
12. Does it pay to invest money in an education? See if you
can get figures to prove your answer to that question?
CHAPTER III
REMITTING MONEY
On account of the heavy expense of shipping actual money,
much of the business of the country is carried on by means of
commercial forms of various kinds.
Postal Money Order
One of the most common forms for sending small amounts of
money is the postal money order. The government charges a
small fee for these orders, varying with the amount of the order.
snoo, Ut Angdet, CaL 193989
United stales Postal Mone y Order
A^C-jT^ — "^
■wnkMMA nemn. nu, mv of piiiBiuwSg
JiL4^)^^||^[2XU
TAC-SDIZLI. or NO VAUUT .
I' ^ " Coupon lofPiTtatOffl*"^
•Jr ' MtnHMnoinnMUM
MOMS THAU LAIWI
IMOieATlDOfI
OP TMi owom
2 THHOII
AMY ALTBlfr
■wrrt
The following
Not exceeding
Exceeding % 2
Exceeding 5
Exceeding 10
Exceeding 20
Exceeding 30
Exceeding 40
Exceeding 50
Exceeding 60
Exceeding 75
table shows the fees for the various amounts:
$2.50 3^
.50 and not exceeding % 5.00 ^i
.00 and not exceeding 10.00 8|i
.00 and not exceeding 20.00 \^i
.00 and not exceeding 30.00 \2i
.00 and not exceeding 40.00 15|i5
.00 and not exceeding 50.00 \%i
.00 and not exceeding 60.00 20^
,00 and not exceeding 75.00 25^
.00 and not exceeding 100.00 30|4
207
208 EIGHTH YEAR
Actual money may be sent by registered mail for a charge
of 10 cents in addition to the regular postage. An indemnity
not to exceed $25.00 will be paid by the government if a first-
class package or letter is lost.
Exercise 1
1. How much will money orders for the following sums
cost: $2.50; $15.00; $30.00; $52.14; $7.26; $76.00?
2. Which will be cheaper, to send $25 in a letter by regis-
tered mail or to buy a postal money order for $25? (The
postage on the letter is extra in both cases.)
3. Which is cheaper, sending $10 by registered mail or
sending a postal money order for $10?
4. What is the fee on a postal money order for $5.00;
for $50.00; for $100.00?
Express Money Orders
Express companies issue express money orders which are
similar in form to the postal money order and for which the
same fees are charged. The table on page 213 may also be used
in computing charges on express money orders.
FMPRrSS MOUC DHUI
*^'".S2Si:ifSS?r*i« - 15- 0000000
• AM PLC-
INOTOOOO^
ftKCMHBnwiMta LJY ^ r^^ - ^^^ !^ ls ^ ^fff^^^fT^;:rT^r^^^rJ^ ! ^ ^^
I SJtJt tmmtmmam m mm
An Express Money Order
REMITTING MONEY— DRAFTS 209
Exercise 2
1, Who purchased the express money order here shown?
2. To whom is this order made payable?
S. How could Mr. Brooks transfer this order to some other
person for collection?
*■ How much will an express money order for $18.75 cost?
8, How much will an express money order for $50 cost?
Bank Drafts
A bank draft is really a check by one bank on another bank.
For regular patrons of the bank who have checking accounts,
most banks write drafts for small amounts without extra
charge as a matter of accommodation. For large amounts
drafts are sold at a premium or a discount, depending on the
state oi the balance between the banks of the two cities involved.
A Bank Draft
Exercise 3
1. Where was the above draft purchased?
2. To whom was it made payable?
8. How can it be transferred to some other person?
210 EIGHTH YEAR
4. On what bank is the draft drawn?
5. A fanner wishes to pay off the mortgage on his farm
that is held by a certain insurance company. He finds that
tjbe rate for a draft on the city where the insurance company
is located is 20 cents per $100. Find the cost of the draft for
$3000.
6. How much would an express money order for the same
amount have cost him?
Checks
Business firms and most individuals have checking accounts
in some bank. Instead of buying drafts, most firms send
checks to settle their accounts. A check is returned by the
local bank to the firm who issues it when the account is bal-
anced. The check thus serves as a receipt for the transaction.
ORpEROl
PA/TOTHFr^^ 5^ >f .^, ^^ ^^JJ^'JJP. ^'j ^^.^f ^^
'^^A/^.^y^.^^^y^/^s^:^ ^^ /^
-^ •^■*-*^
'^^^jy?tZ&ty
AdjC^tjC^'oa^*^*^
A Business Firings Check
Exercise 4
1. What firm issued the above check? In what bank do
they carry their banking account?
2. To whom is this check made payable?
8. When the check is returned to the First National Bank
of Boston for collection, how will they enter it on their accounts?
REMITTING MONEY— CHECKS
211
"^'FiRSTllSmo:
"j/g/T ,A f /4/^
OF €HI€A002-i
PAY TO THE ORDER OF
J 973647
A Personal Check
4. Who issued the above personal check? To whom is it
made payable? Show how this check would have to be indorsed
when it is cashed. (See page 190.)
5. If a certain man has a balance of $125.82 in the bank
on Jan. 1, 1917, and issues three checks as follows: for rent,
$35.00; for light bill, $1.58; for gas bill, $2.56; how much will
he have to his credit in the bank?
6. Mr. Hill issues Mr. Johnson a check for $25.00 to pay
for services rendered. Mr. Johnson loses the check and
promptly notifies Mr. Hill of his loss. How can Mr. Hill
arrange to pay Mr. Johnson without danger of having to pay
twice should the check be found at a later date?
7. Why do banks refuse to cash checks for strangers?
8. Discuss the advantages and disadvantages of remitting
money by means of checks.
Foreign Remittances
Remittances to foreign countries may be made by inter-
national money orders, by foreign express orders or by foreign
drafts called hiU% of exchange.
212 EIGHTH YEAR
Emergency Remittances
When an agent wishes money immediately in order to close
an important transaction, he often finds it an advantage to
have his firm telegraph him the money.
In the telegram in the illus-
THE WESTERN UNION TELEQRAPH compaiiy' tration Richard Doe of Wash-
^«« 1 — ^*^ ^ ington is sending his brother
tC^^^^sZiL^A^Mp^ •^^^. ^^ "^ ^®^ Orleans a
Tragwrf ^o, ^ . Certain sum of money by tele-
^ o^ OL .di^ ^ y7' ^ ^^ graph. In order to prevent
^/a,..^^^y^ — f jy^ ^ ^^ji^f^ ^,>^, Others from leammg about the
^^f a^ /tM-^^uj- ^^4oA^in, < ^,fe amount of money involved in
nL-w« .va^y Mpfit — the transaction, the message is
,__ ^^ expressed in terms of a code.
The word ring in the tel^ram
refers to the amount of money and can be understood only by a person
familiar with that particular code.
Note the writing in the last line. It was made by the sending agent
with his left hand while he was transmitting the message with his right
hand, showing a high degree of efficiency in operation.
Upon the receipt of this message, the agent in New Orleans sends to
John Doe the following notice:
"We have received a telegraphic order to pay you a sum
of money upon satisf actoxy evidence of identity. The amount
will be paid at our office if called for within 72 hours; other-
wise under our arrangement with the remitter the order will
be canceled and the amount thereof refimded."
When money is remitted by telegraph, there is a transfer charge
on the money in addition to the regular charge for the telegram
which is computed on the basis of a 15-word message.
Exercise 6
1. In remitting $25 (or less) by telegraph between certain
cities, the charge for that amount is 60 cents. The telegraph
charges between these cities is 36 cents for a 15-word message.
Find the transfer charge for that amount.
REMITTING MONEY— BY CABLE
213
2. What would be the cost of remittmg $25 by an express
money order? How much cheaper is the express money order
than the remittance by. telegraph given in Problem 1? When is
money usually remitted by telegraph?
8. The cost of a 15-word message between two cities is
35 cents. What will be the total charges for remitting $100 by
telegraph if the transfer charges for the money are 85 cents
per $100?
4. The charges for remitting $200 by telegraph between
those cities are $1.45. How much is charged for the extra
$100? At the same rate per $100 beyond the first $100, what
will be the charges on remitting $1000 between those cities?
Remitting by Cable
If an emergency arises for a quick transmission of money
to a firm or person in a foreign country, money can be remitted
by cable in the same manner that it is telegraphed in this
country. The amount of the money is then expressed in the
money values of the foreign country to which it is sent. The
following illustration shows a form for such a cablegram:
In the cablegram shown in
the illustration ^'Bruzzolo, Lon-
don" stands for the registered
address of the London telegraph
office that pays the money.
"Rabbit" is a guard word neces-
sary in sending such messages.
*'Jewel" is the code word for
"pay to." "John Doe, 76
Downing Street, London" is the
payee. "Bracket" is a code
word which stands for the
amount to be paid John Doe.
^'-^<e>rvCibf£tL ...
<(
Darby" means "from." "Richard Roe" is the name of the sender of the
money and "Jentant" is the code word standing for the signature of the
transfer agent at New York.
214 EIGHTH YEAR
Exercise 6
The charges on sending money by cablegram are $4.65 for
the cable charges (15 words) and 1% premium on the amount
of money sent.
1. Find the total amount that must be paid the agent in
New York to remit $100 to a party in London.
2. What will be the transfer charges on remitting $500
by cable? Find the total amount which must be paid the
transfer agent in this country.
3. If the word "Bracket" stands for $250, how much did
Richard Roe have to pay the transfer agent in New York?
4. Find the total transfer charges by cable on $300, on
$1000, on $5000.
Remitting Money by Wireless
To facilitate business, leading banks and express companies,
in normal times, keep large amounts of money on deposit at
the principal conmiercial centers in the
European countries. During the period of
the European War communication with
certain countries in Europe was maintained
mostly by radio means, and the transmission
of money by "wireless" reached large pro-
MONIY REMITTED BY
WIRELESS
—TO—
knaif lid Anlrli-llnpiy
4MI
Fort iMftrtMra
National Bank
portions at rates indicated in the following problem:
Exercise 7
1. A firm in Chicago remitted $1000 by a wireless radiogram
to a firm in Berlin on Jan. 28, 1917. The charges were quoted
by the bank at $4.00 per order of 6 words, plus the usual postal
charges of 15 cents per order, excess words to be paid at the
rate of 57 cents per word. If the radiogram contained 9 words,
what were the charges on the radiogram?
FOREIGN MONEY AND TRAVEL
Foreign Money
and
Travel
Our trade and
travel among foreign
nations are so exten-
sive that some knowl-
edge of the money
systeans of those nar
lions is a dedrable
acquisition fw any
my or girL
The f oUowing table
l^vee the essential
Facta in the mon^
systems of some of
the leading foreign
countries:
Courtny White Stu lins
Countey
Monty Unit
Equivalent in Lower
Value of Unit
inU.S. Money
Great Britain
£ (pound)
20 shillings
$4.8665
mark
100 pfenn^e
100 centimes
.238
France
.193
Auatoia-Hungaiy..
krone
100 heUer
.203
Itafer
lira
100 centesimi
.193
Spain
100 centimoa
.193
drachma
100 leptBs
100 gulden
100 ore
.193
HollMid
guilder
krone
.402
Den.,Nor.aiid8we.
.268
Russia
ruble
100 kopeks
.518
Japan
100 aen
.498
Portugal
milreis
1000 reis
1.08
Brazil
milreie
1000 reia
.646
All of these systems are centesimal except those of Great Britain,
Portugal and Brazil. Money in the centesimal systems is treated as oiu*
dollars and cent«, the decimal point wparating ttte larger unit from the
smaller denonmiations.
216 EIGHTH YEAR
Exercise 8
1. How many shillings are there in 3 pounds 4 shillings?
2. What is the value in U. S. money of £20?
3. What is the value in English money of $486.65?
4. What is the value in U. S. money of a shilling?
6. 12 pence = 1 shilling. What is the value in U. S. money
of an English penny?
«. Reduce to U. S. money 2 francs, 46 centimes.
Solution: 1 franc = $.193. 2 francs, 46 centimes = 2.46 X
$.193 = $.47285 or 47 cents in U. S. money.
7. What is the simi of 4 francs 5 centimes; 6 francs 15
centimes; 26 francs 10 centimes; and 15 francs 76 centimes?
What is the value of this sum in U. S. money?
8. What is the siun of 20 marks 15 pfennig; 42 marks
26 pfennig; 68 marks 40 pfennig; and 12 marks 20 pfennig?
Express the value of this simi in U. S. money.
9. Add 14 pesetas 10 centimos; 16 pesetas 18 centimos;
25 pesetas 14 centimos; and 26 pesetas 58 centimos. Find the
value of this sum in our money.
10. Add 60 yen, 30 sen; 46 yen, 15 sen; 26 yen, 45 sen;
and 14 yen, 20 sen. What is their exact equivalent in our
money?
Exercise 9
Many travelers in foreign countries use rough estimates
where small sums are spent for personal expenses. A franc or
lira or drachma or peseta is called 20 cents; a ruble or a i^en
a "half-dollar," and a vmrk or a krone a "quarter," etc.
In the following problems the money unit of the country
visited and its centesimal parts are left to be stated by the
pupil:
FOREIGN MONEY AND TRAVEL 217
1. If, when visiting Marseilles, your expense for a luncheon
and for table service is 2.05, for carriage hire 10.15, and for a
souvenir 1.20, how will you compute the total? What will be
its approximate equivalent in American money? What its
exact equivalent?
2. If in Rome the charge for your hotel room is 6.10, for
meals and table service 9.10, for street car and carriage expense
20.15, for a guide 10.20, and for souvenirs 14.50, what will
be the total? What will be its approximate equivalent in
American money?
3. If in Copenhagen you pay 1.90 for a luncheon, and 7.50
for a drive about the city, what will be the cost of both, and
what its approximate equivalent in American money?
4. If a friend writes you from Lisbon that he paid 3000
reis for an automobile ride, what do you understand to be the
cost of the ride in American money?
6. If at Paris he buys a souvenir for 2 francs 50 centimes*
at Rome another for 4 lira 10 centesimi, and at Barcelona
another for 3 pesetas 50 centimos, what is the approximate
sum of the purchases in U. S. money?
6. If a friend in Rio de Janeiro writes to you that he has
invested 5000 milreis in mate, or Paraguayan tea, what do you
understand to be, in U. S. money, the amount of his investment?
7. If in Moscow an American tourist pays for a week's
board and lodgings 16.20, for souvenirs 4.20, and for carriage
and guides 60.00; what is the approximate expenditure for these,
stated in U. S. money? What is the exact amount?
8. If in Rotterdam one of your traveling friends states that
he paid 1.50 to a hack driver and 3.10 for souvenirs, together
with 1.10 each for breakfast, lunch and dinner, what was the
amount of these expenses, roughly stated in U. S. money?
What was the exact amount?
EIGHTH YEAR
Travelers* Checks
Exercise 10
Touiist companies, express companies, and sometimes
banks, issue travelers' checks, in convenient amounts of
$200, $100, and sometimes $20 and $10, or other sums, for
travelers to carry with them on tours to foreign lands. These
are bound together in the form of a folded check book, and
are detachable one at a time.
The purchaser of a book of such checks must sign each one
of them in the office at which he procures it, and f^terwarda,
when he cashes it, at one of the fore^ agencies of the company
or bank issuing it, or at one of their agencies in his own country.
1. If I buy travelers' checks to the amount of $480.00,
and pay J% of the aggregate face of them for the accom-
modation, what do the checks cost me? How much do I
receive for them in London?
2. If, instead of cashii^ all the checks in London, I cash
those for half the amount in Paris, what do I receive for them?
If in Rome what? If in Madrid what?
8. If I cash all the checks in Berlin and Munich, what do
I receive for them?
4. If I cash half the amount of the checks in Moscow and
half of them in Amsterdam, what do I receive for them?
CHAPTER IV
PRACTICAL MEASUREMENTS
Exercise 1. Review of Quadrilaterals
1. State the principle for finding the area of a rectangle.
2. What is the area of a rectangle 16 inches long and 8f
inches wide? (See page 137.)
3. Find the number of square yards in the area of a baseball
diamond which is 90 feet square.
4. How many square inches are there in a sheet of paper
8§ inches by 11 inches? How many square feet of space would
a ream of 600 sheets of this paper cover if the sheets were
placed edge to edge?
6. How many square feet are there in a rectangular garden
15 yards long and 30 feet wide? How many square yards?
6. A certain farm is 1^ miles long and f of a mile wide.
How many square rods does it contain? How many acres?
7. A field 60 rods long and 40 rods wide yielded 360 bushels
of wheat. What was the yield per acre?
8. There are usually 40 apple trees planted on an acre of
ground. How many square feet of space does that allow for
each tree?
9. A ball club bought a field for a ball park. It was 400
feet long and 395 feet wide. How much did it cost at $310
an acre?
10. School architects usually allow 16 square feet of space
as the proper amount for each pupil. How many pupils can
be properly seated in a school room 24' x 28'?
219
220 EIGHTH YEAR
11. How many pupils are there in your school room? Find
the number of square feet of floor space for each pupil, using
the total area of the room for the computation.
12. The area of a rectangle is 96 square inches and the base
is 16 inches. Find the altitude.
13. The area of a rectangle is -3^ of a square foot. The
width is f of a foot. What is the length?
14. Find the area of a parallelogram with a base of 18 inches
and an altitude of 12 inches. (See page 142.)
16. The length of a parallelogram is f of a foot and the alti-
tude is f of a foot. What is its area?
16. Find the area of a trapezoid with its parallel sides
equal to 8 inches and 15 inches and its altitude equal to 12
inches. (See page 144.)
17. Two converging roads form a field in the shape of a
trapezoid. The two parallel sides are 60 rods and 100 rods
and the altitude is 64 rods. How many acres are there in this
field?
18. How much is this tract of land worth at $175 an acre?
Exercise 2. Review of Triangles
1. State the principle for finding the area of any triangle.
2. What is the area of a triangle whose base is 8 inches and
whose altitude is 7 inches? (See page 146.)
3. The area of a triangle is 54 square inches and the altitude
is 9 inches. Find the base.
4. The area of a triangle is ^ of a square foot and the base
is f of a foot. Find the altitude.
6. A triangular flower bed has a base of 3 yards and an
altitude of 4 yards. Find its area in square yards.
PRACTICAL MEASUREMENTS— SQUARES 221
Squares and Square Roots
A square is a rectangle with all of its sides equal.
What kind of angles has a square?
If a side of a square is 4, the base and altitude are
each-4, and the area of the square is 4X4, or 16. ^ Square
16 is called the square of 4. This may be written 4^ = 16.
The small figure 2 at the upper right hand side of the four
is called an exponent. An exponent shows how many times the
number is taken as a factor. For example, 5* means that 5
is taken twice as a factor, or 5X5.
Exercise 3
1. Make a table showing the squares of all numbers from
1 to 25 as follows:
1P=?
12«=?
132=?
142=?
152=?
2. Learn this table so that you can give any square quickly.
3. What are the squares of 30, 40, 50, 60, 70, 80?
Since 16 is the square of 4, 4 may be called the square root
of 16. The two equal factors of 16 are 4 and 4. One of the
equal factors of a number is called the root of the number.
In order to find the square root of a number, we must find
a factor which, when multiplied by itself, will give the number.
Square root is very important in solving problems in right
triangles.
4. What are the square roots of 4, 9, 25, 36, 49, 64, 81, 100,
144, 225, 625?
1*= 1
6*=?
2«= 4
7*=?
3"= 9
8*=?
4* =16
9*=?
6*=25
10*=?
16«=?
21*=?
ir=?
22*=?
18*=?
23*=?
19*=?
24* = ?
20*=?
25*=?
222 EIGHTH YEAR
6. Find the square root of 1296.
The number 1296 is larger than any of the squares that we
have learned, so it is more difl&cult to see the square root of
this number than those in Problem 4. Try different numbers
until you find one which multiplied by itself will give 1296.
There is a much more convenient method of finding the
square root of a number than trying various numbers until
we find the correct one. The following form shows the method
of extracting the square root of a number:
Extracting the Square Root of a Number
1. Begin at the decimal point and point
1296 36 ^ff ^^® number into periods of two figures
9 each (12'960.
66
396 2. Find the largest square (9) in the left-
396 hand period (12). Put its square root (3)
as the first figure of the square root and
subtract the square (9) from the first period (12).
3. To the remainder (3) bring down the next period (96).
4. Take two times the number in the root (3) and use this
product (6) as a partial divisor into the first figure or two
figures of the remainder (396). Place the figure thus obtained
(6) as the next figure of the square root. Also add this figure
(6) to the partial divisor, making the complete divisor (66).
5. Multiply this complete divisor by the last figure of the
root (6).
6. If there are other periods proceed, as in steps 3, 4 and 5.
There is no remainder in this problem.
The square root, then, of 1296 is 36.
By reference to the following diagram on cross section paper
the reasons for the various steps in the preceding problem
can be understood:
PRACTICAL MEASUREMENTS— SQUARE ROOT 223
When the number 1296 is separated into two periods, the
period 12 really stands for 1200 and contMos the square of the
tenS' figures in the root.
The largest square of
tens contained in 1200
is 900 or the square
of 3 tens (or 30). Note
in the diagrajo at the
right the large square
of the three tens (or
30) which contuns 900
of the small squaxea.
In order to find the
units figure, the 900
must be taken from
the 1200, leaving 300
of the small squares.
To these must be added the ne3rt period, 96, making the
total remainder, 396. This means that 396 small squares
compose the two rectangles and the small square at the top
and right-hand side of the figure. Since the two rectangles
have the same length as the large square, each rectat^le
is 3 tens or 30 units long. There are two of the rectangles
and so both of them are 2X3 tens or 6 tens or 60 imits long.
Using 60 as a partial divisor Into the 396, we can find the
altitude of the rectai^es, which we find to be approximately
6 units.
Adding the length of the small square (approximately 6)
to the length of the two rectangles, we have a rectangle which
is approximately 66 units loi^ and 6 units wide:
224 EIGHTH YEAR
When the base 66 of this long rectangle is multiplied by the
altitude 6; we find that the two rectangles and the small square
which formed this long rectangle were composed of 396 small
squares, which made up the remainder after the large square
had been subtracted from the figure.
The square root then consists of 3 tens and 6 units, or 36.
Exercise 4
Find the square roots of the following numbers:
1. 256 8. 3969 16. 3249
2. 1156 9. 5041 16. 116964
3. 1764 10. 11025 17. 173889
4. 4489 11. 18225 18. 822639
6. 3364 12. 1225 19. 123904
6. 5184 13. 6889 20.' 229441
7. 7056 14. 9604 21. 42436
Find the square roots of the following numbers:
1. 3
'3.00'00'00ll.732+
1
27'
200
189
343
1100
1029
34€
>2
7100
6924
If the square root does not come out
as an integer, add ciphers in periods
of two each and proceed as in
other problems. For practical pur-
poses it is not necessary to carry
the result beyond 3 decimal places.
2. 15.
4. 34.
6. 50.
8. 5.
10. 83.
3. 13.
6. 12.
7. 18.
9. 16.
11. 45.
Compare your results in these problems with the values
found in the following table:
PRACTICAL MEASXJREMENTS— SQUARE ROOT 225
SQUAKB ROOTS OF NUMBERS
From 1 to 100, Carried to Three Places of Decimals
Number
Square Root
Number
Square Root
Number
Square Root
1
1
34
5.831
67
8.185
2
1,414
35
5.916
68
8.246
3
1.732
36
6
69
8.307
4
2
37
6.083
70
8.367
5
2.236
38
6.164
71
8.426
6
2.449
39
6.245
72
8.485
7
2.646
40
6.325
73
8.544
8
2.828
41
6.403
74
8.602
9
3
42
6.481
75
8.660
10
3.162
43
6.557
76 '
8.718
11
3.317
44
6.633
77
8.775
12
3.464
45
6.708
78
8.832
13
3.606
46
6.782
79
8.888
14
3.742
47
6.856
80
8.944
15
3.873
48
6.928
81
9
16
4
49
7
82
9.055
17
4.123
50
7.071
83
9.110
18
4.243
51
7.141
84
9.165
19
4.359
52
7.211
85
9.220
20
4.472
53
7.280
86
9.274
21
4.583
54
7.348
87
9.327
22
4.690
55
7.416
88
9.381
23
4.796
56
7.483
89
9.434
24
4.899
57
7.550
90
9.487
25
5
58
7.616
91
9.539
26
5.099
59
7.681
92
9.592
27
5.196
60
7.746
93
9.644
28
5.291
61
7.810
94
9.695
29
5.385
62
7.874
95
9.747
30
5.477
63
7.937
96
9.798 '
31
5.568
64
8
97
9.849
32
5.657
65
8.062
98
9.899
33
5.745
66
8.124
99
100
9.950
10
You will find it an advantage to use the preceding table to find the
square roots of all numbers between 1 and 100. Engineers and advanced
eUidents of mathematics and science use books with similar tables.
226
EIGHTH YEAR
Exercise 6
1. The area of a square is 64 square inches. What is the
length of one side?
2. The area of a square is 40 square inches. What is the
length of one side?
3. A square field contains 40 acres. What is the length
of one side in rods?
4. What is the length of one side of a square whose area
is 81 square yards?
6. What is the length of one side of a square whose area b
64 square yards?
6. By the use .of the table find the square roots of the
following numbers: 17, 56, 97, 62, 43, 35, 2, 5, 77, 32.
Right Triangles
A right triangle has one right angle. The
other two angles of a right triangle are
always acute.
In the right triangle A B C, A C and A B
are called the legs and B C is called the
B hypotenuse.
Suppose the side A C is 3 inches long and A B is 4 inches
long, as shown in the figure below:
Exercise 6
1. How many square inches
are there in the square constructed
on the leg that is 4 inches long?
2. How many square inches are
there in the square constructed
on the leg that is 3 inches long?
vV
■/y
V
/
PRACTICAL MEASUREMENTS— RIGHT TRIANGLE 227
3. How many square inches are there in the square on the
hypotenuse, which is shown to be 5 inches long?
4. How does the square on the hypotenuse compare in
size with the number of square inches in the sum of the two
squares on the legs?
This relation may then be stated in the following principle:
PRINCIPLE: In a right triangle, the square of the hypotenuse
is equal to the sum of the squares of the other two sides.^
Exercise 7
1. The two legs of a right triangle are 15 feet and 20 feet.
Find the hypotenuse.
Solution: 152=225; 202=400. The sum of the squares
on the two legs = 225+400 = 625, which is equal to the square
on the hypotenuse.
The hypotenuse then must be the square root of 625 which
is 25.
Therefore: The hypotenuse is 25 feet long.
2. The hypotenuse of a right triangle is 20 inches and one
of the legs is 12 inches. Find the length of the other leg.
Solution: Since the square on the hypotenuse (400) is
equal to the sum of the squares on the two legs, the square
on either leg must be equal to the difference between the
square on the hypotenuse and the square on the other leg (144).
The square of the unknown leg =400— 144 = 256.
The leg is the square root of 256 = 16. Therefore : The leg is
16 inches long.
8. A right triangle has two legs equal to 6 feet and 8 feet.
What is the length of the hypotenuse?
^This principle was first stated by Pythagoras, a Greek mathematician,
over 2000 years ago.
228
EIGHTH YEAR
These dimensions are very frequently used in constructing
a right angle with cords. By making the two sides 6 feet and
8 feet and then using a 10-foot cord to regulate the spread
of the two sides an accurate right angle can be formed.
Find the missing leg or the hypotenuse in the following
problems: (Carry to three decimal places if the result does not
come out even.)
Leg Hypotenuse
12 in. ?
? 17 in.
32 ft. ?
24 in. 30 in.
11 in. ?
? 18 rd.
36 in. ?
11. What is the length of the diagonal
of a square that is 8 inches on each side?
12. A baseball diamond is 90 feet
square. How far is it from first base to
third base?
13. A congressional township is 6
miles square. How long would a road
be if it ran on the diagonal line of the square? How much
shorter is this road than one which goes along the two sides
of the square to the opposite comer?
14. Draw a square 4 inches on each side.
Divide it into two equal squares.
Suggestion: Draw the two diagonals as shown
in the illustration. Cut along the dotted diagonals,
thus dividing the square into 4 parts. See if you
can arrange these parts so that they will make two
smaller squares.
15. How long is the side of one of the small squares?
PRACTICAL MEASUREMENTS— PROBLEMS 229
16. Two boys were making a model of an automobile in a
wood shop. They were making out a bill
for lumber which they wished to order.
The sides of the hood were 12 inches
apart, and they wished to make the ridge
4 inches above the tops of the sides. Their
problem was to find how wide to order
the slanting boards for the top of the hood.
How wide should they be in order to leave
no waste?
17. A girl wished to put up a window shelf for flowers.
The distance of the edge of the board from the
wall is 10 inches and the bottom of the board
is 16 inches above the baseboard. She wanted
to cut her props so that they would reach from the
outer edge of the board to the top of the base-
board. How long must she cut her props on the
outside edge so that her shelf will make a right
angle with the wall?
18. A ladder 27 feet long leans against a house
from which its base is separated by a distance of 18 feet.
How high from the ground is the top of the ladder?
19. A man has a piece of land in the shape of a right triangle.
He measures the two legs and finds them to measure 21 rods
and 28 rods, respectively. Show how he can compute the
amount of fence which he will need to enclose the field, without
actually measuring the other side.
20. In building a chicken house of the
dimensions shown in the diagram, a man
wished to cover the top with ship-lap
boards which were to extend 6 inches over
the edges at each end. How long must he
order his boards for this roof?
230
EIGHTH YEAR
21. At one comer of a level rectangular field 8 rods long and
6 rods wide is a tower 165 feet high. How long a wire will
be required to reach from the top of the tower to the ground
at the comer diagonally opposite?
Note that you must use two right triangles to solve this
problem.
22. In the figure representing the end of
a bam you find the dimensions given.
How long must the builder order his rafters
for this bam if he wishes them to project
1 foot at the eaves?
23. A man setting a telephone pole which
projects 25 feet above the ground wishes to
brace it with a wire attached 6 feet from the
top of the pole to a stake 30 feet from the base of the pole.
How long must he cut his wire if he allows 3 feet additional for
fastening the brace at both ends?
24. Construct very accurately a right triangle. Then
draw accurate squares on each of the three sides as shown
in the illustration. Extend
the sides of the large square
as shown in the diagram
and draw a line perpendicu-
lar to the dotted line, as
shown in the square on the
long leg. Number the parts
of the small squares and
cut them out. If you
arrange them properly, they
will cover the square on the hypotenuse. See if you can arrange
them in the right order, showing that the sum of the squares
on the legs is equal to the square on the hypotenuse. This is a
practical way of proving the principle on page 233.
%
%
1\
\
•"5
PRACTICAL MEASUREMENTS— PROBLEMS 231
The pitch or slant of the roof of a house is
found by dividing the height above the eaves
by the width of the house. In the illustration
the pitch is 12-5-24, or ^.
26. How high would the ridge of the house
be above the eaves to give a pitch of f ?
26. Find the length of a rafter for a house
with a width of 24 feet and a pitch of f , allowing 1 foot for a
projection at the eaves.
27. The pitch of a house 30 feet wide is J. Find the
length of a rafter for this roof, allowing 1 foot for a pro-
jection at the eaves.
A carpenter can very readily determine the length of a
rafter by using a ruler and the steel square. Along one
arm of the square he lays off a number of inches equal to
the number of feet in f of the width of the house.
Along the other arm he lays off the height of the
ridge above the eaves, using inches to represent
feet. A ruler joining these points as shown in
the illustration will show the number of feet in
the rafter.
-29
■n
-V
-3»
■»
-»
-17
»
-B
-M
-B
-9
-»
-r
6
hs
4
3
-8
-1
? ^^??T??y
28. Find by this method the length
of a rafter for a house 24 feet wide
and a pitch of §.
Equilateral Triangles
The altitude of an equilateral triangle is
a perpendicular drawn from the vertex (C)
to the base (A B). The altitude divides
the equilateral triangle into two equal
right triangles. Measure A D and D B
to show that they are equal.
232
EIGHTH YEAR
Exercise 8
1. An equilateral triangle has each of its sides equal to
12 inches. What is its perimeter?
2. What is the altitude of an equilateral triangle with each
side equal to 10 inches?
Solution : Since A B = 10 inches and A D = D B , then D B = 5
inches. In the right triangle D B C, B C = 10 inches and
D B=5 inches.
102-52= 100-26=75. The square on C D must be 75.
C D then is the square root of 75, or 8.66+ .
Therefore: The altitude of an equilateral triangle with a
side of 10 inches is 8.66+ inches.
3. Find the altitudes of the following equilateral triangles
and fill out the table as indicated:
pROButn
Length or siot or
EQUILATERAL TRIANGLEr
LENGTH or
Altitudi:,
ALTITUDE, -7- SlDt .
I
10
8.66+
.866 4-
2
12
«
?
3
8
?
•
4
16
*?
P
5
6
'?
•
4. What do you find the quotient of the altitude divided
by the side of each equilateral triangle to be?
Since we have found that the altitude of any equilateral
triangle is .866 of the side, we may now use this fact and save
ourselves a great deal of computation.
6. Find the altitude of an equilateral triangle whose side
is 25 inches.
Solution: .866X25 inches=21.65 inches.
6. Find the area of an equilateral triangle whose side is
8 inches; one whose side is 5 inches.
PRACTICAL MEASUREMENTS— CIRCLES 233
Circles
A circle is a figure bounded by a curved
line every point of which is at a given
distance from a point within, called the
center. The bounding line is called the cir-
cumference of the circle.
A straight line drawn through the center
of the circle and terriiinating at both ends
in the circumference is called a diameter of the circle.
The distance from the center to the circumference is called
the radius of the circle. The diameter is how many times
as long as the radius?
Class Experiment
The problem is: To find the ratio^ of the circumference of
any circle to its diameter.
The ratio of the circumference to the diameter (C-r-D) is
known as jd and is designated by the Greek letter tt.
Each pupil in the class should measure very carefully the
circumference of some circular object. This may be done with a
tape line or by measuring with a string and then measuring the
length of the string with a ruler. Then measure the diameter
of the same object. Next divide the circumference by the
diameter and carry out the quotient 4 decimal places.
Enter the results found by each member of the class in a
table similar to the form given below, reduced to decimals:
PUPlL
C IRCUMFERENCi:
DiAMETCR
ir=c-^D.
RlCMARD T^Ot
4.125 in.
1.3125 in.
3.1428+
•
^The ratio of one number to another is the number of times the first
contains the second. For example, the ratio of 8 to 4 is the niunber of
times 8 contains 4, or 2.
234 EIGHTH YEAR
Find the average value of tt for all the pupils in the class and
compare the value which you have found with the accurate
value 7r= 3.1416.
Since ir is the quotient of the circumference divided by the
diameter, the circumference is equal to the diameter multiplied
by TT,
or C = 7rXD.
Since the diameter is twice the radius, C =ir X2 r, or 2irr.
In formulas the sign X is frequently omitted, but the expres-
sion 27rr is understood to mean 2X7rXr. It is much shorter to
write it 27rr.
Exercise 9
1. Find the circumference of a circle whose diameter is
8 inches.
Solution: C = 7rD=3.1416X8 inches =25.1328 inches.
2. Find the circumference of circles with the following
diameters: 12 inches, 10 feet, 15 inches, 5 yards.
3. The radius of a circle is 9 inches. Find the circumference.
4. The circumference of a circle is 50.2656 inches. Since ir
is already known, find the diameter of this circle.
5. A circular flower bed is 8 feet in diameter. How many
bricks must I buy in order to put a border of bricks around
the bed 1 brick thick? (A brick is Sinches long.)
6. A farmer builds a circular bam having a diameter of
40 feet. What is the length of the circumference of the barn?
7. The Equator of the earth is approximately 25,000 miles.
What is the equatorial diameter of the earth?
8. How much fringe is needed to trim the edge of a circular
lamp shade 14 inches in diameter?
PRACTICAL MEASUREMENTS— SHOP PROBLEMS 235
9. How long a piece of tatting would it take to edge the
cuflfs of a girl's sleeves if the cuflfs are 2f inches in diameter?
10. A farmer's roller is 32 inches in diameter. How many
revolutions will the roller make in roUii^ a com row a quarter
of a mile long?
11. A bicycle has wheels 28 inches in diameter, outside
measurement. How many revolutions will each wheel make in
going a mile?
12. A circular wading pool 40 feet in diameter has a concrete
side walk 3 feet wide extending around the border. How much
longer is the outside circumference of this walk than the inside
circumference?
Exercise 10
C^ZD^
1. The trough of a pen tray is
2 inches wide. How wide apart
must I set the points of my compass
in order to draw the semi-circle at each end?
2. If the board is 2f inches wide and the end of the trough
is to be ^ inch from the end, locate the point for the center of
the semi-circle at each end.
8* A boy in the forge shop wishes to make a ring 8 inches
in diameter out of f -inch stock. Allowing 3 times the diameter
of the rod for extra in welding, how loyig must he cut the
piece of stock to make this ring?
4* How long must a rod be cut out of f -inch stock to make
a ring 18 inches, inside diameter? Make allowance for welding.
6. A grindstone 36 inches in diameter makes 40 revolutions
per minute. What is the cutting speed in feet per minute of
this stone? (Find the number of feet of the circumference that
will pass under the edge of a tool in 1 minute.)
236 EIGHTH YEAR
6. Another gnndstone in the shop is only 24 inches in
diameter. How many revolutions per minute must it make to
have the same cutting speed as the grindstone described in
Problem 5?
7. A pulley on a countershaft in a shop ia 14
inches in diameter. How many inches of belt will
pass over this puUey in one revolution?
8. The pulley on a wood lathe is 6 inches in
diameter. How many inches of belt will pass over
this pulley in one revolution?
«. How many revolutions will the lathe pulley
make for one revolution of the pulley on the
countershaft?
10. If the speed of the countershaft is 720
revolutions per minute, what is the speed of the
lathe?
It. If you have a shop in your school, visit it and make
other problems similar to the ones given above
Area of Circles
When a circle is
cut into pieces as
shown in this
illustration,
the pieces are al-
most triangular in
shape, the bases
being slightly
curved. If we arrat^e these triangles in a row with half of
the triangles pointii^ up and halt of them filling in the spaces
between as shown in the diagram on the next page, we should
have approximately a paratleli^ram:
The circle divided ioto triangles
PRACTICAL MEASUREMENTS— CIRCLES 237
The base of this parallelogram
is what part of the circumference
of the circle?
The altitude of the parallelogram is the same as the radius of
the circle.
Since the base of the parallelogram = ^ of the circumference
of the circle (which = 27rr), the base of the parallelogram = 7rr.
The area of the parallelogram = base X altitude or irrXr=7rr*.
But the area of the circle is the same as the area of the
parallelogram. Therefore the area of a circle = 7rr2.
PRINCIPLE: The area of a circle is equal to the square of
the radius multiplied by TT.
Exercise 11
1. Find the area of a circle 8 inches in diameter.
Solution: Radius of circle 8 inches in diameter =4 inches.
Area of circle=OT2 = 3.1416Xl6=50.2656.
Therefore the area of the circle =50.2656 square inches..
2. What is the area of a circle with a radius of 8 inches?
8. Find the area of a circle 3 feet in diameter?
4. Find the area of the 8-inch circle in
the diagram at the left. Find the area of the
12-inch circle. Find the area of the ring.
6. A cow is tethered to a stake in a grass
field by a rope 100 feet long attached to one
of its fore feet. What is the area in-
cluded within the sweep of the rope around the stake?
6. If the rope be attached to one of the hind feet of the
cow, giving the animal a reach of five feet more from the stake,
how much additional area will she have to graze over?
238 EIGHTH YEAR
7. A circular lake three miles in diameter is drained until
it is only two miles in diameter. What area has been reclaimed
by the receding of the water? Draw diagram.
8. By irrigation from a central artesian well, with radiating
ditches extending half a mile in each direction, a circular area
of arid land has been reclaimed. How many acres does it
contain? Draw diagram.
9* If the radiating ditches be extended to twice their length,
what will be the gain in irrigated area? Draw diagram.
10. Bottles two inches in diameter are packed in a box one
foot square, inside measure. How much of the area of the
bottom of the box is covered by the bottles? Would this be
the same if there were but one bottle, and if it were one foot
in diameter? Draw diagram.
11. A certain revolving searchlight illuminates the land to a
distance of five miles. What area is included in the circle of
its illumination?
12. A farmer builds a circular bam having a diameter of
40 feet. Its circular wall will have 3.1416 times the length of
the diameter. What will be the length of it? Suppose this
length of wall were used to enclose a square. What would be
the length of one of the sides? What would then be the area
of the bam?
13. What is the area of the circular bam? What is the gain
in area from having the bam circular in form?
14. A concrete side walk 3 feet wide surrounds a circular
fountain 15 feet in diameter. How many square feet are there
in the surface of the walk?
15. How many 3-inch circles for jelly glass Uds can be cut
from a rectangular piece of tin 24 inches wide and 36 inches
long? How many square inches are left in the waste pieces?
Have pupils bring to class other practical problems on circles.
PRACTICAL MEASUREMENTS— CIRCLES 239
16. Tbe square in the figure at the r^ht is said to be ciVcum-
scribed about the circle. The circle is said
to be inscribed in the square.
If the side of the square ia 12 inches,
what ia the area of the square?
What is the area of the inscribed circle?
17. Divide the area of the inscribed
circle by the area of the square. If your
work is accurate, the result should be .7854. That is, the area
of a circle is .7854 of a square with a side equal to the diameter.
18. From this fact we get the rule: To find the area of a
circle multiply the square of the diameter by .7854.
19. liind the areas of circles 6 inches, 8 inches and 12 inches
in diameter by this rule.
Exerdse 12. Review of Circles
1. How many square feet are there in the area of a circular
flower bed 7 feet in diameter?
3. Two girls made a set of doihes consisting of a center-
piece IS inches in diameter and 6 small doilies 5 inches in
diameter. How many inches of crochet edging did they have
to make to trim all the doilies in that manner?
S. How many square iaches of muslin were wasted in the
squares from which the doilies were cut?
4. Find the area of a circle 3 inches in diameter. Find the
area of a circle 6 inches in diameter. The area of the second
circle is how many times the area of the first circle?
5. In a 4-inch steam pipe the iron is j of an inch thick.
Find the area of the opening in the pipe.
6. Find the area of a cu-cular flower bed 8 feet in diameter.
Find its circumference.
240 EIGHTH YEAR
7. The cold air inlet for a furnace should have the same
area as the sum of the areas of the hot air pipes. If there are
six 6-inch hot air pipes leading from the furnace, what should
be the area of the cold air inlet?
8. If the cold air inlet is rectangular in shape and has a
length of 15 inches, what should be its width to furnish sufficient
air for the six furnace pipes?
9. A circular asbestos pad is 7 J inches in diameter. How
many of these pads can be made from a piece of asbestos padding
30 inches square? Draw a diagram to show the arrangement
of the circles.
10. How many square inches of waste material would be
left in cutting out these circular pads from the 30-inch square?
Hexagons
A regular hexagon is a six-sided figure with equal sides and
equal angles.
A regular hexagon may be inscribed in a
circle by taking the compass spread to the
length of the radius used in drawing the
circle and marking off six arcs intersecting
the circumference as shown in the figure at
the left. Then join the six points of division
as indicated to form the regular hexagon.
Exercise 13
1. Construct a regular hexagon with a
ruler and compass as directed above.
2. Divide the regular hexagon into six
triangles as shown in the figure at the left.
How do these six triangles compare in
size? Why?
PRACTICAL MEASUREMENTS— SOLIDS 241
8. Find the area of an equilateral triangle with a side
equal to 6 inches. (See page 238.)
4. Since the six equilateral triangles of the hexagon are all
equal, show how to find the area of a regular hexagon.
6. Find the area of a regular hexagon with each side equal
to 6 inches.
6. What is the perimeter of the regular hexagon described
in the preceding exercise?
7. Find the area of a hexagon with a perimeter of 48 inches.
Find the area of a square with the same perimeter. Also find
the area of a circle with a circumference of 48 inches. Which
figure contains the greatest area for the given perimeter?
8. Why do bees have hexagonalnshaped cells? Consider
both area and convenience of arrangement.
Measurements of Solids
We have been studying triangles, rectangles, trapezoids,
hexagons, circles, etc. All of these figures have two dimensions,
length and breadth. The term polygon is a general term,
meaning many-sided, which applies to all of these figures.
A figure which has three dimensions, length, breadth and
thickness, is called a solid.
The term solid does not mean that the figure be composed
of some compact material, for it may apply equally well to an
empty bin, box or jar.
There are certain solid figures with which we ought to be
familiar because we see them about us in daily life.
A prism is a soHd having two bases which are equal and
parallel and whose lateral (or side) faces are parallelograms.
The most common prisms are triangular and quadrangular.
242
EIGHTH YEAR
Triangular Prism Quadrangular Prism
Triangular glass prisms are used for bending rays of light.
They are used in some forms of opera glasses. The luxfer
prisms are used in upper parts of thrwinSows of large rooms
to bend and throw the light farther across the room. You
wiU find how a prism bends a ray of Hght in your science work.
The most common forms of quadrangular prisms are rec-
tangular solids such as bins, rooms (rectangular in shape),
boxes, freight cars, bricks, etc.
Exercise 14. Area of Surface of a Prism
In finding the area of the surface of a prism, we are using no
new principles. We simply find the areas of the two bases
and the areas of the lateral surfaces and add these to get the
total surface of the prism.
1. Find the total surface of a room 15 feet long, 12 feet wide
and 10 feet high.
2. What is the area of the surface of a triangular glass
prism 3 inches long and whose bases are equilateral triangles
with each side equal to 1 inch?
3. What is the area of the surface of a brick 8 in. x 4 in. x
2 in.?
4. What is the area of the surface of a rectangular block of
wood whose length is 4 feet and whose bases are 6 inches square?
6. Find the number of square inches of cardboard in a box
6 in. X 3^ in. X if in. without a top.
PRACTICAL MEASUREMENTS— PRISMS 243
Volumes of Prisms
If you made a quadrangular or rectangular
prism out of inch cubes as shown in the figure
which is 3 ini:»hes long, 3 inches wide and 3 inches
high; how many cubes would it take to make
one row along the bottom? How many such rows are there
in one layer? How many layers are there in the prism? How
many cubes are there in the volume of the prism? How
many inch cubes are there in the volume of the prism? The
volume of a prism is generally expressed in cubic units, though
it may be expressed in gallons, barrels, bushels, and various
other measures which are made up of a certain number of cubic
units. A short way of thinking the above process is:
PRINCIPLE: The volume of a prism is the product of the area
of the base and the altitude.
The above prism is a cube, which has 6 equal square faces.
The volume of the cube is equal to (3 X 3) X 3, or3*. The expres-
sion 3^ is read 3 cubed and means that the volume of a cube is
equal to the cube of its edge.
Exercise 16
1. What is the volume of a rectangular prism 12 inches long,
8 inches wide and 6 inches high?
2. How many cubic feet are there in a box 4 feet long,
3 feet wide and 2§ feet high?
3. How many cubic inches are there in a brick? (A brick
is 8^ inches long, 4 inches wide and 2^ inches thick.)
4. How many cubic inches are there in a cubic foot? How
many bricks would make a cubic foot if there was no mortar
between them? 22 bricks are figured as making a cubic foot
of wall. How many bricks are saved by the space occupied
by the mortar?
244 EIGHTH YEAR
6. An excavation for a house is 40 feet long, 32 feet wide
and 4 feet deep. How many loads of .earth were removed?
(1 cubic yard = 1 load.)
6. A bin is 20 feet long, 8 feet wide and 6 feet deep. How
many bushels of wheat will it hold? (1 bushel = how many
cubic inches?)
7. What is the volume in cubic feet of a rectangular horse
trough 6 feet long, 3 feet wide and 2^ feet deep?
8. How many gallons will the tank in Problem 7 hold?
(1 cubic foot = how many gallons?)
9. The swimming tank in a certain club house is 40 feet
long, 20 feet wide and has a uniform depth of 5 feet. How
many gallons of water are there in this tank?
10. A freight car is 30 feet long, 8^ feet wide and 4 feet deep.
How many tons of anthracite coal will it hold if 1 ton of anthra-
cite coal occupies 34 cubic feet of space?
11.* A rectangular block of ice is 30 inches long, 24 inches
wide and 9 inches thick. How much will it weigh if a cubic
foot of ice weighs 57.5 pounds?
12. An excavation for a house contains 6000 cubic feet.
If it is 40 feet long and 30 feet wide, how deep is it?
13. A bin 22^ feet long and 6 feet wide must be how deep
to contain 576 bushels, estimating the bushel at 1 j cubic feet?
14. A wagon box is found to have the following inside
measurements: 36 inches wide, 26 inches high and 10 feet
4 inches long. How many bushels of com on the cob will it
hold if 4000 cubic inches of corn on the cob = 1 bushel?
16. A rectangular com crib 20 feet long and 12 feet wide is
filled with ear com to a depth of 10 feet. How many bushels
of com does the crib hold?
PRACTICAL MEASUREMENTS— FARM PROBLEMS 245
Exercise 16
Problems Prepared by a Fanner
1. I sold my neighbor a crib of com 20 feet long, 9 feet
4 inches wide and 10 feet 2 inches high. How many bushels
of com were in this crib, counting 4000 cubic inches to the
bushel?
2. A neighbor asked me to help him measure three cribs
of com which he had sold. We found the cribs to measure as
follows:
Crib 1 — 9 ft. 3 in. long, 9 ft. 1 in. wide, 8 ft. 5 in. high.
Crib 2—9 ft. 3 in. long, 8 ft. 11 in. wide, 8 ft, 4 in. high.
Crib 3 — 9 ft. 4 in. long, 8 ft. 11 in. wide, 8 ft. 4 in. high.
How many bushels were there in the three cribs? (4000 cubic
inches = 1 bushel.)
8. How many bushels of com are there in a frame crib
20 feet long, 10 feet wide and 9 feet high if there are 20 studding
2''x4''x9 feet long to be deducted from the contents on account
of bemg on the inside of the crib?
4. I sold 20 wagon loads of com to be measured in wagons,
counting 4000 Cubic inches per bushel. How many bushels
were there in the 20 loads if the wagon box was 10 feet 6 inches
long, 3 feet 1 inch wide and 2 feet 1 inch high?
6. How many tons of hay are there in a mow 36 feet long,
14 feet wide and 17 feet high, allowing 512 cubic feet per ton?
6. I sold a stack of hay which was 24 feet long, 14 feet wide
and had an average height of 15 feet. How much did I receive
for the hay at $10 per ton? (Allow 512 cubic feet per ton.)
7. How many tons of hay are there in a mow 32 feet 6 inches
long, 12 feet 8 inches wide and 14 feet high?
246 EIGHTH YEAR
Cylinder
A cylinder is a solid bounded by a uniformly
curved surface and two parallel circular bases.
The cylinder, on account of the small amount
of material in its walls, is one of the most common
of the solid forms in practical use. Cisterns, stove
pipes, water pipes, hot water tanks, boilers and
^ ^ silos are usually cylindrical in shape.
PRINCIPLE: The Yoltune of a cylinder is equal to the area of
the circular base multiplied by the altitude (or height).
Exercise 17
1. Find the volume of a cylinder whose base is 6 inches in
diameter and whose altitude is 20 inches.
2. A cistern is 6 feet in diameter and 8 feet deep. How
many gallons of water will it hold? (1 cubic foot = 7.5 gallons.)
3. A barber once gave me this problem. "I have a hot-water
tank 14 inches in diameter and 60 inches high. How many
gallons of water does it hold?" What answer should I have
given him?
4. A fanner has a silo 12 feet in diameter and 35 feet high.
How many tons of silage will it hold, counting 34 pounds to
the cubic foot?
5. A cylindrical boiler is 3 feet in diameter and 12 feet
long. If it is half full of water, how much water does it contain?
6. A bushel measure contains 2150.42 cubic inches. If it
is 12 inches in diameter, how high is it?
7. A cylindrical bucket 8 inches in diameter and 15 inches
high will hold how many gallons?
8. Bring to class for solution any problems you can find
on the volumes of cylinders, such as gasoline tanks, cisterns,
. standpipes, stock watering tanks, etc.
PRACTICAL MEASUBEMENTS— THE SILO 247
The silo is one
of the chief factora
in successful dairy-
ing and cattle ris-
ing. It is usually
filled with com, the
stalks and ears be-
ing chopped up
while still green.
To secure the
for the beat preser-
vation of sil^e, the silo should be of a height equal to at least
twice its diameter. The greater the height of the silo, the
greater will be the weight of the ;^lage and the more it will be
compressed. The cylindrical form allows the greatest area in
proportion to the wall space and also offers less friction in the
settling of the silage.
Exercise 18
1. If the silo in the above illustration is 14 feet in diameter
Eind filled to s depth of 28 feet, what is the total weight of the
silage, the average weight being 38 pounds per cubic foot?
2. How many days will this silage last a herd of 20 cows,
allowing each cow 35 pounds each day?
S. How long will a silo 15 feet in diameter and filled to a
depth of 32 feet feed a herd of 30 cattle, allowing 1 cubic foot
of silage for each head?
4. In order to prevent silage from spoiling, a layer 1 ^ inches
deep must be fed each day. If my silo is 12 feet in diameter
and filled to such a depth that it weighs 36 pounds per cubic ■
248 EIGHTH YEAR
foot, how many cows should I keep to feed a layer of that
depth, allowing each cow 38 pounds each day?
The weight of silage varies from about 32 pounds per cubic
foot for 18 feet in depth to about 43 pounds per cubic foot for
a depth of 36 feet.
B. A certwi silo is 14 feet in diameter and is filled with sil^e
to a depth of 25 feet. U the silage weighs 36^ pounds per
cubic foot, what is the amount of it in tons?
6. How long will this silage last a herd of 24 cows, allowing
each cow 40 pounds each day?
7. I wish to build a silo large enough to supply a herd of
20 cows for 190 days. Plan the dimensions for a cylindrical
silo, allowing about 1 cubic foot per day for each cow. (See
Problem 4 for minimum depth that must be fed each day to keep
the silage from spoiling.)
nUUGATION
Elephant Butte Dam, New Mesico
The Elephant Butte Dam, built across the Rio Grande
' River in New Mexico by the United States Reclamation Service
IRRIGATION 249
is 1250 feet long and 200 feet high. It is 18 feet wide at the top
and 215 feet wide at the bottom. 610,000 cubic yards of
masonry were used in the construction of this immense dam.
Water for irrigation is measured by the acre^foot, which is
the amount of water necessary to cover an acre to a depth of
one foot.
Exercise 19
!• An acre-foot is equal to how many cubic feet of water?
2. The storage capacity of the Elephant Butte Reservoir
is 2,642,292 acre-feet. This is equal to how many cubic feet
of water?
3. What is the storage capacity in gallons of this reservoir?
4. The state of Connecticut has an area of 4965 square
miles. How deep would the water stored in the Elephant
Butte Reservoir cover an area equal to the state of Connecticut?
5. The water surface of this reservoir is 42,000 acres. Find
the average depth of water in the reservoir.
6. The Roosevelt Dam in the Salt River Valley of Arizona
stores up 1,284,200 acre-feet. The surface of this reservoir is
16,329 acres. What is the average depth of the reservoir?
7. It is estimated that 27,000 horse power of electric energy
can be developed from the water in the Roosevelt Reservoir.
If this energy is worth $50 per horse power per year, how much
revenue would this yield per year if it were all used?
8. A weir (a device for measuring the amount of water)
shows that a certain box in an irrigation canal is delivering
water at the rate of 2 cubic feet per second. How long will it
take to irrigate 40 acres of land, supplying ^ of an acre-foot per
acre?
260
EIGHTH YEAR
9. Land was offered in the Salt River Valley, Arizona, at
$30 per acre before the Roosevelt Dam was built. Unimproved
land sold at about $100 per acre after the irrigation system
was completed. The area of the completed system is 250,000
acres. Find the increase in the value of the land as a result of
the building of this dam.
10. A farmer raised 8 tons of alfalfa hay per acre on irrigated
land worth $200 per acre. He sold this hay at $10 per ton. If
his expenses were $25 per acre, what were his profits on a field
of 20 acres of alfalfa? What per cent was this on the value of
the land?
11. A truck farmer planted a 10-acre irrigated tract in pota-
toes on Feb. 10. He harvested this crop on May 10, making
a profit of $100 per acre. On July 25 he planted com and in
the autumn of that year sold the roasting ears so as to yield
a profit of $60 an acre. What was the. total profit on the 10-
acre tract for that year?
12. Find other examples of irrigation projects and make
problems similar to the ones in this exercise.
GOOD ROADS
The Lincoln Highway
When the Lincoln Highway is finished from New York to
San Francisco, it will be a magnificent and useful memorial to
the great president for whom it was named. This road is
planned to be concrete throughout its entire length of over
3000 miles.
GOOD ROADS
Exercise 20
1. In 1916 the distance on the Lincoln Highway from New
York to San Francisco was 3331 miles. How many days will
it take a touring party to make the journey if th^ drive 8
hours per day at an average speed of 15 miles per hour?
3. The distance from Boston to New York by road is 234
miles. How far is it from Boston to San Fraacisco by way <A
the Lincoln Highway?
8. Of the distance from New York to western Indiana,
659 of the 802 miles of the Lincohi Highway are hard roads.
How much will it cost to complete the rest of this section of the
road at $12,000 a mile?
i. U the average cost for concrete roads b S13,000 per mile,
what will be the total cost of the Llncohi Highway from New
York to San Francisco when completed?
B. Mention other important state and national highways
with which you are familiar.
Exercise 21. The Construction of Good Roods
1. The maximum grade
of ascent or descent for im-
poHant roads has been
fixed, generally, at 5%, or
5 feet of rise or fall hi 100
feet of length. For a rise
of 528 feet, what would be
the length of road, at this
maximum grade?
s. Gutter grades, at the
Sides of roadways, should
have a minimum fall of 6 inches in 100 feet to the culverts.
If the culverts are 600 feet apart, how much will the gutters
8k)pe to meet them at this minimum fall?
252 EIGHTH YEAR
3. For a road 15 feet or less in width, the middle line, or
crown, should be 5 j inches higher than the sides. For a greater
width of road, the crown should be raised ^ inch for each foot
of distance from the boundary. What should be the height
of the crown of a road 18 feet wide? — ^24 feet wide?
4. A road commission found that 26,509 square yards of
concrete roads cost $23,154. If the roads averaged 15 feet wide,
find the average cost per mile of the concrete roads in that
locality.
5. The same commission found that 13,699 square yards of
brick-paved roads cost $20,294. Find the cost of brick pave-
ment per mile for an 18-foot surface.
6. 651,123 square yards of macadam roads were found to
cost $401,470. Find the cost per mile of a 15-foot macadam
road.
7. A tar binder is often placed on macadam roads to hold
the fine particles of crushed stone together. About 2 gallons
are required for each square yard. If the binder costs 8 cents
per gallon, what will be the cost of the binder for a mile of
macadam road 15 feet wide?
8. The earth work on a certain road averaged about 5§60
cubic yards per mile. Find the cost of this earthwork at 28.5
cents per cubic yard.
9. In building a burnt-clay road in the South for 300 feet
as a test, the following expenses yrere incurred:
30 J cords of wood at $1.30 per cord;
20 loads of bark, chips, etc. at 30 cents per load;
Expenses for labor and teams^ — $38.30.
What was the cost of the 300-foot road? What would a
mile of this road cost at the same rate?
10. If a ton of broken rock for a macadam road will cover
3.13 square yards of surface, how many tons of this material
GOOD ROADS 253
will be required for a macadam road a mile long and 15 feet
wide covering it to the same depth?
11. A county road commission decides to build 4 miles of
macadam roads each year at an estimated average cost of
$7600 per mile. The state pays ^ of this expense. If the
assessed valuation of the county is $3,800,000, what will be
the tax rate for hard roads in this county?
r—T'CT- — — r- ^'-O- ^ — 7^^— ^T
Cross Section of a Concrete Road
Concrete for road purposes should consist of a mixture of
1 part of cement to 2 parts of sand to 3§ parts of gravel or
crushed stone.
12. The cross section of the concrete road shown in the
diagram shows the concrete to be 6 inches thick. How many
cubic yards of concrete are there in a mile of this road?
13. The crown of this road shows a fall of 3 inches in half
the width of the road. Find the fall per foot.
14. Under each edge of the concrete a longitudinal drain
ditch is dug and filled with loose stone. How many cubic
yards of stone will it take to fill a mile of these ditches if they
are S'^xlO''?
15. How much stone will it take to fill 120 lateral drains for
each side of the road per mile, the drains being 8'^xl0''xl0'?
16. How much would the stone cost for both longitudinal
and lateral drains at $1.00 per cubic yard?
17. How much would it cost to haul this stone at 50 cents
per cubic yard?
18. How much would the concrete cost for a mile of this road
at $6.00 per cubic yard?
EIGHTH YEAR
Mr. Davis lives 2 miles from a hard road on which there is
no grade exceeding 5%. A certdn city, where he markets his
produce, is located on the hard road 6 miles from the point
where his branch road meets the hard road. Mr. Davis sold
his crop of 1260 bushels of wheat to a firm in the city.
19. The road leading from his farm to the good road was so
rough and hilly that he could only haul 18 two-bushel sacks
of wheat to a load. How many such loads would he have had
to haul to market the wheat in this manner?
20. If he had hauled two loads per day, what would have
been the cost of hauling in this way, counting Mr. Davis and
his team as worth $4.00 per day? Find the cost per bushel.
31. On the good road a team could haul 35 sacks of 2 bushels
each at a load. Had the good road extended to his farm, what
would have been the cost of marketing the wheat at $4.00 per
day for 2 loads? Find the cost per bushel.
32. Comj)are the cost per bushel for hauling on a good road
with the cost per bushel on the unimproved road.
38. Mr. Davis decided to hire an extra team to haul sacks
from his farm to be transfered to his w^on at the hard road.
He then hauled the large loads from that point to the city. By
this system they marketed the wheat in 6 days. At $4.00 per
day, for each team, find the coat of marketing the wheat in
this way.
24. How much was saved over the method described in
Problem 19?
CHAPTER V
GRAPHS
Graphs are used so extensively to illustrate statistics that a
knowledge of how to make them and how to read and interpret
them should be obtained by every one.
The Pictorial Graph
The pictorifil graph uses
pictures of the things to
be compared, showing dif-
ferences in the numbers
of the tliii^ by the relative
sizes of the pictures. In
the pictorial graph in the „ ^__ _ _ , ^ . „. ..
'^ o- r Courtesw Office of EipeniriBiitatftUom,
illustration a comparison is u. s. Depdrtment of Agncuitu™
made of the eggs laid by a hen the first year (Fig. 1), the sec-
ond year (Fig. 2) and the third year (Fig. 3) . Which year was
the most productive? How many ^gs did the ben lay each
year? The exact number
of eggs can not be told by
such a graph. Such a graph
merely enables us to get a
general impression of the
numbers compared.
Pictorial graphs are much
improved when the num-
bers represented by the pi(v
tures are also shown in the
graph. The graph at the
left shows an improved
~Coart«y InWrn.tion.1 Harve.Wr Co. tyP^ of pictorial graph.
255
256
EIGHTH YEAR
The Line Graph
A line graph is a much more accurate way of representing
certain kinds of statistics. Line graphs are also much more
easily made than pictorial graphs.
Suppose that the wholesale prices of eggs for a certain year
are to be represented by a line graph. The prices averaged
as follows for the different months: Jan. 30i; Feb. 2Qi; Mar.
24f{; Apr. 18f{; May 17f{; June 17ff; July 17ft; Aug. 17^; Sept.
19ff; Oct. 22j4; Nov. 25j4; and Dec. 29ff.
On the cross section paper let the vertical lines represent the
different months and the horizontal lines represent the prices
from to 36, increasing 4 cents from one horizontal line to
another.
On the January vertical line a
dot is placed half-way between the
28|!t line and the 32^ Une, thus
representing 30ff for January. On
the February line a dot is placed
one-fourth of the distance from the
28ff line to the 32f!f Une, representing
29^ for February. After the dots
for all the months have been located
in this manner, a broken line is
drawn to connect them. This graph represents very clearly
the fall and rise in the prices of eggs during that year.
1
lit
in
t 1
» 3 " « I
■ < ui o a
•1
1
M
\
■■
^
J
\
4
/
V
y
iT
\
.^
^
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'
Exercise 1
1. From this graph give the wholesale prices of eggs for the
following months: March, April, July, September, October,
November and December.
2. During what four months did the average price of eggs
remain the same?
GRAPHS 257
3. How did the decline in price from February to April
compare with the rise in price from August to December?
4. The production of coal in long tons for the United States
for the years 1905 to 1914 was as follows:
Year
Anthracite
Bituminoua
1905
69,405,958
281,230,252
1906
63,898,803
306,084,481
1907
76,487,860
352,408,054
1908
74,384,297
296,903,826
190»
72,443,624
338,987,997
1910
75,514,296
372,339,703
Iftll
80,859,489
362,195,125
1912
75,398,369
401,803,934
1913
81,780,067
427,190,573
1914
81,090,631
377,414,259
Suppose that we represent the
years on the vertical lines. The next
step is to determine how many tons
are to be represented by the distance
from one horizontal line to another.
Suppose that we decide on a graph
19 squares high. The smallest num-
ber of tons is 63,698,803 and the largest number is 427,190,573,
the difference between these numbers being 363,491,770.
Dividing the difference by 19, we find that the most convenient
number to represent the distance from one horizontal line to
another is 20,000,000. The numbers in the table can be plotted
only approximately. 69,405,958, the first number of tons of
anthracite coal, may be represented by a dot slightly less than
half-way from the 60,000,000 line to the 80,000,000 line.
Draw the graphs for both anthracite and bituminous, repre-
senting the anthracite by a solid line and the bituminous by
a dotted line. Compare your graph with the one in the book.
In which one of these kinds of coal did the production increase
more rapidly during this period?
258 EIGHTH YEAR
6. A pupil made the following grades on his practice exer-
cises for two weeks: Feb. 1, 80; Feb. 2, 87; Feb. 6, 100; Feb. 6,
83; Feb. 7, 78; Feb. 8, 93; Feb. 9, 100; Feb. 12, 93; Feb. 13, 97;
Feb. 14> 100. Draw a line graph to show his record.
6. The immigration into the United States each year since
1907 is shown in the table at the
J5^;;;;;;;;;;^^782SJ left. Draw a line graph to show
1909. ,,,..,... 751786 *^® increases and decreases for the
1910 1,041,570 various years. In what year during
1911 878,587 this period was immigration largest?
^^^2 838,172 What year shows the least number
1913 1,197,892 .. _._ x o rr i ,.
-g- . 1 218 480 unmigrants? How do you account
1915 .......... 326 Voo ^^^ ^^® rapid drop for the years
1916 298^826 1915 and 1916?
7. The cost per pupil for education in the United States
for the years 1901 to 1914 is
1901 $21.23 1908 $30.55 , • xu x ui n/r i
1902 21.53 1909 31.65 shown m the table Make
1903 22.75 1910 33.33 ^ lin^ graph to show the
1904 24.14 1911 34.71 costs for the various years.
1905 25.40 1912 36.30 What does the graph show
1906 26.27 1913 38.31 ^bout the cost per pupil for
^^ 28.25 1914 39.04 ^i^i, p^^od? "^ ^ ^
8. Keep a record of the tt^mperature at 9:00 o'clock at the
school house for a month and plot the graph for the temperature
record for that month.
The Bar Graph
The bar graph is one of the easiest to construct and interpret.
For comparative purposes it is superior to other forms of
graphs because the size of a number is shown by the length
of the bar. Thus only one dimension has to be considered,
while in pictorial graphs two or three dimensions must be
considered.
The illustration at the
right shows a typical bar
graph. The lei^hs of the
bars are drawn to represent
the numbers written at the
right of each. In this graph
the longest bar is one inch
and represents 5.4 tons.
The bar representing brome
grass (1.3 tons) must then
be drawn approximately
^ inch long, and the bars
representil^ the yields of Couiuay IntenuxJaiutl HurvesUr Ca
clover and timothy must be drawn to the same scale.
Exercise 2
1. Draw a bar graph showing the comparative values of
the products of the leading industries in the United Statea for
a recent year as shown in the followiI^; table:
Industry Value of Product
1. SUughterii^ and packing $1,370,568,000
2. Foundriea and machine ehopa 1,228,475,000
8. Lumber and timber 1,166,120,000
4. Iron and flteel 985,723,000
5. Flour and grist mills 883,684,000
6. Printing and publishing 737,876,000
7. Cotton goods 628,392,000
8. Men'a clothing 668,077,000
Suggestion: A suitable scale for determining the length of the bars
in the above problem is 1 inch =$300,000,000.
a. In 1900, 40.5% of the inhabitants of the United States
were Uving in cities of 2500 or more inhabitants. In 1910,
46.3% of the people were living in cities of this size. Show the
comparison between these two years by a bar graph.
280 EIGHTH YEAR
S. Draw a bar graph representing the production for
crude petroleum in the United States as shown in the table:
1904 4,916,663,682 1910 8,801,364,016
1905 5,658,138,360 1911 9,258,874,422
1906 5,312,745,312 1912 9,328,756,156
1907 6,976,004,070 1913 10,434,740,660
1908 7,498,148,910 1914 11,162,026,470
1909 7,649,639,508 1915 .16,806,372,368
The Distribution Graph
Another form of graph used extensively by the United States
government in its reports
is the distribution graph.
The distribution graph in.
the illustration shows the
distribution of poultry in
the United States. Each
dot in this graph repre-
sents 1,000,000 fowls.
The first Step in the con-
struction of such a graph is
to determine the number for each dot. Then determine the
number of dots for each state and arrange them in some syste-
matic order. From the distribution graph for poultry, name the
chief poultry-producing states in our country.
Exercise 3
1. Find the population for each county in your state and
make a distribution graph showing the distribution of popula-
tion in your state.
2. On a map of the United States draw a distribution graph
showing the distribution of horses in the United States according
to the census of 1910, which was as follows:
GRAPHS
261
California 445,349
Kentucky 425,884
Tenneaaee 333,025
Virginia 318,831
Montana 304,21
Colorado 284,647
Washington... 2eg,S01
Oregon 261,627
Arkansas 245,861
Miasistiippi . . .
West Virginia. 176,530
Louisiana 175,814
New Mexico . . 175,057
N.Carolina... 162,783
Wyoming 150,98
so that you will get at least one dot tor Rhode
Island. Make your number per dot as large as passible, however, so that
there will not be so many dots for the states containing large numbers.
Iowa
.1,449,652
lUinoia
.1,402,649
Texas
.1.125,834
Kansas
.1,099,738
Missouri . . .
.1,035,884
Nebraska..
. 971,279
Ohio
. 888,027
Indiana, . . .
. 785,954
Minnesota. .
. 738,578
Oklahoma. .
. 708,848
S. Dakota. .
, 645,639
N. Dakota.
. 625,984
V'isconsin. .
. 608,657
Michigan. .
. 602,410
New York.
,. 587,393
Plan your numbers
Maryland 150,159
Alabama 132,611
soTpa 118,583
Utah 111,135
107,210
Arizona 93,803
New Jersey. .. 88,239
Vermont 80,556
South Carolina 79,105
Nevada 65,717
Massachusetts. 64,109
Connecticut... 46,248
46,154
Florida 45,029
Delaware 31,943
Rhode Island. 9,527
The Circle Graph
The circle graph at the right rep-
resents the approximate per cents
of the different food substances in
peanuts.
The circumference of a circle is
divided into 360 equal parts called
degrees. The angle showing the pro-
portion of fat cuts off 29.1% of 360 degrees (360°) or 104.76°.
1. Find the nmnber of degrees in the angles for each of
the other food substances in the peanut.
2. In alfalfa 65% of the food value is in the leaves and
35% in the stem. Draw a circle graph to show the relative
proportions of each. Use a protractor to lay out the angles.
CHAPTER VI
PRACTICAL MEASURING INSTRUMENTS
The Thermometer
i The Fahrenheit thermometer is the standard
measm« of temperature m the United States.
A thermometer consists of a small glass tube
ending in either a spherical or a cylindrical bulb.
At the temperature of your room, the bulb and
part of the tube is filled with a liquid (usually
mercury).
Hold the bulb of a thermometer at your mouth
and slowly blow on it. What happens to the
mercury? The heat from your mouth has caused
the mercury to expand. Hold the bulb for a
few moments in some cold water. What change
has taken place in the column of mercury in
the tube?
The thermometer can thus be used to measure
the temperature of the air and certain liquids.
There are two important points on a Fahrenheit
thermometer: the freezing point of water, which
A Standard jg marked 32° above zero, and the boiling point
"^ of water, which is marked 212° above zero.
Most scientists use the Centigrade thermometer, which has
the freezing point marked 0° and the boiling point marked 100°.
Exercise 1
1. Find from a physics book or the encyclopedia how a
thermometer is made. Explain to the class how the freezing
and boilii^ points are found.
PRACTICAL MEASURING INSTRUMENTS 263
2. How many d^rees are there between the freezing and
boiling points'on a Fahrenheit thermometer?
In order that temperatm'es above and below zero may be
distinguished, the signs + and — are usually used; +20°
meaning 20° above zero and —20° meaning 20° below zero.
8. What is the difference in degrees between a temperature
of +20° and a temperature of -20°?
4. At a certain city the temperature on a certain day at
noon was 25°. At midnight of the following day the tempera-
ture was —4°. How many degrees had the temperaturefallen?
Give the changes in the temperature indicated by the follow-
mg readings:
5. +50° to +32^ 9. - 5° to +10^ 18. +4(f to +101°
6. +15° to- 2r 10. +32°to+98§° 14. - r to- 16^
7. +77° to +92^ 11. + 2° to +36° 16. -16° to+ 15^
8. +60° to +43° 12. -20° to +32° 16. +98§°to+10l|°
At government observatories, the temperature is taken each
hour. The f ollowii^ extract from a daily paper shows a portion
of the weather record in a certain city on Feb. 9, 1917:
12 midnight 4 7 a. m — 1
1 a. m 3 8 a. m — 2
2 a. m 2 9 a. m
3 a. m 1 10 a. m 2
4 a. m 11 a. m 4
5 a. m — 1 12 noon 4
6 a. m — 1
17. What was the maximum, or highest, temperature during
the time indicated?
18. What was the minimum, or lowest, temperature?
19. What was the range or change in temperature during
the 12 hours indicated?
>o
:o
264 EIGHTH YEAR
SO. Keep a d^y record of the outade temperature at the
school house. Leave this for the pupils of next year's class.
They vill be able to make some interesting comparisons with
the record that they are keeping.
The Barometer
A barometer is an instrument to measure the
pressure of the air.
A simple barometer may be made by inverting
a tube, filled with mercury, in a dish of mercury.
If the tube is longer than 30 inches, the mercury will
drop from the end of the tube, leaving a vacuum
above it. The pressure of the. air on the surface
of the mercury in the dish will support a column of
mercury 30 inches high at sea level. If one goes up
in a balloon or climbs a mountain, the column of
mercury in the tube will gradually fall because
the higher above sea level one rises the less air there
is to press down.
The barometer is a very important instrument
in predicting weather conditions. When the
barometer is very law, stormy weather usually
A Standard resulte, and when the barometer is extremely high,
Barometer fair weather usually results.
Exercise 2
1. Suppose the barometer tube has an area of 1 square
inch at the base, and the air supports a column of mercury
30 inches high. How much is the pressure of the air per square
inch, if mercury weighs .49 pound per cubic inch?
Solution: A column of mercury 1 square inch at the base and 30 inches
high contains 30 cubic inchee. 30X.49 pounds = 14.7 pounds. Since the
column of mercury weighs 14.7 pounds, the air pressure must be 14.7
pounds on each square inch of surface.
PRACTICAL MEASURING INSTRUMENTS 265
2. Find the number of square inches on the top of your
desk. How much pressure does the air exert on the top of this
desk?
8. The area of an average person's body is 30 square feet.
Find the total pressure, which the air is exerting on our bodies.
Our bodies are built to withstand this enormous pressure.
If we go up a high mountain, the outside pressure becomes so
much less that the pressure of the blood is apt to break the
blood vessels, and bleeding at the nose and ears often results.
The Hygrometer
It is important not only to know whether the
air is light or heavy as shown by the barometer,
but also to know how much moisture it contains.
The instrument for measuring the amount of
moisture in the air is called a hygrometer.
One of the common forms of hygrometers is the
wet and dry bulb type. One of the thermometers
is an ordinary thermometer; the other thermom-
eter has its bulb covered with a wick which is
dipping in a can of water. Evaporation of any liquid has
a cooling effect. Drop some gasoline on the back of your
hand and see how cool it feels when it is evaporating into the
air. If there is a very little moisture in the air, the water will
evaporate rapidly from the wick and cool it. The tyei ther^
mometer will then read lower than the dry thermometer.
If there is a great deal of moisture in the air, the evaporation
will not be so rapid and the difference in the readings of the two
thermometers will not be so great. By the use of tables pre-
pared for this hygrometer, the amount of moisture in the an-
can be found.
The amoimt of moisture in the air is expressed in terms of its
reiative humidity. If we say that the relative humidity of the
EIGHTH YEAR
air is 65%, that means that the air now contains 65% as much
moisture as it is capable of holding. The relative humidity
of a livii^ room should be between 50% and 65%. If the air
gets too dry, moisture will evaporate too rapidly from the
body and chill the skin. The pores of the skin will then be
closed, preventing the elimioatioa of certain waste products
through the glands of the skin. If the air of a room is too dry,
an open vessel containing water should be placed on the stove
or radiator to supply the necessary moisture.
WEATHER REPORTS
WEATHER FORECAST
For City and vicioity—
Partly oloudy WedDBi-
day and Thunday,
probably loo.l Ibun-
dcnhciwars. coatinued
warm WedaMday; not
■a warm Thundsy;
Wodnesday. beoomiiif
variable 'Hiursday.
For Central territm^-
Partly oloudy Wed-
ueadav and TburHJay,
probably local thua-
I TEMPER ATI! RB
■SI
itZ-
■ti
iV.m'.'.
A Daily PapH'a Weather Rmid.
One of the most
beneficial depart-
ments of our govern-
ment is the weather
bureau. By means
of observations taken
in various cities scat-
tered all over the
country, weather fore-
casts can be made
which save farmers
and shippers thou-
sands of dollars.
The weather record
of the preceding day
is shown at the left
as it appeared on a
certain day in a large
daily paper. We have
now studied some of
the instruments which
are used in makii^
these observations.
PRACTICAL MEASURING INSTRUMENTS 267
By reference to the above record answer the following ques-
tions:
1. What was the mean temperature for the day?
2. Was this temperature wanner or cooler than is usually
observed on this particular day of the year?
8. What was the difference between the maximum and
the minimum temperature for the day?
4. Has the weather during this year since Jan. 1 been
warmer or cooler than the average year's temperature?
6. Did any rain fall during the day? Has as much rain
fallen during this year since Jan. 1 as is usually observed?
(The amount of rainfall is measured each day by the amount of water
falling in an open vessel with perpendicular sides.)
6. From what direction was the wind blowing? What
was its velocity?
(The velocity of the wind is measiu^ by an instrument called an
anemjofmeUr^ which may be described as a cupnshaped windmill so arranged
that it shows the velocity of the wind by the rapidity with which the
wind makes it revolve.)
?• What was the relative humidity of the air at 7 a. m.?
At 7 p. m.? Explain what is meant by relative humidity f
8. What was the change in the pressure of the air, as
measured by the barometer, between 7 a. m. and 7 p. m.?
9. From the preceding observations and other similar
ones made in other cities scattered over the country, the weather
forecaster makes predictions on what the weather will be.
What was hip forecast?
10. Bring in other daily records clipped from your daily
papers an^ compare the records and forecasts with this one.
268 EIGHTH YEAR
Uses of Weafher Reports
By taking observations over this country and Canada,
forecasters are able to warn farmers and shippers of storms
and cold waves. Rain storms usually sweep over the country
from the southwest to the northeast, taking several days to
travel across the country. Farmers can thus be warned of
an approaching storm and make their plans accordingly.
Shippers pack perishable produce in cars to withstand certain
temperatures. If a cold wave is approaching, they must pack
their cars to withstand the lower temperature. In the summer,
more ice must be put in the refrigerator cars if a hot wave is
approaching. The government issues bulletins to shippers
telling them what temperatures they may expect.
Exercise 4
1. A farmer had, in process of curing, five acres of new mown
hay. Counting on fair weather and failing to profit by his
daily paper's "Weather Forecast," he had his crop damaged to
the extent of 35% during an unexpected rainstorm. How
much did he lose, on 11 tons of hay, counting the full market
value at $11.40 per ton?
2. In a certain fruit belt the temperature dropped unex-
pectedly, over night, from 51 degrees to 30 degrees above zero.
The peach crop that year in a certain locality yielded 3768
baskets. In the season following, under normal conditions,
the yield was 7348 baskets. What was this increased product
worth at 55^ per basket?
3. In some localities the temperature of the air is kept
higher by building fires all over an orchard. If the fruit growers
in the locality described in the preceding problem had heeded
the warning issued by the government and built suitable fires,
how much loss might they have prevented? ,
PRACTICAL MEASURING INSTRUMENTS 269
4. A farmer observed that the weather report said: "Con-
tinued dry weather may be expected." He draped an old
mower wheel between the rows of his com, thus forming a mulch
and conserving the moisture in the ground by preventing its
evaporation. His jrield was 40 bushels per acre. Another
farmer who paid no attention to the reports of the weather
bureau and knew nothing of dry farming methods plowed his
com deep and his ground dried out so that his yield was only
25 bushels per acre. If both farmers had equally good land
and prospects for com, how much did the first farmer make
per acre by dragging his corn, if it sold for 75f5 per bushel?
6. The precipitation ih a certain township in one season
was 26.8 inches. The wheat yield that year in the township
aggregated 137,540 bushels. In the succeeding year the pre-
cipitation during the same period was 19.7 inches, and the
wheat yield aggregated 68,430 bushels. What was the differ-
ence in the value of the crops at 95f5 per bushel?
6. A gallon contains 231 cubic inches. An acre of ground
contains 43,560 square feet. What would be the weight, in
tons, of a rainfall of one inch in depth over a quarter-section of
land, estimating the weight of each gallon of water at 8§
pounds?
7. A fruit grower in Georgia shipped a carload of peaches
which were damaged by a hot wave striking the country while
the car was on the way. Having insufficient ice to withstand
the hot wave, the peaches were damaged 2b^ per bushel. If
the car contained 420 bushels of peaches, what was the shipper's
loss due to the change of weather? He might have prevented
this loss if he had heeded the government's warning.
8. Tell of any instances in which you have heard of farmers
or fruit growers profiting by the weather reports m the news-
papers.
9. Bring to class newspapers containing weather reports.
270 EIGHTH YEAR
THE ELECTRIC METER
If we bum coal under a boiler, we generate steam. This
steam may be used to run a steam engine which in turn may
run a dynamo which generates an electrical current. This
electric current supplies the power for electric lights, electric
motors and runs our street cars and interurban lines.
Steam engines and gas engines are generally rated by the
horse power in this country. We say the engine in an automo-
bile is 40 horse power or 60 horse power.
■
Electric energy is measured in terms of kilowaUs. A kilowatt
is equal to 1 J horse power. Thus an engine rated at 40 horse
power would be rated at 30 kilowatts.
Electric light companies generally measure the current you
use in terms of kilowatt-hours. A kilowatt-hour is equal to
the use of 1 kilowatt of energy for 1 hour. For clearness we
may say that a kilowatt-hour is equal to the energy which a
good horse would supply in working steadily for 1^ hours.
Electric meters are instruments used to measure the amount of
electrical energy which we use.
How to Read an Electric Meter
Beginning at the left
indicator on the dial we see
that the reading is some-
where between 2000 and
3000 because over this dial
we see that these figures are
read in thousands. Going to the right we see hundreds, tens,
ones, and tenths dials. We can easily read such a dial because
it is just like writing numbers with figures in thousands, hun-
dreds, tens, units and tenths. As we read the dial we take the
figure that the dial is at or has just passed. The reading is
2438 kilowatt-hours.
Amjk
5
y Inte^rdtin^ Watt-Meter V^sX
Type K.
PRACTICAL MEASURING INSTRUMENTS 271
1000 s
1005
lOS
1 s
Kilowatt - Hours
The dial at the right is the
same as the preceding dial
except that the tenths indi-
cator is absent.
Some meters have differ-
ent dials on them. If the
dial on your meter at school or at home is different, work out
the method of reading it and then check your result by the
reading on the light bill. If you can not read it, have the officer
of the company, who calls each month to get the reading,
explain how it is read.
Exercise 6
1. What is the reading on the dial with 4 indicators on it?
2. The reading of the meter of Problem 1, for the previous
month, was 1782. How many kilowatts has the family used
during the past month?
8. If the local rate is 12^fi per kilowatt, what was the light
bill for last month?
4. Many light companies have a sliding scale for the use of
electrical energy.
The following shows a bill of a company which generates its energy by
water power. Note the low rates for energy from water power.
Meter Readings Dec. 13. . . . 2416
Nov. 13. . . . 2368
Total consumption in k.w.hrs. 48
First 9 k.w. hrs. ® 10c= $0.90
Second 9 k.w. hrs. @ 6c = .64
30 k. w. hrs. excess
over 18 @ 3c= .90
Gross Bill $2.34
18
Date: Dec. 22, 1916.
Discount on first 18 hrs. if paid on
or before Jan. 1, @ Ic per k. w.
Net BiU $2.16
6. The reading on Jan. 13 of the meter described in
Problem 4 was 2458. (Problem 4 gives the reading for Dec. 13.)
Figure out the bill for this month according to the plan shown
in Problem 4.
272 EIGHTH YEAR
6. A company in a small village charges 15^ per kilowatt
hour for their electrical energy. How^ much will a family pay
which uses 16 kilowatts during a certain month?
7. Draw a diagram, similar to the one shown in the book,
of the dial of some electric meter which is convenient for you
to read. What is the reading of the meter shown by your
diagram?
8. Determine the system of computing charges for your
community. Get some actual readings from bills in your
community and make a problem. Present it to the class for
solution.
9. Electric cars are run by storage batteries. They can be
charged by running an electric current through them. After
they are disconnected from the charging current they will
give back the energy stored up on their plates. Find the cost
of charging a storage battery. How many miles will this
battery run the car in which it is used? Find the cost per mile
for the current necessary to run this electric car.
10. Find the number of miles a gallon of gasoline will run
an automobile of about the same weight. Find the cost per
mile of the gasoline. Compare this cost per mile with that of
the electric car.
THE GAS METER
Uluminating gas is made from soft coal by driving off the volatile gases
by means of fires under closed retorts. This gas is then run through
several processes to take out the impurities which are driven off with the
gas. The purified illuminating gas is then pumped into large tanks where
it is kept under a pressiu*e which forces it through the pipes to the con-
sumers.
The consumption of illuminating gas is measured in terms of
cubic feet. The gas meter records the number of thousand
cubic feet used. The indicators on the dial at the left are
PRACTICAL MEASURING INSTRUMENTS 273
labeled 100 thousand, 10
thousand and 1 thousand.
They really read in 10
thousands, thousands and
hundreds. Hence the cor-
rect reading is only one-
tenth the reading as indi-
cated on the dial.
The reading on the dial at
the right as above corrected is 87,300.
Exercise 6
1. The reading on my gas meter on Oct. 27 was 83,800.
On Nov. 27 it was 85,600. What was my gas bill for the
month, gas selling at 00^ per 1000 cubic feet?
Solution: Nov. 27 85600
Oct. 27 83800
1800 number of cubic feet consumed.
1800 cubic feet at 90f( per thousand = 1.8X90^ =$1.62 (gross bill.)
2. If I am allowed a discount on this bill of 10|i5 per 1000
cubic feet if I pay it within 10 days, what is my net bill?
8. Problem 1 gives the reading for Nov. 27. If my reading
for Dec. 27 is 87,400, what is my gas bill for the month of Dec?
(Find both gross and net bill, using the same rates as given
in Problems 1 and 2.)
4. If I use 2400 cubic feet of gas during the month of July,
what is my gas bill at 90^ per thousand cubic feet and 10^ per
thousand cubic feet discount if paid within 10 days?
5. If you live in a city where gas is used, find the cost per
thousand cubic feet. Is there a discount for prompt payment?
274 EIGHTH YEAR
6. Get an old gas bill and make a problem similar to the
ones given above and present it to the class for solution. Check
their solution by the amount as stated on the bill.
THE STEAM GAUGE
The steam gauge is an instrument to
measure the pressure of the steam in a
boiler. These gauges can also be used to
indicate the pressure of compressed air in
tanks. They are usually graduated to
read pressure in so many pounds to the
'square inch. The gauge shown in the
illustration shows no pressure, the pointer standing at zero.
*
Exercise 7
1. How many pounds of pressure must be put in an auto*
mobile tire to make it sufficiently hard?
2. A safety valve is placed in a boiler so that the pressure
will not become too great and explode the boiler. Ask the
janitor of your school building how many pounds of steam his
boiler will carry before the steam forces its way out of the
safety valve.
8. Most steam heating plants have low pressure boilers.
Locomotives and engines have high pressure boilers. Ask an
engineer how many pounds he aims to carry on his engine.
4. The pressure of the atmosphere is about 14.7 pounds per
square inch. The steam gauge reads additional pressure above
the pressure of the air. For example, if a steam gauge reads
14.7 pounds, we say the boiler is under two atmospheres of
pressure inside and only one atmosphere of pressure on the
outside. If the gauge reads 29.4 pounds, what would be the
pressure on the inside and outside?
PRACTICAL MEASURING INSTRUMENTS 276
UEASUKEMENTS OF THE EARTH'S SURFACE
Short distances on land are measured
by means of the aurveyor'a chain^ which
W^9
is sixty-six feet long and has one hundred
links. Sarreyor-. Ctoln
Distances on the water, and loi^ distances by land, are
Dteasured by observing the sun and other heavenly bodies,
which seem to pass over the heavens and entirely around the
world in twenty-four hours.
Distance east and west measured in this way is called longi-
tude. This old word meant length; and the ancient peoples
who lived on the shores of the "loi^-east-and-west" Mediter-
ranean Sea supposed that the lengOi of the world was east and
west. They did not know that the world is round and they
gave us the word longitude.
It is customary to measure lon^tude from some great
observatory, where the heavenly bodies are observed through
the best instruments. Since the one at Greenwich ^in nij)
near London, England, is the best known in the world, longitude
is generally reckoned from that one.
To make the distances east and west, imaginary lines are
drawn north and south from the North
Pole to the South Pole. These imaginary
lines are called meridiana. All places
between the poles along the same meridian
have the same longitude.
The Equator, which crosses every merid-
ian at r^ht angles hajf-way between the
poles, is the line from which distance is measured in degrees
north and south. Imaginary circles to indicate latitude, or
distance north or south from the Equator, are called paraUele
qf latitude.
276
EIGHTH YEAR
THE MEASUREMENT OF TIME
Suppose it is noon at the place where you live and the sun
is directly south of you. As the earth rotates from west to
east, the sun seems to move westward and noon travels with
the sun. Since the earth rotates on its axis once in 24 hours,
the sun will seem to pass over 360° of longitude in 24 hours,
or 15° of longitude in 1 hour.
Exercise 8
1. If it is noon where you live, how long will it be before
it is noon 15° west of you? 30° west of you? 45° west of you?
2. What time is it 16° west of you? 30° west of you?
45° west of you?
3. How long has it been since the sun was directly over
the meridian 15° east of you? What time is it at a place 15°
east of you? What time is it 30° east of you?
For convenience, time must be reckoned from a certain
meridian. This meridian has been chosen as that of Greenwich,
England. All longitude west of this meridian to the 180th is
called west longitude and all longitude east of this meridian to
the 180th is called east longitude.
STANDARD TIME 277
i. If it ia noon at Greenwich, what time will it be 15° west
of Greenwich? 30° west of Greenwich?
5. If I set my watch at Greenwich and carry it west with
me to longitude 90° west without re-setting it, how much too
fast will it be?
6. Philadelphia is in about 75° west longitude. When it
is noon at Greenwich, what time is it in Philadelphia?
7. Since there are about 60° of longitude between the
extreme east and west coasts of the United States, what is
the difference in time between a city in Maine and a city in
western Oregon?
Standard Tune
All places on the same degree of loi^tude have the same
local time, however far apart they may be north and south;
but by far the greater amount of travel in the world is in an
easterly or westerly direction, and to one traveling east or
west the local time changes constantly. It is especially impor-
278 EIGHTH YEAR
tant that railways shall have an unvarying standard of time
for long distances. Hence a system of Standard Time has
been adopted for this great country, by which its area has
been divided into four great time sections, known as the Divi-
sions of Eastern Time, Central Time, Mountain Time and
Pacific Time.
At all points in any one of these Divisions, the time is made
artificially the same. When it is noon in the Eastern Division,
it is 11 o'clock in the Central Division, 10 o'clock in the Moun-
tain Division and 9 o'clock in the Pacific Division. Thus
the Divisions are, successively, one hour apart.
When travelers going east or west arrive at the boundary
line of one of these divisions, they set their watches ahead or
back, to correspond with the time in the next division. The
Southern Pacific Railway makes no use of Mountain Time,
but passes directly through from Pacific Time to Central Time.
It will be noted that the Maritime Provinces of the Dominion
of Canada make use of what is called Atlantic Time, which is
the time of the meridian of Long. 60° W. This time is not
employed in the United States.
Exercise 9
1. When it is 12:15 a. m. at Chicago, what time is it in
New York (Standard Time)?
2. When it is 4:32 p. m. at San Francisco, what time is it
in Chicago?
3. When it is 9:45 at New York, what time is it at
Denver?
4. Detroit is now under Eastern Time. How much differ-
ence is there between the time in Detroit and the time at
Cincinnati, which is in the Central Time belt but has practically
the same longitude?
INTERNATIONAL DATE LINE 279
6. BufiFalo, being at the line of division between Eastern
Time and Central Time, makes use of botti. How far apart
are clocks and watches found to be in a city so situated? Men-
tion some other cities on the dividing lines of Standard Time
Divisions?
6. If El Paso should make use of Mountain Time it would
have the time of what meridian? Would this be near the local
time of the place?
The International Date Line
When ME^ellan's men returned to Spain from their voyage
around the world, they found that
they were a day behind in their time.
There must be some place, then, where
people travelling west or east can chaise
a day in time. It would be very incon-
venient for this change to be made in
any thickly populated area of the world.
The nations of the world have agreed
upon such a line passing along the 180th
meridian with a few variations as shown
in the map. A person travelling west
adds a day to bis calendar when he crosses
ther international date line. If he travels
east, he goes back a day on his calendar
when he crosses this line.
Exercise 10
1. If a ship crosses the international date line going west
at 11:50 p. m. Saturday, how long will it be Sunday on board
the ship?
2. If a ship crosses the international date line going east at
midnight Sunday, how lon^ will it be Sunday on the ship?
CHAPTER VII
THE METRIC SYSTEM
Weights and Measures
Over a century ago, in the time of the French Revolution,
a conunission of able men was formed to devise a convenient
system of weights and measures to replace the clumsy systems
then in use in the countries of Europe. They proposed the
metric system, a scheme so scientific in plan and so convenient
in its use that it has grown in favor over the world, until now
it is used around the globe, except among the English-speaking
peoples. Even in the United States and in the British Empire
it is in use in a limited way, being employed very generally
in scientific laboratories and is recognized by law. '
The need for a more general knowledge of this system in
this country is growing from day today, in view of our increas-
ing trade with the nations which use it exclusively. Without
mastering it we cannot readily understand the trade catalogues
of their business houses or the bills sent us for articles purchased;
nor can we make them readily understand our own price lists
and bills of goods sold to them without writing these in terms
of the metric system. No ambitious pupil of the present day
can afford to slight the metric system in his study of arithmetic.
This commission measured very carefully a portion of the
meridian running through Paris and estimated, from this
measurement, the distance from the North Pole to the Equator.
They then took one ten-millionth of this distance as the stand-
ard measure for length and named it the meter.
Since they wished to base their scheme upon a decimal ratio,
they selected the Greek prefixes deka, meaning ten; hekto,
280
THE METRIC SYSTEM
281
meaning hundred; kiloy meaning thousand, and myria, meaning
ten thousand, for the multiples of any unit of measure, and the
Latin prefixes deci, meaning 3^; centij meaning xiirj ^^^ ndUi,
meaning xo^nrj ^^^ *^® fractions of any unit of measure.
Instead of learning an entirely new set of names for each table
as we have to do in our dumsy English system of weights and
measures, all we have to do in the metric system is to learn one
new unit for each table, and, by prefixing the roots, the new
tables can be formed.
Metric Table of Length
10 miUimetera (mm) =1 centimeter (cm.)
10 centimeters.
10 decimeters. .
10 meters
10 dekameters.
10 hektometers
10 kilometers. .
= 1 decimeter (dm.)
= 1 meter (m.)
= 1 dekameter (Dm.)
^ 1 hektometer (Hm.)
= 1 kilometer (Km.)
= 1 myriameter (Mm.)
The following is an illustration of a decimeter divided into
10 equal parts called centimeters (cm.). Each of these centi-
meters is also divided into 10 equal parts called millimeters
(mm.). Along the base of the ruler is shown a scale in inches.
This shows that a decimeter is slightly less than 4 inches.
A meter =39.37 inches.
nTTTTm
mTTTm
^
2cm. ocm 4cm 5cm 6cm 7bm 6cm 9aTi lOcm
TTTNT
±
tin
2in
3in
Exercise 1
1. A meter stick is how many times as long as the decimeter
shown above?
2. If you have access to a work shop, construct a meter
stick from another as a model or use the scale in your book.
282 EIGHTH YEAR
3. A meter equals how many centimeters?
4. A dekameter is equal to how many meters?
6. A kilometer is equal to hew many meters?
6. Change 355 millimeters to centimeters.
Since 10 millimeterB » 1 cm., 355 mm.s=355 ^l]n.-^10 mm. » 35.5, the
number of cm. This shows the convenience of the metric system in chang-
ing from one unit to another — ^we merely move the decimal point to the
right or left the required number of places.
7. Change 8750 mm. to meters.
8. Change .5 km. to Dm.
9. Change 345 meters to km.
10. A rod in our English system is equal to how many meters?
11. Find the length and width of your school room in meters.
12. Measure the length and width of your desk in centimeters.
13. Draw a line on the blackboard a meter in length without
looking at a meter stick. Now measure it and see how many
centimeters you have missed it.
14. Measure the lengths of Objects in your school room after
you have first estimated their length, using the different units
meter, decimeter and centimeter in your estimates.
16. A kilometer is equal to what decimal fraction of a mile?
In France they estimate the distance between two cities in kilometers
instead of miles as we do here.
Metric Table of Square Measure
The square centimeter is one of the most common of
the units of square measure in scientific work. As
shown in the exact reproduction at the left, it is a
square 1 cm. on each side.
Find the number of square centimeters in a square inch.
I
laouARc
KZNTVICTCR
THE METRIC SYSTEM 283
100 sq. millimeters (sq. mm.) — 1 sq. centimeter.
100 sq. centimeters (sq. cm.) = 1 sq. decimeter.
100 sq. decimeters (sq. dm.) =1 sq. meter (sq. m.).
For measuring land the following units are used:
1 sq. meter = 1 centare (ca.)*
100 centares ~1 are (a.).
100 ares =1 hectare (Ha.).
A hectare is equal to about 2.471 acres.
Exercise 2
1. What is the area of the top of your desk in square
centimeters?
2. Draw a square meter on the floor without using a meter
stick. Use the meter stick to check your estimated square
meter.
3. A friend of mine in Argentina writes that he has planted
20 hectares of wheat. How many acres of wheat has he planted?
4. What part of an acre is an are?
6. Reduce 45675 sq. mm. to square meters. (Remember
that the multiplier is 100 in square measure instead of 10.)
6. Make 5 problems that involve square measure.
Metric Table of Volume
1000 cu. millimeters (cu. mm.) = 1 cu. centimeter.
1000 cu. centimeters (cu. cm.) = 1 cu. decimeter.
1000 cu. decimeters (cu. dm.) = 1 cu. meter.
In measuring wood a cubic meter is called a stere.
A cubic centimeter is a cube 1 cm. long, 1 cm. wide and 1 cm.
high. The exact size of a cubic cm. is shown in the illustration
at the right.
Find the nmnber of cubic centimeters in a cubic inch. 1 cu.
cm. is what part of 1 cu. in.?
284 EIGHTH YEAR
Exercise 3
1. Make a cube 1 decimeter long, 1
decimeter wide and 1 decimeter high. An.
open cubical box may be made by making
I each line in the pattern shown at the left
^ 1. decimeter long. The four sides may be
turned up at the dotted lines and the comers
HdiM sewed or pasted together with some kind of
gummed paper.
2. In a stere are how many cubic centimeters of wood?
8. A shipment of guanacaste wood from Central America
forms a pile two meters high, 1 meter broad and 30 meters
long. How many decasteres does it contain?
4. How many cubic meters of earth are removed to make an
excavation 12 meters long, 8 meters wide and 1.5 meters deep?
6. What will be the cost of teaming in the removal of 2500
cubic decimeters of gravel at $1 per cubic meter?
6. A cubic meter is equal to about 1.3 cubic yards. How
many cubic yards would there be in the excavation described
in Problem 4?
Metric Table of Capacity
The cubical box described in Problem 1 of the preceding
exercise if made correctly will hold exactly 1 cubic decimeter.
This is taken as the unit of capacity and called the liter (lee-ter).
A liter is equal to about 1.057 quarts.
lOmilliliters (ml.) =1 centiliter (cl.)
lOcentiliters =1 deciliter (dl.)
lOdeciliters =lliter (L.)
lOUters =ldekaliter (Dl.)
lOdekalitera =1 hektoliter (HI.)
lOhektoUters =lkiloUter (Kl.)
THE METRIC SYSTEM
285
Exercise 4
1. How many cubic centimeters are there in a liter?
2. If milk costs 8 cents per liter, what is the cost of a deka-
liter of milk?
8. Reduce 8 dekaliters to deciliters.
4. An aquarium 2 meters long, 1^ meters broad and 1
meter deep contains how many liters?
6. A bin in a certain granary is 4 meters long, 3 meters
broad and 176 centimeters deep. How many hektoliters does
it contain?
6. A hektoliter is equal to about 2.837 bushels. How many
bushels of wheat will the bin described in Problem 5 hold?
7. Change 245 liters to hektoliters.
8. Make 4 problems involving the metric table of capacity.
Metric Table of Weight
If a cubic centimeter of distilled water be
weighed at a temperature of 39° F. it will
weigh exactly a gram. 1000 of these
grams make a kilogram (or kilo for short).
A kilogram, then, is the weight of a cubic
decimeter or liter of distilled water at
the temperature of 39° Fahrenheit.
10 miUigrams (mg.)
10 centigrams
10 decigrams
10 grams
10 dekagrams ,
10 hektograms ,
10 kilograms
= 1 centigram (eg.)
= 1 decigram (dg.)
= 1 gram (g.)
= 1 dekagram (Dg-)
— 1 hektogram (Hg.)
= 1 kilogram (Kg.)
=1 m3rriagram (Mg.)
10 myriagrams =1 quintal (Q.)
10 quintals =1 Metric Tan (MT.)
286 EIGHTH YEAR
Exercise 6
A kilogram is equal to about 2.204 pounds.
1. A gram is equal to how many centigrams?
2. A kilogram is equal to how many grams?
8. How many grams are there in a metric ton?
4. How many pounds are equal to a metric ton?
6. Linseed oil is only .935 as heavy as distilled water.
How many grams will a liter of linseed oil weigh?
6. Gasoline is only .7 as heavy as distilled water. How
much will a Uter of gasoline weigh?
7. I weighed myself on a standard metric scale in a phy-
sician's office and found my weight 74 kilograms. Find my
weight in pounds.
8. The average weight^ of boys 13^ years old is 38.48
kilograms. Find their average weight in pounds.
9. The average weight of girls 13^ years old is 40.24
kilograms. Find their average weight in pounds.
10. How many pounds do you weigh? Express this weight in
kilograms.
11. A farmer in Argentina measures his wheat by the hekto-
liter. A hektoliter = 2.837 bushels. A bushel of wheat weighs
60 pounds. From these facts find the weight of a hektoliter
of wheat in kilograms.
12. A cubic decimeter of gold weighs 19.3 kilograms. How
many pounds avoirdupois weight does a cubic decimeter of
gold weigh?
13. A cubic foot of water weighs 62.5 pounds. How many
kilograms are there in the weight of a cubic foot of water?
14. Make three problems which involve the metric table
of weights.
iFrom Table B, Rowe's "Physical Nature of the Child."
THE METRIC SYSTEM 287
Exercise 6
Prom the information already given in connection with the
metric system find the following equivalents:
1. A meter =? feet? 6. A quart =? cu. in.?
2. An inch =? cm.? 7. A cu. meter =? cu. ft.?
8. A mile = ? km.? 8. A pound = ? grams?
4. An are =? sq. yd.? 9. A cu. in. =? cu. cm.?
6. A gallon =? liters? 10. A rod =? meters?
Exercise 7
1. At 40 cents a meter, what will be the cost of 2.5 deci-
meters of ribbon?
2. A book is 4 centimeters thick between the covers: It
contains 400 pages. How many leaves are there in 1 millimeter
of thickness?
3. Sound travels in dry air at the rate of 1087 feet in a
second. How many meters does it travel?
4. How many seconds would elapse between the flash and
the report of a gun if I was a kilometer away?
6. Lead is about 11.4 times as heavy as distilled water.
How many pounds will a liter of lead weigh?
8. A bale of hay weighs 40 kilograms. Find its weight in
pounds.
7. A field is 40 rods long. How many meters long is the
field?
8. What is the cost of 150 decimeters of cloth at $1.25 per
meter?
9. I am 5 feet 10 inches tall. Find my height in centi-
meters. Find your height in centimeters.
CHAPTER vni
EFFICmNCT IN THE HOME
A Southern Colonial Bungalow'
When one decides to build a house, he is interested in seeing
two things : an exterior view of the finished bouse and a floor
plan, showing the arrangement and sizes of the various rooms.
The floor plan of the Southern Colonial Bungalow is ehottn in 0>6
flluBtration on the next page.
Exercise 1. A Study of the Floor Plan
1. What are the outside measurements of the house,
excluding the front porch?
2. Read the azes of the various rooms from the floor plan.
3. How lai^e ia the front porch?
4. How many chimneys are shown in the plan?
5. Would you make any changes in the plani if you were
going to build this house?
'Acknowledgment is made to the "Gordon-Van Tine Homee," Daven-
■ '' a p. 109), aud for the
EFFICIENCY IN THE HOME
289
Exercise 2. Cost of the House
1. The basement excavation was 1.8 yards deep. Find
the number of cubic yards of earth that was excavated. See
the floor plan for the dimensions of the house. The basement
isr the same size as the
house, exclusive of the front
porch.
2. In excavating for the
basement of the house,
there were 200 cubic yards
of earth removed. Find the
cost of excavating at 25
cents per cubic yard.
3. In the foundation the
following materials were
used: 42 perch^ of stone
at $5.00 per perch; 40
cubic yards of poured con-
crete at $5.50 per cubic
yard; and block and foot-
ings costing $195. Find the
total cost of the foundation.
4. The contractor
charged for 120 square
yards of cement floor at 80
cents per square yard. Find the cost of cementing the base-
ment.
6. The plastering was estimated at 600 square yards at
36 cents per square yard. How much did the plastering cost?
6, The carpenter labor amounted to 833 J hours at 60 cents
per hour. Find the total amount paid the carpenters.
*A perch =24i cubic feet.
Po^c n
ft:
L^E^
■5"
290 EIGHTH YEAR
7. The rear chimney was 35 feet high and cost $1.30 per
linear foot. Compute the cost of this chimney.
8. The other items in the cost of the construction of the
house were: Lumber $669.00; miUwork $239.00; hardware
$132.00; paint (material and labor) $190.00; brick for porch
work $80.00; fireplace (chimney, hearth, stone, etc.) $105.00;
wiring $14.00; and hot-air beating plant $129.00. . Find the
total cost of these items.
9. Find the total cost of the house as shown by the various
items described in Problems 1 to 8 inclusive.
10. Find the total cost of the excavating, the foundation
and the cement floor of the basement.. These items amounted
to what per cent of the total cost of the house?
11. The cost of the carpenter labor was what per cent of the
total cost of the house?
12. The total cost of the lumber, millwork and hardware
was what per cent of the cost of the house?
Exercise 3. Furnishing a Home
1. What size rugs would you buy for the living room and
the dining room? What are the advantages of rugs over
carpets?
2. Would you buy rugs for the two bed rooms? If so,
what size would you buy?
3. How many shades would be needed for the bungalow?
4. Would you put linoleum on the kitchen floor? Linoleum
is made in 6-ft., 9-ft. and 12-ft. widths. Which one of these
widths would be used on the kitchen with the least waste?
6. Make out a list of the various articles of furniture which
you would buy to furnish this home and the approximate cost
of each article. Find the total cost of these furnishings.
EFFICIENCY IN THE HOME
291
6* An expert in interior decorations and home furnishings
suggested the following as a model list of furniture for this
five-room bungalow. Find the total cost of furnishing the
bungalow in this manner:
Living Room (Antique Mahogany)
Davenport, with damask, valour or tapestry covering flOO . 00
Chair to match 55 . 00
Sofa table to go with davenport if used in front of fireplace 37. 50
Overstuffed arm chair with velour, tapestry or damask covering . . 50 . 00
Occasional chair or rocker in cane or upholstered 18 . 50
Sofa, and table at each end of sofa, each 12 .00
Living room table, 30"X54" 45.00
Book case, 4' wide 40 .00
Best Grade Wilton Rug, 10' 6"X 13' 6" 122.00
Dining Room (Tudor Wahiut) 7^ gjjow how you would
^^«* *7^^ furnish this house with an
Serving Table 38.00
Extension Table 58.00
Cabinet 60.00
Arm Chair 22.00
Side Chairs, 5 at $13.50 67 . 50
WUton Rug, 11' 3"X 13' 0". .110.00
Chamber No. 1 (American Wahiut)
Bed— Full size $42.00
Spring and Mattress 38 . 50
Chest of Drawers 66.00
Dresser 65.00
Night Stand 8.00
Side Chair and Side Rocker, ea. 9 . 00
Wilton Carpet, 9' X 11' 46.00
Chamber No. 2 (Ivory Enamel)
Bed— Full size $48.00
Spring and Mattress 38 . 50
Chest of Drawers 36.00
Toilet Table 47.00
Night Stand 10.00
Toilet Table Bench 10.00
Side Chair and Side Rocker, ea. 11. 75
Wilton Carpet 9'Xll' 46.00
allowance of $800 to cover
all expenses for furnishmgs.
Get prices on furniture from
the local dealer in making
your estimates.
8. Furnish the house on
an allowance of $500.
9. Which would be the
better plan if your allow-
ance were too small: to buy
a full equipment of cheap
furniture or to buy fewer
pieces of higher-priced furni-
ture?
10. What articles would
you provide for the front
porch? Estimate the cos^
of these articles*
292
EIGHTH YEAR
Exercise 4
The house plan shown in this illustration is the one for the
house shown on page 109.
16-0
1. Compare this plan with the plan of the bungalow. Which
one would you prefer for a home? Why?
2. Estimate the cost of furnishing this house, listing the
various articles and their prices as in the preceding exercise.
3. Discuss size of rugs, number of windows, etc., for this
plan as outlined in Exercise 1.
Exercise 6. Expenses of a Home
1. How many tons of coal would be needed to heat this
home for a year? Get estimates from owners of houses of about
the same size.
•
2. How much does coal cost in your community? Estimate
the cost of the coal at that price.
EFFICIENCY IN THE HOME 293
8. Compare the cost of burning hard coal and that of soft
ooal for a house of this size.
4. If the kitchen range were a coal stove, how many tons
would be needed to supply the stove per year? Find the cost
of the coal for cooking purposes for a year.
6. If gas is used in your community, find .the cost per month
for the average family. What is the total gas bill for a year?
6. If estimates for both coal and gas can be obtained,
compare the costs to see which is the more economical.
7. Secure actual data from the homes in your community
and estimate the cost of lighting a home for a year.
8. Estimate the table expenses^ for a family of 4 to 8 persons
per month?
Campfire Girls
In order to encourage girls to become efficient as home
managers, honors are granted to Campfire Girls for the following
achievements:
1. Save ten per cent of your allowance for 3 months.
2. Plan the expenditures of a family under heads of shelter,
food, clothing, recreation and miscellaneous.
8. Have a party of ten with refreshments, costing not more
than one dollar.
4. Market for one week on $2.00 per person.
6. Market for one week on $3.00 per person.
6. Give examples of 5 expensive and 5 inexpensive foods
having high energy or tissue-forming value. Do the same for
foods having little energy or tissue-forming value.
Choose one of the above achievements to work out and report
on it to the class at a later date.
*A review of the section on Food Values at this point will be of assistance
in planning the food for the family, use. A very elaborate and profitable
treatment can be made of this topic.
294
EIGHTH YEAR
Exercise 6. Keeping the Family Budget
Efficiency in a business enterprise demands that the income
and expenses of every department be known. Likewise effi-
ciency in the home demands that the home managers apportion
the family incomes in the most advantageous manner.
A large business corporation made out a suggestive budget
for the benefit of their employees. They suggested that the
daily expenses be entered on an account sheet similar to the
following:
Budget Estimate for a Family of Five
Date
Food
30%
Shelter
20%
Operating
Expenses
10%
Clothing
15%
Contingency
25%
1
2
3
4
5
6
7
8
9
10
•
.
etc. to the close dof each month.
EFFICIENCY IN THE HOME 295
Under food they included meat, groceries, vegetables, bakery
and dairy products, and any meals at hotels or restaurants.
Shelter included rent or payments on owned home, interest on
mortgage, taxes, fire insurance, and upkeep of the house.
Operating expenses comprise heat, light, fuel for cooking, ice,
hired help, laundry, telephone and replacement of home fur-
nishings. Contingency includes savings, educational expenses,
church dues, club dues, concerts, personal expenses and expenses
for health and recreation.
1. If the family income is $75 per month, find the amounts
that should be included under the various headings of the
suggested family budget.
2. Find the amounts for family incomes of $100, $125 and
$150 per month.
3. Keep a family budget at home for a month and see how
the amounts expended for the various apportionments compare
with the percentage of the suggested budget.
4. Another expert on home economy suggested the following
classification: Rent, 25%; food, 25%; clothing, 15%; education,
10%; luxuries, 5%; miscellaneous expenses, 10%; savings, 10%,
Find the monthly apportionments of this budget for an income
of $125.
5. Compare the apportionments for the two budgets.
Which is the most suggestive and helpful to a home manager?
6. Bring to the class any other budgets for distributing
the family income among various headings and compare these
budgets with those presented in this chapter.
7. Does the location (in a large city, a small city, or the
country) affect the per cents apportioned among the various
items of a budget? Show why.
296
EIGHTH YEAR
EFFICIENCY IN BUSINESS
The boys and girls in the upper school grades are the coming
business men and women. If you study the things that lead
to efficiency in business, you will find that scientific pi
and economy in management are the essential factors.
The printing trade is here used for illustration only,
lessons will apply to other industries as well.
The
Exercise 7
Mr. Franklin, with $5000 to invest in the printing business,
rented floor space 50'x28'.
The accompan3ring diagram will show how this space was
laid out, by an expert, to insure the greatest working corwenience,
the proper proportion of expenditures in equipment and the
highest utility of space.
After a careful study of the floor plans, Mr. Franklin pur-
chased the material and furniture listed on the following page,
which it was found would give him a complete and well-pro-
portioned working outfit.
EFFICIENCY IN BUSINESS 297
Wood and Steel Equipment $ 850.00
Machinery, including Motors 1,830.00
Type, Spaces and Quads, Borders, Ornaments, Brass Rule, Iron
Furniture, Quotation Quads, etc 1,435.00
Miscellaneous material such as Quoins, Mallets, Planers, Brushes,
Benzine Cans, Ink, Knives, Roller Supporters, Composing
Sticks, Galleys, and all the small tools necessary in a printing
plant 110.00
1 Office Desk 55.00
1 Counter (built in) 42.00
1 Show Case 62.00
1 Typewriter 85.00
4 Chairs (average, $7.75) 31.00
Total
What balance did he have remaining as working capital?
There was still another necessary preparation for the safe
conduct of the business, viz., the establishment of a cost system
to include the overhead charges (see page 62) and a properly
classified schedule of wages for the three separate departments
of the work as below shown :^
Composing Room wages $0.50 per hour
Overhead charges — Rent, Heat, Light, etc 1.00 per hour
Net cost per working hour .$1.50 per hour
Press Room wages (Gordons) 30 per hour
Overhead charges — Rent, Heat, Light, Power, Insurance,
Taxes, etc 65 per hour
Net cost per working hour $0.95 per hour
Bindery wages — Girls 21 per hour
Overhead charges — Rent, Heat, Light, Insurance, Taxes,
etc 24 per hour
Net cost per working hour $0.45 per hour
*The "cost system^* enabled Mr. Franklin, at the end of each week,
auicklv to determine whether the business of each department was con-
aucted at a vrofit, or, if at a losSy to make the necessary correction and
thus avoid further risk and loss.
298 EIGHTH YEAR
Mr. Franklin ordered his paper from a wholesale paper
house, by the ream, in sheets of various sizes, weights and
grades, including the standard lines specified in the second
column of the problems below.
Let us now find the largest number of circulars 5"x7" that
can be cut from a sheet 2l"x36"^
Solution: 3 7
2Zx30
= 21
0x7
Note that 5 is canceled into 36, 7 times, the fraction being discarded.
Show the amount of waste in square inches.
Find the number of circulars, or pieces of paper of the sizes
given in the first column, that can be cut vrith the least waste
from the sizes given in the second column, and show the amount
of waste for each in square inches.
1. Si'xll" from 17''x22''
2. 4' X bl' from 22' x 28'
8. Si'xll" from 22'x34'
4. 4|' x 8' from 24' x 36'
6. 6 J' x 9' from 25' x 38'
r
Exercise 8
1. For 9. certain job of printing, 2 reams of book paper
were needed, weighing 80 pounds to the ream, and costing
8 cents per pound. The composition (type setting) required
8 hours, the press work 6 hours and the bindery work 3 hours.
What was the net cost based on the "working hour" rates
given in the table on page 303?
^In arriving at the amount of paper required for a job, printers by the
use of cancelkition are able to see at a glance the sized sheet they may
have in stock from which they can cut with the least waste.
6. 6i'
X 9'
from
26'x29'
7. r
xlC
from
28' X 42'
8. 8'
xlOl"
from
32' X 44'
9. 9'
xll'
from
35' X 45'
.0. 9'
xl2'
from
38'x50'
EFFICIENCY IN BUSINESS 299
2. If the printing office added 20% for profit, what was the
total cost of the job to the customer?
3. Mr. Howe, a merchant, ordered 6000 handbills, size
6^"x9", for Ms anniversary dry goods sale. How many reams
of paper were required for this job if cut from sheets 25"x38"?
4. If the paper cost 6 cents per pound and weighed
60 pounds to the ream, what did the paper cost?
6 If the composition required 1^ hours and the press work
2 hours, what was the cost of these two items at the net prices
given in the table?
6. If Mr. Franklin added 20% for his margin of profit on
the job, what did the 6000 handbills cost Mr. Howe?
7. A High School Glee Club ordered 500 programs for their
annual entertainment, size (before folding) 6 J"x9", printed on
both sides from stock weighing 100 pounds to the ream. How
many sheets 25"x38" were required, and what was the cost of
the paper at 10 cents per pound?
8. If the composition required 5 hours and the press work
4 hours, what was the charge to the Glee Club, counting in the
office charge of 20%?
9. A graduating class ordered 1500 programs, size 4"x6".
What paper size given in the table cut to the best advantage,
and how many sheets were required?
10. A School Board ordered 2000 letterheads, size 8|"xll".
If these were cut from sheets 17''x22'', of paper stock costing
9 cents per pound, and weighing 90 pounds to the ream, the
composition requiring 1 hour, and the press work 2 hours, and
20% was added for profit, what was the total charge for the job?
11. Find some printed program, estimate its cost based on
the tables given, submit your figures to your local printer, and
see how near you have reached the correct amount.
SUPPLEMENT
The purpose of this section is to provide additional work in
simple equations to supplement Chapter III of Part I, and to
give material for additional work in measurements in con-
nection with Chapter IV of Part II.
. While this section is intended to be optional, it offers valuable
training in preparation for algebra and geometry and should
be used when time permits.
I. SIMILAR FIGURES
Similar figures are figures having the same shape.
All squares are similar to each other because they all have
the same shape. In the same way all circles are similar. All
rectangles are not similar to each other. Rectangles A and B
are similar to each other because they have the same shape,
each being twice as long as wide. Rectangles B and C. are
not similar because C is 5 times as long as it is wide and B is
only 2 times as long as it is wide.
Exercise 1. Ratio and Proportion
Ratio and proportion are very convenient tools to work with
in discussing similar figures. It will be to our advantage,
then, to master the uses of these tools before going further
into the study of similar figures.
The ratio ol one number to another is the number of times
the first contains the second.
300
SIMILAR FIGURES 301
The ratio of 15 to 3 is the number of times 15 contains 3,
which equals 5. The ratio of 15 to 3 may be expressed as
follows: 15 : 3 reads "the ratio of 15 to 3" or -^. The fraction
is an excellent way of expressing a ratio because it indicates
the division idea of a ratio. -^, the ratio of 15 to 3 = 15-^ 3 = 5.
A statement that two ratios are equal is called a proportion
as 15 : 5 = 24 : 8. The four numbers in this proportion are
called the terms of the proportion. The first and last terms of
a proportion are called the extremes and the second and third
terms are called the means, 15 and 8 are the extremes of the
above proportion and 5 and 24 are the means.
What is the product of the extremes, 15 and 8?
What is the product of the means, 5 and 24?
How does the product of the means compare with the product
of the extremes of the proportion?
See if the same relation exists between the products of the
means and extremes in the following proportions:
1. 10 : 5= 8 : 4. 6. 18 : 6 = 15 : 5.
2.60:15 = 12: 3. 6.30:6 = 25: 5.
3.48: 8 = 12: 2. 7.15:7=45:21.
4. 4: 2 = 36:18. 8. 6:5 = 18:15.
If we should try a very large number of these proportions,
we should find that the same relation holds true. This relation
may be e;cpre3sed in the
PRINCIPLE: In any proportion the product of the means is
equal to the product of the extremes.
If one term of a proportion is unknown, by means of this
principle the unknown term can be found. Let X represent
the unknown term.^
«
^By putting the value of the unknown term in place of X after it has
been found and ^en finding whether the product of the means equals
the product of the extremes, a check upon the correctness of the work is
shown.
302 EIGHTH YEAR
40:X=24:3
24 XX or 24X= product of the means.
40 X 3 = 120= product of the extremes.
Therefore: 24X=120
(Check: 40 : 5= 24 : 3)
120 = 120
Exercise 2
Fmd the value of X in each proportion:
1. 27:12=X: 8. 6. 21 : 18= 56: X. 11. 9: 3=X: 6,
2. 14:X = 26:13. 7. X: 28= 10: 7. 12. X: 12 = 20: 5.
3. 35: 7 = 15: X. 8. 3.5:2.5 = .21: X. 13. 16: 6=X:18.
4. X: 7=36: 6. 9. 9 : 5=X:10. 14. 21:X=14: 8.
6. 18:12= X: 6. 10. 8: X= 16: 8. 16. f : f = X: f.
PRINCIPLE: In similar figures the corresponding dimensions
are proportional.
c
If the triangles ABC and M N O are similar (that is, the
same shape), the corresponding dimensions are proportional:
AB:MN = CD:OP.
Exercise 3
1. Suppose A B = 16 inches ; N M = 10 inches ; C D = 6 inches.
Find O P.
Solution: Put those values in the above proportion:
16 : 10 = 6 : X.
16X=60 (the product of the extremes = product
of means).
X=^ or 3f . Therefore: O P or X=3f in.
k
SIMILAR FIGURES 303
2. Two rectangles axe similar. The base of the first is
12 inches, the base of the second is 8 inches and the altitude
of the second is 6 inches. What is the altitude of the first?
Caviion: Be sure to keep the right order — ^base of 1st : base
of 2nd — alt. of 1st : alt. of 2nd.
3. In the iabove triangles A B = 16 inches, MN = 10 inches
and A C = 7 inches. Find the side M O.
Exercise 4. Similar Triangles
1. To measure the height of a tree.
Method: Measure the shadow
A B of the tree. Set up a stick F D
whose length you have measured,
so that it is perpendicular to the
surface of the ground. Measure the
shadow of this stick.
The triangles ABC and D E F are similar.
The shadow of tree A B : shadow of stick D E = height of
tree A C : height of stick F D.
2. If A B = 30 feet; D E = 22 inches and D F = 36 inches,
find the height of the tree.
Caviion: Both expressions in the same ratio must be ex-
pressed in the same unit of measure.
3. A tree casts a shadow 42 feet long. At the same time
a stick 5 feet high casts a shadow 3 feet long. How high is
the tree?
4. Another method of measuring the height of the tree
. is to construct a large right triangle out
of strips of lumber. Make it so that the
legs of the right triangle are 3 and 4 feet
long. If equal legs are put on this triangle
it is much easier to make the accurate
measurements.
304
EIGHTH YEAR
Move the triangle back and forth until a person with his
eye at B can just see the top of the tree along the edge D B.
Measure the distance from B to the tree. ABE and D C B
are similar triangles. The length of the legs of the triangle
measuring instrument must be added to A E to give the whole
height A E.
5. Suppose A B = 50 feet, B C = 3, feet and D C=4 feet,
what is the height of the tree? Allow 3 feet for the legs.
6. To measure the distance across a pond.
Measure B C, D C and E D.
Triangles ABC and D C E are
similar.
ThenBC : DC=AB : ED.
Suppose BC = 150 feet; DC =90
feet; and E D = 50 feet. Find A B.
7. To measure the width of a stream.
Select some object such
as a tree on the opposite
bank at B. Set a stake at
A and lay ofif a line A D.
Lay ofif D C as nearly par-
allel to A B as possible.
Set a stake at any point O
in the line A D. Move
back along the line D C until the stake at O is in line with the
tree at B. Set a stake at this point C. Measure A O, O D
and D C. The triangles A O B and C O D are similar.
By means of this pair of similar triangles we get the pro-
portion:
AB : CD=AO : O D.
8. If CD = 100 feet, A = 50 feet and O D = 25 feet,
find A B, the width of the stream.
SIMILAR FIGURES
305
9. A boy desiring to measure the width of an impassable
riVer flowing through level land drew on the edge of the bank,
parallel with the stream, a base line, at each end of which
he drove a stake to which he attached the end of a ball of
twine. At one end of the base line, with an instrument, he
sighted a small spot in a rock on the opposite bank, and noted
the angle made by the
line of sight with the base
line. He then turned his
instrument to an equal
angle on the other side
of the base line, and had
an assistant carry the twine
a long way along the line
of sight. At the other
end of the base line he sighted the same spot in the rock,
then turned his instrument to an equal angle on the other
side of the base line, and had his assistant carry the second
ball of twine along the line of sight. From the point where
the strings crossed, he measured straight to the base line,
and announced the measure as being that of the width of
the stream. Was this correct? Explain your answer.
10. By placing a mirror on the
ground and moving up or back
until the top of the object to be
measured is seen in the mirror, the
height pf any object can be found.
ABC and B D E are similar triangles and C A distance from
the eye to the ground; A B, the distance from one's feet to the
mirror = D E, the height of the object : B D the distance of
the mirror from the object. If AB = 10 feet; C A = 5 feet;
B D = 25 feet, find DE.
Have pupils find other methods of measurements involving the use of
similar triangles.
^\a^/i\.rvltfW
306
EIGHTH YEAR
n. CONES AND PYRAMIDS
A p3rramid is a solid having for its base a triangle, rectangle
or other polygon, and having for its lateral faces triangles
meeting at a point called the vertex.
Triangular Pyramid Quadrangular P3rramid
Cone
A cone is a solid having for its base a circle, and bounded by
a curved surface tapering uniformly to a point called the apex.
Construct a hollow quadrangular prism out of cardboard.
Construct a hollow quadrangular pyramid with a base and
altitude equal to the base and altitude of the prism. Fill the
pyramid with sand and see how many times it must be emptied
into the prism to fill it. You will find that it takes 3 pyramids
full of sand to fill the prism. The volume of the prism is equal
to the product of the area of the base times the altitude. The
volume of a pyramid is ^ of the product of the area of the base
times the altitude. In the same way it can be shown that the
volumes of a cone is one-third of the volume of a cylinder of the
same base and altitude.
PRINCIPLE : The volume of a pjrramid or of a cone is equal to
one-third of the product of the area of the base times its
altitude.
Exercise 6
1. What is the volume of a cone having a base 7 inches in
diameter and a height of 9 inches? Solution:
3.5X3.5X9X3.1416
Volume = ^
t, find the volume of a pyramid having a base of 64 square
feet and an altitude of 6 feet.
8. A marble cylindrical shaft 1 foot in diameter imd 10 f^t
high is capped by a marble cone having the same diameter
at the base. The altitude of the cone is equal to its diameter.
Find the volume of the shaft and cone.
4. The Pjrramid of Khufu, in Egypt, has a square base,
measuring 750 feet on each side, and its height was originally
482 feet. Find in cubic yards its contents as originally com-
pleted, according to these figures.
A globe or sphere is a solid bounded by an evenly curved
suri'ace every point of which is equally distant from a point
within called the center.
m. SPHERES
A cubical block of wood may be made
into a sphere having its diameter equal
to the width of the cube. The wood that
is removed lies chiefly at the comers and
along the edges of the cube. If very
exact weights are made of the cube and
of the sphere, the sphere will be found to
we^h .5236 as much as the cube. Since
the volume of the cube is equal to the cube of its edge and the
diameter of the sphere is equal to the edge of the cube.
PRINCIPLE: The volump of a sphere is equal to .SSaS times
the cube of Its dUmeter.
[Se: page 243.]
Exercise 6
1. Find the volume of a sphere 4 inches in diameter.
Solution: .5236X(4X4X4)=33.5104, number of cubic
inches in volume of sphere.
308 EIGHTH YEAR
2. Find the volume of a sphere 6 mches in diameter.
8. If the earth were a perfect sphere exactly 8000 miles
in diameter, what would be its volume in cubic miles?
' 4. A globe 3 feet in diameter is how many times the size of
a globe 1 foot in diameter?
6. A wood turner makes a wooden ball 3 inches in diameter
from a 3-inch cube. What part of the wood is wasted in making
the ball?
6. Measure the circimiference of a regulation baseball.
Find its diameter. How many cubic inches are there in the
volume of the baseball?
Surface of a Sphere
If a croquet ball be sawed into two equal halves and cord be
wrapped around the curved surface and then around one of the
flat circular surfaces where the ball was sawed, it is fpund
that it requires twice as much twine for the curved surface of
one of the halves as for the circle. It therefore requires four
times as much cord for the whole surface of the sphere as a
circle of the same diameter. Since the area of a circle =7rr*,
the area of the surface of a sphere =4xr2.
7. Find the surface of a sphere 8 inches in diameter.
Solution: Area of surface of a sphere =47rr*.
47rr2=4X3.1416X(4X4) =201.0624.
The area of the surface of this sphere «" 201.0624 sq. in.
8. Find the surface of a sphere 5 inches in diameter; 6 inches
in diameter; 10 inches in diameter.
9. The radius of the earth is approximately 4000 miles.
Find the approximate number of square miles in the earth's
surface.
10. Find the number of square inches of leather in a r^^-
ation baseball cover. (Use measurements found for Problem 6.)
EQUATIONS 309
IV. SIMPLE EQUATIONS
Exercise 1
An equation is a statement of the equality of two quantities.
For convenience in writing equations, letters are generally
used to stand for the unknown numbers.
For example, if we wish to solve the following problem, we
will find it convenient to use an equation:
1. A newsboy sold twice as many papers today as he did
yesterday. During the two days he sold 96 papers. How
many did he sell each day?
We may let the letter X stand for the unknown number of papers sold
yesterday. Then 2X stands for the number of papers sold today.
X H-2X = the total number sold.
But 96 = the total number sold
Therefore X +2X = 96.
or3X=96.
The expression 3X =96 is an equation because it is a statement of the
eqiiality of 3X and the number 96.
If 3X = 96, X =96-^ 3, or 32.
and 2X = 2X32, or 64.
Solve the following problems by using equations:
2. A farmer bought 20 rods of chicken wire fencing. He
wished to make a lot twice as long as it was wide. Find the
number of rods in the length and width of the chicken lot.
Suggestion: Let X= the number of rods in the width. Remember
that there are four sides to be considered in getting the perimeter of the
lot.
3. Mary is twice as old as her brother. The sum of their
ages is 21 years. Find the age of each.
4. A real estate dealer bought a lot on which he built a
house costing three times as much as the lot. If the total
cost of the house and lot was $5200, what was the cost of each?
310 EIGHTH YEAR
6. The sum of three numbers is 84. The second is twice
as large as the first and the third is twice as large as the second.
Find the three nimibers.
6. A farmer has a farm of 80 acres. He has a certain
number of acres in oats; twice as many acres in pasture and
hay as in oats; and five times as many acres in com as in oats.
How many acres has he in each?
7. The area of a rectangle is 56 square inches and the
width is 4 inches. Find the length.
Let X=the length. Then 4 times X or 4X=the area.
8. The area of a field is 80 square rods. The length is
32 rods. Find the width, using an equation as shown in Prob-
lem 7.
Exercise 2
As shown on page 49, an equation may be represented by
a balance. The two sides will therefore balance or remain
equal if we take the same quantity or number from both sides
or if we add the same numbers to both sides.
Suppose we wish to find the value of X in the equation XH-6 = 19.
If we take away 6 from the left side, we shall have left merely the un-
known number X. But if we take 6 from the left side, we must also*
subtra-ct it from the right side to keep both sides of the equation equal to
each other.
X-f6 = 19
Subtracting : 6 = 6
X = 13
If we wish to find the value of X in the equation X— 3=5, we must
add 3 to the expression X— 3 to make it equal to X because X— 3 means
three less than X, the unknown number. If we add 3 to the left side of
the equation, we must also add 3 to the right side to keep both sides of
the equation equal.
EQUATIONS 311
X-3=:5
Adding: 3=3
X =8
Find the value of X in the following equations:
1. X+5 = 12. 11. X+11 = 15.
2. X-4= 9. 12. 3X-- 5=13.
8. 2X+3 = 17. 18. 5X+ 2 = 27.
4. 3X+1 = 10. 14. 2X- 6=12.
5. 2X-2= 8. 16. X-13=19.
6. 6X+4 = 19. 16. 9X+ 4=49.
7. 2X-5 = 11. 17. 3X- 2=13.
8. X+7 = 15. 18. 4X+ 3 = 21.
9. 4X+3 = 19. 19. 7X- 5 = 16.
10. 7X-3 = 11. 20. 5X+ 6 = 26.
Exercise 3
1. The sum of two consecutive numbers is 27. What are
the numbers?
Suggestions: Let X=one number. Then the next (consecutive) num-
ber is X-fl. The two numbers X+X-fl =27 or 2X+1 =27.
Solve the equation 2X-}-l =27 for the value of X.
2. John is 4 years older than Louise. The sum of their
ages is 24 years. Find their ages.
8. Two newsboys made 45 cents selling papers. One made
7 cents more than the other. How much did each make?
4. A farmer bought a horse and a cow for $185. The horse
cost $55 more than the cow. How much did each cost?
6. The sum of two numbers is 80. One is 20 larger than
the other. Find the two numbers.
6. A lawyer received $26.60 for collecting a debt on a
commission of 5%. Find the amount of the debt.
Equation: $26.60= .05 XX.
312
EIGHTH YEAR
Per Cents of Food Substances in the Various
American Food Products
Protein
Fat
Cmrbo-
hydrates
Ash
(mineral)
Water
Refuse
White bread
9.2
8.9
9.8
9.2
16.7
6.4
1.0
26.8
3.3
3.0
2.5
16.7
16.5
14.5
13.7
16.9
3.2
13.7
16.1
14.9
. 6.0
1.8
1.4
7.1
7.0
1.3
1.4
1.4
0.9
1.3
0.7
0.9
0.7
1.0
0.4
8.0
0.4
"0.3
0.8
1.0
0.7
0.6
0.5
0.9
0.2
0.3
1.9
4.3
2.3
11.5
8.6
3.8
6.6
4.6
5.8
7.5
5.2
19.5
6.9
1.3
1.8
9.1
1.9
7.3
1.2
85.0
35.3
4.0
.5
18.5
16.1
7.8
23.2
25.5
27.5
2.1
6.8
18.4
3.0
1.3
0.1
0.6
0.7
0.5
0.1
0.2
0.3
0.1
0.4
0.2
0.4
0.2
0.2
0.4
0.3
0.1
"0.3
0.4
1.2
0.5
0.1
0.4
0.6
0.1
"2.6
0.3
3.0
30.2
33.7
8.3
4.9
41.6
25.6
31.3
33.3
29.1
26.6
53.1
52.1
73.1
75.4
66.2
77.9
••••••••
3.3
5.0
4.8
4.5
'i".i
4.3
"*"".4
3.3
14.7
21.9
22.0
16.9
7.7
4.8
8.9
5.7
10.8
4.6
3.9
2.6
2.5
2.2
79.0
88.0
100.0
70.0
81.0
96.0
10.8
14.3
14.4
5.9
8.6
12.7
7.0
2.7
4.6
70.6
74.2
68.6
9.6
3.6
0.6
45.9
22.9
4.3
6.2
6.2
18.6
6.8
1.1
1.6
2.1
1.0
2.1
.9
3.0
^ 3.8
0.7
0.7
0.5
0.8
0.7
0.8
0.7
3.1
1.3
0.7
0.8
0.9
1.1
0.8
0.9
1.7
1.0
0.9
0.9
0.5
0.6
1.1
0.4
0.5
0.4
0.8
0.4
0.4
0.1
""0."3
0.6
0.4
0.3
0.4
0.4
0.6
0.1
0.3
1.2
2.4
3.1
1.1
2.0
0.4
1.4
1.1
0.8
1.1
.0.7
1.6
.6
35.3
35.7
5.9
12.6
7.7
13.6
11.0
30.8
87.0
91.0
74.0
51.7
58.2
50.3
44.0
50.7
89.0
45.4
42.4
52.9
88.3
62.6
55.2
68.5
74.6
70.0
77.7
78.9
62.7
66.4
44.2
94.3
81.1
80.5
56.6
12.3
11.4
63.3
48.9
58.0
62.5
63.4
76.0
85.9
37.5
44.8
13.8
18.8
13.1
2.7
2.6
.6
21.1
5.4
1.4
1.8
1.4
6.9
1.0
16.4
17.5
14.3
16.6
3.3
33''7
22.7
35.6
20.0
20.0
20.0
15.0
10.0
30.0
20.0
50.0
lO
15.0
40.0
25.0
35.0
25.0
30.0
27.0
10.0
5.0
59:4
50.0
10.0
10.0
45.0
49.6
86.4
15.0
25.0
62.2
52.4
53.2
24.5
58.1
Graham bre&d -
Soda crackers
Corn meal
Oat meal
Buckwheat
Butter
Cheese
Milk
Buttermilk
Cream
Beef
Veal
Pork..._
Mutton.
Sausage ^
Soups
Chicken
Turkey
Fish
Oysters
Potatoes
Sweet potatoes
Beans
Peas
Beets
Cabbage
Onions
Turnips
Parsnips
Squash ... , , .
Tomatoes
Cucumbers
Lettuce
Rhubarb
Rice
Tapioca
Sugar
Molasses .
Honey
Candy —
Apples
Bananas
Grapes
Lemons
Oranges
Pears
Strawberries
Watermelon
Muskmelon
Dates — dried
Figs — dried
Raisins — dried
Almonds
Brasilnuts
Butternuts
Chestnuts
Cocoanuts
Hickory nuts
Filberts
Pecans.... -
Peanuts
Knfflish walnuts
INDEX
PAGE
Addition . . 6-10, 14-18, 156-8
Angles 135-136
Applied decimal problems 38
Applied fraction problems 41-44
Applied insurance problems . 109
Applied measurement problems,
140-141, 149-154
Applied percentage problems, 66-68
Approximation problems . . 178
Bank discount .... 188, 189
Bank draft 191
Bankrupt (broken bench) 180
Banks and banking 179
Barometer 264
Bills of exchange . . .211
Bonds 199-a02
Book binding 153
Book paper 152
Boy scouts 140, 141
Boy's cash account 120
Business forms .... 113
Business transactions ... 77
By-products 67
Cabling money .... 213
Calories 73
Campfire girls 293
Cashier's memorandum . 126
Checking accounts 182
Checks 183, 210
Clearance sales .... 80
Colonial bimgalow 288
Commercial discounts 81
Commissions .... 92, 174
Compound interest 187
Cones 306
Cotton 69,70
Coupons 201
Customs duties .... 100
Daily products . . . 63-65
PAGE
121
169
36
39
37
36
Day book and journal
Decimals 34,
addition of
division of
multiplication of . . .
subtraction of .
Discounts 79, 175
Division drills, . 4-22, 103-107
Efficiency in business . 296
Efficiency in the home 288
Electric meter .... 270, 271
Emergency remittances . . 212
Equations . . . 48, 309
Exchange . . . . 190
Express money order . 208
Express rates .... 130, 131
Family budget . . . 294,295
Federal reserve banks 181
Food products 71
Food values . . . 72-76, 312
Foreign money and travel, 215-217
Fractional equivalents 46
Fractions — Conmion
decimal .
addition of
division of
multiplication of
review of
subtraction of
Freight rates
Gardening .
Good roads
Graphs .
bar .
circle .
distribution
line
pictorial
23
34
25,26
30
29
23, 167
26
131, 132
. 141
. 250
. 255
258,259
. 261
. 260
256,257
. 255
House building and furnishing, 289
313
314
Hygr
Insur
ace
fire
life
Incoi
Indoi
Insur
Inters
Inter
Inter.
Invei
Inves
Inroi
Irrig!
Lines
Makj
Makj
Metr
tal
tal:
tat
tal
tal
Mixe
Mom
Mon
Moti
Mult
Nati<
National expenses
National revenues
Overhead charges .
Paper and printing
Parallelogram .
Parcel post
Partial payments'
Pay roll
Percentage . . .
Perimeter . .
To avoid fine, this book should be returned on
or before the date last stamped below
BOM-
-40
99
. 100
62, 297
149-154
. 142
127-129
89
125-126
45, 77, 170
. . 138
Thermometer .
Time drafts
Trapezoid .
Travelers* checks
Triangles
Trust companies
Type sizes .
Weather reports
Wireless
Writing numbers
145-
PAOI
. 207
133, 219
180
245
61
306
300
2
118
137
207
113
186
127
235
pli.
. 160-164
i 164-166
' . . 191
. 199
! . , 247
! . .301
. 4-22
. 159,164
' . . 307
. . 221
• . . 179
'. 194-198
2, 158, 159
95, 176
. 212
. 262
191-193
. 144
. 218
148, 226, 231
. 179
. 161
266-268
. 214
3