(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "The public school arithmetic and mensuration [microform]"

IMAGE EVALUATION 
TEST TARGET (MT-S) 







1.0 



I.I 



If 1^ I 



M 

2.2 
12.0 



1.8 





L25 


1.4 


III '•* 




^ 


6" - 




► 



V] 



<^ 



/J 



^a 






7: 







y 






/^ 



Photographic 

Sciences 
Corporation 



23 WEST MAIN STREET 

WEBSTER, N.Y. 14580 

(716) 872-4503 




/. 






it 



/a 




CIHM/ICMH 

Microfiche 

Series. 



CIHM/ICMH 
Collection de 
microfiches. 




Canadian Institute for Historical Microreproductions / Institut Canadian de microreproductions historiques 





Technical and Bibliographic Notas/Notes tachniquas at bibliographiquas 



The Institute has attempted to obtain the best 
original copy available for filming. Features of this 
copy which msy be bibliographically unique, 
which may alter any of the images in the 
reproduction, or which may significantly change 
the usual method of filming, are checked below. 



D 



Coloured covers/ 
Couverture de couiour 



I — I Covers damaged/ 



D 



D 
D 
D 
D 

n 



Couverture endommagia 

Covers restored and/or laminated/ 
Couverture restaur^e et/ou pelliculie 



[~~1 Cover title missing/ 



D 



Le titre de couverture manque 



Coloured maps/ 

Cartes giographiques en couleur 



Coloured ink (i.e. other than blue or black)/ 
Encre de couleur (i.e. autre que bleue ou noire) 



Coloured plates and/or illustrations/ 
Planches et/ou illustrations en couleur 



Bound with other material/ 
Reli4 avac d'autres documents 



Tight binding may cause shadows or distortion 
along interior margin/ 

La re liure serrie peut causer de I'ombre ou de la 
distorsion le long de la marge intArieure 

Blank leaves added during restoration may 
appear within the text. Whenever possible, these 
heve been omitted from filming/ 
II se peut que certaines pages blanches ajouties 
lors d'une restauration apparaissant dans le texte, 
mais, lorsque cela 6tait possible, ces pages n'ont 
pas iti film^as. 

Additional comments:/ 
Commentaires supplimentaires; 



L'Institut a microfilm^ le meilleur exemplaire 
qu'il lui a iti possible de se procurer. Les details 
de cet exerT')plaire qui sont peut-^tre uniques du 
point de vu.» bibliographique, qui peuvent modifier 
une image raproduite, ou qui peuvent exiger une 
modification dans la mithoda normale de filmage 
sont indiquAs ci-dessous. 



rn Coloured pages/ 



D 



D 



Pages de couleur 

Pages damaged/ 
Pages endommagies 



p~1 Pages restored and/or laminated/ 



Pages restauries et/ou pelliculies 

Pages discoloured, stained or foxei 
Pages d^color^es, tachetAes ou piquees 

Pages detached/ 
Pages ditachees 

Showthrough/ 
Transparence 

Quality of prir 

Qualit^ inigale de I'impression 

Includes supplementary materii 
Comprend du materiel suppl^mentaire 

Only edition available/ 
Seule Edition disponible 



I ^ Pages discoloured, stained or foxed/ 

I I Pages detached/ 

r~7| Showthrough/ 

r~] Quality of print varies/ 

r~~| Includes supplementary material/ 

r~~| Only edition available/ 



Pages wholly or partially obscured by errata 
slips, tissues, etc., have been ref limed to 
ensure the '*est possible image/ 
Les pages* ro aloment ou partiellement 
obscurcies par un feuillet d'srrata, une pelure, 
etc., ont iti filmies d nouveau de facon <l 
obtenir la meilleure image possible. 



This item is filmed at the reduction ratio checked below/ 

Ce document est filmi au taux de reduction indiquA ci-dessous. 



10X 








14X 








18X 








22X 








26X 








30X 






















y 































12X 



16X 



20X 



24X 



28X 



32X 



The copy filmed here hes been reproduced thanks 
to the generosity of: 

National Library of Canada 



L'exemplaire filmA fut reproduit grAce A la 
g4n4rositA de: 

BibiiothAque nationale du Canada 



The images appearing here are the best quality 
possible considering the condition and legibility 
of the original copy and in iteeping with the 
filming contract specifications. 



Las Images suivantes ont 4t6 reproduites avec is 
plus grand soin, compte tenu de la condition et 
de la nettetA de rexempiaire f ilm6, et en 
conformity avec ies conditions du contrat de 
fiimage. 



Original copies in printed paper covers are filmed 
beginning with the front cover and ending on 
the last page with a printed or illustrated impres- 
sion, or the back cover when appropriate. All 
other original copies are filmed beginning on the 
first page with a printed or illustrated impres- 
sion, and ending on the last page with a printed 
or illustrated impression. 



Les exemplaires originaux dont la couverture en 
papier est imprim6e sont filmte en commen^ant 
par le premier plat at en terminant solt par la 
dernlAre page qui comporte une empreinte 
d'impression ou d'illustration, soit par le second 
plat, salon le cas. Tous les autres exemplaires 
originaux sont filmAs en commenpant par la 
premiere page qui comporte une empreinte 
d'impression ou d'illustration et en terminant par 
la dernlAre page qui comporte une telle 
empreinte. 



The last recorded frame on each microfiche 
shall contain the symbol ^^> (meaning "CON- 
TINUED"), or the symbol V (meaning "END"), 
whichever applies. 



Un des symboles suivants apparaltra sur la 
dernlAre Image de cheque microfiche, selon le 
cas: le symbols — ► signlfle "A SUiVRE", le 
symbole ▼ signlfle "FIN". 



Maps, plates, charts, etc., may be filmed at 
different reduction ratios. Those too large to be 
entirely included in one exposure are filmed 
beginning in the upper left hand corner, left to 
right and top to bottom, as many frames as 
required. The following diagrams illustrate the 
method: 



Les cartes, planches, tableaux, etc., peuvent §tre 
f llmAs A d« i tsMX de rMuction diffArents. 
Lorsque le document est trop grand pour Atre 
reproduit en un seul clichA, II est fiimA A partir 
de Tangle supArieur gauche, de gauche h droite, 
et de haut en bas, en prenant le nombre 
d'images nAcessaire. Les diagrammes suivants 
illustrent la mdthode. 



32X 



1 2 3 




1 


2 


3 


4 


5 


6 



PUB] 



Anthorizt 



c 



THE 



PUBLIC SCHOOL ARITHMETIC 



AND 



MENSURATION^. 



Authorised for use in the Public Schools of Ontario hy the 

Minister of hVucation. 



NEW EDITION. 



TORONTO : 
CANADA PUBLISHING COMPANY, 



(LIMITKD). 



)0'0 



PS 



'-^. I 



\2nteied lu-cording to Act of Parliamejit of Canada, in the year 1!M)0. by the 
Canada Pubmshino Company (Limited), In tlie Office of the Minister 
of Agric'ulture. 



PREFACE. 



The main purposes which liavo been kept in view by the 
authors of this Arithmetic are — (1) to aid a pupil in becoming 
aeeiinite and rapid in calcukition; (2) to train him in 
independent thinking and in applying his knowledge of 
nximbor to the actual business transactions of life; (3) to aid 
the teacher in assigning s.pplieations of the various principles 
which have been explained. The classification of the problems 
has been given with this last aiu) mainly in view. 

Explanations of theory and all formal rule? have been 
omitted, the authors believing that teachers can best supply 
what is necessary in these respects, as the pupils are led to a 
clear comprehension of the principles which should be explained 
by the teacher before the pupils are required to examine the 
problems. It may be here stated that the exercises and 
problems are mainly intended to be used as applications of the 
theory taught. While no direct explanation of theory has been 
given, much lias been suggested by the character of the 
problems and by their arrangement. 

The definitions have been carefully prepared and stated in 
such a way that it is believed the pupil will find little difficulty 
in understanding them. 

Numerous mechanical and practical exercises on the 
fundamental rules for seat work form an important feature of 
the book. In many eases the answers to the mechanical tests 
have been omitted to enable the teacher to judge of the progress 
of his pupils in accuracy and rapidity. 

The exercises are a well -graded and progressive series, 
carefully arranged to develop the reasoning powers of the 
pupil, and at the same time to familiarize him with the 
important practical applications of the science of number. 

The Metric System has been introduced to meet the growing 
demands of the time. 



CONTENTS. 

Facie 

I.— Dkf'Nitions, Notation, Numeratkin 7 

II.— TnK Simple Kules— 

I. AdtUtiou 11 

II. Subtntetion 22 

III. Multiplication 30 

IV. Division 37 

V. MiscellaneouH Exercises 43 

III. — Compound Numbers- - 

Tables, Definitions, Etc 50 

IV.— Simple Applications op i.ie Previous Rules— 

I. Bills and Accounts GO 

II. Simple Measurements (53 

Carpeting 64 

Plactering 06 

Wall Paper 67 

Board Measure 68 

Rectangular Solids 69 

III. Sharing 72 

IV. Averages 75 

V. — Factors, Cancellation, Measure^, and Multiples — 

I. Factors 78 

II. Cancellation 79 

III. Measures... 80 

IV. Multiples 82 

VI. — Fractions — 

I. Definitions, Notation and Numeration 84 

II. Reduction of Fractions 85 

III. Addition of Fractions 90 

IV. Subtraction of Fractions 92 

V. Multiplication and Division of Fractions 95 

VI. Complex Fractions 101 

VII. -G. CM. and L. CM. of Fractions 102 

VIIl. Denominate Fractious 103 

IX. Applications of the Previous Kules 105 



Vl C'ONTKNTS. 

Vil. — DKf'IMAI.S— 

I. DefiiiitioTis, Notation and Nuinovation 115 

II. Addition of Dccinmls 117 

III. Subtnu'tion of J)t'<'inialM 118 

1\'. iMultipliciition of Dfciniuls 121 

V. Division of Doeinials 122 

VI. Reduction of IhMdniiils 124 

VII, Applications of tlic I'lcvioiiH Rules 125 

VIII.— Pkuckntaoe - 121) 

IX. — API'MCATIONS of PF,K('KNTA(iK— 

I. Trade Discount 134 

II. Profit and Loss Hid 

III. Commission 1;{S 

IV. Insurance 140 

V. Taxes 142 

VI. Simple Interest 144 

VII. Compound Interest 14G 

VIII. Bank Discount 147 

IX. Stocks and Dividends 14J> 

X. F^quation o£ Piiyincnts ir)2 

X. — Pautnership ir)4 

XI.— Invom'TIon and Ev<)r,i"ri(»x — 

1. Involution loG 

II. Square Root 1.'58 

III. Cube Root ir.9 

XII. — Mensuration IGl 

XIII. — The Metric System of Weights and Measures.... 172 
XIV. — Miscellaneous P^xercises — 

I. Cireulatiuf? Decimals 177 

II. Problems Relating to Work Done 180 

III. Clock Problems 181 

IV. Problems Involving Velocity 182 

V. Problems Involving the Sum and Difference of 

Two Numbers 183 

VI. Review Exercises for Third Class 185 

VII. Review Exercises for Fourth Class 187 

VIII. Review Exercises for Fifth Class '. 190 

XV.— Answers 198 



ARITHMETIC. 



CHAPTER I. 



DEFIINITIOINS. INOTATIOIN. INUMERATIOIN. 

A Unit is a single thing or a definite quantity; as 
1 lK)f)lv, 1 foot, 1 score, 1 four-oiinee weight, i half- 
ounce weight. 

A INumber is that which is applied to a unit 
or to a group of units for the purpose of answering 
the question ' ' How many ? " or " How much ? ' ' 

Arithmetic is the science whi<'h treats of numbers 
and the art which uses them in computation. 

Numbers are either Concrete or Abstract. 

A Concrete INumber is one whi(*h names the kind 
of unit used; as 4 tons, 6 horses, 3 dozen eggs, 5 
half- ounce weights. 

An Abstract INumber is one in which the kind of 
unit is not named, as 4, 6, 9, 17. 

Notation is the expression of numbers by means of 
symbols. 

Arabic Mctation is the expression of num))ers by 
means of figures. 

Roman INotation is the expression of num])ers by 
means of (certain letters called liomati Numerals. 

Numeration is the reading or writing in words of 
a number expressed in symbols. 



8 



1. 
2. 
3. 
4. 
6. 
6. 
7. 
8. 
9. 
10. 



(> 
If) 

i<; 

94 

2:{ 

(53 

4'J 
2H 
79 



AKITIIMKTIC. 




EXERCISE 1. 




rords tlic 


followinR 


: — 


T) 


9 


7 


21 


12 


31 


(>! 


71 


81 


9;i 


30 


47 


H({ 


68 


76 


:i4 


43 


45 


78 


87 


91 


2;') 


52 


20 


95 


59 


(59 


48 


84 


04 



8 


4 


i:i 


17 


18 


92 


74 


49 


07 


.'{2 


54 


50 


19 


24 


02 


82 


90 


97 


46 


100 



EXERCISE II. 

Write In words the following;: — 



1. 


500 


700 


800 


200 


000 


400 


2. 


830 


470 


(509 


714 


800 


990 


3. 


007 


700 


070 


7(50 


901 


109 


4. 


847 


784 


478 


748 


874 


487 


5. 


205 


400 


507 


705 


570 


750 


6. 


4705 


5843 


91(58 


2049 4905 


4231 


7. 


8007 


8070 


8700 


7080 7008 


9045 


8. 


50(58 


9008 


0202 


1508 3746 


5780 


9. 


21.34 


1234 


1243 


4321 4132 


8009 


10. 


9001 


1009 


9001 


9100 9010 


9080 






EXERCISE III. 






• 


Write 


in words tlie following: — 








1. 


40870 




54089 


30070 




91111 


2. 


54089 




40058 


39007 




40100 


3. 


81095 




59100 


95101 




37098 


4. 


819075 




891492 


294710 




410101 


5. 


210010 




918005 


231040 




217000 


6. 


1470931 




3790842 


910010 




2103001 


7. 


3091000 




4007007 


190100 




3019047 


8. 


17091807 




93704905 


903705 




21010101 


9. 


40097000 




30910405 


9317900 




70000005 


10. 


2309400100 


91491591(591 


1013210012 


7060700001 



EXERCISE IV. 

Write in figures: — 

1. Fifteen; twenty-one; tliirty-four; seventy-eight; eighty - 
seven; nineteen; ninety-one. 



DEFINITIONS, •.OTATION, NUMERATION. 







2. One hundred; one hundred and seven; three hundred and 
Hix*«'»'n; four hundred and forty; nine hundred and nine; nine 
hundred and nineteen; nine hundred and ninety-one. 

3. One thousand; one thousand, four liundred and two; eijcht 
thousand and six; eijfht thousand and sixty; two thousand, four 
hundred and ninety-six. 

4. One thousand and eleven; ten thousand, six liundred and 
four; twenty-nine thousand, four hundrtid and seventy; eighty 
thousand, nine hundred and ninety. 

r-t. Eight hundred and four thousand and sixteen; two 
hundred and ninety-one thousand, seven hundred and four. 

6. One million, one hundred and one thousand and one; five 
million, four thousand and thirty. 

7. Nine hundred and fifty-four million, eight hundred and 
six. 

8. Seven million, seven hundred and seven thousand, seven 
hundred and seven. 

0. One hundred and forty-six million, one hundred and 
forty-seven thousand and forty-seven. 

10. Five hundred and thirty-six million, three hundred and 
forty -seven thousand, nine hundred and seventy -two. 

11. Six billion, ninety-five thousand, one hundred and 
forty-eight; seven hundred billion and one. 

12. Ninety-nine billion, thirty-seven thousand and four. 

13. Eight hundred and sixty-four billion, five hundred and 
thirty-eight million, two hundred and seventeen thousand, nine 
hundred and fifty -three. 

14. Forty billion, four million, four hundred thousand, four 
hundred and fourteen. 

15. Forty-nine trillion, fifty-eight thousand, seven hundred 
and ninety-eight. 



Write in Roman numerals 



1. 


5 


2. 


15 


3. 


25 


4. 


49 


5. 


109 


6. 


240 


7. 


404 


8. 


796 


0. 


875 


10. 


973 


11. 


1900 



EXERCISE 


V. 


erals : 
6 


8 


16 


18 


26 


28 


45 


94 


104 


105 


249 


394 


444 


499 


789 


777 


857 


578 


9(55 


999 


1889 


1899 



9 
19 
24 

98 
219 
388 
589 
766 
894 
987 
1849 



4 

•14 

44 

99 

329 

356 

594 

699 

984 

944 

1904 



10 



ARITHMETIC. 



i£XERCISE VI. 

Write in figures: — 

1. XV, XC, XCIV, LXIX, XLIV, XCIX, LXXXIX, CX. 

2. CXI, CIX, CXLIV, CCXXIX, DIV, CCXLIX, DCCIX. 

3. CDIV, DCCXXX, DXL, CDXLIV, DXXIX, DCXXIV. 

4. DCCCXXXIII, CDLXXXIV, CCCXXXIII, CDXXXIV. 

5. DV, CDXXX, CCXCVII, CCXLIV, CCCXXIII, DLV. 
G. MCXI, MD, MXIV, CMXC, CMXCIX, AICCCLIV. 

7. MCCXC, MDLV, MCDXLJV, MIX, MCCXXII, ^ICDXC. 

8. MMCCXXII, CMXLVII, MCMVI, MCD, MCvIIX, MDLV. 
y. MDCCXLIV, MCDXLIX, MDCLXVI, MMIX, MCXIX. 

10. MDXCIX, MCM, MCMI, MDCCCXCIX. 



EXERCISE VII. 

1. Write in Arabic Nrnnerals the smallest number that can 
be expressed by two figures ; by three ; by four. 

2. Write in Roman Numeruls the largest number that can be 
expressed by three figures. 

15 . What is the effect of writing a letter of less value before 
one oi a larger valuef Give four examples illustrating this, 

4. To the left of only what letters can I be placed in Roman 
Notation? 

"). To the left of only what letters can X be placed in Roman 
Notation i 

6. Write the significant ngures and express each in Roman 
Notation. 

7. What letters in Roman Notation are never repeated? 

8. Write in words the following sentences: — The earth is 
92890000 miles distant from the sun. The lei.gth of the equator 
is- 'i:{827033 yards. The cheese factories of Ontario produced 
13r'->b:?91G pounds of cheese in 1897. The milk used in making 
*iiis cheese was 1455937148 pounds. In 1898 the 98 creameries 
lii '.''i'" returns to the Bureau of Industries produced 9008992 
pounds of butter, valued at 1632234 dollars. 

9. What numbers can be expressed by means of the letters 
V and X taken separately or in combination? 

10, Express "n Arabic Numerals all the numbers of three 
figures that can be expressed by means of the letters X and G 
taken together or separately. 



CHAPTER II. 



THE SIMPLE RULES. 



I. ADDITIOIN. 



Addition is the process of linding a number equal 
to two or more numbers of the same kind. 

Tlie Addends are the numbers to be added together. 

Tlie Sum is the single number which results from 
the addition. 

The sign of addition is +, called plus, and when 
placed between two numbers it shows that these are 
to be added. 



1. 



2. 



8. 



4. 





EXERCISE VIII. 








14 


41 


52 


42 


33 


21 


23 


12 


12 


21 


32 


13 


25 


15 


123 


421 


241 


222 


234 


321 


110 


345 


333 


311 


231 


242 


102 


123 


132 


313 


123 


410 


321 


321 


134;-) 


2111 


1012 


1000 


4443 


2231 


4001 


3421 


1234 


2224 


2423 


2403 


1323 


2423 


1201 


3000 


3121 


4231 
5231 


5341 


2100 


5123 


4112 


7111 


7231 


4132 


5234 


4211 


5000 


3412 


G210 


7110 


5341 


3123 


4123 


3111 


4231 


0204 


4351 


5201 



11 



12 



5. 





AUITHMETIC. 






71112 


52123 


71241 


71122 


82013 


41231 


41024 


32026 


20311 


41012 


51640 


62301 


41010 


42133 


50601 


41013 


70021 


52401 


54332 


41203 



6. 2031+1234+3122-f 1010+100. 

7. 1207+3040+2430+112+2000. 

8. 51+3027+2000+1500+1320. 

9. 21021+12+32+2700+12000+102+21. 
iO. 12201+21+142+23000+2100+2012. 



EXERCISE IX. 

1. John has 10 cents; Bob has 25 cents; Harry has 14 cents. 
How many cents have thev together? 

2. A cow cost $21, a pig $14, and a sheep $12. How much 
did all cost? 

3. A farmer drew five loads of wheat to market. He had 41 
bushels in the Ist load, 42 in the 2nd, 40 in the 3rd, 42 in the 
4th, and 44 in the 5th. How many bushels were in the five 
loads? 

4. I walked 21 miles on Monday, 22 on Tuesday, 21 on 
Wednesday, and 23 on Thursday. How far did I walk in the 
4 days? 

5. A train goes 31 miles the Ist hour, 30 the 2nd, 32 the 3rd, 
and 31 the 4th. How far has it gone in the 4 hours? 

6. The population of four cities is as follows: the first 
111203, the second 21.n23, the third 11221, and the fourth. 
611222. What is the total population of these four cities? 

7. A merchant bou.crht four pieces of cloth. The first was 
203 yards long, the eeeoud 321, the third 223, and the fourth 
222. How many yards were in the four pieces? 

8. An ocean steamship sailed 312 miles on Tuesday, 324 
miles on Wednesday, 320 miles on Thursday, and 411 miles or 
Friday? How far did it sail on these 4 days? 

9. A steamship leaving Montreal for Liverpool had on board 
415 cattle, 240 sheep, and 131 horseB. How many head of live 
stock were on board? 

10. A history consists of 4 volumes. In the first there are 
412 pages, in the second 410, in the third 415, and in the fourth, 
431. How many pages are there in the entire history? 



d on board 
ead of live 







ADDITION 


> 




13 






EXERCISE 


X. 






1. 323 


233 


123 


312 


311 


2323 


232 


222 


132 


123 


233 


3211 


333 


333 


213 


323 


322 


2332 


233 


310 


231 


333 


113 


3123 


312 


232 
2133 


321 
2323 


223 
3213 


333 
23132 


2323 


2. 3233 


32133 


3233 


3032 


3223 


2133 


21332 


32332 


2332 


3321 


3332 


3321 


33213 


32223 


3123 


3333 


2332 


2332 


23323 


23322 


3321 


2332 
21321 


3212 
32212 


3323 
23213 


32133 


12233 


3. 31333 


23213 


32132 


23213 


21332 


31232 


23223 


32123 


22321 


31220 


32132 


21332 


32213 


32233 


31223 


33303 


32013 


21321 


33223 


32213 


20301 


10332 


32103 


33233 


13322 


32132 


21303 


12321 


23321 


13321 


32332 


21331 


33233 


4. 34124 


41234 


24134 


41234 


41341 


21314 


31413 


32134 


24413 


44341 


24143 


44143 


24130 


24341 


34123 


24132 


34124 


21321 


24133 


43214 


41244 


41421 


34143 


40143 


40241 


43441 


32412 


34134 


21414 


21434 


30213 


14234 


22141 


21414 


34140 


24143 


T). 13412 


41324 


41321 


51321 


32132 


51324 


4G712 


62132 


35326 


41324 


46213 


42676 


3r)273 


41653 


45624 


41324 


24132 


25014 


24134 


25623 


52334 


50604 


3(5213 


30629 


4r)0o2 


32134 


41302 


60621 


41621 


46532 


3r)213 


43253 


10343 


40132 


41321 


42624 


0. 41324 


41324 


41321 


32562 


41324 


41321 


34120 


16213 


62162 


31416 


30143 


41032 


604(52 


40123 


42342 


20413 


62143 


40162 


30(521 


30(523 


62103 


401(52 


40132 


32162 


41032 


43216 


66552 


41324 


40110 


41314 


41(521 


2U32 


45625 


51602 


62162 


62132 



14 



ARITHMETIC. 



7. 



5232 
4013 
6217 
3017 
1472 
1213 



41321 
00213 
41002 
41321 
42321 
41021 



32134 
22343 
402()2 
S21(i3 
41323 
41021 



413212 
413210 
413210 
4()r)271 
017172 
312711 



3121 
4137 
5702 
3502 
5213 
4134 



37124 
34135 
25312 
40352 
70712 
34372 



8. 81876 


41342 


21341 


41832 


41372 


41783 


413^2 


48324 


62437 


41072 


47726 


47807 


34027 


78772 


24167 


32171 


68783 


87710 


18704 


40724 


82416 


42313 


27107 


37872 


31241 


37802 


37137 


57717 


27178 


47132 


01375 


41371 


41683 


87071 


37183 


41367 


9. 41340 


41837 


41372 


41672 


41834 


41837 


21347 


08773 


46837 


37183 


67832 


41678 


70827 


41701 


46713 


63784 


41786 


38678 


48372 


37450 


48783 


32487 


67138 


32168 


48372 


75071 


67187 


67137 


41687 


41767 


41071 


38710 


38147 


47183 


48371 


89168 


0. 41071 


13716 


41371 


41372 


71324 


41674 


00872 


41372 


02710 


48637 


67168 


34187 


41876 


67187 


04701 


24873 


32417 


62184 


86716 


47183 


37124 


21437 


03418 


67132 


40713 


80713 


37072 


67138 


40728 


48667 


87241 


40713 


48372 


63418 


87832 


47183 




EXERCISE 


XI. 




1. 370693 


732894 


507] 


126 


770655 


764845 


777777 


555123 


432733 


007755 


999999 


531234 


456789 


567643 


554488 


888888 


135789 


579040 


219872 


998877 


777777 


973124 


843757 


876464 


776654 


666606 


70383 


984329 


597777 


897987 


245678 


507890 


432173 


66466 


764896 


457896 


2. 348037 


460375 


963] 


[72 


849652 


962847 


272405 


841681 


300725 


361728 


777888 


530034 


239724 


403;: 


48 


412381 


888999 


109871 


763256 


721003 


035403 


789789 


093036 


437891 


387356 


872545 


678678 


704543 


825432 


241653 


400223 


897987 


233038 


285678 


u03'J 


80 


294867 


387047 


428432 


310720 


5321 


70 


811230 


480578 



ADDITION. 



15 



37124 
34135 
25312 
40352 
70712 
34372 



3897(53 
210045 
76080(5 
(53(5215 
253734 
251600 
575453 
807720 



403521 

687489 
324061 
530724 
623452 
487(538 
290731 
803256 



278321 
829248 
171320 
20(>782 
461027 
589203 
248639 
730461 



576037 
213744 
764368 
305216 
436720 
823284 
217436 
592301 



364728 
246374 
478369 
287456 
93(5478 
184369 
678456 
286397 



4. 379623 


891371 


889977 


789 


8000000 


7542 


919198 


732894 


723 


667755 


25320 


171296 


555123 


674 


44332 


57644 


1478(57 


456013 


1674 


3355778 


908176 


182371 


579646 


19006 


986754 


73409 


929292 


843751 


1916 


71347 


3147 


292929 


984329 


■ 986986 


981675 


67039 


777777 


432173 


97979 


19198 


5. 3824442 


67124332 


25927871 


3267362 


7778889 


4563358 


31734324 


71684655 


2152837 


4581986 


1612119 


19524324 


69351437 


4627792 


3599872 


5121223 


53414325 


35927212 


3564465 


2998767 


8232535 


57384327 


21614892 


2152322 


9887651 


6348442 


42624329 


74321572 


4617777 


8776548 


3454384 


75218671 


69987452 


3564416 


7665434 


2563125 


83186438 


25654232 


2152362 


6554326 


4673995 


41986974 


71381011 


4617727 


5443213 


6. 6739484 


87665163 


94358975 


95639888 


99888777 


5263898 


57946295 


2848 


86872569 


22586972 


9688626 


43937568 


9184 


11191993 


57486976 


7445853 


89264339 


45339 


32384345 


21586972 


6899438 


2613 


987672 


95339888 


93456975 


8123814 


9155 


93783891 


85372569 


46556972 


4598603 


5278 


26753984 


14891173 


25496977 


2355792 


87667549 


66344839 


36684845 


47556979 


1773424 


49623 


94982172 


71739188 


21457979 


7. 4008811 


31412 


657118 


294044 


95299 


1854239 


30088 


182595 


199639 


8720834 


705 


150 


5520 


17228 


436292 


14872 


1500 


525 


17370 


400283 


6498119 


5363277 


497454 


41762 


2344900 


1 055308 


3187 


57768 


482511 


12137980 


371498 


18015 


23247 


1027 


11089359 


4040559 


4(5976 


990019 


1088534 


3633750 


12526543 


1278225 


2150113 


9414575 


295984 



-«^ia.. 



16 



3 




ARITIFMETIC. 






8 


1288153r) 


624564 


2610287 


6214458 


131917 




2171188 


209840 


373898 


1530581 


3400/17 




9947r)2:{, 


213954 


2297433 


2142822 


28()0765 




683069 


1957 


109897 


417 


25396S 




9243811 


2434454 


1364034 


296259 


71894 




3086160 


3975 


477438 


4494680 


41729 




8071370 


7088142 


585138 


31211 


535955 




7065878 


1011492 


2043283 


4925889 


11212616 




4346234 


21191 


559619 


137990 


4286131 




7834359 


203572 


1627164 


2981652 


517562 


9. 


6967056 


3196563 


1108476 


185658 


57636799 




9487210 


365756 


375396 


1601190 


63927094 




79766094 


49741413 


10071301 


13121498 


19154873 




4146290 


95921 


970738 


2130102 


25981652 




34449379 


20819542 


10196".71 


14487351 


7165.3431 




39878418 


2505034 


4481ii70 


15367691 


62327299 




995670 


316508 


129692 


49 


29987988 




2981850 


4970 


487233 


1066277 


7565487^^ 




8139585 


177681 


1364378 


1619386 


61321716 


10. 


8529883 


27932143 


93789391 


22872769 


75700757 




3593652 


53969235 


26745984 


75191997 


36471241 




9658934 


49265558 


66357839 


96484343 


75057906 




6475424 


87647389 


94946172 


81539885 


44346505 




3757873 


87931693 


93787391 


12872568 


91753002 




3363662 


53929135 


26782644 


.35791979 


77647300 




8829744 


49298258 


66359199 


96284343 


76044071 




2293413 


87651589 


94945222 


81339885 


82872633 




7958882 


87973397 


93787511 


12672568 


99872517 




8175659 


75982231 


65781737 


35891219 


86297761 




( 


EXERCISE XII. 


- 




1. 


Add togeth 


er 763, 4663, 37, 49763, 


6178, and 671. 




Add together 15, 7896 


, 1, 13, 106, 113, 156, 100, 


and 2201. 


3. 


Add togeth 


er 100375, 406780, 467300; 


), 4112, 2478, 


79, !Uid8. 


4. 


Add together 123405, 


2354210, 79431 


27, 36547, and 789. 


5. 


Add together 275L32, . 


345007, 4567801, 365, 1896, 


and 78G9. 


6. 


Add togeth 


er 70, 189, 


3684, 72, 8967, and 798. 




7. 


Add togeth 


er 982, 369 


, 764, 8, 89, 75, and 396. 




8. 


Add togeth 


er 7, 89, 8, 


7098, 38, 471 


, 78, and 1899. 


9. 


Add together 968, 777 


, 78, 408, 700, 


9009, and 7 


. 


10. 


Add together 7698, 4, 


790, 87, 3694, 


78, and 897 


• 



i.iion 


'^H 


3400717 




28(507<)r) 




•jriiujes 




71894 




41729 




r):{r)9r>5 




11212616 




4286131 




5l7r)62 




57636799 


a 


63927094 




19ir)4873 




25981652 




716."i3431 




62327299 




29987988 




7565487'^ 




61321716 




75700757 




36471241 




75057906 




44346505 




91753002 




77647300 




76044071 




82872633 




99872517 




86297761 




671. 




)0, and 2201. 




78, 79, and 8. 


■; 


and 789. 


\ 


)6, and 7809. 


i 


1. 


i 


6. 




1899. 




li 7. 




897. 


■ 




^ 



ADDITION. 
EXERCISE XII.I. 



17 



1. 7634129+ 7634-f830604-|-937+856312+37140+694713284- 
85'j4695. 

2. 9093+846295+37G05f54+57312858+581401+393+4301201. 

3. 51316281+7413819+543628+71434-717562+8319886. 

4. 79+;'*(53+900832+8632+473423+644+1000000. 

5. 789632+71+879002+876+970+329449. 

6. 92+853+7654+65432+543210+4321098+321976+2109+ 
1098+182. 

7. 6290+704+713+4631+5214+289+3102+41. 

8. 483+9000+648+3750+9840+24680+5096. 

9. 103421538+120952657+116843889+116491051. 
10. 82+92+102+873+824683+2000201+489076. 

EXERCISE XIV. 

1. B^ind the sum of 27, 36, 45, 52, 8V, 29, 16, and 11. 

2. A farmer has five fields of grain. In the first there are 
27 acres; in the second, 42 acres; in the third, 97 acres; in the 
fourth, 86 acres; and in the fifth, 102 acres. How many acres 
are there in the five fields? 

3. James has 27 marbles; John has 83; Harry has 116; and 
Tom 46. How many have they all? 

4. James rode 17 mi]es on Monday, 23 miles on Tuesday, 
41 miles on Wednesday, 36 miles on Thursday, 17 miles on 
Friday, and 24 miles on Saturday. How far did he ride during 
the 6 days? 

5. A farm cost $4816, a house $2345, a horse and buggy $158, 
and a cow $34. How much did all cost? 

6. A drover had 327 sheep, 245 cows, 584 pigs, and 117 
horses. How many animals had he in all? 

7. In a~i orchard there are 417 apple trees, 176 peach trees, 
245 plum trees, and 47 pear trees. How many trees are there 
in the orchard ? 

8. Add 294, 421, 76, 109, and 217 together, and express the 
result in Roman numerals. 

9. In 1897 the population of the County of Oxford was as 
follows i Townships, 28780; Towns, 15801; Villages, 1810. 
What was the total population of the county in 1897? 

10. To the sum of 14, 17, 25, and 96, add the sum of 18, 12, 
19, and 25. 



18 



ARITHMETIC. 



EXERCISE XV. 

1. Tom had 17 mnrbles; ho houj?ht 5 mor«*, and his brother 
gave him IS. How many had he then f 

2. A man paid $22 for a suit of clothes; *$2 for a hat; $6 for 
a pair of boots; and $1") for underwear. What did he pay 
for all? 

3. John's book has 216 pages; Mary's, 492; and Harry's, 
162. How many jtages are there in the three books? 

4. A man travelled 247 miles on Monday, 36 miles on Tues- 
day, and 17 miles on Wednesday. How far did he go in the 
three days? 

5. Find the sum of 47 cents, 93 cents, 107 cents, 483 cents, 
and 270 cents. 

6. Add $128, $1275, $468, $17, and $12. 

7. A man spent $127 one day, $47 another, and $96 another. 
How much did he spend altogether? 

8. Edwin had 35 cents: he found 16 cents, and his brother 
gave him 47 cents. How much had he then? 

9. A man wheeled 37 miles on Monday, 46 on Tuesday, 34 
on Wednesday, 52 on Thursday, 28 on Friday, and 11 on 
Saturday. Ho- v far did he wheel altogether? 

10. A man began business with $3795. His gain the first year 
was $824; the second, $491; the third, $726; the fourth, $1211; 
and the fifth, $809. What is he now worth? 



EXERCISE XVI. 

1. Find the sum of all the numbers, from 749 to 760, 
inclusive. 

2. Three men bought a farm. The first paid $2468; the 
second, $2032; and the third, as much as the other two. Find 
the cost of the farm. 

3. Ella picked 378 baskets of berries, and Jane picked 58 
more than Ella. How many did both pick? 

4. A schoolroom is 32 feet long and 21 feet broad. How 
many feet is it round the room? 

5. Willie gave John 37 cents and Mary 48 cents. He had 
as many cents left as he had given away. How many cents had 
he at first? 

6. A farmt?r bought a pig for $19, a cow for $39, a sheep for 
$13, and a horse for as much as he paid for the pig and the 
cow. How much did he pay for all? 

7. My brother gave me 32 cents; my father gava me 8 cents 
more than my brother, and my mother. gave me as much as 
both. How much money did I receive? 



ADDITION. 



19 



8. Helen spent 117 cents for books, 121 cents for ornnjjes, 
44 cents for peacheH, l.'Jl cents for sugar, and had 87 cents left. 
How much had she nt first? 

9. A farmer has lo acres of whwit, 29 acres of barley, 17 
a^'res of peas, 19 acres of corn. The rest of the farm is in 
pasture, and there are as many acres of pasture as of grain. 
How many acres has he altogether? 

10. A drover >)ought 27 sheep for $11.'5 from one farmer; from 
a second, he bought 35 sheep for $142; and from a hird, 28 
sheep (or $1.32. How many sheep did he buy, and how much 
did they cost him? 



EXERCISE XVII. 

1. Find the sum oi $42, $9136, $254, $29, and $530. 

2. At the World's Fair a man spent $37 the first week; $46 
the second; $84 the third; and $9o the fourth. His other 
expenses were $87. How much did he spend during the four 
weeks ? 

3. In 1897 the population of the County of Essex was 431.54; 
of Kent, 44183; of Elgin, 29659; of Norfolk, 29231; of Haldi- 
mand, 2^263; and of Welland, 30305. What was the total 
population of these six counties? 

4. In 1896 the debenture debt of Ontario was as follows: Of 
township^, $2866904; of towns, $9598063 ; of villages, $1163096; 
and of cities, $37471231; of counties, $1848982. What was the 
total ^ jbenture debt of Ontario? 

5. A drover bouj^ht three flocks of sheep. The first contained 
967, the second 133 more than the first, and the third 450 more 
than the second. How many sheep did he buy altogether? 

6. Sarnia is 62 miles west of London: Ijondon is 115 miles 
west of Toronto, and Toronto is 333 miles west of Montreal. 
How far is it from Sarnia to Montreal ? 



7. T lost $29 by selling a-horse for $71. 
horse cost me ? 



How much did the 



8. For how much must I sell a horse which cost me $91, so 
as to gain $29 ? 

9. John has 27 cents more than Willie, who has 84 cents. 
How much money have both together? 

10. The first of three number" is 846, the second is 987, and 
the third is as much as the other two. Find the sum of the 
three numbers. 



20 



ARITHMETIC. 



EXERCISE XVIII. 



H 1 1 
l! Il 



1. A boat Bails from St. Catharines to Toronto, 45 miles; 
from Toronto to Montreal, 93.") miles; and from Montreal east- 
ward a distance eijiial to that from bt. Catharine*? to Montreal. 
Find the total distance sailed. 

2. Add 675, one Taillion and nine, four thousand and six, 
302, fortj -one thousand six hundred and four, 21436, ninety- 
seven, 84, and ninety-one thousand four hundred and seven. 

3. 1 bought wheat for $4')i)i], corn for $2347.1, oats for $8796. 
I sold the wheat at a gain of $1404, the corn at a gain of $6525, 
and the oats at a gain of $204. How much did I get for allf 

4. After selling 1016085 oranges, a merchant had two lots 
left, one containing 69756 and the other 85619. How many 
oranges had he at first? 

5. A man sold a horse for $986, and three cows for $680 
each. He lost $125 on the horse and $220 on each cow. How 
much did all cost him? 

6. How many times does a clock strike in 12 hours? 

7. I bought wheat for $7962, corn for $12649, oats for $8763. 
I sold the wheat for $780 more than the cost, and the corn and 
oats at a gain of $1685 on both. How much did I get for all? 

8. A lady paid $380 for a piano, $275 more than that sum for 
furniture, and*$2675 for a house, and has still $8375 in the bank. 
What sum had she at first? 

9. A fai'mer gave to each of his three sons $6580, .and to his 
daughter $920 more than to two sons. How much did he give 
away altogether? 

10. A man gave his wife $10560, his two sons $7325 each, and 
his daughter $485 more than a sou's share. How much did he 
give away? 

EXERCISE XIX. 



1. In 1S97 the population of the townships of Ontario was 
1113530; of the towns, 312947; of the villages, 1.33560; and of 
the cities, 430940. What was the population of Ontario in that 
year? 

2. In the B'vttle of Waterloo it is said that of the soldiers 
engaged 36273 were Briti«)i, 7447 were Hanoverians, 8000 were 
Brunswickers, and 21000 were Belgian, whilst there were about 
75000 French. How many were there of the four allies, and 
how many combatants were there altogether? 

3. A father leaves an estate to" his son, daughter and wife. 
To his son he leaves 5355 dollars, to the daughter 500 dollars 
more than to the son, and to the wife 1500 dollars more than to 
the daughter. What was the amount of the estate ? 



ADUITIUN. 



21 



1, 45 miles; 
mtreal eiint- 
trO Montreal. 

ind and six, 
436, ninety- 
nd Heven. 
,ts for $8790. 
ain of $6525, 
;et for allf 

had two lots 
How many 

)W8 for $680 
li cow. How 

lurs? 

its for $8763. 
the corn and 
get for all? 

that sum for 
) in the bank. 

iO, .and to his 
did he give 

325 each, and 
much did he 



' Ontario was 
]3560 ; and of 
ntaric in that 



4. John threw a hall 34 yards up the road, and another 43 
yards down the roml. How fur must he walk to bring them 
both ba<'k agiiin ? 

5. The first of four numbers is 4768, the second is 170 
more than the first, the third is 90(5 more than the second, and 
the fourth is as much as the other three. What is the sum of the 
four imnibcrsf 

6. Mary bought a book for which she gave 95 cents; Maudo 
bought oiH' for which she gave 13 cents more than Mary; aiul 
Maude's book cost 23 ci'iits less than Jane's. Find the cost 
of .lane's book. 

7. Find the number of days in a year — the days of the 
respective months being as follows: January 31, February 2H, 
March 31, April .30, May 31, June 30, July 31, August 31, 
September 30, ()ctol»er 31, November 30, December 31. 

8. Adam lived 930 years; Seth, 912; Enos, 905; Cainan, 
910; Mahaleel, 895; Jared, 962; Enoch, 365; Methusaleh, 969; 
Lamt^ch, 777; Noah, 950; Shem, 600; Arphaxad, 438; Salah, 
433; Heber, 464; Peleg, 239; Keu, 239; Serug, 2:10; Nahor, 
148; Terah, 205; A>»raham, 175; Isaac, 180; Jacob, 147; 
Joseph, 110; Moses, 120; Joshua, 110. What is the sum of all 
their ages? 

9. Water-mills were invented in the year 555 after Christ; 
windmills 744 years after water-mills; pumps 126 years after 
windmills; printing 15 years after pumps; watches 37 years 
after printing; the spinning-wheel 53 years after watches; 
the steam-engine 119 years after the spinning-wheel; the fire- 
engine 14 years after the steam-engine; the spinning-frame 98 
years after the fire-engine; and the electro-magnetic telegraph 
71 years after the spinning-frame. In what year was the electro- 
magnetic telegraph invented? 

10. A man bequeathed his estate as follows: To each of his 
two sons, $12450; to each of his three daughters, $6500; to his 
wife, $650 more than to both the sons; and the remainder, 
which was $1000 more than ho had left to all his family, he 
gave to benevolent institutions. What was the whole amount 
of his property? 



f the soldiers 
ns, 8000 were 
re were about 
ur allies, and 



ter and wife, 
er 500 dollars 
1 more than to 

e? 



oo 



ARITHMETIC. 



II. SUBTRACTIOIN. 

Subtraction is tlio process of ftndiiijf ilie differenco 
between two iiuinbers of the same kitid. 

The IMInuend is the number from whieli tlie other 
number is taken. 

The Subtrahend is the number whieli is taken 
from the minuend. 

The Difference or Remainder is the num1)er 
found by taking the subtrahend from the minuend. 

The sign of Su])traetion is — , called minKs, and 
when written between two numbers it shows that the 
number after it is taken from the one before it. 

EXERCISE XX. 



». 



4. 



i). 



59 


07 


29 


47 9() 


87 


99 


23 


54 


t() 


21 32 


52 


73 


786 


938 


897 


984 


593 


898 


245 


412 


504 


421 


242 


452 


674 


849 


928 


547 


693 


989 


52 


417 


415 


231) 


451 


472 


8947 


5986 


9397 


8946 


4918 


4765 


4312 


3241 


4152 


4235 


3807 


1234 


70846 


89476 


91708 


.59487 


49387 


.39587 


50314 


13012 


40532 


23152 


29245 


21432 



6. 35276 40547 48456 57345 73840 904782 
21042 31023 22304 31021 21413 130531 



45987 
21257 


47543 
31213 


48053 
32423 


49735 
13425 

54398 
51281 


50347 
12345 


98764 
12321 


38704 
32532 


74820 
50412 


45708 
42323 


01895 
()2352 


78456 
.32012 



i(» (lifFcroiKM' 

•li tlic Otllt'l* 

•h is taken 

he number 
ninuend. 
mhu(s, and 
wa that the 
re it. 



87 


J)9 


52 


73 


503 


808 


212 


452 


G03 


989 


451 


472 


1918 


4705 


5807 


1234 


)387 


39587 


)245 
1840 


21432 


004782 


1413 
5347 


130531 


98704 


2345 
1895 


12321 


78450 


2352 


32012 



428357 
423142 


SUBTRACTION. 

028954 039847 
523412 032123 


718047 
715415 


li 

905783 
120321 


4370<)8 
312415 


800087 
304015 


705347 
705123 


308718 
123718 


470084 
412382 



10. 



EXERCISE XXI. 

1. A niiui had 151 i-ows. JIu sold 40 of them. How many 
hail \w Wat 

2. Harriet and VAh'ix tofrctln'r liavo 83 littln fhickons, of 
which Harriet owns 43. How many btdonff to Kllenf 

3. A man boiijrht n horse for $\27 and sold it for $104. How 
much did he losef 

4. A hook has 210 pajjes. Tom has read 103 pages. How 
many pages has lie yet to read? 

5. A merchant having bought 587 gallons of syrup, sold a 
pertain quantity and hud 315 gallons left. How many did he 
sell? 

0. A man paid 275 dollars for a horse and buggy; the horso 
cost 125 dollars. What was the price of the })Uggy? 

7. In one year a merchant sold 1578 barrels of flour and 
1324 barrels cf sugar. How many more barrels of flour did lie 
sell than sugarf 

8. A drover having 1465 sheep sold 233 of them. How many 
had he renniining? 

9. A farmer has two farms containing together 875 acres. 
Tn one farm there are 442 acres. How many are there in the 
other? 

• 10. A fanner liouglit a farm for 4f3()00 and sold it for $4200. 
How much did he gain? 



EXERCISE XXII. 



1. 



90 


40 


50 




00 


70 


80 


100 


35 


13 


27 




31 


40 


29 


75 


327 


930 




574 




928 


726 


850 


142 


484 




381 




182 


145 


160 


590 


700 




40G 




732 


824 


751 


143 


178 




184 




185 


108 


328 


3450 


3700 




4870 




5340 


5938 


9418 


1235 


2340 




2527 




2128 


2970 


5493 



u 



'"*- 


ARITHMETIC. 








4'J:J8 


5129 6248 


7206 


7462 


4915 


L'HiC} 


as?-) 498:5 


:{K94 


59158 


.'5897 



427:56 
24:582 



53829 
28596 



61705 
28483 



80727 
45384 



49376 
31949 



57146 
29418 



9. 



400300 
295246 

500000 
273827 

506207 
49185 



500200 
:J9:5186 

400000 
285458 

402508 
84274 



700400 800500 
398327 496478 



600000 700000 
365879 486347 



604506 703605 
89251 78382 



300700 
12:5456 

400000 
267410 



802507 
76832 



600500 
287684 

800000 
120076 

907608 
30709 



10. 924:590 705180 527082 816141 423453 700600 
4:52412 44:5544 232154 1:55212 141514 123416 



1. From 

2. From 

3. From 

4. From 

5. From 

6. From 

7. From 

8. From 

9. From 
10. From 



1. 

o 

3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 



EXERCISE XXIII. 

924 take 379; from 970 take 182. 
1000 take :!78; from 1111 take 999. 
2450 take 1097 ; from 6040 take 644. 
44444 take 14847 ; from 44444 take 15789. 
50505 take 27895; from 55,555 take 48776. 
6G6666 take 278954; from 600000 take 123007. 
100600 take 99999; from 777777 take 297998. 
486413 take 164184; from 418786 take 219186. 
600078 take 142368; from 300007 take 108819. 
672246 take 487128; from 578472 take 169386. 



EXERCISE XXIV. 



6005- 
8002- 
8003- 
6005- 
9004- 
6003- 
7035- 
7023- 
8021- 
8064- 



-2:547 
-2636 
-2746 
-2748 
-2615 
-2846 
-2648 
-2896 
-;3472 
-2397 



7825-3569 
H412— 3756 
9000—1234 
7018—6243 
8765-5999 
6200—4756 
8006—7184 
8574—6497 
74S2— :5597 
8100—6718 



9012- 
7064- 
7000- 
7000- 
8000- 
8000- 
9000- 
9000- 
6324- 
6245- 



-3684 
-2768 
-2546 
-3748 
-5318 
-3526 
-3725 
-2745 
-2538 
-3789 



:t 



■a 



SUBTRACTION. 



25 



7462 
5938 

49376 
31949 


4915 

3897 

57146 
29418 


300700 
123456 


600500 

287684 


400000 
267410 


800000 
120076 


802507 
76832 


907608 
30709 


423453 
141514 


700600 
123416 



EXERCISE XXV. 



44. 

e 15789. 
e 48776. 
take 123007. 
ako 297998. 
take 219186. 
take 108819. 
take 169386. 

9012- 
7064- 
7000- 
7000- 
8000- 
8000- 
9000- 
9000- 
6324- 
6245- 



-3684 
-2768 
-2546 
-3748 
-5318 
-3526 
-3725 
-2745 
-2538 
-3789 



is 



r 
I 



1. 


.56739— 24316 


36751- 


-2S976 


431250—153697 


2. 


68507—47623 


90006- 


-29384 


920503—476829 


3. 


47865—12341 


71020- 


-.-)43(i7 


523146—286759 


4. 


72006—48315 


43002- 


-27659 


647352—268574 


5. 


65043- -17872 


71300- 


-450.35 


502304—186475 


6. 


81000-25143 


64434- 


-25679 


625030—274384 


7. 


90000—30906 


76456- 


-29898 


720301—368596 


8. 


90503—47628 


56307- 


-18497 


842003—459687 


9. 


41009—31214 


70000- 


-39458 


715324—369857 


10. 


43020—36748 


78536- 


-47658 


900500—465783 




EXERCISE XXVI. 




1. 


8467321—3478271 




700' 


rOOO— 2009001 


o 


3178632—1478371 




6789012—700999 


3. 


9004100—30012 




764.89687—999999 


4. 


100010110—990991 




7000000—636363 


5. 


49716368—42894938 


7400002—123807 


6. 


3714908—2916409 




5000005—900009 


7. 


37080605—2934716" 


> 


10101011—303033 


8. 


23456789— 149307()8 


27689714—9337778 


9. 


1000000—11 




476.- 


5879—707070 


10. 


4000000—199091 




5005005—1234567 



EXERCISE XXVII. 

1. How much must be added to 76 to make 150? 

2. Take 713968 from one million. 

3. From 9410068 take 3090801. 

4. What is the difference between 76104 and 108403? 

5. The greater of two numbers is 705, and the difference 
between them is 29. Find the smaller number. 

6. Find the remainder, after taking 7854 as often as possible 
from 57692. 

7. What number taken from one million will leave 473916? 

8. To what number must 8764 be added to make 11342? 

9. 7900000— 467846— 7()4839. 

10. From the difference between 287368 and 789560, take 
360194. 



2G 



AUITHMKTIC. 



EXERCISE XXVIII. 

1. A man l»ad 374 nhcep and sold 28;"). How nianv had he 
left? 

2. James has I'lT') ; Tom has $'MH. How much more has 
James than Tom f 

3. If a man receives $3415, and si)end8 $2947, how much lias 
he left? 

4. If I buy 47964 bushels of wheat and sell 23796 Imshels, 
how many bushels are left ? 

5. Mr. Jones has $7698 and Mr. Williams $5919. How much 
more has Mr. Jones than Mr. "Williams? 

6. I bought a farm for $7916 and have paid $5748. How 
much do I still owe for the farm? 

7. A owed B $378 and paid him $329, and gave him a cow for 
the balance. What was the value of the cow? 

8. A man started to walk 3400 miles, and has finished 1968 
miles. How far has he yet to go? 

9. In 1897 the population of Ontario was 1990977; in 1886 it 
was 1828495. How much had the population increased during 
*;his period? 

10. In 1897 there were 940236 milk cows in Ontario; in 1888 
there were 781559. How many miik cows had been added to 
the cattle of Ontario during this period? 

EXERCISE XXIX. 

1. A merchant sends $4796 to his agent to buy goods, and 
receives $3989 worth. How much does the agent keep? 

2. James bought 98 marbles and then sold 59 of them. How 
many had he left? 

3. In an army of 24907 men, there are 10908 who are over 
36 years )f age. How many are younger? 

4. I sold a farm for $4713 and gained $897. What did it 
cost me ? 

5. There are 525600 minutes in a year, and 173964 in the 
first four months. How many minutes are there in the rest of 
the year? 

6. Jane has two books containing 736 pages, and one has 
297. How many has the other? 

7. A railway cost $63475916, and of that sum $41968959 have 
been paid. How much is still owing? 

8. A boy starts from Montreal for Vancouver, a distance of 
14680000 feet, and travels 8379164 feet. How far has he yet 
to go? 



SUBTRACTION. 



27 



9. In 1897 there were 312947 persons in Ontario living in 
towns, and 430940 living in cities. How many more persons 
lived in cities in Ontario than in towns? 

10. In Ontario in 1883 there were 53513032 pounds of cheese 
niaimfactured, and in 1897 13736291G pounds. How many more 
pounds were manufactured in 1897 than in 1883? 

EXERCISE XXX. 

1 . A boy paid 52 cents for a geograpliy and 25 cents for an 
arithmetic. How much inore did lie pay for the geograpliy tliau 
for the arithmetic? 

2. A boat had 720 passengers and lauded 438 at a port. 
How many remaiued on the boat? 

3. A man began bnsiues« with $15264 and lost $3271. How 
much had he let'tif 

4. A man had $100. He paid $65 for a buggy and the rest 
for harness. How much did the harness cost? 

5. Sir Isaac Newton died in 1727 at the age of 85. When 
was he l>orn? 

(5. Gladstone was born in 1809 and died in 1898. To what 
age did he live? 

7. The Universitv of Camltridge was founded in 915. How 
old was it in 1898? ' 

8. Mount Logan, the highest mountain in Canada, is 19500 
feet high. How much higher is it than Mt. Blanc, the highest 
mountain in Europe, which is 15812 feet high? 

9. At an election there were 2784 good ballots cast. The 
successful candidate received 1459 votes. How many votes 
were given to the defeated candidate? 

10, In 1898 the population of Greater Loiidon was 6291000, 
and of Greater New York it was 2321644. How much did the 
population of Loudon exceed that of New York? 

EXERCISE XXXI. 



1. ^11 a school of 489 scholars there are 267 girls. How 
mauy more girls tlian boys are in this school? 

2. I bought a house for $2127. I paid $365 for repairs, and 
then sold it for $2690. How much did I gain? 

3. A miller bought 1000 bushels of wheat from one farmer, 
and 500 bushels from another. After selling 825 bushels to one 
merchant and. 460 to another, how mauy had he left? 



28 



AUITIIMKTIC. 



4. A {^eiitleraan at his death left 12000 dollars to be divided 
between his wife, his son and his two daughters. To each of 
the daughters he gave 287") dollars, to the son aOOO dollars, and 
to his wife the remainder. What was the wife's portion? 

5. A man bought a horse for $175 and another for $216. He 
sold both for $42;{. How much did he gain? 

G. A man is worth $175968. Of this $29347 is in real estate; 
$14743 in bank stock; $23928 in railway bonds, and the rest is 
in the bank. How much is in the bank? 

7. A cattle drover bouglit cattle for $19376. He paid $8949 
in cash, gave a cheque on the bank for $3249, and his note fcr 
the balance. For liow much was the note drawn? 

8. There are 1760 yards in a mile. Find by su])traetion 
how many miles there are in 8937 yards, and how many yards 
remain. 

9. Two persons are 375 miles apart; they travel towards 
each other; at the end of one day, one has travelled 93 miles 
and the other 57 miles. How far apart are they still? 

. 10. At an election 12572 votes are taken, of which the suc- 
cessful candidate received 7391. By what majority was he 
elected? 



EXERCISE XXXII. 

1. A man deposits in the Ontario Bank 2374 dollars. At 
one time he draws out 897 dollars, at another time 543 dollars, 
and at a third time 689 dollars. How much still remains in 
bank? 

2. A man was 21 years old in 1896. In what year will he 
be 75 years old? 

3. A gentleman dying left 4500 acres of land to his wife, his 
son and his daughter. To his wife he gave 1564 acres, to his 
son 1449 acres, and to his laughter the remainder. What was 
the daughter's portion? 

4. A gentleman 83 years old has two sons; the age of the 
older son added to his makes 128 years, and the age of the 
younger son is equal to the difference between the age of the 
father and that of the older son. How old is each of his sons? 

5. A man bought three estates; for the first he gave $5260, 
for the second he gave $3585, and for the thii-d he gave as 
much as for the first two together. He afterwards sold tliem all 
for $15280. Did he gain or lose, and how mucli^ 

6. James has 25 marbles; John has 32. The first time they 
played John won 7, but the next tinn; James won 13. How 
many marbles has each now? 



SUBTRACTION. 



29 



7. On a farm of 112 acres there are 14 acres in wheat, 15 
acres in barley, 12 acres in oats, 17 acres in peas, 9 acres in 
hoed crop, and the rest in pasture and bush. Ilow many acres 
are in [»aHtur(» and bush? 

H. How many days are there from June 28th to September 
oth, inc'hisive? 

9. James and Henry have together 45 marbles; Henry and 
John have togetiier 63 marbles; John and William have together 
HI marbles; William has 45 marbles. How many marbles has 
James? 

10. In 1897 the population of Ontario was 1990977; in 1896 it 
was 1972286; in 1895 it was 1957390, and in 1894 it was 1936219. 
By how much did the population increase during 1894, 1895 and 
1896 respectively? 

EXERCISE XXXIII. 

1. From th(i difference between 17496 and 5378 take the 
sum of 4125 and 1247. 

2. Simplify 2187+374—1763+9436—1479+8161—3948. 

3. The sum of three numbers is 2897. One of these is 794, 
another is 497. Find the other. 

4. What must be added to 1000000—6093 to give 3746918— 
94786? 

5. The sum of six numbers is 40917. Five of them are 4876, 
9127, 4763, 8294, and 7328. What is the sixth number? 

(). What nuTuber added to the sum of 7089, 987, 3469, 58732, 
29 and 4:536, will make one million? 

7. What numl>er must be taken from the difference ]>etwe» n 
3789 and 7968 to leave 1645? 

8. What number added to 1271 will give the sum of 40370, 
.3684 and 30916? 

9. From the sum of all the odd numbers l»etween 436 and 
448 take the difference between 39476 and 38979. 

10. The subtrahend is the sum of 784, 965, and 1894. The 
niinuend is the difference between 7689 and 19785. Find the 
remain ier. 

11. The sum of four numbers is 45364. The first number is 
5215, the second is 457 more than the first, and the third is 128 
It'ss tlian the first and second together. Find the fourth 

UUnilKM'. 

12. The remainder is 7894 after 9462 has been subtracted 7 
times from a certain number. Find the uumJ»er. 



80 



ARITHMETIC. 



III. MULTIPLICATION. 

l\1ultiplication is the process of finding the sum of 
a number called the multiplieand, repeated as many 
times as inhere are units in another number called the 
multiplier. * 

The Mlultiplicand is the number to be multiplied. 

The IMultiplier is the number by which the multi- 
plicand is to be multiplied. It shows how often the 
multiplicand is to be repeated as an addend. 

The Product is the result of the multiplication. 

The multiplier and the multiplicand are called the 
Factors of the product. 

THE MULTIPUCATIOIN TABLE. 



Twice 


Three 


Four 


Five 




Six 


Seven 


times 


times 


times 


times 


times 


1 is 2 


1 is 3 


1 is 4 


1 is 5 


1 


is 6 


1 is 7 


2 . . 4 


2 . . 6 


2 . . 8 


2 . . 10 




. . 12 


2 . . 14 


3 . . 6 


3 . . 9 


3 . .12 


3 . . 15 


3 


. . 18 


3 . . 21 


4 . . 8 


4 . . 12 


4 . . 16 


4 . . 20 


4 


. . 24 


4 . . 28 


5 . . 10 


5 . . 15 


5 . .20 


5 . . 25 


5 


. . 30 


5 . . 35 


6 . . 12 


6 . .18 


6 . .24 


6 . . 30 


6 


. . 36 


6 . . 42 


7 . . 14 


7 . .21 


7 . . 28 


7 . . 35 


7 


. . 42 


7 . . 49 


8 . . 16 


8 . .24 


8 . . 32 


8 . . 40 


8 


. . 48 


8 . . 56 


9 . . 18 


9 . . 27 


9 . . 36 


9 . . 45 


9 


. . 54 


9 . . 63 


10 . . 20 


10 . .30 


10 . .40 


10 . . 50 


10 


. . 60 


10 . . 70 


11.. 22 


11 . . 33 


11 . . 44 


11 . . .55 


11 


. . 66 


11 .. 77 


12 . . 24 


12 . . 36 


12 . .48 


12 . . 60 


12 


. . 72 


12 . . 84 



Eight 


NMne 


Ten 


El«>ven 


Twelve 


times 


tiiiies 


times 

1 is 10 


times 


times 


1 is 8 


1 is 9 


1 is 11 


1 is 12 


2 . . \G 


2 . . 18 


2 . . 20 


i) »)>) 


2 . . 24 


3 . . 24 


3 . . 27 


3 . . 30 


3 . . 33 


3 . . 36 


4 . . 32 


4 . . 36 


4 . . 40 


4 . . 44 


4 . . 48 


5 . . 40 


5 . . 45 


5 . . 50 


5 . . 55 


5 . . 60 


6 . . 48 


6 . . 54 


6 . , 60 


6 . . 66 


6 . . 72 


7 . . 56 


7 . . 63 


7 . . 70 


7 . . 77 


7 . . 84 


8 . . 64 


8 . . 72 


8 . . 80 


8 . . 88 


8 . . 96 


9 . . 72 


9 . . 81 


9 . . 90 


U . . 99 


9 . . 108 


10 . . 80 


10 . . 90 


10 . . 100 


10 . . 110 


10 . . 120 


11 . . 88 


U . . 99 


11 . , no 


11 . . 121 


11 . . 132 


12 . . 96 


12 . . 108 


12 . . 120 


12 . . 132 


12 . . 144 



MULTIPLICATION. 



81 



the sum of 
3(1 as many 
V called the 

multiplied. 

I the multi- 
»w often the 
id. 

plication . 
3 called the 



Seven 
times 



6 


1 


is 7 


12 


2 


. 14 


18 


3 


. 21 


24 


4 


. 28 


30 


5 


. . 35 


36 


6 


. . 42 


42 


7 


. . 49 


48 


8 


. . 56 


54 


9 


. . 63 


60 


10 


. . 70 


66 


11 


. . 77 


72 


12 


. . 84 



Twelve 
♦ imes 



1 is 


12 


o 


24 


3 . . 


36 


4 . . 


48 


5 . . 


60 


6 . . 


72 


7 . . 


84 


8 . . 


96 


9 . . 


108 


10 . . 


120 


11 . . 


132 


12 . . 


144 



1. 3040204 
o 



11. 5789645 



EXERCISE XXXIV. 

4302432 423042 340243 



5 



5 



8950()94 



5478946 



4897649 
5 



3204302 



o 


974234 


4963241 
2 


879716 
2 


9847456 


7084567 
2 


3. 


768064 
2 


578467 


708096 
2 


598746 
2 


967865 


4. 


863428 
2 


768497 
2 


700608 
2 


367496 
o 


784967 
2 



5. a456454 3454645 4543456 6534356 3545464 
3 3 3 3 3 



6. 8768475 9647364 8769456 9484965 7899486 
3 3 3 3 3 



7. 3404134 
4 


634243 
4 


4137404 
4 

978649 
4 


1678343 
4 


6783437 
4 


8. 54:{7489 
4 


6789013 
4 


345987 
4 


4139764 
4 


9. 230456 
5 


5432061 
5 


3475264 
5 


2536472 
5 


1234567 
5 



10. 4597045 9682469 7893086 7080904 7684963 



8647649 



12. 3741064 34071064 3718643 41890701 4196804 
6 6 (i 6 6 



82 



ARITHMETIC. 



EXERCISE XXXV. 



1. 4375780 
6 


0892405 



5080700 



3(589427 
() 


784(5952 



2. 7890905 
() 


4709(547 



8490790 



0894579 



887799(5 



a. 7450948 

7 


7045093 

7 


8450784 
7 


9009078 

7 


7084905 
7 


4. 245078 
7 


37425(54 

7 


5420034 
7 


4253042 

7 


700(5457 

7 



5. 4087900 4087054 3090874 4897054 9870543 

7 7 7 7 7 



6. 3042054 32400(55 4004503 2345035 4352073 
8 8 8 8 8 



7. 4794086 8887(55(5 9234507 7890543 0700809 
8 8 8 8 8 



8. 7684907 2503128 1536211 3306525 5010323 

8 8 8 8 8 



9. 1234505 5043204 2073465 4234507 5704507 
9 9 9 9 9 



10. 3004789 0478975 8090403 5408795 7864087 
9 9 9 9 9 



11. 1760689 5311695 3155093 1534091 5135491 
9 9 9 9 9 



12. 7689745 7000068 9506078 5078943 7684796 
10 10 10 10 10 



MULTIPLICATION. 



33 



EXERCISE XXXVI. 

1. Multiply n7Sr)417H:{ hy 2, hy li, ».y 4, by f), by G, by 7. 

2. Multiply 47H(JO():{U4 by 2, by :{, by 4, l>y '>, by (J, by 7. 
;{. Multiply :{7S()41H:t4 by 2, by ;{, liy 4, l)y fi, by <5, by 7. 
4. Multiply 4()H:{71«:{4 l»y 2, l>y ;}, by 4, l»y f), by (i, by 7. 
'.. Multij.ly HyiSO(»:;47 by 4, by 5, by 0, liy 7, by 8, by !). 
«>. Multiply ()()7S9019r) by 4, by f), by G, by 7, by 8, by 1). 
7. Multiply H(i7H:{4071) by 5, by (5, by 7, by 8, l»y 9, by 10. 
H. Multiply G78:{418»5<) by .^), by 0, by 7, by 8, by !), by 10. 
J). Multiply 478:{780()r) by 5, by G, by 7, by 8, l»y 9, by 10. 

10. Multij.ly 418:J4784G by 5, by G, by 7, by 8, by 9, by 10. 

EXERCISE XXXVII. 

What are the factors of 15? of "^1 ? of 28? of 42? of Uf)? 

1. Multiply 4879 by the factors of 15, of 28, of 18, of 'A'k 

2. Multij.ly 6785 by the factors of 14, of 18, of 25, of 42. 
:{. Multiply 708G by the factors of .•{2, of 3'J, of 42, of 49. 

4. Multiply 9584 by the factors of 21, of 45, of 49, of 54. 

5. Multiply 2539 by the factors of 24, of 25, of 3G, of 63. 

6. Multiply 6407 by the factors of 32, of 45, of 54, of 72. 

7. Multiply 7685 by the factors of 48, of 50, of 60, of 70. 

8. Multiply 9685 by the factors of 70, of 80, of 90, of 100. 

9. Multiply 7689 by the factors of 45, of 54, of 63, of 81. 
10. Multiply 4875 by the factors of 30, of 40, of 50, of GO. 

EXERCISE XXXVIII. 

1. Multiply 78546 by 21, by 31, by 41, by 51, by 71. 

2. Multiply 68095 by 61, by 71, by 81, by 91, by 19. 

3. Multiply 789G7 by 13, by 17, by 19, by 29, by 37. 

4. Multiply 64758 by 78, by 87, by 95, by G4, by 59. 

5. Multiply 47896 by 234, by 345, by 456, by 579. 
G. Multiply 97640 by 567, by 892, by 347, by 638. 

7. Multiply 90070 by 325, by 257, by 689, by 976. 

8. Multiply 76847 by 306, by 405, by 708, by 704. 

9. Multiply 98764 by 4008, by 7006, by 5009, by 9040. 
10. Multiply 87009 by 5090, by 7080, by 7096, by 9007. 



:h 



ARITHMETIC. 



EXERCISE XXXIX. 

1. A train riiiiH L'~) iiiili-s iiii hour. How t':ir tlocs it run in 
4H lionrH? 

2. Mr. Brown luis I'WIG liorsen. Wluit uro lln-y worlii at 

;{. How many ouncj-s are there in :{7U(»8 pounds, it' tln-re are 
IG ounces in one jtoundf 

4. The earth in its annual journey around tiic sun moves 
altout (iKOOO miles an hour. J low far does it mov«f in a day, or 
24 hours f 

[). Find the cost of 7H1)(5 ytirds of cotton at H cents a yard. 

G. In a ^rove there are 9 rows of trees and 7H trees in each 
row. How many trees are there in the f^rovef 

7. How fai' can a iiorso travel in 'M'ui Incurs at tlic rate of 8 
miles' an hour? 

8. How many hills of corn are there in a litld containing 
42(» rows, and 224 hills in a T-owi' 

9. What will G5 miles of plunk -road cost at 2007 dollars per 
mile? 

10. How many lemons are there in 24:5 boxes, each box 
containing 309 lemons? 

EXERCISE XL. 

1. A merchant V)ought 1275 barrels of sugar of ,300 pounds 
each at 4 cents a pound. Find tlie cost of the sugar. 

2. A merchant bought 27 bales of cloth, each bale eontaluing 
'}.1 pieces, and each piece containing iiG yards. How many 
yards were there in all? 

3. How many nails will it take to shoe 74 horses, if there 
are 8 nails in each shoe? 

4. How far will a train go in 87 days at 30 miles per hour? 
(1 day=24 hours). 

5. How many inches are there in 475G yards, there being 
3 feet in a yard and 12 inches in a foot? 

G. A man buys 4795 pounds of tea at 5 cents an ounce/ 
What did he pay for it? (10 ounces=l pound). 

7. Find the cost of 78 bales of cotton, each bale containing 
412 yards at 15 cents per yard. 

8. Find the value of 68 farms of 120 acres, eacli at $25 per 
acre. 

9. There are 60 minutes in an hour and 24 hours in a day. 
How many minutes are there in 3G5 days? 

10. The Montreal Star hasa daily circulation of 146819 copies. 
How many papers will be sent out in G weeks of G days each? 



MI'I.TIPMCATIOK. 



35 



in it vm\ in 

y \vt)l'tll ut 
it' tlu'n< are 

SHU mONM'H 

ill ii day, or 

iits a yiu<l. 
vi-vH in •■acli 

lit' I'iitc of H 

I coiitainiiif^ 

7 dollars per 

s, each box 

' 300 pounds 
ar. 

e eoiitaraing 
How many 

I'si's, if there 

es Iter hour? 

Iliere being 
ts an ounce.* 

e containing 

•h at $2;') per 

urs in a day. 

46819 copies. 
G days each? 



EXERCISE XLI. 

1. Multiply tho suni of all the odd nuinin'is Itetwoen 'M niid 
40 by the sum of all the evei numhers between ;{7 and 47. 

2. A drover }>ought 475KJ eiittle at $4') each, and 4iM;{7r) sheep 
nt $5 each. How much more did the sheep cost than the cattle;' 

;{. A farmer sold 'J."» cords of wood at $'A pi-rconl aii<l received 
in jtaynieiit four $'J0 bills. What change must lu* give liack/ 

4. Kind the aujoimt of the following bill: — 
14 pounds ri(M' nt, 4 cents a pound. 
8 yards cotton nt 7 <'ents a yard. 
19 spools thread at 4 cents a spool. 
73 pounds sugar nt 5 cents n pound. 

r». A drovei- liough. 124 cows at $.")7 each, and 71) horses nt 
$90 ea<'h. How much more did the horses cost than the cows? 

(!. The drover sold the cows in last (piestion at a gain of $13 
each, and the horses at a loss of $20 each. Did he gain or lose, 
and how much? 

7. A merchant liought 473G turkeys in London at 75 cents 
each, aTui sent them to Montreal at a cost of 5 cents each. 
Here he sold them for $4730. How much did he gain on the 
transaction? 

8. A merchant luid 793 yards of cloth. He sold 120 yards 
to one nuin and 304 yards to another. What is the remainder 
worth at 8 cents a yard? 

9. Two persons start from the same point, and travel in 
oj)))osite di ections. One travels 29 miles a day, and the other 
32 miles a day. How far apart will they be in 17 days? 

10. A drover bought 127 head of cattle at $34 a head, niul 97 
head at $47 a head, and sold the whole lot at $40 a head. What 
was his entire profit or loss? 

EXERCISE XLII. 

1. The two factors of a certain nundjer are 428 and 403. 
What is the number? 

2. The three factors of a certain number are 187, 29, and 43. 
What is the number? 

3. Find the continued product of 11, 13, 17, 19, and 23. 

4. One of the three equal factors of a number is 407. Find 
the numl»er. 

5. The multiplicand is 40009 and the multiplier is the 
number whose ructors a " .">, 7, and 11. Find the product. 



86 



ARITIIMKTir. 



<5. Tho multiplicand is th« UiflTi'n'uco iM'twcM-n one million 
iumI ono thou8)in(l and one. Th«> nniltiplier in tliu Huui of 407, 
70'J, and U(>:i. Find l\u> product. 

7. TliH difference between two numl>ers i^^tlle product <)f 4',)7 
and .'iOf). The Hirniller of the two nuinbei-H Ih lUOlOO. Multiply 
tho lar^^er number l>y .')0()0. 

H. The ditTerence between two numbers iH.^)0()7. The >.'r(«ater 
number is thu product of 70(1.') and UOOM. Find vh:: smaller 
number. 

y. How much must be taken from the product of .^>07 and 
7i{r> to ^et tho product (tf r>()7 and iVAiif 

10. From the Hum of •)r>XH7 antl 7«>XJ>S, take the ditTerence 
between 78X87 and 97X8.'). 



EXERCISE XLIII. 

1. Multiply the sum of I'JOG and 7ri7{) by their difference. 

12. How nnieh is the product of 579 and 758 greater than the 
product of 577 and 758* 

;{. Multiply together all the uumbers that end in IJ, 5, 7, or 
9, between 12 and 20. 

4. Multiply the greatest number that can be expressed by 
four figures by the greatest one expressed by three figures. 

5. From the product of 9009 and 7007, take the product of 
7090 and 7909. 

6. If Mr. Brown owns 3 houses, the first worth $2783, the 
second 3 times, and the thiil 7 times as much as the first, what 
are the 3 houses together worth? 

7. A drover bought a drove of 33 oxen, paying as many 
dollars for each ox as there were oxen in the drove. He paid 
$514.85, and gave his note for the balance. For how much does 
he give his note? 

8. The area of Ireland is 32535 square miles, and 5096490 
acres are cultivated. How nuiny acres are uncultivated, there 
being 640 acres in a square mile? 

9. A field of oats has 19 rows of stooks ; each row has 37 
stooks in it, and there are 12 sheaves in a stook. How many 
stooks are in the field? How many sheaves? 

10. The sum of 4 numbers is 20000; three of them are 4785, 
5769, and 2807. Multiply the sum of the greatest and least by 
the sum of the other t"'c. 



DIVISION. 



37 



II g as many 
e. He paid 
w much does 

and 5096490 
ivated, there 

1 row has 37 
How many 

em are 4785, 
and least by 



IV. DIVISION. 

Division is t]i<» pnxM'ss ]»y which, \vh«'ii th«' itroduct 
mid out' fnrfor an- ^iv«'ii, thf ofin r farfor is t'ouiid. 

The Dividend, tiic j^ivm pnMlm't, is Mic iimiilHT 
to Im' divided. 

Tiie Divisor, the pivcMi fjictor, is th«' nutidMM- hy 
which the <livideiid is to l)e divi(h*d. 

The Quotient, the faetor to be found, is tlie result 
of Ihe division. 

The Remainder is wlmt is over wlien tlie dividend 
does not contain the divisor an e.xaet number of times. 

Thus, The Dividend is ecjual to the proihict of the 
Pirisor and Qnotii nl, increased l»y the RemnimUr. 

Tlie sij.ii of Division, written — , shows that the 
number )re('edinj^ it is to be divided by the nund)er 
foHovviii}^ it. 

EXERCISE XLIV. 

NoTK. — It is recommended that this exercise ]»e worked by 
the Long Division plan. 



1. 
«> 

3. 
4. 
5. 
(i. 
7. 
H. 
9. 



'J4— 2 
4(58—2 
9(53—3 
484-4 

r)85-7-5 
(518— (5 
749—7 
9(58-8 
819—9 



10. 4r)(i8— 8 

3. 2)428042 

2. 2)157996 

3. 3)3960(59 

4. 4)534768 

5. 5)1847(50 



40-2 
472-2 
699—3 
568—4 
(535—5 
3(5(5—6 
847—7 
H40— 8 
918—9 
7389—9 



96—2 
836—2 
(587—3 
730—4 
205—5 
480-6 
574-7 
928—8 
729-9 
5243—7 



EXERCISE XLV. 

2)208462 2)242680 



2)135794 
3)156945 

4)784724 
5)501035 



2)351792 
3)40:?716 
4)813492 

5)741800 



2)424820 
2)537958 
3)804957 
4)674508 
5)357185 



84—2 
946^2 
87(5^3 
624-^4 
745^5 
9(50-0 
945-7 
728—8 
360-^9 
2709^9 



2)462860 
2)315970 
3)745683 
4)562732 
5)9276.50 



38 



AniTIIMRTlO. 



«;. (i)»;s47r»(! 

7. 7)7\4HV2 

H. H) 728128 

!». y)'Ji47:M 

1(1. 8)810L'48 



(!)()rj:}4'j 

7)!Mr)707 
8)!(14(i4() 

!tj8:t4r)(n 
u)Do;{(ir)4 



())H417r)2 
7)r)847(i(i 

8)8iM:j»;o 

!»)47r):!()2 

i>) 748r):5«j 



EXERCISE XLVI. 



())9;n47(; 

7):{214()l 
8)7412;i2 

!»)<)8478;{ 

7)i2:{4r)U 



(5)700002 

7)(i;no4:{ 
8)i48r.:5(; 
;i)r>48:}7!> 
7)y:j47(5o 



1. Divide 

2. Divido 
:{. Divido 
4. Divide 
il. Divide 
(5. Divido 

7. Divide 

8. Divide 
<J. Divide 

10. Divido 



4178():J4 
()7();{40() 
40(i78()7 
G78:5S()7 
41(5708() 
4078(iO:{ 
3070(542 
3070412 
4012(578 
3070804 



by 2, by ',], by 4, l)y f), 
by 2, by 3, by 4, by .^), 
]>y 2, by 3, by 4, by .'), 
by 2, by 3, by 4, by f), 
by 3, by 4, by 5, by (5, 
by 3, ])y 4, by 5, by G, 
l>y '5, l»y 4, by 5, by G, 
}»y 4, by f), by G, by 7, 
by 4, i»y 5, by G, by 7, 
by 4, by 5, by 6, by 7, 



i»y <», 


I'y 7, 


by 8. 


I'y <i, 


I'y 7, 


by 8. 


i»y <i, 


by 7, 


by 8. 


I'y 0, 


by 7, 


by 8. 


I'y 7, 


'•yH, 


hy !). 


i'y7, 


i»y8, 


v>y 9. 


i>y7, 


by 8, 


by 9. 


I'ys, 


by 5), 


by 10. 


i'y«, 


by 9, 


by 10. 


by 8, 


by 9, 


by 10. 



*^i 



EXERCISE XLVII. 

1. At $;i ]H'r ynrd, iiow niaiiy y.ards of silk onn be Iton^lit I'oi' 
$48? For $84? 'For $132? For $2(M? 

2. Divide $968 eciuully iiniong 8 persons. 

3. If I buy 12 horses for $900, liow much will one horse cost? 

4. If flour costs $8 a barrel, how many barrels can be bought 
for $2(532 f 

5. A grocer packed 994 pounds of butter in 7 tubs of equal 
size. How many pounds did he put into each tub? 

6. Seven bales of cotton weighed 3(508 pounds. What was 
the average weight per luile? 

7. If 5 carloads of iron weigh 7532;) i)ounds, what would be 
the avera,ji' weight of one carload? 

8. In 1 i-oek there are 8 quarts. How many pecks are there 
in 4250 quarts? 

9. A ship worth $38125 was owned in ecjual shares by 5 men. 
Find the share of each. 

10. At six dollars a ton, how many tons of coal can be bought 
for $2274 ? 



DIVISION. 



30 



EXEKCISE XLVIII. 

1. A Hliip sailed across the Atlantic Oceaii, a distance of 
'JHHO miles ill days. J low far did it sail each day? 

L*. In one mile there are r)280 feet. How many yards are 
there in a mile, there bein<^ '.I feet in one yardf 

;{. The wages of 8 men for one week were 104 dollars. How 
much did each earn per week? 

4. How long will a bicycle rider who goes at the rate of U 
miles pel' houi- take in going 117 miles? 

.'). Find the price of a dozen oranges at two for five cents. 

(5. A drover bought 11 head of cattle for 352 dollars. What 
was the price per head? 

7. An excursion train consisted of five passenger cars and 
carried -8") persons. What was tlie average number of pas- 
sengers in a car? 

8. If a locomotive runs 289(5 miles in 8 days, what is the 
average run per day? 

9. The sun is 9;{000000 miles from tlm earth. Light travels 
tills distance in about 8 minutes. What is the velocity of light? 

10. Four farthings make a penny. How many pence are 
there in 22008 farthings? 



i 



•e bought for 



EXERCISE XLIX. 

1. Divide 022,14 by 51, by 01, by 71, by 81, by 91. 

2. Divide 17253 by 31, by 41, by 71, by 81, by 91. 
:j. Divide 127551 by 41, by 51, by 01, by 81, by 101. 

4. Divide 105243 Vjy 01, by 71, by 81, by 91, by 301. 

5. Divide 594130 by 401, by 801, by 901, by 500, by 704. 
0. Divide 471582 by 301, by 501, by 201, by 007, by 809. 

7. Divide 095847 by 611, by 721, by 821, by 541, by 441. 

8. Divide 437650 by 531, by 651, by 751, by 654, by 885. 

9. Divide 904375 by 825, by 925, by 795, by 333, by 555. 
10. Divide 704578 by 972, by 492, by 954, by 870, by 385. 



EXERCISE L. 

1. Divide 987C54 by 912, by 922, by 934, by 975, by 942. 

2. Divide 785469 by 845, by 876, by 889, by 892, by 875. 

3. Divide 870549 by 777, by 78^^ by 795, by 799, by 789. 

4. Divide 987054 by 078, by 089, by 695, by 699, by 697. 



40 



ARITHMETIC. 



r». Dividf 7Sr)9()7 by 508, by nST, by ')[)(]. by HSO, by .lOS. 

(). Divide 7»)()(W() by 485, l)y 490, })y 491, by 478, by 497. 

7. Divide 87()497 by :507, by :{78, by :W9, by :J99, by ;590. 

H. Divide 700000 by 285, by 290, by 278, by 294, by 289. 

9. Divide 1000000 by 49, by iW, by 29, by 17, by 19, by :i7. 

10. Divide 12:54507 by i:{, by 17, by 18, by 19, by 29, by :{9. 





EXERCISE LI. 








1. 


Divide 17:J255 by the factors of 15; 


of 18; 


of 21; 


of 25. 


l> 


Divide 87045C by tiie factors of 24; 


of 30; 


of 30; 


of 42. 


3. 


Divide 954708 by the factors of 45; 


of .54 ; 


of 50; 


of 03. 


4. 


Divide 743045 by the factors of 25; 


of 32; 


of 30; 


of 40. 


5. 


Divide 875976 by the factors of 32; 


of 35; 


of 42; 


of 54. 


C. 


Divide 900007 by the factors of 30; 


of 42 ; 


of 72; 


of 81. 


7. 


Divide 397486 by the factors of 30 ; 


of 40; 


of 50; 


of 60. 


8. 


Divide 780978 by the factors of 00 ; 


of 70; 


of 80; 


of 90. 


9. 


Divide 987641 by the factors of 100; 


of 200; 


of 300 


; of 400 


10. 


Divide 987685 by the factors of 500 ; 


of 600 ; 


of 700 


of 800 



EXERCISE Lll. 

1. Divide 470880 by 6 times 12. 

2. Divide 337103025 by 861. 

3. How often is 77 contained in 37704821? 

4. Divide 7364063 by 7 times 7. 

5. Divide 888888 by the continued product of 3, 7, 8, and 11. 

6. By what number must 129546 be divided that the quotient 
may be'27f 

7. Divide the continued product of 12, 5, 183, 18 and 70 by 
ttie continued product of 3, 14, 9, 5, 20, and 6. 

8. The product of two numbers is 2177280; one of them is 
the continued product of all the even numbers between 5 and 
13. Find the other number. 

9. What number besides 7087 will exactly divide 68070635? 

10. When a certain number is divided by 478, the remainder 
is 205 and the quotient the same as the divisor. Find the 
dividend. 

EXERCISE Llll. 

1. The distance from Montreal to Vancouver is 2948 miles. 
How long will it take a man to walk the distance at 22 miles 
per day? 






.f busl 



DIVISION. 



41 



^ 


i>y 


r.98. 


s, 


I'y 


497. 


9, 


by 


:{9(). 


4, 


by 


2S9. 


y 


19, 


by -M. 


y 


29, 


by :59. 


f 21; 


of 2r). 


f 


:ui; 


of 42. 


E 


r)() ; 


of g:{. 


f 


:u> ; 


of 40. 


)f 4l>; 


of M. 


)f 


72; 


of 81. 


)f 50; 


of GO. 


)f 


80; 


of 90. 


of 300 


; of 400 


^t 700 


; of 800 



, 7, 8, and 11. 


M 


,t the quotient 


•1 


18 and 70 l)y 


1 


ne of them in 
etween 5 and 


g 


ie cmiomr^ ? 


:'** 


the remainder 
or. Find the 


:S 


is 2948 miles. 
?e at 22 miles 


•1 



2. If $.^40^)l is equally divided among 17 men, what sum 
will each receive? 

;{. A miie contains G.'WfiO inclies. How many steps of 24 
inches each will a boy take in walking a mile? 

4. How many pounds of 16 ounces each are there in 473G48 
ounces? 

5. A man paid $ir)i;i4 for cf«ttle at $23 each. How many 
head did he i)uy? 

0. Tn 42 acres there are 6720 square rods. How many square 
rods are there in one acre ? 

7. If a steamship sails 1144.5 miles in 35 days, what is the 
average speed per day f 

8. The area of a country is 8315 square miles, and the 
population is 2286625. How many people are there to each 
Sipiiire mile? 

9. If 2800 sacks of coffee weigh 470400 jjounds, what is the 
average weight i)er sack? 

10. If 1 man can finish a work in 261 days, how long would 
29 men recjuire to do the work? 

EXERCISE LIV. 

1. There are 320 rods in a mile. How many miles are there 
in 572K0 rods? 

2. There are 3() inches in a yard. How many yards are 
tiiere in 34S9624 Inches? 

3. How many miles are tliere in 33440 yards, there being 
1760 yards in one mile? 

4. There are 48 j)otinds in a bushel of barley. How many 
bushels are there in a load of barley of .3072 pounds? 

5. A farmer l»rought 30(50 ])Ounds of jmtatoes to market. 
How many Itushels had he, there being (50 pounds in each 
bushel of potatoes? 

6. In a bin of oats there are 8330 i>ounds. How many 
l)usliels ar«^ there in the bin, there being 34 pounds in eneh 
bushel of oats? 

7. ^'liere are 160 acres of land in a nuarter Rection. How many 
quarter sections are there in a township containing 23040 acres? 

8. A cubic yard contains 27 cubic feet. How many cubic 
yards are there in a heap of earth containing 2025 cubic 
feet ? 

9. There are 196 pounds in a barrel of flour. How many 
barrels are there in 40572 poutids of flour? 

10. A pile of wood contains 90112 cubic feet. How many cords 
p,re there In It, there being 128 cubic feet in one cord of woodf 



42 



AHITHMKTIC 



EXERCISE LV. 

1. How many times can 7H })o taken fiom tlio <'ontinued 
product of i:{X 7X1012* 

2. Find the sum of all the numbers between 90 and ISO that 
are exactly divisible by llj. 

;i. Divide the sum of 4077, ;59(), and 8745)1, })y the diff<'rence 
between (i;{84 and 7492. 

4. Find the value of :{()984X 2739(5^761. 

5. What is the true remainder when 69472') is divided by the 
factors of 10;')? 

(). Hew often can you take the sum of the even numbers 
between 241 and 253 from forty thousand and fourteen. 

7. If 213X84X190X264 be divided })y 30X56X36, what 
will the quotient be? 

8. When 82965;j is divided by 1022, the remainder is 811. 
What is the quotient? 

9. Divide 41579 by the factors of 42, and find the true 
remainder. 

10. The quotient of one number by another is 74; tlie divisor 
is 321, and the remainder is 95. Whatjs the dividend? 



EXERCISE LVI. 

1. The divisor is 77; the quotient is 97; there is no 
remainder. Find the dividend. 

2. The dividend is 632; the quotient is 27; the remainder 
is 11. What is the divisor? 

3. The 'divisor and quotient are equal to each other, each 
bein<^ 794 and the remainder is the largest possible. Find the 
dividend. 

4. The divisor is 801 ; the quotient is 403, and the remainder 
the largest ]»ossible. Find the dividend. 

5. The divisor is the difference between 204 and 2^58; the 
quotient is their sum, and the remainder is the largest ]>ossible. 
Find the dividend. 

6. Find the least numl»er which must be added to 17634 to 
make it exactly divisilde by 236. 

7. What number besides 364 will exactly divide 89180? 

8. Of wiiat number is ;}45 Itotli divisor and (puttient? 

9. When 169 is added to the dividend it is exactly divisible 
by 7H5, the (piotient being 978. Find the dividend. 

10. Find the smallest number which, subti'ucted from 78654, 
will make it exactly divisible by 458. 



th( 



MIS(!KLI-.\NKOlS KXKK(MSES. 



43 



livided by tlio 



the reniiiiiHler 



'a\ to 17634 to 



V. IV1ISCELLAINE0US EXERCISES. 
EXERCISE LVII. 

1. Tlie i)laypfround is 93 steps lonp and 47 wide. How many 
Hteps >\ill a boy take in iio'xu^ around it tliree times? 

2. From 479'JO take 3H1219, and to the result add 4901 > 

3. Simj.lifv 4K7 + 19(5+ 14732 — 1984 — 4756 + 1734— 1S96 + 
4111412—1739648. 

4. Find thevahieof 761+276—849+98—121—317+963+438. 

5. Multiply 68754 by 6 and by 8, and add the products. 

6. Multiply 59846 l>y 1))8 and by 105, and subtract the products. 

7. In a mile there are 1760 yards. How many inches are 
there in 4 miles? (12 inches=l foot; 3 feet=l yard). 

8. Multiply 500302 by 40102. 

9. Divide 275264 by 736, and multiply 45697^ by 78, and 
sul>traet one result from the other. 

10. Find the amount of the following bill: 

473 yards cotton at 7c. a yard. 
916 pounds tea at 40c. a pound. 
19 pounds raisins at lie. a pound. 

EXERCISE LVIII. 

1. Multiply seventeen thotisand nine hundred .ind forty- 
three l»y 5079^ 

2. A ])erson earned $85 a month and spent $2 a day. How 
nnich did he save in 1896? 

3. A numl)er divided by 243 gives 4713 for quotient and 89 
for remainder. Find the number. 

4. How manv times is the i)roduct of 75 and 109 contained 
in the sum of 2063014, 17005000, 469, 30214707, and 3885? 

5. Find a number which multiplied by 369 will give the 
same iiroduct as 615X18;{57. 

6. Wliiit number multiplied bv 86 will give the same i»roduct 
as 163X430. 

7. Find the quotient when the i»roduct of 86947 :ind 248 is 
divided by 217. 

8. A man Itought 52 liors»'s at .t75 each, and 214 jiigs at $\\ 
each. How mucli more tiiiin +()000 did all cost.' 

9. The divisor is 473(5, the (|U(»tient 299, and the remainder 
the largest number ]>ossible. Whiit is t!ie dividend? 

10. A grocer bought 16 cheese each weighing 70 jtounds for 
10080 cents, and «old it at 11 cents a pound, How much did he 
gain? 



44 



ARITHMETIC. 



EXERCISE LIX. 

1. A carpoiiter ♦■iiftaf^es 4 men nc $2 each por day. flow 
much will they earn in 7 weeks? 

2. JV farmer owes his grocer 2640 cents; he gives in jtayment 
147 pounds of butter. What is the butter valued at per lb, 

;{. "A drover sold 495 sheep and 27;') laml)s for .fIJiJOO; he 
received $y apiece for the lamba. How much did he get for 
each sheep f 

4. A man bought ducks at 47 cents each and sold them at 
100 cents a pair. What did he pay for the ducks which he sold 
for 2800 cents? 

f). A man bought 5 pounds nails at 4c. a pound; ') gallons of 
oil at 1(5 cents per gallon; a stove for $l~) and an ixe for .$2. 
How much change will he get out of a $20 bill? 

(). A man bouglit a horse for $7') and :hen exchanged it for 
[) slieep and $G2. If a sheep is worth $7 Hnd his gain? 

7. If I give $78;}0 for 90 head of cattle and sell them at $H)') 
ejich. How much is the gain? 

8. A farmer sold 97 cattle at $65 each, and with the money 
l)ought sheep at $i;j each. How many did he buy? 

9. What numl>er divided by 3008 gives 3875 for <iuotient and 
1397 for remainder? 

10. A man earns $75 a month and spends $50 a month, how 
long will it take liim to pay for 60 acres at $40 an acre? 

EXERCISE LX. 

1. A certain number was divided by the factors of 35; the 
qtiotient was 72, the first remainder 2 and the last remainder (i. 
What is the number? 

2. I bought 28 barrels of sugar, each weighii\g 310 pounds 
net, at 1200c. a barrel and sold it at 6c. ajtound. Find the gain? 

3. Two i»ieces of cloth of e(|ual length cost 5()00c. and 7600('. 
respectively; the first piece cost 70 cents a yard, find the price 
per yard of the second piece? 

4. What is the least number that nmst bo added to 10000000 
to make the sum exactly divisible by 653? 

5. A number was divided by the factors of 77, the quotient 
was 137, the first remainder 9, the second 6. What is the 
dividend ? 

6. A farmer exchanged 162 Inishels of wheat at 160c. per 
bushel for 27 barrels of flour. What was the value of fiour ;^er 
barrel ? 

'. A grocer bought 126 pounds of tea at 68c. a ])ound. Ho 
kept 18 pounds and sold the rest at 80 cents a pound How 
much move money did he receive than Ue paid out? 



MISCELLANEOUS EXERCISES. 



46 



8. A frciith'HiMn s]>«'iit durinp: tlu' yonr IHIK} ^\{) n day mid 
laid away ^KK) a nioiitli. Wliat was his inconicf 

J). Find a nimilM'r s'lcli that it' it U' added L':5 tiiius to :;7<)(ll 
ill.- siiiii will Ik- 4(Hi(K». 

Id. The itrodtu't of two imniltcrH is l'J7«);{74 and lialf of one of 
tlu'U) is ;J1L"J. What is the other? 



i month, how 



EXERCISE LXI. 

1. If 2 oranfict'*^ ^'^^^ ^' cents, find the oost of 9 oranges. 

L*. If 9 pounds of riee cost 36 cents, what will 4 pounds of 
rice cost? 

;{. If John walk 27 miles in 9 hours, at the same rate how 
far will he walk in seven hours* 

4. If 12 yards of cloth cost $.'30, find the cost of 17 yards of 
the same kind of cloth. 

;'). If 17 tons of coal cost $102, find the cost of 25 tons. 

0. If $40 laiy 20 yards of cloth, how many yards can be 
bought for $00? 

7. If ir)0 yards of cloth are required to make 15 dresses, 
how many dresses can be made from 210 yards? 

8. If 17 men can husk 1088 bushels of corn a day, how many 
bushels can 27 men husk in the same time? 

9. If a train goes 21G miles in 8 hours, how long will it take 
to go 297 miles at the same rate? 

10. If 2800 sacks of coffee weigh 470400 pounds, what will be 
the weight of U^oO sacks? 



d to 10000000 



EXERCISE LXII. 

1. If 7 men can do a piece of work in 9 days, in how many 
days can 3 men do the same work ? 

2. Ten men can finish a piece of work in 57 days; how long 
will it take 6 men to do it? 

3. If 12 men can build a wall in 30 days, how long will it 
take 18 men to do it? 

4. If a garrison of 150 men have provisions for 45 days, how 
long will they last 250 men? 

5. How long will it require 20 horses to do the work of 24 
horses for 15 days? 

(]. If 25 men can do a piece of work in 9 days, how many 
men will be required to do it in 15 days? 

7. If a drain is dug by 36 men in 100 days, how many men 
would be required to dig it in 80 days? 



46 



AKITHMKTIC. 



S. A i»i»*«'«' of work was to h:ivo Iku-ti ]>«'i'forin(Ml ])y (!0 men 
in 4") days, but a iiuiuh*'!' worn MiHcliar^^fil and so tin* work lasted 
50 days. How many were discliarj;ed? 

9. A fyarrison of 1200 men had provisions to last 4 months, 
but in a battle a number were killed and the i)rovisions lasted 
the remainder 5 months. How many were killed If 

10. If 25 men can do a pieee of work in li6 days, how many 
men will be required to do '.i timen as much work in 12 days? 



EXERCISE LXIII. 

1 . Divide 36 marbles between two boys so that one may have 
4 more than the other. 

2. Two boys together liave 50 marl»les and one has ten more 
than the other. How many has eachf 

'.i. Two loads of wheat toj^ether contain 85 V)ushols and one 
has 7 bushels more than the other. How many busliels are 
there in eaeh load? 

4. Two pieces of cloth tojsjether contain 100 yards; one of 
the pieces is 16 yards longer tlum the other. How long is each? 

5. There are 94 examples in two exei'cises. There are 6 
more in one than in the other. How many are there in each 
exercise? 

6. The sum of the ages of two boys is 27 years, and one is 
3 years older than the other. How old is each? 

7. In a game of cricket two boys together made 47 runs. 
One made 9 more than the other. How many did each make ? 

8. At an election 240 persons voted. There were two 
candidates and the successful one beat his opponent by 18 votes. 
How many votes did each receive? 

9. In two journeys a bicycle rider rode 157 miles. He rode 
23 miles farther the second journey than the first. How far did 
he go on each journey? 

10. Two skaters race for an hour round a circular course. 
The sum of the number of circuits made is 387. The winner 
beats his opponent by exactly 3 rounds. How often did each 
go round the course? 

EXERCISE LXIV. 

1. A number when divided by 5 gives 3 for remainder, and 
when the quotient is divided by 7 the new quotient is 241 and 
the remainder is 4. Find the number. 

2. The remainder after division is 97; the quotient is 342, 
and the divisor is 91+97+342. Find the dividend. 



MISCELLANEOUS EXERCISES. 



47 



ne may have 



las tt'n more 



:}. A drover houglit I'J7 (-attic at .$.")(» each, and 93 more at 
$45 each. He lost 1 of tlu* first lot and 'J of the second, and 
sold all the r»«Ht at $(5;') euch. Find his f?ain. 

4. A train starts from Toronto for C^ucIk'c, HIG miles away, 
at 2li miles per hour. At the same time another starts from 
(Quebec for Toronto at 21 miles per hour. How far from Toronto 
will they meet? 

5. A man earns $1180 per year. He spends $348 during the 
year. How much does he save per week if 52 weeks make a 
year? 

G. A newsboy buys 120 papers at 2 cents each and sells them 
all at 2 for 8 cents. How much dees he gain? 

7. A wagon loaded with coal weighs 2612 pounds. The 
wagon alone weighs 1112 pounds. If the load is woi-th 450 
cents, what will be the cost of a ton of 2000 pounds? 

8. In a stack of hay there are 23G88 pounds. A buys it at 
!j<15 per load of 2632 pounds. How much is the stack worth? 

9. Multiply the greatest of the following numbers by the 
least, and divide the product by the other number: 324, 510, 108. 

10. A merchant was in business 17 years. He gained $2240 a 
year during the first G years and $3036 a year afterwards. What 
was his whole gain? 



otient is 342, 



EXERCISE LXV. 

1. From the sum of 47916, 842, 4983 and 1714, take 47168; 
multiply tho remainder by 184, and divide the result by 46. 

2. If 75 bushels of wheat cost 6375e., for how much must 1 
sell 63 bushels to gain 252c. on what is sold? 

3. A grocer gave 153 barrels of flour at 900e. a barrel for 81 
barrels of sugar of 170 pounds each. What did sugar cost per 
pound ? 

4. The product of three numbers is 7650, and the product 
of two of them is 450. What is the other number? 

5. A man gave 50 geese and 35 turkeys for 55 bushels of 
wheat at 100c. a bushel. If turkeys are worth 90e. each, what 
are geese worth? 

G. If 65 bushels of wheat cost 8450c., what should 195 
bushels cost, when the price has fallen 20c. a bushel? 

7. A grocer pays 20864c. for syrup at 128c. per gallon. 
Some leaks out, and the rest is sold for 25920c. at 180c. per 
gallon. How many gallons leaked out? 

8. A drover bought 68 cattle at $47 each. He sold half of 
them at $54 each and the rest at $45 each. How much did he 
gain? 



liBulB 



48 



ARITHMETIC. 



9. A nncrcliiuit l»<>ii^,'lit 4S yards clotli iit 02 cvuU a yanl nnd 
81 yiinis iit 7">c. a yanl. Ho s«>M tlio first lot at Sic a yaid 
and tlif latt«'r at HiU-. a yard. Fiiul his total j^aiii. 

Id. If 1!> liorst'H aii*l 'JS cows are worth .tl.M'_':», and 1 I horses 
are worth pj'.i'>, lind tin? value of lil cows. 

EXERCISE LXVI. 

1. How many fj-eent pieces are there in IToc-fllOc-j-lOle. 
+2()r)e.? 

2. How many luilf-dollar pieces are there in 1710c. +2940c. 
+1 5250.+ 1775c.? 

3. How much greater is IS times $1054 tlian 9 times $3307? 

4. A person Itonj^ht a inimber of cows at ^'<iS each and as 
many liorses at $90 each. He paid $2814 for all. How many 
of each did ho btiy? 

5. If 120 feet of lumber cost 240c., what will 900 feet cost? 

0. If 17 tons of hay cost $204, liow many stacks of liay, each 
containing 9 tons, can be bought for $1 1H8? 

7. A merchant bought 07 i>ieees of cloth of 94 yards each at 
240c. a yard. He sold it all at 288c. a yard. How much did ho 
gain? 

8. A farmer bought land at $49 per acre and an equal 
quantity at $78 per acre. He paid altogether $31750. How 
many acres did he buy? 

9. If 17 yards of silk cost 5100c.. how many bushels of potatoes 
at 55 cents a bushel must be given for 11 yards of silk? 

10. If 5 hats cost as much as 9 pairs of gloves, and one pair 
of gloves cost 125c., how many hats can be bought for 3825c.? 

EXERCISE LXVil. 

1. A man bought wheat at 47 cents a bushel and sold it at 50 
cents a bushel. He gained 327045c. How many bushels did 
he buy? 

2. A merchant bought 13 bales of cloth of 27 pieces each, 
and each piece contained 34 yards. What is it worth at 17 
cents a yard? 

3. A moulder has 17385 pounds of metal. Find the least 
number of pounds he must buy in order to mould cannon balls 
weighing 08 pounds each and use all the metal. 

4. A jeweller sold 15 clocks and 22 watches. For the clocks 
he got $12 each, and for a watch 7 times as much as for a 
clock. How much did he get for all? 

5. A man bought 103 barrels flour at $9 a barrel; 15 barrels 
were spoiled, and the rest sold at $11 a barrel. Did he gain or 
lose, and how much? 



MISf'KLLANKors KXKKC'ISKR. 



49 



I II liorm'rt 



fi. Tf 4 Ituslicls (if wlifiit of (!0 ])nini(ls ciM-li will iiiiiko 1 
hnncl (if ll(»tir, how iniiiiy itoiiiids of wheat will he nMiuiri'd for 
1(50 barrels of flour? 

7. I borrowed from A OaSfic. ; from B, 40:510.; from (\ 
101 HHe., and from J), DOHc. 1 paid E u debt of 197580. How 
much had I leftf 

8. I ])ou{;ht :J24 i)onv.,ls of tea for LU.'JOOc. If I sold it at an 
ndvaneo of 15 eeiils a pound, what was my whole gain and my 
Belling ]»ri(*e j>er ]»oun(ll' 

9. How mueh tea at 46 cents a pound must be given in 
cxelmnge for 18 gallons of maple synip at 92 eents a gallon? 

10. What number multiplied by 79 will give the same product 
as 1279 multiplied by 55.'{? 



EXERCISE LXVIII. 

1. In a division question the divisor is 8 times nnd tho 
quotient is 7 times the remainder. What is the dividend, tke 
renuiinder being 1()8? 

2. It two steamers leave Quebec for Liverpool at the same 
tinie, one going 18 miles and the other 14 miles an hour, how fur 
will the first be ahead of the second in 37 hours? 

;{. By selling 31 horses for $3100 I lose $155. For what 
should I sell 16 horses to gain $597? 

4. If 59 articles cost 4307c., for how much must 23 of them 
be sold to gain 183c. on those sold? 

5. A drover bought 84 horses for $11424. He sold them at 
$108 each. Find his gain. 

0. Two equal sums were divided, the one among 9 men, the 
other among a number of boys. Each man received 300c. and 
each boy 18e. How many boys were there? 

7. The salary of the President of the Fiiited States is 
$.50000 a year. What sura may he expend each year, and yet 
save $75584 in 4 years, his term of office? 

8. A man bought a farm for $3012. He sold half of it at $50 
an acre for $2408. How many acres did he buy and what dM 
he give per acre? 

9. Two men had an equal interest in a herd of cattle. One 
took 72 at $35 apiece and the other took the rest at $42 apiece. 
How many cattle were there in the herd? 

10. A man travels due north for 7 days at the rate of 37 miles 
a day. He then returns on his path at the rate of 29 miles a 
d;iy. How far is he from the starting-point at the end of 12 
days' travel? 



CHAPTER III. 



COMPOUND INtlVIBERS. 
I. TABLES, DEFIINITIOINS, AIND REDUCTION. 

A Simple quantity is one expressed in terms of a 
single unit, as 4 yards, 5 miles, 16 onnees. 

A Compound quantity is one expressed in terms 
of more tlian one unit, as 4 yards 2 feet. 

Reduction is the proifess of (Oianjjing the unit or 
denomination of a simpki or eompound quantity 
without changing tlie value of the quantity. 

Reduction Descending is the i>roeess of ehang- 
ing a quantity from units of a higher denomination 
to those of a lower denomination. 

Reduction Ascending is the process of changing 
a quantity from units of a lower denomination to 
those of a higher denomination. 

Canadian Money. 

100 pentH (ct.) = l dollar, or $1. 
Ten Mills make one cent. The mill is not coined. 

EXERCISE LXIX. 

Reduce the following to cents: — 

1. 7 dollars 25 cents; 4 dollars Scents; 5 dollars and 5 cents. 

2. 30 dollars 4 cents; 100 dollars 90 cents; 3000 dollars. 

3. $7.0(5; $10.45; $80.07; $100.90; $27.05; $404.04. 

4. $100.01; $1000; $101.81; $1000.01; $70007.70. 

5. $371.75; $575.49; $6184.72; $378.84; $907.09. 

Reduce the following to dollars or to dollars and cents: — 



6. 700 cents. 

7. 1001 cents. 

8. 27010 cents. 

9. 97000 cents. 
10. 470S41 cents. 



3084 cents. 

57648 cents. 

47006 cents. 

2000007 cents. 

1010101 cents. 
50 



44968 cents. 

10000 cents. 

7400007 cents. 

4710071 cents. 

20600609 cents. 



TAHI.KS, DKKINITIONH, ANI> RKDUCTION. 61 

StcrMnfl, or English (Money. 

4 farthingH (fiir.) = l penny, or Id. 
12 pence =1 shilling, or 1h. 

20 shillingH =1 pound, or £1, 

21 Hhillings =1 guinea. 

A farthing is written Jd. ; two fartliings, M. 

EXERCISE LXX. 

Hodiire to farthings: — 

1. Hd.; 124d.; 375d.; 451d. ; 784d.; 1960d.; 7000d. 

Kedn('(« to pence: — 

2. OS.; 71s.; lOOs. ; 241s.; 3C9s. ; 2978.; 9000s. 

Hcduce to shillings: — 

;{. C7; i:i7; €90; £419; £48 178.; £100 12s. 

Keduce to farthings: — 

4. 58. Gd.; 88. 4d. ; lOs. fid.; 12s. 3 far.; 19s. 9d. ; £10. 
T). CO 10s. ; £4 18s. ; £7 8d. ; £5 l.'Js. lOd. ; £50 lOs. 5id. 

licduoe to pence: — 

<). 30 far. ; 720 far. ; 425 fur. ; 900 far. ; 1000 far. ; 2700 far. 

Reduce to shillings: — 

7. 80d.; 168d.; 37r«d. ; 1805d. j 17G89d.; SOOOd. 

Reduce to pounds: — 

8. 80s. 764s. 1879s. 4.567s. 

9. 768d. 3689d. 7416d. 87651 d. 
10. 3084 far. 7689 far. 45672 far. 78947 far. 



Avoirdupois Weight. 

16 ounces (oz.) =1 pound, or 1 lb. 
100 pounds =1 cental, or hundredweight, or 1 ewt. 

20 hundredweight=l ton, or 1 t. 
7000 grains (gr. ) =1 pound avoirdupois. 
437A grains =1 oz. avoirdupois. 

14 lb. =1 stone. 

Avoirdupois weight is used for weighing all articles, except 
the ]»reeious metals, jewels, and medicines when dispensed. 

In Great Britain 2240 lb. make a ton, called the long ton. 



sSassfaK: 



iiBMi 



52 



ARITHMETIC. 



Troy Weight. 

24 fcrains (gr.) =^1 pennyweight, or 1 dwt. 
20 penny\veight8= 1 ounce, or 1 oz. Troy. 

12 ounces =1 pound, or 1 lb. Troy. 

480 grains =1 oz. Troy. 

57G0 grninfj =1 pound Troy. 

Troy weight is used for weighing the precious metals, gold, 
silver, and platinum. 

Apothecaries* Weight. 

20 grains (gr.) = l scruple, or 1 ^ _ 

3 scruples =1 drair, or 1 3 

8 drams =1 ouncu, orl ^^ 

12 ounces =1 T>ound, or 1 Bb. 

Apothecaries' weight is used in compounding medical 
prescriptions. 

Long, or Linear Measure. 

12 inches (in.) = l foot, or 1 ft. 
3 feet =1 yard, or 1 yd. 

5 J yards =1 rod, or 1 rd. 

320 rods =1 mile, or 1 mi. 

mi. =320 rd.=1760 yd. --=5280 ft,^80 cfiains. 
A huTid, used in measuring horses, --4 in. 
A knot, used in navigation, =6086 ft. 
A fathom, used in measuring depth at sea, =6 ft. 
Gunter's Chain, used in measuring land, = 100 links. 
1 chain=4 rd.=22 yd. =66 ft. =792 in. 

Square, or Surface Measure. 

144 square inches (sq. in.) = l square foot, or 1 sq. ft. 

9 square feet =1 square yard, or 1 sq. yd. 
30i square yards =1 square rod, or 1 sq. rd. 
160 square rods =1 acre, or 1 A. 

640 acres =1 square mile, or 1 sq. mi. 

10000 square links (sq. 1.) =] square chain, or 1 sq. "h. 

10 square chai'.is =1 acre. 

^4840 sq. yd. 
160 acres =1 quarter-section. 



TABLES, DEFINITIONS, AND REDUCTIONS. 



53 



Cubic, or Volume Measure. 

1728 cubic inches (on. in.) = l cubic foot, or 1 eu. ft, 
27 cubic feet =1 cubic yard, or 1 cu. yd. 

128 cubic feet =1 cord, or 1 cd. 

Firewood and rough stone are measured by the cord. 

A cord is equal to a pile 8 ft. long, 4 ft. wide, and 4 ft. high. 

Dry Measure. 

2 pints (pt.) = l quart, or 1 qt. 
4 quarts =1 gallon, or 1 gal. 
2 gallons =1 peck, or 1 pk. 
4 pecks =1 bushel, or 1 bu. 

In Great Britain gr.iin is sold by the quarter (8 bushels). 

Certain articles are sold not by bulk, but by weight. The 
following table gives the weight of a bushel of a number of 

these: — 



Dried Apples, 22 lb. 
Oats, 34 lb. 
Barley, 48 lb. 
Buckwheat, 48 lb. 
Timothy See'l, 48 lb. 
Flax Seed, 50 lb. 
Indian Corn, 56 lb. 
Kye, 56 lb. 



Fine Salt, 56 lb. 
Beans, 60 lb. 
Peas, 60 lb. 
Clover Seed, 60 lb. 
Wheat, 60 lb. 
Potatoes, 60 lb. 
Turnips, 60 lb. 
Onions, 60 lb. 



Liquid Measure. 

2 pints {pt.) = l quart, or 1 qt. 
4 quarts =1 gallon, or 1 gal. 

The Imperial gallon contains 277*274 cu. in. 

A cubic foot of water weighs 1000 oz. or 62i lb. and contains 
Gi gal. Thus a gallon of water weighs 10 lb. 

Time Measure. 

60 seconds (sec.) = l minute, or 1 min. 

60 minutes =1 hour, or 1 hr. 

24 hours =1 day, or 1 da. 

7 days =1 week, or 1 wk. 

,'565 days =1 common year, or 1 yr. 

I)(i() days :=1 leap yt;M'. 

Tliirty days have Septehil>er. 
A]>ril, »luiie and November. 

'V\u' other months, cxM-cpt Fcltruary, liavc ;J1 days each. 
Felti'uai'y has 28 days, except in leaj* year, wheii it has 2iK 



Sj«e 



54 



ARITHMETIC. 



The leap years are those whose numbers can be divided 
exactly by 4, except in the ease of the even hundreds. These 
must be exactly divisible by 400. Thus 1892, 1896 and 1600 
were leap years; 1894, 1897 and 1900 were not leap years. 

Each day is considered to commence at midnight. 
Circular, or Angular Measure. 

60 seconds (") = 1 minute, or 1'. 
60 minutes =1 degree, or V. 
360 degrees =1 circumference, or 1 C. 

A degree of the circumference of the earth at the Equator 
contains 60 geographical miles, or 69' 16 statute miles. 



Miscellaneous Units. 

12 units =1 dozen, or 1 doz. 

12 dozen — I gross, or 1 gro. 

12 gross =:1 great gross. 196 lb. 

20 units. =1 score, or 1 sc. 200 lb. 



24 sheets=l quire, or 1 qr. 
20 quires=l ream, or 1 rm. 

= 1 barrel of Hour. 

= 1 barrel of pork. 



29 lb. 
7 t. 1200 ll>. 

nso oz. 

:J671S4 oz. 



128 lb. 
7 t. b') oz. 

7162 oz. 

789641 oz. 



29 ft. :} in. 145 It. (i in. 



EXERCISE LXXI. 

Reduce to ounces Avoirdupois: — 

1. 2 lb. 5 lb. 

2. 2 t. 3 t. 50 11». 

Reduce to pounds Avoirdupois :- 

3. 36 oz. 480 oz. 

Reduce to tons: — 

4. 4216 lb. 82161 lb. 

Reduce to inches: — 

5. 7 ft. 9 ft. 8 ill. 

Reduce to yards: — 

6. 27 ft. 464 in. 
Reduce to square inches: — 

7. 8 sq. ft. 17 sq. ft. 100 sq. in. 

Reduce to square yards: — 

8. 78 sq. ft. 876 sq. ft. 3()89 sq. in. 

Reduce to cultic inches: — 

9. 3 (Ml. ft. 5 cu. ft. 9 fii. ft. 121 (Ml. ft. 100 (mi. in. 

Reduce to cords: — 

10. 1768 cu. ft. 5768 cu. ft. 9764 cmi. ft. 96."341 cu. ft. 



37'6i") in. 



f) sq. yd. 



17854 in. 



^q. ft. 



17(5415 s<|. in. 



TABLES, DEFINITIONS, AND REDUCTIONS. 



55 



96 qt. 1 pt. 
568 pt. 



EXERCISE LXXII. 

Reduce to pints j — 

1. 4qt. 7 qt. 
Reduce to gallons: — 

2. 27 qt. 761 qt. 

Reduce to bushels: — 

3. 4768 lb. wheat. 

Reduce to pints: — 

4. 3 gal. 5 gal. 1 qt. 

Reduce to gallons : — 

T). 17 pt. 245 pt. 

Reduce to seconds: — 

6. 7 mill. 5 sec. 17 hr. 15 min. 

Reduce to days: — 

7. 120 hr. 71856 min. 
Rediu-e to seconds: — 

8. 24' 768' 17" 

Reduce to degrees: — 

9. 700' 



471 qt. 1 pt. 
9765 pt. 



57896 lb. oats. 76891 lb. rye. 

7 gal. 3 qt. 9 gal. 1 qt. 1 pt. 

7689 pt. 2010 pt. 

5 da. 1 hr. 7 min. 

33333 min. 796841 sec. 

34° 15' 19" 



956' 



7689" 



S«'lect the leap years out of the following: — 
10. 1760 1815 1800 1837 

EXERCISE LXXIII. 



1856 



171° 51" 
76451" 
1890 



Add the following: — 


1. 


£ 


s. d. 




24 


12 6 




25 


13 9 




17 


18 10 




15 


7 8 


o 


c\v*. 


lb. oz. 




17 


xG 14 




18 


21 10 




18 


16 7 




i-1 


9 4. 


3. 


vd. 


ft. in. 




15 


I 7 




23 


2 9 




35 


6 



2 11 



£ 


s. 


d. 


25 


16 


8 


17 


13 


9 


14 


17 


11 


16 


10 


7 


t. 


cwt. 


lb. 


40 


16 


16 


16 


18 


94 


47 


15 


87 


21 


9 


75 


yd. 


ft. 


in. 


3 


o 


10 


4 


') 


5 


5 





6 


4 


2 


7 



£ 


s. 


d. 


123 


14 


6 


137 


18 


10 


246 


19 


11 


301 


8 


9 


t. cwt. 


lb. 


oz 


7 17 


15 


15 


18 14 


47 


12 


19 8 


76 


10 


9 20 


87 


14 


y*i- 


ft. 


in. 


17 


2 


11 


14 


1 


9 


12 


1 


7 


13 





6 



I 



56 



ARITHMETIC. 



4. bu. i»k. qt. 

5 1 3 

6 I 1 
2 
3 2 

5. gal. qt. \)t. 

13 2 1 

2 3 

15 

_ 7 1 _1 

Subtract the followint?; 

G. £ s. d. 

7 9 6 
4 5 9 



V>ii. ])k. qt. i»t. 

6 3 5 1 

8 16 1 

9 2 5 

7 3 4 1 

da. hr. mill. see. 

15 18 50 49 
1 13 59 59 
4 23 4 

10 11 1 4 



f?Hl, 


qt. 


pt 


36 


') 


1 


42 


1 


1 


25 


3 





28 


3 


1 



10. 



t. 


ewt. 


lb. 




27 


14 


56 




16 


18 


94 




1)U. 


l.k. 


qt 




56 


1 







27 


3 


1 




da. 


hr. mill. 


sec 


5 


16 


21 


18 


2 


22 


12 


37 


o 


/ 


,'/ 




48 


51 


17 




17 


57 


28 





£ 


s. 


d. 


50 





1 


30 


10 


10 


yd. 


ft. 


in. 


14 


1 


4 


10 


2 


11 


bn. 


]>k. 


qt 


27 


1 


1 


18 


1 


3 



wk. da. hr. min. sec . 

1 2 13 40 30 

2 6 10 8 3 
5 22 55 45 

2 3 4 1 15 



ewt. lb. oz 
20 45 7" 
16 22 13 

yd. ft. ill. 

54 

6 19 

gal. qt. pt, 
4 10 
3 2 1 



wk.da. hr. rain. sec. 
3 4 23 45 30 
1 6 16 30 45 



25 36 15 

18 45 36 



c. yd. eft. c.iii. p. yd. eft. c. in. 

48 16 1000 100 760 

16 2^ __! 245 4824 1 000 

EXERCISE LXXIV. 



Multiply the following: 
1. 



£ 


s. 


d. 


£ 


H. 


d. 


ewt. 


lb. 


oz 


13 


5 


10 
5 


75 


15 


8 
6 


15 


18 


9 
9 



3. 



t. ewt. IV). oz. 
7 14 16 7 

8 

bu. pk. qt. i)t. 
4 2 3 1 



4. gal. qt. ]>t. 
15 2 1 
12 



yd. 


ft. 


ill 




17 


1 


11 
12 




bu. 


pk. 


qt. 


l»t 


7 


3 


7 


1 
12 


dit. 


11'. mill. 




17 


17 


17 
9 





yd. 


ft. 


in. 


87 




9 
11 


gal 


qt. 


pt. 


4 


3 


1 
7 


da. lir. 


mill. 


sec , 


5 19 


41 


52 

8 



TABLES, DEFINITIONS, AXD REDUCTIONS. 



57 



qt. 


pt. 


2 


1 


1 


\ 


3 





3 


1 


min.sec. 


40 


30 


8 


3 


5a 


45 


1 


15 


t. lb. 


oz 


45 


7 


; 22 


13 


I. ft. 


in. 


i 





3 1 


9 


il. qt 


. pt. 


4 1 





3 2 


1 




. 


D ' 


ft 


:5 36 


15 


S 45 


30 


•.ft. 


0. in 





760 


24 


1000 



lb. 


o/,. 


18 


9 




9 


. ft. 


ill. 


Ml 


9 




n 


ll. qt. 


pt. 


3 


1 




7 


. mill 


Hce 


1 41 


52 




8 



5. 


17' 41' 57" 

t 


84" L>7' 28" 
5 


f. yd. eft. 
7 24 


e.in, 
245 
11 


J 


Divitl 


t- tlu' followiiif^: — 




0. 


£ s. d. 
4)81 17 8 


& 8. d. 
7)36 7 5 


cwt. lb. 
6)47 15 


oz. 
4 


r 




t. cwt. lb. oz. 
8)20 5 16 8 


yd. ft. in. 

6)75 2 6 


yd. ft. 

1;)83 2 


in. 
3 




8. 


bu.pk. qt. pt. 
7)34 2 5 1 


bu.pk. gal. qt. 
9)73 1 1 1 


gal. qt. 
5)78 


pt. 

1 




y. 


gal. qt. pt. 
7)30 2 1 


hr. min.st'. 
9)1479 57 36 


diX. hr. mill 
3)563 17 47 


. sec. 
51 




10. 


4)77° 2' 48" 


7)876° 5' 48" 


e.yd. eft. 
9)178 14 


c.in. 

81 





EXERCISE LXXV. 

Divide the following: — 

1. £30 6s. 8d. by £2 6s. 8d. ; £8 18s. by 5s. 6fd. 

2. 3 t. 16 cwt. by 19 lb. ; 1 t. 16 cwt. 83 lb. 12 oz. by 105 
lb. 4 oz. 

3. 44 yd, 2 ft. 9 in. by 33 in. ; 7 yd. by 6 in. 

4. 78 A. 71 sq. rd. by 1 xV. 3 sq. rd. ; 100 sq. yd. by 1 sq. ft. 
36 sq. in. 

5. 327 eu. ft. 1094 eu. in. by 1 cu. ft. 14 cu. in. ; 74 cords 
by 148 eu. ft. 

6. 87 bu. by 1 qt. 1 pt. ; 29 bu. 1 pk. 1 qt. 1 pt. by 5 pt. 

7. 33 gal. 3 qt. by 1 qt. 1 pt. ; 30 gal. 2 qt. 1 pt. by 7 pt. 

8. 12 hr. 48 min. by 16 sec. ; 8 da. 3 hr. by 1 hr. 15, miu. 

9. 2° 42' 30" by 2' 5"; 7,C. by 1° 30'. 

10. 35 rm. by 15 sheets; 75 rm. 15 qr. by 5 qr. 

EXERCISE LXXVI. 

1. Wliat is the height of a horse that stands 14 hands high? 

2. How many pints of molasses are there in a hogshead 
containing 63 gallons? 

3. Find the number of hours in January. 

4. How many parcels, each weighing 15 lb. 4 oz., can be 
made from 1 ton, and what weight will be remaining? 



m 



m 



% 



58 



ARITHMETIC. 



f). If nil onnoo of i>iiro pnld is worth C3 17s. lO^d., find thr 
value of 11 l»ar of pur** f^ohl wj-ifjclilii};; 2 ll». G o/,. 

(}. What IS the value of K2 marks, when a mark is worth 
138. 4i\.1 

7. A rect.aiffular box is 4 ft. 4 in. long, 1 ft. 10 in. wide and 
17 in. deep, outside measurement. Find the lengtli of a string 
that will go round it — (1) lengthwise, (2) crosswise. 

8. The angles of a triangle contains 180^. One angle is 
42° 36' 45", another is 29° 42' 37". Find the third angle. 

9. If the posts in a telegraph line are 45 yards apart, how 
many are there in 9 miles? 

10. If the wool from a sheep each year weighs 7 lb. 8 oz., 
find the value of the wool from a flock of 300 sheep at $19.()0 
per cwt. 

EXERCISE LXXVII. 

1. A merchant bought tobacco at $55 a cwt., and sold* it at 
4 cents an ounce. How much did he gain on 3 cwt.? 

2. How many telegraph poles are there in 1(5 mi. 80 rd. of 
line, the poles being 4 rd. apart? 

3. Find the cost of a pile of wood containing 3328 c. ft. at 
$4 per cord. 

4. A farm is 50 chains long and 20 chains wide. How many 
yards long are the boundary fences? 

5. Find the value of 17 sq. miles 85 ae. of land at $15 per 
acre. 

6. Find the number of minutes from 17 minutes to ten in 
the forenoon till 25 minutes past three in the afternoon. 

7. A grocer bought a cheese weighing 45 lb. 6 oz. He sold 
2 lb. 4 oz. to one woman, 1 lb. 8 oz. to a second, and 3 lb. 
12 oz. to a third. How much of the cheese remains unsold? 

8. A cubic foot of water weighs 62 lb. 8 oz. How many 
tons of water are there in a tank containing 480 c. ft.? 

9. A gallon of water weighs 10 lb. How many gallons art* 
there in the tank in question 8? 

10. Find the cost of grading a railroad 57 miles long at $5.50 
per yard. 

EXERCISE LXXVIII. 

1. How many tons of provisions are required to feed 480 
men for 60 days, if each man receives 3 lb. 2 oz. each day? 

2. How many silver spoons, each weighing 2 oz. 8 dwt., can 
be made from a bar of silver weighing 12 lbs. ? 

3. How often can 2 ft. 3 in. be subtracted from 81 yards? 



TABLES, DEFINITIONS, AND REDUCTIONS. 



5U 



4. If Mar> takes 'J miii. 20 see. to reiul a l)af,'o ol" a book, 
how many such pa^^es ean sh« read in I{r> minutes? 

T). If a bicycle rider jroes 2 miles 'Ait rods every (i min., how 
far will lie go in '2 hours? 

(). A merchant bouf?ht 7H0 yards of doth at J)s. lid. a yard, 
iind retailed it at 12s. Id. a yard. Find his total gain. 

7. If it costs 12s. Gd. more to build a fence ^5 yards long 
thiin one IJO yards long, find the cost of building 75 yards of 
such fence. 

8. A man bought 3G72 lb. of oats at 27 cents a bushel and 
3136 lb. of rye at 4G cents a bushel. How much had he to pay? 

9. Seventy-five bushels of wheat at 68 cents a bushel will 
buy how numy yards of cloth at 85 cents per yard? 

10. A merchant bought 71) reams of foolscap, for which he 
paid $237. How nnich did he pay for a quire? 

EXERCISE LXXIX. 

1. A merchant sold to one man 19 gal. 3 qt. 1 pt. of 
molasses; to another he sold 27 gal. 2 qt. 1 pt., and had 48 gal. 

1 i)t. left. How much had he at first? 

2. Out of a cask having 27 gal. 1 pt. of vinegar, 14 gal. 

2 qt. were sold. How much remained in the cask? 

3. A farmer sold six loads of wheat which grew on one field, 
as follows:— The first weighed 47 bu. 36 lb., the second 48 bu. 
15 \h., the third 47 bu. 35 lb., the fourth 47 bu. 55 lb., the 
fifth 48 bu. 19 lb., and the sixth 38 bu. 56 lb. How much 
wheat grew on this field? 

4. There are 12 acres in the field referred to in the last 
example. Find the yield per acre. 

5. A clock which gains 45 seconds every 8 hours is set right 
at noon on Monday. When it is 8 o'clock in the evening of 
Wednesday what time will the clock show? 

6. Find the weight of two dozen sterling silver spoons, each 
one weighing 2 oz. 4 dwt. 

7. If 2 lb. of gold are coined into 89 guineas, find the value 
of i)ure gold per ounce. 

8. 7000 grains make a pound Avoirdupois, and 5760 grains 
a i)ound Troy. How many pounds Avoirdupois are of the same 
weight as 350 lb. Troy? 

9. Find the cost of feeding 120 horses for 20 weeks when 
hay is $8 a ton and oats 30 cents a bushel, if a horse eats 20 lb. 
of hay and 10 quarts of oats a day? 

10. A wagon with 128 packages weighs 2 t. 60 lb. If the 
wagon weighs 1 t. 140 lb., find the average weight of a package. 






CHAPTER IV, 



SIMPLE APPLICATIONS OF THE PREVIOUS RtLES. 
I. BILLS AND ACCOUNTS. 

A Debtor, in business transactions, is a pureliasor, 
or a person wlio receives money, goods, or servi(^es , 
from another. 

A Creditor is a seller, or a person who parts with 
money, goods, or servi(*es to another. 

A Bill is a detailed statement of goods sold or of 
services rendered, and of payments, if any, made. It 
should show the place and time of each transaction, 
the buyer and seller, the quantity, price and cost 
of each article, and any payments received. 



Mrs. F. S. Brown. 



Form of a receipted Bill. 

Toronto, Jan. 12, 1900. 



Bought of Hii.r. & Weir. 



»ee. 


26 




( < 




27 




28 




u 




( ( 



12 yd. Calico, @ 16 ct. . . . 
2 Silk Scarfs, @ $1.35 . . . . 
30 yd. Linen Crash, @ 21 ct. . 
4 pair Kid Gloves, @ $1.50 . . 
Ik doz. spools Cotton, 60 ct. 
1 piece Ticking, 42 yd., @ 37 ct. 



Received Payment, 



1 


92 




70 


6 


30 


6 


00 




90 


15 


54 



$33 



Henry F. Wat^^rbury, 

for KtLL & Weir. 

60 



36 



BILLS AND ACCOUNTS. 



61 



i 



RULES. 



Li'chaser, 
servi(^es 

arts with 

old or of 
aacle. It 
usaction , 
and cost 



12, 1900. 



1 


92 




70 


6 


30 


6 


00 




90 


15 


54 


$:j3 


36 



EXERCISE LXXX. 

Make out Bills for the following, supplying names of places 
and dates where necessary: — 

1. Mrs. James Brown bought of John Marsh: — pair shoes 
(li) .$3.25, 8 yd. silk @ $2.40, 3 pair gloves @ $1.25 and 9 collars 
(a) 25 ct. 

2. Mrs. John Green sold Charles Jenkins: — 75 bu. apples (ff>j 
S5 ct., 5 tons hay @ $10.85, 50 bu. potatoes @ 60 ct. and 50 
cabbages @ 10 ct. 

3. John Smith sold Peter Brown: — 25 horses @ $115, 143 
cows @ $27, 24 oxen @, $45 and 175 sheep @ $5.50. 

4. J.ames Sparrow bought of Messrs. Jones & Son: — 52 lb. 
butter @ 18 ct., 16 yd. silk @ $1.45, 23 pair boots @ $2.40, 19 
lamps @i $2.35 and 28 lb. sugar @ 6 ct. 

5. Mrs. R. Philp bought of the R. Simpson Company: — 6 
l»ureaus @ $8.75, 3 easy chairs @ $15.25, 12 dining chairs @ 
$4.(50, 15 mattresses @ $4.50, 2 tables @ $18.75 and 4 mirrors 
@ $9.75. 

6. Samuel Purdy sold Mrs. T. Jones: — 125 lb. sugar @ 8 ct., 
17 bbl. flour @ $7.75, 48 lb. lard at 11 ct., and 48 lb. meat 
13 ct. 

7. Mrs. T. Rorer bought of Messrs. Jones & Co.: — 4 yd. 
cloth @ $1.25, 12 pair stockings @ 38 ct., 6 pair kid gloves @ 
$1.15 and 27 yd. ribbon Qt} 5 ct. 

8. Simon Brown sold Mrs. T. Smith:— 21 lb. butter @ 22 
ct., 12 lb. cheese © 16 ct., 114 doz. eggs @ 15 ct., 23 qt. milk 
@ 6 ct., 27 bu. potatoes at 45 ct. and 32 bu. carrots @ 40 ct. 

9. Mrs. Blake bought of the T. Eaton Company: — 2 lb. 
candy @ 15 ct., 5 books @ 25 ct., 3 slates @ 12 ct., 2 quires 
l>aj)cr @ 10 et., 1 box pens @ 35 ct., and 1 box slate pencils 
@> 10 ct. 

10. The R. Simpson Co. sold Mrs. P. Scott: — 25 lb. sugar @ 
7 ct., 32 lb. tea at 45 ct., 84 11). coifee @ 35 ct., 62 lb. raisins 
(<i/ 9 ct., 39 lb. currants @ 8 et. and 47 lb. biscuits @ 10 ct. 

EXERCISE LXXXI. 

Make out bills for the following, supplying names of places 
and dates where necessary: — 

1. .Tames Smith bought of Edward Jones: — 75 cords hard- 
wood @ $4.50, 10 tons coal @ $6.50 and 15 cords pine @ $2.50. 
He ]»aid cash $150. 

2. Peter Douglas sold James Rogers: — 10 lb. sugar @ 5 ct., 
(5 lb. tea @ 35 ct., 8 lb. colTee @ 25 ct., 5 lb. rice at 7 ct., and 
9 lb. cheese @ 16 ct. He took in exchange 4 bags potatoes at 
90 cts. and the balance in cash. Make out a receipted bill. 



IR. 



■1 



m 



ARITHMETIC. 



3. William Taylor bought from John McMurtry:— 10 lb. 
sugar @ 8 ct., 6 lb. tea @ 45 ct., 1 set dishes @ $10. .50, 1.') lb 



soap @ 
another. 



15 ct. He paid $5 iu cash at one time and $1 at 
Make out tin* bill. 



4. Thexton Bros, bought from RoV>ert Smith:— 25 tons hay 
® $7.r)0, 66 bu. rye Qi^, 40 ct., 104 bu. barley (n), iV.i ct. and 9H 
bu. wheat @ 72 ct. They give iu exchange 5 bids, flour Oi} 
$7.25, and 75 lb. oatmeal @ 3 ct. and the balance in cash. 
Make out a receipted bill. 

5. Smith & Weir bought from Thomas Scott:— 1140 lb. 
wheat @ 84 ct. per bu., 1802 lb. oats @ 45 ct. per bu., 540 bu. 
peas© ^0 ct. and 1200 !b. barley @ 48 ct. per bu. On Oct. 17, 
1899, he received $100 in cash and the balance on Oct. 28. 
Make out a receipted bill. 

6. Mrs. Brady bought from Smith & Jones:— 7 doz. eggs @/ 
18 ct., 19 lb. soap @ 11 ct., 10 lb. butter at 22 ct., 13 lb. cheese 
@ 17 ct. and 20 lb. rice @ 4 ct. She gave in exchange 5 geese 
weighing 54 lb. @ 6 ct. and the balance in cash. Make out a 
receipted bill. 

7. Mrs. R. Porter bought from Jones & Co., Belleville: — 
27 yd. flannel Qi} 80 ct., 32 yd. calico @ 9 ct., 6 pair gloves at 
90 ct. and 16 yd. muslin (a) 12 ct. She paid $10 cash. Make 
out her bill. 

8. John Smith bought of Hill & Groves, London: — 16 yd. 
silk (a>, $1.15, 72 yd. ticking @ 14 ct., 42 yd. shirting @ 15 ct., 
12 yd. flannel @ 40 ct. and 24 yd. print @» 13 ct. He paid 
cash. Make out a receipted bill. 

9. Thomas Taylor bought of Lewis & Sons, May 5: — 5 doz. 
coat hooks @ 35 ct., 7 door knobs @ 20 ct., 25 lb. nails @ 4 
ct., June 1st, 5 door locks © 75 ct., 12 doz. screws at 7 ct., 3 
sets fire-irons @ $3.15. Thomas Taylor sold Lewis & Sons, 
June 10, 1 pair boots @ $3.50, 1 pair rubbers @ 75 ct. The 
balance was paid June 20. Make out a receipted bill. 

10. Henry Philps sold to Aaron Brown: — 75 yd. Bri.ssels 
carpet @i 96 ct., 1 piece cotton, 31 yd., @/ 11 ct., 1 box hooks 
and eyes @ $1.75, 1 piano cover @ $5.50, 1 table cover @ 
$3.25. Brown worked 10 days @ $1.40 per day for Philps and 
paid the balance in cash. Make out a receipted bill. 

11. June 14, 1899, Samuel Farwell bought the following 
items of H. J. Thompson & Co. : 9 lb. of paint at 12 ct. a 
pound; 10 rolls of paper at 20 ct. a roll; 28 rolls at 8 ct. a roll; 
44 rolls at 10 ct. a roll; 4 rolls at 25 ct. a roll; 34 yards of 
border at 6 ct. a yard; .58 yards at 2 ct. a yard; 60 yards at 1 
ct. a yard. July 7, 1899, Mr. Farwell returned 3 rolls of paper 
at 8 ct. a roll, 5 rolls at 10 ct. a roll, and 5 yards of border at 6 
ct. a yard. Make out Mr. Farwell's ivccount. 



SIMPLE MEASUREMENTS. 



G3 



II. SIMPLE IV1EASUREIVIEINTS. 

A Rectangle is a flat surface bounded by four 
straight lines and having its four angles equal to one 
nnother. 

A Square is a rectangle contained by equal sides. 

A Rectangular Solid is a space enclosed by six 
rectangular surfaces. 

EXERCISE LXXXII. 

Draw the followinj^ rectangles and find their perimeter: — 

1. 2 in. by ii in., 4 in. by 3 in., 5 in. by 6 in., 4 in. by 4 in. 

2. Tlu3 ceiling of a rectangular room is 16 ft. by 12 ft. Find 
its perimeter. 

3. A rectangular lot is 50 yd. long and 40 yd. wide. Find 
the cost of fencing it at 25 ct. per yard. 

4. How many boards 12 ft. long are there in a fence round a 
rectangular lot 60 yd. long and 40 yd. wide, the fence being 5 
boards high. 

5. The posts in a fence round a rectangular lot 60 ft. by 144 
ft. are 6 ft. apart. Find the cost of digging the post holes at 
5 ct. each. 

6. How much will it cost to fence a farm 200 rods long and 
80 rods wide at $1.25 per rod? 

7. How much will it cost to fence both sides of a road for 1 
mile with wire which weighs 1 lb. per rod and costs 8 ct. per 
lb., the fence being 5 wires high? 

8. A square cattle ranch is 2 miles long, how many yards of 
fencing will enclose it? 

D. How much will it cost to enclose a mile square with wire- 
fencing at $4.50 per chain? 

10. A rectangular room is three times as long as it is wide. 
Its perimeter is 320 feet. Find its length and width. 

EXERCISE LXXXIII. 

1. Find the area of each of the following rectangles: — 



34 ft. by 36 ft. 


32 ft. by 38 ft. 


72 yd. 


by 78 yd. 


2. Find the number 


of acres in each 


of the 


following 


rectangular fields: — 








36 rd. by 40 rd. 


25 rd. by 64 rd. 


75 rd. 


by 32 rd. 


70 rd. by 96 rd. 


48 rd. by 50 rd. 


38 rd. 


by 80 rd. 



3. How many square feet are there in a board 18 ft. long 
and 12 in. wide? 



64 



ARITHMETIC. 



4. How many sciimre yards are thfro in :i rt'ctaii>?ular floor 
33 ft. by l»l ft.f 

5. A Bqiiare garden is 48 yd. long. How many Kqiiaro yards 
doeH it contain f 

6. A close board fence 6 ft. liigh and 100 yd. long is to bo 
painted. How numy square yards are tliere in the fence? 

7. How numy square inches are there iu the surface of a 
brick 8 in. long, 4 in, wide, and 2 in. deep? 

8. How many square foet are there in the walls of a rectan- 
gular room I'J ft. high, 28 ft. long and 1(5 ft. wide? 

9. A rectangular i)]ot 00 ft. by 130 ft. has a path roiind the 
outside 5 ft. wide. Find the number of square feet iu the 
path. 

10. How many square feet are there in a board 18 ft. long 
and 13 in. wide at one end, 19 in. wide at the other. 



EXERCISE LXXXIV. 

1. A rectangular floor contains 48(5 s(i. ft. It is 27 ft. long; 
find its width. 

2. A rectangular surface contains (i48 sf|. yd. If it is 108 
ft. long, find its width. 

3. A rectangular field containing 1(5 acres is G4 rods long. 
IIow wide is it? 

4. A rectangular field containing 18 acres is 80 rods long. 
Find the cost of fencing it at $1.25 per rod. 

5. A rectangular lot contains 1(500 sq. yd. Its length being 
240 ft., find the cost of fencing it at 25 ct. per foot. 

6. How many boards 12 ft. long would be required to enclose 
a rectangular lot containing 9600 sq. yd. with a straight fence 5 
boards high, the lot being 240 ft. wide, 

7. The walls of a room contain 96 sq. yd. The room is 12 
ft. high. Find its perimeter. 

8. A bought a farm containing 220 acres. If it is 176 rods 
wide, what will it cost to fence it iu at $1.25 per rod? 

9. To paint a close board fence 6 ft. high at 15 ct. per sq. 
yd. costs $36. Find the length of the fence. 

10. At $25 an acre a farm costs $2000. This farm is 200 rd. 
long. • Find the cost of fencing it at $1.25 per rod. 

CARPETIINCi. 

In computing how nnicli carpet is needed for a room 
there are two modes of procedure — (1) the mathema- 
Heal, where the quantity equal to the floor space is 



SIMPLE MEA8URKMKNTS. 



C5 



found, and (2) tlio p)'((r(iral or (wbifnu'i/, whcro the 
iimiilMT of strips of cjirix't r('«|i.ir('d is first found, 
imd, an allowance beinj^ made for nuitchint? tln^ 
pattern as well as turning? iind<'r ait the side when 
necessary, the ([uantity reciuired is then computed. 



EXERCISE LXXXV. 

1. Find what length of ciupt't 30 iti. wide is required for a 
H'ctanK'iln''' room 24 ft. by 15 ft. 

12. A r«'('tan{,'ular floor ^(5 ft. by 25 ft. is to bo covered with 
oilcloth GO in. wide. How many yards will be rc(niiredf 

;{. How many yards of carpet 27 )u. wide will cover a 
rectangular room 18 ft. by 12 ft. 

4. A rectangular room is 27 ft. by 17 ft. 6 in. How many 
yanls of cari)et 27 in. wide will cover it? 

5. There is a square room 42 ft. long to be covered with 
carpet 1 yard wide. How many yards are required? 

G. Find the cost of carpeting a rectangular room 24 ft. by 18 
It. with carpet 27 in. wide at 90 ct. per yard. 

7. A rectangular room 15 ft. by 12 ft. is covered with carpet 
:») in. wide which costs 65 ct. per yard. Find the cost. 

8. Find the cost of carpeting a rectangular room 36 ft. by 20 
ft. with carpet a yard wide at $1.25 per yard. 

9. Find the cost of carpeting a rectangular room 12 f1 . by ^S 
ft. with carpet 27 in. wide at 75 ct. a yard. 

10. Find the cost of carpeting a stairway of 24 steps, each 
step being 11 in. wide and rising 7 in., with carpet at $1.05 per 
yard. 

EXERCISE LXXXVI. 

1. How many strips of carpet 36 in. wide are required to 
cover a rectangular room 27 ft. by 18 ft. — (1) if the strips run 
lengthwise, (2) if they run crosswise? 

2. How many strips of carpet 27 in. wide are needed to 
cover a rectangular room 18 ft. wide, if the strips run 

lengthwise? 

3. How many strips of carpeting 30 in. wide are needed for 
a square room 40 ft. long? 

4. How many strips of oilcloth GO in. wide are required to 
cover a room 40 ft. wide, the strips running lengthwise of the 
room? 

"). A rectangular room, 22 ft, 6 in. wide, is covered with 
carpet 27 in. wide. How many strips are there? 



* •.I 



'cm 



66 



ARITHMETIC. 



6. How many yards of carpet 30 in, wide will be required 
for a rectangular rooru 27 ft. V)y 20 ft., the strips running 
lengthwise of the room ? 

7. How many yards of carpet 36 in. wide are needed for a 
rectangular room 24 ft, by 18 ft., the strips running lengthwise 
of the room? 

8. Find the cost of carpeting a rectangular room 24 ft. l>y 

21 ft., witli carpet a yard wide at $1.05 per yard, the strips 
running lengthwise of the room. 

9. Find the cost of carpeting a rectangular room 27 ft. by 
20 ft., with carpet 27 in. wide at $1.10 per yard, the strips 
running crosswise of the room. 

10. Find the cost of carpeting a rectangular room 30 ft. l>y 

22 ft., with carpet 30 in. wide at $1.25 per yard, the strips 
running crosswise of the room. 

PLASTERING. 

Ill reckoning tlie area to be plastered in a room, 
there are two methods of procednre— (1) the mafhema- 
tiraJ, wliere the exact number of square yards is found 
l)y finding the total area within the boundary line of 
the work, and from thi leducting the area of all the 
openings; and (2) the irbitrarij or practical method. 
In this case the total i.i'ea within the boundary lines 
of the work is found. From this area, half the are?i 
of the doors and windows is subtracted. The nearest 
whc^ d number of square yards in the remainder is the 
area for which the plasterer is to be paid. 

EXERCISE LXXXVil. 

1. How many square yards of plastering are there in the . 
ceiling of a rectangular room 30 ft. by 24 ft. ? 

2. How many squar(^ yards of plastering are there in tlie 
walls of a rectangular spf-ce 38 ft. long, 25 ft. wide and 12 ft. 
high ? 

3. How many square yards of plastering are there in the 
walls and ceiling of a rectangular rocm 30 ft. by 24 ft. and 
12 ft. high? 

4. Find the cost of plastering the ceiling of a rectanguhw 
room 24 ft. by 18 ft. at 19 ct. per square yard. 

5. Find the cost of plastering a surface equal to the walls 
and ceiling ot a rectangular room 27 ft. by 18 ft. and 12 ft. 
high at 23 ct. per square yard. 



^^- 



SIMPLE MEASUREMENTS. 



67 



6. A rectjuij?ul!ir room 27 ft. by 18 ft. and 10 ft. high has 3 
doors, each 7 ft. by 4 ft.; '.i windows, eaeli (5 ft. by 3 ft., and 
1 window G ft. by 4 ft. Find the area to \m plastered on the 
walls only — (1) mathematically, (12) practically. 

7. Find the cost of pljiHterin<j: the walls only of a rectangular 
room 30 ft. by 'J4 ft. and 112 ft. high, there being 3 doors, each 
8 ft. by 5 ft.; 3 windows, each 7 ft. by 4 ft., and 1 window 
() ft. by f) ft., at 20 ct. ])er sq. yd. — (1) mathematically, (2) 
pi-aetically. 

8. At 25 ct. per sq. y^.., And the cost of plastering tlie walla 
of a rectangular room 25 ft. by 20 ft. and 10 ft. high, there 
being 2 doors 7 ft. by 5 ft., 3 windows (5 ft. V)y 3 ft., and 1 
window 5 ft. by 4 ft. — (1) mathematically, (2) practically. 

9. At 25 ct. per sq. yd., find the cost of plastering the walls 
and ceiling of a rectangular room 24 ft. by 21 ft. and 12 ft. 
liigh, there being 3 doors 8 ft. by 4 ft. and 3 windows 7 ft. by 
4 ft. — (1) mathematically, (2) practically. 

10. At 27 ct. per sq. yd., find the cost of plastering the 
ceiling and walls of a hall 3G ft. by 27 ft. and 14 ft. high, 
there being 2 doors 9 ft. by 8 ft. and 9 windows 7 ft. by 4 ft. — 
(1) mathematically, (2) practically. 



M 



WALL PAPER. 



Ill Canada and in the United States, wall paper is 
usually made into rolls 8 yd. long: <>i' donl)le rolls 
IG yd. long and 18 in. wide. In Great Britain the 
usual width is 21 iu. 



EXERCISE LXXXVin. 

1. How many yards of pape. '''' in. wide will paper the 
ceiling of the room in example 1, last exercise? 

2. How many yards of paper 21 in. wide are required to 
pai)er the walls of the room in example 2, last exercise? 

3. How many yards of paper 18 in. wide will paper the walls 
iiiid ceiling of the room in example 3, last exercise? 

4. How many yards of paper 18 in. wide will pap^u- the 
ceiling of the room in example 4, last exercise? 

5. How many yards of paper 18 in. wide will paper the 
walls and ceiling of the room in example 5, last exercise? 

6. How many yards of paper 36 in. wide will paper the 
walls of the room iu example 6, last exercise? 

7. The room in example 7, last exercise, is papered with 
piiper 18 iu. wide. How much is "required for the walls and 
ceiling? 



<'A 



B\ 



!?;• .1 



asm 



68 



ARITHMETIC. 



8. The walls of the room in example 8, last exercise, are 
papered with paper 21 in. wide. How nmch is needed? 

9. Find the cost of covering the plaster of the room in 
example 9, last exercise, with paper 18 in. wide at 15 ct. ]>er 
roll of 8 yards. 

10. Find the cost of papering the walls and ceiling of the 
hall in examjjle U), last exercise, with paper 18 in. wide at 
25 ct. per roll of 8 ^ards. 

BOARD MEASURE. 

Boards one inch or less in thickness are sokl by tlie 
square foot. 

Thus, a board 18 ft. long, 1 ft. wide and 1 in. or 
less thick contains 18 ft., board measure. 

Boards more than an inch thicik are sold by the 
number of feet, board measure, to which they are 
equivalent. 

Thus, a plank 18 ft. long, 1 ft. wide and 3 in. 
thick contains 54 ft., board measure. 



EXERCISE LXXXIX. 

1. Find the number of board feet in the following :- 

(a) A board 12 ft. long, 9 in. wide and 1 in. thick. 

(b) A board 18 ft. long, 16 in. wide and 1 in. thick. 

(c) A board 16 ft. long, 18 in. wide and 1 in. thick. 
{(i) A board 16 ft. long, 9 in. wide and 2 in. thick, 
(e) A board 16 ft. long, 10 in. wide and 3 in. thick. 
(/) A board 18 ft. long, 16 in. wide and i in. thick. 
(g) A board 16 ft. long, 9 in. wide and i in. thick. 

2. How many feet of lumber are there in a close board fence 
5 ft. high, 660 ft. long, the boards being 1 in. thick? 

3. How many feet of lumber are there in 100 pieces 14 ft. 
long, 6 in. wide and 6 in. thick? 

4. How much lumber is required to put a 12 in. board 
around a rectangular field 220 yd. by 150 yd.? 

5. How many ft. of lumber are there in a sidewalk 160 yd. 
long, 8 ft. wide, the ])lanks being 2 in. thick? 

6. How many feet, board measure, are there in 8 planks, 
4 in. thick, 18 ft. long and 16 in. wide? 

7. How much lumber is there in 220 yards of fencing, con- 
sisting of 5 six-inch boards? 



SIMPLE MEASUREMENTS. 



69 



'W 



8. A pile of lumber consists of 250 boards, each 16 ft. long, 
10 in. wide and 3 in. thick. How many board feet are there f 

9. Find the cost of 500 planks, 10 ft. lont?, 12 in. wide and 

3 in. thick, at $20 per thousand, board measure. 

■ 10. What is the value of a pile of inch lumber consisting of 
2000 boards 15 ft. long and 12 in. wide at $18 per thousand? 

RECTANGULAR SOLIDS. 
EXERCISE XC. 

1. How many e. ft. of air are there in a rectangular room 
18 ft. by 16 ft. and 10 ft. high? 

2. How many c. ft. of timber are there in a rectangular 
stick 35 ft. long, 3 ft. wide and 2 ft. deep? 

3. How many cubic yards of stone are there in a rectangular 
pile 15 ft. long, 12 ft. wide and 9 ft. high? 

4. How many cubic yards of earth are taken from a cellar 
30 ft. long, 21 ft. wide and 9 ft. -eep? 

5. White pine weighs 24 lb. per cubic foot. What is the 
weight of a rectangular stick of such timber 28 ft. long, 3 ft. 
wide and 2 ft. thick? 

6. What will the digging of a cellar 18 ft. long, 15 ft. wide 
and 9 ft. deep cost at 45 et. per cubic yard? 

7. A gravel pit 60 ft. wide and 360 ft. long is excavated to 
the uniform depth of 17 ft. How many cubic yards of gravel 
are removed? 

8. How many cubic yards of stone and mortar are in the 
fourrdation of a barn 60 ft. long and 36 ft. wide, the wall being 
2 ft. thick and 8 ft. high? 

9. How many cubic feet of masonry are there in the founda- 
tion of a house 40 ft. long and 30 ft. wide, the vtaii being 9 ft. 
high and 2 ft. thick? 

10. Find the cost of 24 rectangular blocks of stone, each 9 ft. 
by 6 ft. by 5 ft., at $5.75 per cubic yard. 

EXERCISE XCI. 

1. How many cords of wood are there in a pile 24 ft. long, 
16 ft. wide, 10 ft. high? 

2. Find the number of cords of wood in a pile 48 ft. loirg, 
14 ft. high and 12 ft. wide. 

3. Find the number of cords in a pile of wood 120 ft. long, 

4 ft. wide and 8 ft. high. 

4. How much should be paid for a pile of 4-foot wood, 
128 ft. long and 7 ft. high, at $3 per cord? 



•'-m 
till 



■n>s 



■"Tlfgl 



70 



ARITHMETIC. 



.". Find the value of l(i pileis of w^oil, each 24 ft. long, 

4 tv. wide, 8 ft. high, at $2.25 per cord. 

G. Find the cost of a pile of wood 112 ft. long, 5 ft. wide 
and 8 ft. high, at $2.15 per cord. 

7. There are GO cords of wood in u pile 8 ft. wide and 12 ft. 
high. How long is the pile? 

8. There are ;{5 cords of wood in a pile 14 ft. high and 64 
ft. long. How wide is the pile ? 

9. Tiie cost of a pile of wood at $3 per cord is $;{60. It is 
240 ft. long and 8 ft. wide. How high is tiie pile? 

10. At $2.25 per cord a pile of wood is worth $2;{G.25. It is 

5 ft. wide and 12 ft. high. How long is the pile? 

EXERCISE yxil. 

1. There are 70 e. yd. of earth taken from a cellar 18 ft. 
long and 15 ft. wide. How deep is the cellar? 

2. A rectangular room 30 ft. by 25 ft. contains 8250 c. ft. of 
air. How high is the room? 

3. In a pile of wood there are 6 cords. The i)ile is 4 ft. 
wide and 8 ft. high. How long is it? 

4. A stick of square timber contains 180 c. ft. It is 30 ft. 
long and 2 ft. wide. How thick is it? 

5. A brick wall 2 ft. thick and 40 ft. high contains 89G0 
c. ft. How long is the wall? 

6. A l)rick contains 64 c. in. How many bricks are there in 
a rectangular pile 12 ft. long, 8 ft. wide .and 7 ft. high' 

7. There are 3072 c. ft. of masonry in a stone wall 8 ft. high 
and 2 ft. tliiek. How long is the wall? 

8. If the wall in example 7 is the stone foundation of a barn 
60 ft. long, how wide is the barn? 

9. A rectangular box 48 in. long and 30 in. deep, inside 
measurement, contains 25 e. ft. How wide is the box? 

10. A rectangular cutting 360 yd. long and 25 ft. wide has 
17000 c. yd. of earth taken out of it. What is the average 
depth of the cutting? 



EXERCISE XCIII. 

1. Two-foot wood is piled 6 feet high. How long must the 
pile be to contain 3 cords? 

2. How much will it cost to have a tin roof put on a stable, 
each slope of which measures 25 ft. by 14 ft. at $5.75 per 100 
sq. ft.? 



n 



SIMPLE MEASUREMENTS. 



71 



3. From a lot 40 rods square IGO sq. rods wtM-e sold. Wlint 
is the value of the remainder at $120 per acre? 

4. A cubic foot of black spruce weif^hs 2K lb. Find the 
wcifjfht of 10 planks of this wood, each 16 ft. long, 1 ft. wide 
and o in. thick. 

f). A ton of hard coal occui)ies 4L* c. ft. How many tons of 
hard coal will a bin 1(5 ft. long, 12 ft. wide and 7 ft. deep holdt 

0. How many tons of water will a tank 1<) ft. long, 12 ft. 
wide and 8 ft. deep hold? (1 c. ft, weighs 1000 oz.) 

7* A street (»()0 ft. long and 24 ft. wide lias to be filled in to 
the depth of li ft. How many cubic yards of earth wil' be 
required? 

8. Find the cost of laying a tile drain a mile long at 15 ct. 
per foot. 

9. What will it cost to enclose a mile square with wire 
fencing at $4.50 per chain? 

10. What will it cost to shingle a barn, the roof of which is 
80 ft. long and the slope on each side 30 ft. at $1.50 por 100 sq. 
ft.? 

EXERCISE XCIV. 

1. How much will it cost to ])aint a close board fence G ft. 
high around a rectangular lot 36 yd. by 32 yd. at 12 ct. per sq. 
yd.? 

2. What length of road 66 ft. wide will contain one acre? 

3. How many rectangular sods each 20 in. by 9 in. will be 
required to sod a rectangular lawn 60 ft. by 75 ft.? 

4. What must be the depth of a wagon box 10 ft. long and 4 
ft. wide that the contents may be 120 c. ft.? 

5. A rectangular box is 6 ft. 8 in. long, 4 ft. 6 in. wide and 
3 ft. deep, inside measurement. Find the cubic content of the 
box. 

6. A bicycle wheel is 10 ft. 1 in. around the tire, and turns 
17280 times in a journey from A to B. How far is A from B? 

7. What length of board 16 in. wide will contain 20 sq. ft.? 

8. What length of board 15 in. wide will contain 11 sq. ft. 
;{G sq. in.? 

9. How many square yards of oilcloth will be required to 
cover a rectangular room 20 iiu, 3 in. long and 16 ft. wide? 

10. A rectangular box 11 ft. 3 in. long and 5 ft. 4 in. wide 
contains 300 cu. ft. How deep is the box? 



Ill 



m 



72 



ARITHMETIC. 



III. SHARIING. 

EXERCISE XCV. 

1. Divulo !f40 bt'twoiMi two )»oys so that one may have $6 
more thau tlie otlier. 

2. James and Thomas have 41) yd. of cloth, and James has 
11 yd. more tlian Thomas. How many has each? 

',i. Divide 84 marbles between James and Robert, giving 
Robert 12 more than James. 

4. Divide $99 between two boys, giving one $1.50 more than 
the other. 

'). Divide $50000 between A and B, giving B $4000 hiSs than 
A. 

0. A hovso and bnggy are wortli $375, and the liorse is worth 
$55 more than the bnggy. Find the value of each. 

7. A man earned $790 in two years. In the first year he 
earned $54 more thau the 2nd, find the amount earned each 
year. 

8. Two trains start at the same time from Montreal and 
Harnia, a distance of 508 miles. When they meet one has gone 
M miles less than the other. How far has each gone? 

9. 750 votes were polled for two candidates. The elected 
one had a majority of 34. How many votes had each? 

10. A house and lot together cost $5750. The house cost 
$3250 more than the lot. Find the cost of each. 



EXERCISE XCVI. 

1. A yacht and its fittings cost $0400. The yacht cost 
$3840 more thau the fittings. Find the cost of each. 

2. A farmer raised 4375 bu. of wheat in two years. In the 
second year he had 247 bu. more thau iu the first. How many 
bu. had he in each year? 

3. A merchant bought $4908 worth of hardware and groceries. 
The groceries cost $484 less thau the hardware. Find the cost 
ot the hardware. 

4. The perimeter of a rectangular field is 1200 yd. and the 
length is 119 yd. greater thau the width. Find the length and 
width of the field. 

5. Three times the sum of two numbers is 1830, and one is 18 
more than the other. Find the numbers. 

0. Four times the sum of two inimbers is 3984, and one is 72 
less than the other. Find the numbers. 



SHARING. 



78 



<! t 



7. Two men topfether chopped 52 cords of wood. One 
chopped 3 cords 50 c. ft. more chan the other. How much did 
each cho])? 

H. Two adjacent fields together contain 20 acres. The larger 
contains 90 sq. rods more than the other. Find the area of each 
lieUl. 

9. Two men are ten miles apart. They walk straight 
towards each other, and when they meet one has gone 90 rods 
less than the other. How far has he walked? 

10. Two loads of hay together weigh 3 t. 8 cwt., and one 
weighs 12 cwt. more than the other. Find the weight of each. 

EXERCISE XCVII. 

1. Divide 120 marbles between two boys giving one three 
times as many as the other. 

2. Two books together contain 762 pages, and one has twice 
as nniny pages as the other. How many p'tges are in each? 

[i. Two pieces of cloth together contain 115 yards, and one 
piece is 4 times as long as the other. How long is each? 

4. Two houses are together worth $12250. One is worth 4 
times as much as the other. Find the value of each. 

5. Two men have together $243. One has $18 more than 
twice as much as the other. How much has each? 

(). Two lots are together worth $607. One is worth $27 more 
than thrice tiie other. Find the value of each. 

7. Two farms are together worth $139.50. One is worth $150 
more than three times the other. Find the value of each. 

8. Find the length and breadth of a field whose perimeter is 
240 rods and the length three times the breadth. 

9. A and B together own 120 acres, A having 24 acres more 
than B. A sells his part at $84 an acre and B sells his for the 
same amount of money. What does B get per acre? 

10. At an election 4977 votes were polled. The successful 
t-aTulidate received 17 votes more than three times as many as 
liis oi>ponent. How many votes did each receive? 






EXERCISE XCVIil. 

1. Divide $84 between two men, giving the first $3 as often 
as the second gets $4. 

2. A mixture of 210 bu. of oats and peas is made up as 
follows: — For every 2 bu. oats there are 5 bu. i)eas. How 
many bushels are there of each? 

3. A roll of bills contains $153. It is made up of an equal 
number of $5 bills and $4 bills. How many are there of each ? 



^'!ii 



74 



ARITRMETIC. 



4. Divide $19500 between two men so that when the first 
f^ets $2 the second may get $3. 

5. Two books together contain 605 pages. B^or every five 
pages in the first bool< there are six pages in the second. How 
many pages are there in each book? 

6. Divide $120 among three men so that when the first gets 
$1 the second may get $2 and the third $'l. 

7. Divide 150 marbles among t' ~ boys so that when t'le 
1st gets 2 marbles the 2nd may get . :.d I . 3rd 5. 

8. A sum of money, $2.40 is made n of Ir-- ct. pieces, t( n 
ct. pieces and twenty-five ct. pieces and the ^.-XAie number 3f 
each. How many are there of each? 

9. Divide $1120 among A, B, and C, so that A may have 3 
times as much as B, and C may have as much as A and B 
together. 

10. Three houses are together worth $16410. The first is 
worth twice as much as the other two together and the second 
is worth $570 more than the third. Find the value of each. 

EXERCISE XCIX. 

1. A man sold three sheep for $31. For the second he 
received $2 more than for the first, and for the tliird $3 more 
than for the second. How much did he receive for each? 

2. Three men weigh 456 lb. The 1st weighs 18 lb. more 
than the 2nd and the 2nd 18 lb. more than the 3rd. Find the 
weight of each. 

3. Three pieces of cloth contain 444 yd. The 1st has 25 yd. 
more than the 2nd but 19 yd. less than the 3rd. Find the 
length of each piece. 

4. Three loads of hay weigh 6400 lb. The 1st weighs 200 
lb. more than the 2nd and the 2nd 400 lb. more than the 3rd. 
Find the weight of the 1st. 

5. Three pigs weigh 402 lb. The 1st weighs 27 lb. nfbre 
than the 2nd but 48 lb. less than the 3rd. How much does 
each weigh? 

6. In three days A rode 125 miles upon his bicycle. The 1st 
day he went as far as on the other two days all but 5 mi. 
The 2nd day he rode 15 mi. less than the 3rd day. How far did 
he go each day? 

7. The perimeter of a triangular field is 249 rd. The 1st 
side is 36 rods longer than the 2nd but 42 rd. shorter than the 
3rd. How long is each side? 

8. In three books there are 108G pages. The 3rd has 74 
more than the 2nd and 196 more than the 1st. How many 
pages are there in each book? 



AVERAGES. 



75 



9. In three years a man saved $1593. In each year he saved 
$81 more than in the preceding one. How much did he save 
each year? 

10. Three bins contain 573 bu. of wheat. The Ist has 110 
bn. more than the 3rd and 53 bu. less than the •2nd. How many 
bushels are there in each bin? 

11. The cost of 5 bu. of oats and 8 bu. of wheat is $(>.80 and 
the cost of a bu. of wheat is 33 ct. more than a bu. of oats. 
Find the cost of a bu. of oats. 

12. A box contained 286 marbles, red, blue, and white. 
There were 192 red and white, and 199 blue and white. How 
many of each kind were in the box ? 

IV. AVERAGES. 

The Aggregate of a nuni])ei' of qnantitios of tlio 
.same kind is their entire number, or sum. 

The Average of a number of quantities of the 
same kind is the quotient arising from dividing 
their sum by the number of addends; thus, the 
average of 4,^8 and 9 is (4+8+9)-3, or 7. 

EXERCISE C. 

Find the aggregate of the following: — 

1. 47, 275, 368, 495, 784 and 6. 

2. 571, 0, 100, 367, 2461, 78, 96 and 10. 

3. 6746, 89745, 3689, 4875 and 78964. 

Find the average of the following : — 

4. 5 and 9; 7 and 13; 4, 8 and 15. 

5. 9, 12, 16 and 19; 0, 7, 12, 15 and 21. 

6. 26, 37, 49 and 60; 27, 0, 0, 16, 25 and 28. 

7. A man trolling caught three fish; the 1st weighed 16 lb., 
the 2nd 11 lb., and the 3rd 15 lb. Find their average weight. 

8. A's age is 45, B's 30, C's .35, D's 60, E's 70 years. What 
is the average of their ages? 

9. A man sold goods in six days to the following amounts: 
$80, $75, $92, $64, $210, $193. What did his sales average per 
day? 

10. Seven houses are worth, respectively, $10000, $12000, 
$8500, $7525, $4260, $4180, and $3200. What is their average 
value I 



ittl 



76 



ARITHMETIC. 



EXERCISE CI. 

1. Tho avpi'njjo woipht of 9 boys is 73 \h. 't oz. Find tlieir 
nfXfiff'di^tt* weipfht. 

2. The nvornge speed of a triiiii for 1*2 hours is 21 mi. 120 
rd. Find the distajiee travelled during that time. 

3. A farmer sells loads of wheat havinj? an averapje of 45 
bu. 30 lb. per load. Find the value of tho loads at 75 ct. per 
liushel. 

4. A woman sells 12 turkeys of an averjipe weipfht of 13 lb, 
8 oz. What did she receive for the lot, turkeys being worth H 
ct. per lb. 

5. A farmer brought to market a load of 15 hogs of an 
average weight of 2 ewt. 35 lb. What was the aggregate 
weight of the hogs? 

0. The aggregate weight of turkeys is 113 1)». I oz. What 
is the average weight of a ttirkey? 

7. A train goes 333 mi. in 10 lir. What is the average speed 
per hour? 

8. In one of the classes in a school the aggicgate attendance 
for the week was 225. What was the average attendance each 
of the five days ? 

9. A earns $3900 in a year. What does he earn each week, 
there being 52 wks. in a year. 

10. The aggregate weight of 24 tubs of Itutter is 591 lb. Find 
the average weight of a tub. 



EXERCISE Cll. 



1 . Bouglit 1 cow for $36, and 2 others for $30i a piece. 
What was their average cost ? 

2. A grocer mixes 9 lb. of sugar at 5 ct. a jmund with IS lb. 
at 8 ct. a pound. What is a i)Ound of the mixture worth? 

3. A jeweler mixes 20 oz. of gold 18 carats fine with 12 oz. 
10 carats fine. How fine is the mixture? 

4. A grocer sold 7 lb. of tea at 55 ct. per lb. and 21 lb. at 35 
ct. per lb. What was the average price? 

5. A grocer mixed 20 lb. of sugar of a certaiji kind with 40 
lb. worth 9 ct. per lb. The whole was worth 8 ct. per lb. 
What was the price of the first kind of sugar? 

6. I bought 500 bu. of wheat, part at 70 ct. per bu. and the 
rest at 75 ct. per bu. The average price was 72 et. per bu. 
How many bu. of each kind did I buy? 



AVER AUKS. 77 

7. The ftvcrnj^c iM'i^lit of 4 boys is 5 ft. 1 in. Wluit \h t\w 

iK'i^'lit of u fifth boy, tlie uv«'i'ag«' hei^'lit of the five being 4 ft. 
11 hut 

K. The aggregate weight of ') men is 800 lb. Tlie aggregate 
weiglit of tliree of them in ,'iJli lb. Find the average weight of 
the otlier two. 

9. A ])erson mixes 1 lit. of his best eoiTee with ') lbs. at Is. 
4d. a lb., and produei s a mixture wortli Is. 4id. a lb. What is 
the priee of liis best eoffee/ 

10. If 1") lb. of sugar are bought at 4d., jind 24 lb. at 6^d., 
iind if the two quantities ar«' tlien mixed and sold at 7d., how 
much will be gained/ 



EXERCISE cm. 

1. The weights of some hogs are as follows: 250, 320, 27'), 
H22, 415, 2i:{, 244, 214 and 195 pounds. What is the average of 
tiieir weights atid their aggregate weight? 

2. In 1898 the value of hay and clover grown in the counties 
bordering on Lake fh-ie was as follows: — Essex $5;J019.'{, Kent 
$()9;{773, Elgin $(539646, Norfolk $404300, Haldimand $597953, 
and Welland $559775. VV^hat was the average value of this 
croj) per county? 

3. If a doz. eggs weigh 1 lb. 8 oz., what is their average 
weight? 

4. A merchant mixes 4 lb. of coffee worth 32 et. a pound 3 
lb. worth 35 ct. and 2 lb. worth 41 ct. What is the mixture 
worth a pound? 

5. Of candidates for office, 7 were 20 yrs. old, 12 were 22, 12 
were 23, and 1, 24. What was the average age of the 
candidates? 

6. A drover bought 30 cows at $22 a head, 40 at $25 a head, 
30 at $28 a head. What was the average price per head? 

7. A merchant mixed 24 lb. of sugar at 5 cents a pound, 30 
11). at 6 ct. and 26 lb. at 10 ct. What is the average price of 
the mixture? 

8. A merchant bought 2000 lb. of wool at 47 ct. ])ev 
pound, 3000 lb. at 43 et., 5000 lb. at 49 et. and 8000 lb. at 45 ct. 
Wliat was the average cost i)er lb. ? 

9. In a factory a certain number of men receive $13 each 
per week, 4 times as many receive $9 each per week, and 10 
times as many receive $5 each per week. What is the average 
weekly wage per man? 

10. A goldsmith combined 8 oz. of gold 21 carats fine, 12 oz. 
22 carats fine, 18 oz. 20 carats fine, with 28 oz. of alloy; required 
the fineness of the composition. 



'"ik-S 



CHAPTER V. 



FACTORS, CAINCELLATIOIN, MEASURES. AND MULTIPLES. 

I. FACTORS. 

Whole Numbers, or Int('<?t'rs,are oitlior Odd or Erf h. 

An Odd INumber is a nimihcr not cxactlv ilivisihlo 
by 2, as 7, J), &(\ 

An Even Number is a nnnibcr oxactlv divisible bv 
2, as H, 10, &i',. 

A Factor of a iiuinbcr is a number wliieh will 
divide the given iminber exactly, as 2, 3, 4 or 6 is a 
factor of 12. 

A Prime Number is one which has no integral 
factors, ex(^ept itself and ouf, as 13. 

A Composite Number is one which has other 
integral factors than itself and one, as 12. 

The Prime Factors of a composite number are 
the prime numbers which, multiplied together, prodm^e 
that number; thus, 2, 3 and 5 are the prime factors 
of 30. 

EXERCISE CIV. 

Find the prime factors of the following: — 

1. 12 56 84 

2. 196 231 252 



.3. 876 948 1052 

4. 1095 1113 1127 

5. 1202 1214 1218 
Find the prime numbers in the following: — 

(i. 781 797 821 

7. 1157 1187 2067 

8. 2543 2521 2007 

9. 2273 23:!9 2417 
10. 3397 3197 3013 

78 



30. 
384. 
1059. 
1156. 
1555. 

1437. 
2117. 
2013. 
2967. 
3119. 



OANCKLLATION. 



79 



EXERCISE CV. 

rind tho prime fuetors common to the following: — 

140 and .'JH."). 
4129 and 1001. 
H8S and 948. 



1. 



4. 

(). 

7. 



r)() and 70 
10.~> and 'J:M 
.')y.') and ir»47 



4K4 and 470 (548 and r)40. 

7120 and 748 9()0 and 912."). 

Write the numbers less than 100 of wiiich 3 i8 a factor. 

Write the numbers between 700 and 800 of which 1 1 is a 
factor. 

8. Find the larpjest factor otlier than the number itself of 
each of the following? numbers:— (JO, I'Jf), 825, r)79, and 88(5. 

9. Find three prime numbers that will divide each of the 
following:— 30, 105, 385, 1001, 3553. 

10. Resolve the followinp; into as many pairs of factors as 
possible:— 60, 150, 100, 240, 3(i0. 

II. CANCELLATION. 
Cancellation is tlin process of rejecting erinftl 
fjKitors from both Dividend and Divisor, and thereby 
greatly shortening the operation of Division. 

EXERCISE CVI. 

1. Divide 15X16X18X20 by 5X8X3X4. 

2. Divide 7X24X30X35 by 14X36X70. 

3. Divide 60X66X80X90 by 15X20X88X180. 

4. Divide 75X85 X 120 XI 14 by 57X102X125. 

5. Divide 48X54X60X72 by 36X54X18X80. 

6. Divide the continued product of 7, 8, 9, 12, 18 and 24 by 
the continued product of 3, 4, 6, 6, and 6. 

7. Divide the continued product of 16, 18, 20, 24, 25 and 27 
by the continued product of 4, 9, 30, and 36. 

8. A lot is planted with potatoe. There are 75 rows; each 
row has 120 hills, and each hill has on an average 16 potatoes. 
How many bushels are there, if it takes 20 potatoes to fill a 
gallon? 

9. Five pieces of cloth, each containing 60 yd., worth $1.50 
per yard, are exchanged for 6 pieces, worth $1 per yard. How 
many yards are there in each piece of the latter? 

10. A bicycle rider goes at the rate of 10 miles per hour for 
12 hours a day during 16 days. How many days must another 
ride at the rate of 8 miles per hour for 6 hours per day to go 
as far? 









80 



ARITHMETIC. 



III. MEASURES. 

A IVIeasure of n number is one of the factors of 
that number. 

A Common IVIeasure of two or more numbei-s is 
a factor common to the {^iven numbers. 

The Greatest Common IVIeasure (G.C.M.) of 
two or more numbers is the largest factor common to 
the given numbers. 

Numbers tliat have no common factor otlier than 
one are said to be prime to one an otlier. 



EXERCISE evil. 



Find the G.C.M. of: 



1. 


i 


12 and 


56 


48 and 128 


65 and 91. 


2. 


2 


10 and 455 


230 and 506 


210 and 294. 


3. 


288 and 


360 


352 and_384 


336 and 884. 


4. 


27, 


36, 


108 


32, 48, 128 


56, 63, 315. 


5. 


75, 


225, 


500 


210, 462, 546 


546, 462, 882. 


0. 


216, 


360, 


405 


168, 132, 352 


146, 365, 219. 


7. 


36o, 


511, 


803 


192, 576, 1760 


671, 781, 1441. 


8. 


G39, 


873, 


747 


808, 568, 1112 


455, 403, 481. 


9. 


352, 


992, 


672 


550, 770, 1210 


154, 210, 420. 


0. 


luOl, 


1365, 


1820 


715, 1001, 1287 


1615, 969, 2261. 



EXERCISE CVIII. 

1. What is the length of the longest pole that will Pleasure 
84 ft., 56 ft., and 70 ft.? 

2. What is the length of the longest stick that will measure 
15 ft. 7 in. and 18 ft. 5 -i.? 

3. What is the largest number that will divide 202 and 266 
so as to leave 7 and 11 as remainders respectively? 

4. What is the greatest equal length into which throe trees 
can be cut, the first being 84 ft. long, the second 105 ft., and 
the third 119 ft.? 

5. What is the greatest width of carpet that will fit three 
rooms — the first being 18 ft. wide, the second 22 ft. 6 in. wide, 
and the third 29 ft. 3 in.? 

6. A rectangular field 611 ft. by 364 ft. is fenced with rails 
of equal length, and this the greatest possible. The fenc-^ 
being straight, what is the length of a rail? 



MEASURES. 



81 



7. A farmer has 441 bn. of oats, 567 bu. of wheat, and 315 
bu. of rye. He wishes to make exact loads of the same 
number of bushels of each kind of grain, and have as few loads 
as possible. How many bushels will there be in a load? 

8. Three debts of .$200, $1250 and $300 were paid with bills 
of the same denomination. How might the debt have ])een 
paid? How was it paid if the bills were the largest possible? 

9. B has $620, C $1116, and D $1488, with which they agree 
to purchase horses at the highest price per head that will allow 
each man to invest all his money? What will be the cost of 
each horse? 

iO. How many rails will Inclose a rectangular field 14599 feet 
long by 10361 feet wide, provided the fence is straight, and 
7 rails higl>, and the rails of equal '' ngth, and the longest that 
can be used? 

EXERCISE ex. 

Find the G.C.M. of the following: — 



1. 


1008 and 


1026 


1225 and 


2247 


2761 and 


3263. 


2. 


1391 and 


2247 


1866 and 


3421 


1957 and 


2987. 


3. 


4004 and 


5772 


4427 and 


7219 


7813 and 


9015. 


4. 


2542 and 


5487 


4735 and 


6629 


3029 and 


3961 . 


5. 


2951 and 


3477 


4559 and 


7003 


4055 and 


7299. 


6. 


8128 and 


8472 


5544 and 


8008 


7956 and 


9724. 


7. 


15444 and 


13068 


69615 and 


92872 


23673 ami 


60203. 


S. 


45H62 and 


29026 


43155 and 


81564 


53712 and 


659(51 . 


9. 


15249 and 


27807 


30429 and 


88641 


18577 and 


20006. 



10. 13230, 44100, and 118125 



720100, 913330, and 211109. 



EXERCISE ex. 

1. Find the G.C.M. of 1365 and 1785, and from this find all 
tlu' common measures of these two numbers. 

2. Find the G.C.M. of 37 d. 13 hr. and 55 d. 5 hr. 

3. Find the G.C.M. of 7 mi. 259 yd. and 11 mi. 407 yd. 

4. Find the G.C.M. of 6 bu, 1 pk. 1 gal. and 10 bu. 3 pk. 1 gal. 

5. What is the largest number that will divide 2000 leaving 
a remainder of 11, and 2708 leaving a remainder of 17? 

6. Find the greatest laimber that will divide 13956 and 
14565, and leave a remainder of 7 in each case. 

7. Find the greatest number tliat will divide 2293, 4245 and 
."):U8, and leave i-emainders 18, 20 and 23 respectively. 

S. Whiit is the largest number of men amongst whom 209 
.'ip])]es and 3(51 oranges can be distributed, so that every man 
gets as many apples and as many oranges as any other man? 



Ei 



1-1* 



82 



ARITHMETIC. 



9. Two masses of silver, weifjhing 1169 oz. an;l 139.'? oz., 
respectively, are eacii to be made, without loss, into medals of 
the same weij^ht. What is the weight of the largest possible 
medal? 

10. A farmer has 1134 sheep and 1260 lambs. He forms them 
into separate flocks, with the same number of animals in each 
flock. The flocks being the largest possible, how many animals 
are in each? 

IV. MULTIPLES. 

A IVIultiple of a imml)or is the product ()l)t}iined 
by multiplying tlie given number by any whole 
number. 

Thus, if 7 is multiplied sueeessively by 1, 2, 3, 4, .">, 
&(^, the products 7, 14, 21, 28, 35, &c,., are multiples 
of 7. 

From this, it follows that every multiple of a 
number is exactly divisible by that number. 

A Common IVIultiple of two or more numbers is a 
iium))er which is one or more times each of the given 
numbers. 

Thus, 24 is a common multiple of 2, 3, 4, 6, 8, &c. 

The Least Common Multiple (L.C.M.) of two or 
more numbers is the least number that is one or more 
times each of the given numbers. 

EXERCISE CXI. 



Find the L.C.M. of the following:— 



1. 


4, 


6, 8 


6, 8, 


10 


2. 


5, 


15, 25 


25, 30, 


40 


3. 


5, 


7, 9 


12, i:^, 


17 


4. 


12, 


IS, 24, 30 


18, 30, 30, 


42 


f). 


32, 


48, ()4, 72 


30, 40, 50, 


CO 


6. 


14, 


18, 20, 21 


51, 187, 1.53, 


105 


t . 


10."), 


198, 242 


312, 429, 572, 


715 


8. 


510, 


,^)95, G80 


432, 840, 693, 


(iOO 


9. 


19;')-), 


2001, 3451 


2041 , 8470, 


3423 


10. 


1554, 


1058, 18058 


4410, 7350, 


7875 



8, 10, 12. 

36, 48, 60. 

13, 15, 19. 

24, 36, 42, 56. 

60, 66, 72, 77. 

203, 429, 494, 570. 

287, 451, 455, 715. 

253, 345, 414, 495. 

2743, 400l», 4199. 

2001, 4278, 4495. 



MULTIPLES. 



88 



9;i oz., 

jdals of 
possible 

ns them 
in eac'li 
animals 



3, 4, r>, 
lultiples 

>le of a 

ibers is a 
:lie given 

6, 8, &(^ 
of two ov 
} or more 



10, 


12. 


48, 


GO. 


15, 


19. 


i, 4'2, 


56. 


), 72, 


77. 


), 494, 


570. 


1,455, 


715. 


>, 414 


495, 


4()0it, 


4199. 


4278, 


4495 



EXERCISE CXII. 

1. Find the L.C.M. of the first six even nuni])ers. 

2. Find the smallest number of apples that can be arranged 
in gi'OU])s of 8, or 9, or 15, or 20 each. 

.'J. Find the L.C.M. of the prime numbers between 4 and 18. 

4. Find the L.C.M. of all the odd numV)ers between 8 and 16. 

5. What is the least number from which 16 and 24 may each 
be taken an integral number of times? 

(). Find the least number that can l)e divided by 7, 20, 28 
and ;J5 respectively and leave 3 as remainder in each case. 

7. What number is the same mi Itiple of 7 that 1962 is of 9? 

8. Divide the L.C.M. of 23949 and 26610 by their G.C.M. 

9. What is the shortest piece of wire that can be cut into 
exact lengths of either 6 ft., 8 ft. or 10 ft.? 

10. Wliat is the capacity of the smallest cistern the full 
contents of which will exactly fill a four-gallon, a ten-gallon 
or a fifteen -gallon measure a certain number of times; 

EXERCISE CXIII. 

1 . What is the smallest delit that can ]>e ]>aid with an exact 
number of 2-dollar, or 4-dollar, or 10-dolIar i>ills? 

2. What is the gresitest weight of which 1 t. 19 cwt. 4H 11). 
iind 4 t. 14 cwt. 47 lb. are multiples? 

'.). What is the greatest weight of which 2 t. 4 cwt. 18 lb. 
and 5 t. 4 cwt. 34 lb. are multiples? 

4. How often does the L.C.M. of 5, 12, .36, 42 and 84 
contain the G.C.M. of 7266 and 8022? 

5. A rides at the rate of 6 miles per hour, B at the rate of 
1(1 miles per hour, and (' walks at the rate of 3 miles per hour. 
Find the shortest distance each may go in an integral number 
of hours. . 

6. What is the least number which divided by 8, 9, 10 and 
12 respectively gives in each case a remainder of 5? 

7. What numbers less than 200 leave 2 .as remainder when 
divided by 3, or 4, or 5, or 6. 

8. What is the smallest quantity of wheat that can be taken 
lo market in either 20, 25, 30, or 40 bushel loads? 

9. The prodiu't of four consecutive numbers is 43680. What 
lire the numbers;' 

111. One pound Avoirdupois weight contains 7000 gr. and one 
pniind 'i'roy weight 57(50 gr. Find the least weight whicli can be 
expressed integrally in l)oth Troy and Avoirdupois pounds. 



■ •,^1 



CHARIER VL 



FRACTIONS. 



I. DEFIINITIOINS, INOTATIOIN AIND INUMERATIOIN. 

A Fraction is a number whieh expresses one or 
more equal parts of a wJiole, or unit. 

A Common or Vulgar Fraction is expressed by 
two num))ers, one above and the other below a short 
horizontal line; thus *, ro, iiud /a are Common, or 
Vulgar frjietions. 

The Denominator is the nuniber below the line, 
and shows into how many equal parts the whole, or 
unit is divided. 

The Numerator is the number above the line, and 
shows the number of equal parts in the fraction. 

The numerator and denominator are calle'i the 
Terms of the fraction. 

A traction indicates also the quotient arising;, irom 
dividingr the numerator l)v the denominator. Thus 

4 

f means 

i. Four of the parts when a unit is divided into 

five equal parts, 
ii. The quotient when four is divided by live, 
iii. One-fifth of tour units. 



tXERCISE CXIV. 



Express in fif;«i!'ps: — 
I. Two-thirds; 
'J, Five ei^-.iths; 
;{. Six-sevenths- 



'ihree- fourths ; Four- fifths. 
Five-nintlis; P''ive-twelfths. 
Six-tlnrteeuth:- ; Six-seventeenths. 
4. Seven-twenty 3i'!its; Sevt-n-twelfths; Seven-thirtyseconds. 

84 



ii\ 
Ml 

oi 

«> 

b<i 






1 









rioiN. 

s one or 

•essecl by 
w a short 
union, or 

the line, 
wlioU', or 

line, and 
tion. 
;alle<l tlie 

Isin^^ ii"f>»^ 
,r. Thus 

Ivided into 
)V tive. 



lis. 

llt'ths. 
Iiteeuths. 
lirty seconds. 





REDUCTION. 






Write in words: — 








5. f 


1 


4 


A. 


6. i\ 


H 


il 


H. 


7. H 


H 


^1 


il. 


Explain tlie meaning of 


the following 


fnietionB: — 




8. f in. 


f ft. 


B a. 


$t\ . 


9. I hr. 


H 


1 3 
21 


1^\. 


10, 1 cord. 


H cwt. 


Ub. 


h t. 



85 



II. REDUCTION. 

A Proper Fraction is one of which the nunier- 
iitor is less than the denominator, as j;, L 

An Improper Fraction is one of whili the 
numerator is equal to or greater than the denomin- 
ator, as r, V . 

A mixed Number is a number which consists of 
the sum of a whole number and a fraction, as 21. 

A fraction is in its lowest terms when the numer- 
ator and denominator are prime to each other. 

Similar Fractions are those that have a common 
denominator, as f , f , i and V". 

When the terms of a fraction are both mutti- 
plied by the same number or are both divided by 
the same number, the value of the fraction is 
not altered. 

A Simple Fraction is one in w^hich the terms 
are ])oth whole numliers and which expresses one or 
more of the equal parts of unity, as f, |. 

A Compound Fraction is one which expresses 
one or more of the equal ])arts of a fraction, as I of 
3, a or T. 

A Complex Fractio^i is one in which one or 

i 4 2] 



'Mm 



l>otli terms 'are fractir-Tis, a.- 



■>, Oj, Si;, 



•-Ar^-. ^-> 






86 



ARITHMETIC. 



EXERCISE CXV. 

Redupe to improper fractions: — 



1. 


2i 


4J 


21 


43. 


2. 


ek 


7i 


81 


41. 


3. 


51 


6* 


8 A 


9.^. 


4. 


18 i 


192 


2U 


25L 


5. 


43 i\ 


101 1 


1411 


262V5. 


6. 


163 t*j 


275 ^ 


4611^ 


403^1. 


7. 


20711 


H.lO^r 


908 y 


78U]. 


8. 


310A 


5694 3 


678,V:t 


6982V0. 


9. 


1001, V 


OCrin 


8080f,l 


7000 i,V, 


10. 


7018A 


705?!!? 


368 l-n 


37^1 01. 



EXERCISE CXVI. 

1. .John has two apples. To how many boys can he give 
half an apple? 

2. Among how many jrirls must -5 melons be divided 'lat 
each may receive i of a melon r 

;>. How many fifths are there in ii api>les? 

4. How many persons will 5^ cords of wood supply, if each 
one receivjs i cord? 

5. A gave $i to each one of a number of boys. He gave 
away $151 . How many boys were there? 

6. Express both '1 and 7 as fractions with denominator 15. 

7. (^liunge 48 to ninths and 57 to tenths. 

8. What fractions with denominator 24 are equivalent to 3, 
5, 8, and 12, respectively? 

9. A walked a mile each quaricr hour. He walked for 3i 
hours. Hi w far did he go? 

10. To make badges i yd. 'oug for n :;lass, 5^ yd. of ribbon 
are needed. How many pupils arc tiiere in the class? 

EXERCISE CXV5K 
Reduce to whole numbers or to mixed numbers: — 



1. 


f 





1 5 

8 


3. 


S 5 


4. 


Hi 



¥/ 



¥ 


¥. 


V 


.{ 5 
T2- 


H 


u. 


w 


8 «H 
^5 



REDUCTION. 



87 



i), 
G. 

mm 

i. 

H. 

!). 

10. 



H31 
I 35 
H (Ml 
1 1 ff 

4 » t » 
24 

76 84 

2:1 

8 :< 6 
4 1 
925 



21 f mi. 



54 I 
1 2:1 

6 01 

700 1 

830 1 
fill ' 

764 
3 1 



gal. 
cords. 



9 7 8 
1 5 I 

5 2 3 1. 
52.7 

6 89 7 
1 9 3 f 
6 8 1 

« 7 

^V da. 

36 9 
TT 



yd. 



1 (I n I) 
7 3 . 

17 18 
1 I 3 3 • 

76 84 9 
223 1 

8 5 6 7 
8^3 • 

253 
S 

6 94 
TT 



11). 



oz. 



EXERCISE CXVIII. 

1. How much money has John who has $'/? 

'J. If a basket of peaclies holds i bu., how many ])ushels are 
tliere In ;{69 baskets? 

15. A walked from X to Y at the rate of a mile each i hr. 
He walked h^ hr. How far is it from X to Y? 

4. A druggist has 97 psiekages of medicine, eaeh weighing 
h lb. How many pounds does the medicine weigh? 

5. How many bushels of wheat are there in 964 bags, eaeh 
oontaining i bu.? 

6. Which is the he.ivier — 786 packages, each holding i lb., 
or 6'J9 packages, each holding i lb. ? 

7. Express ^ in., fs lb., H:- oz., eaeh as a whole inimber. 

8. A bottle holds i gal. of wine. How many gallons are 
there in 5 doz. such bottles? 

9. The perimeter of a rectangular room is -^ ft. It is' four 
feet longer than wide. Find the length and width of the room. 

. 10. A farmer sold a load of oats consisting of 79 bu. at $i 
per bushel. How much did he get for the load? 

EXERCISE CXIX. 



1. 


Reduce i, 


i and | , 


each to twelfths. 







h 


r and i, 




twenty-fourths. 


3. 




f, 


t and 1, 




eighteenths. 


4. 




3 


f and A, 




twentieths. 


5. 




!, 


f and A, 




thirtieths. 


G. 







f and 1, 




twenty-fourths. 


7. 




i 


fV and IL 




thirtieths. 


s. 




f, 


1 and i 




forty- seconds. 


5). 




5 

8, 


i\ and i\, 




forty-eighths. 


0. 




5 


rV and H, 




sixtieths. 



iii 



88 



ARITHMETIC. 



EXERCISE CXX. 



1. llediKH' 
'> 

3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 



1. 
^1. 
3. 
4. 
5. 
G. 
7. 

i. 

9. 
10. 






1 2 

30 
4 4 
26 
.id 

2 6 
4(1 
1 4 
4ft 
66 
93 

68 



1 
T55 
20 

3 5 

n 
u 

25 
*0 

4 4 

80 

1 5 

3 5 
51 T 

9 1 
3?f 



and 
and 
and 
and 
and 
find 
and 
and 
and 
and 



is, 

4 9, 
\l 

38 



20 

97r, 

1 4 3 
34 1 , 
316 
6 24, 



each 



to fourths. 
' tifths. 
sevenths, 
ninths, 
eleventlis. 
eighteenths, 
twentieths, 
twenty-fourths, 
rhirty-tirsts. 
fifty-seconds. 



EXERCISE CXXI. 

Supply numerators in |=t? 






1 ( 



4 = 33 

l=TTr 






I 2 
16=4 

84 
14 4 = T? 

Supply denominators in |=*® 

" " "535 

II = 

it " "11154 

12 = 

it a "81 

12 = 

" " 4^8 2 



3 
6- 

5 
9- 

6 
13- 

15- 
25- 

T 5 _ 
1 - 

7 _ 
11- 

H-- 

6 
TT= 

8 
^4 = 

3 8 



'8 
=7T 

-m 
'-T 

-T 

. 28 

.12 1 

-.7 2. 
.1 



6 

■a. ; 
t 

1 
1 1 - 

1T = 5"5 
1 4 

an-- 

5 5 
TS2 = 

1 I 

1 s — 

y 6 3 
it = 

9 
2Tt = 

9 
TS = 






-1^ 

44 



feXERCiSE CXXII. 



Reduce to equivalent fractions in lowest terms: 



1. 


1 


2. 


H 


3. 


80 
TTJ 


4. 


AV 


5. 


3 2 
T57 


6. 


4» 2 


7. 


2 6 40 
2])To- 


8. 


1242 

2 3 2 ;t 


9. 


56 8 
TT f T 


10. 


3 1 
-10 9^3 



9 
T2" 

27 
4? 

9 
T5S 

1 5 9 
5TT 

19 2 
3 1 

2 7 5 5 

3 3TF 

3 6 2 
IT 9 3 

2 112 
T T TT 4 

2 2 7 7 
2 8971 



42 

¥8 

72 

25 

2 09 
21 5 

36 5 
"5TT 

1428 
T530 

26 5 1 

326 5 
"9¥T0Tr 

2 6 194 



8 1 
3 

2 14 4 12 

20 4 — 



7 
28. 

3 6 
63. 

1 5 
2J5- 

22 1 
2ff0. 

3 1 6 

T4 6 • 

1 144 
170 • 

226 8 
3444. 

47 7 
6T9^D. 

6 53 9 

T¥7-g^3- 

3 6 73 



IS. 

lis. 

^nths. 

^ths. 

-fourths. 

firsts. 

iconds. 

^— n 

1 t _44 
1 S = 
19 6 3 

n ^^ 

« H 1 

2fi = 

9 3 

Id— • 

14 4 12 

2 4=^" 



1 
28. 

36 

6 3'- 

1 5 » 

221 

3 1 6 
T4 fi- 
ll 44 

22 6 8 
3 4 4 4 • 

4 '•0-5 

6 53 9 
T 2¥¥3 • 

3 6 13^ 







HKDUCTION. 






89 




EXERCISE CXXIII 


• 






Keduee to 


equivalent f ruet 


IOI18 having leant common 


denominator: 


1. 


1 and i 


H and 


5 
1 6 


A 


and |]. 


2. 


'\ and 2\ 


5 and 


2\ 


A 


and n. 


3. 


2 and 3 


i and 


1 
6 


i 


and J . 


4. 


3 and I 


7 and 


5 
9 


A 


and "6. 


5. 


I and 9 


": and 


A 


i 


and A. 


6. 


i\ and TT 


A and 


iPi 


A 


and 2^. 


7. 


6 Jtnd h 


i\ and 


i\ 


f\ 


and 2^. 


8. 


A and t\ 


9 and 


n 


A 


and li. 


9. 


iV and 11 


1 1 and 


2 3 
2t 


U 


and 42. 


10. 


U and A 


2 8 and 


'h 


24 


and 12. 



EXERCISE CXXIV. 

Keduee to equivalent fractions with least common denominator; 



1. 


t, 


2. 


I 


3. 


A., 


4. 


6 

'1» 


5. 


A, 


6. 


i\, 


7. 


A, 


8. 


8 
T5, 


9. 


1, 


10. 


9, 



5 
12 

4 

25 

6 

1 
T2, 

1 1 

T8, 

A, 

ii, 
11 

5 

1 H» 

A, 



and 


t\ 


and 


^V 


and 


U 


n 


and 


11 


and 


u 


and 


-A 


and 


tV 


and 


A 


and 


M 


and 



1 3 

14 

1 1 
T8 



1 1 
^4 

1 1 

36 



EXERCISE CXXV. 



3 

I» 

2 

Tf, 

3 

19) 

2 
5» 

3 

4, 

1 1 
1 &, 

1 7 
24? 

1 7 

2 , 

5 
I 1 , 

1 H 

2 6? 



3 
14 

6 
TJ 

5 

7 8 



5 

T, 

1 7 

2 0, 

1 3 
2f, 

5 

'IT, 
5 

t, 

23 

4 5' 



and 
and 
and 



4 

46' 



2 

8 
2T 

tV 

1 1 
14 

1 3 
24 

1 1 
2f 

2S 
I 8 



and 
and 
and 
and 
and 
and 
and 



1 II • 

1 1 

4 2- 

1 9 
24- 

1 5 

28- 

-A. 

1 3 

71- 



Which is tlie greatest and which the least of the following 
fractions? 

1. 

2. 

3. 

. 4. 



f, I and f 




4 , 


i and |. 


17 6 .,,,/] 5 

21, T ana 6 




f, 


-A and I. 


4, Ti and U 




1, 


A and 1 . 


A, At, 2'8 and 


1 1 

3 6 


At, 


U, U and 11 



90 



AIUTHMKTIC. 



Armn^«' the followinp: fnictioiiH in onlcc (tf lunpfnitiuU' : — 

\L ki, U and A A A 11 1 1 



7. 



1 



1 1 

B 1 



3)) t 



3 



3« 
» 1 



t\ Jiiid 

1 it, JO HlUl HO 



24, 
4 

I's, 1^8, 2 6 and U 



.•ind U. 
I'^s, L^. and U. 



H. Find a fniftion with 00 for (Icnominutor intcnnt'diatc in 
valiH' Ix'twcon I and J;. 

y. Find a fraction with H4 for dcnoniiniitor ^'rcater than f; 
and k'HK than ". 

10. Find a fraction witli 72 for denominator as much U-sh 
tlian g as it is j^rcatcr tlian i'^^. 

EXERCISE CXXVI. 

Kcduce the following eonijtound fractions to 



1. 

2 

3. 
4. 
5. 
G. 
7. 
8. 
9. 
10. 



of 



G 
1 1 

I of ^ 

^ Of H 



i of 1 I 



of 



1 

2 
J 

2 
IT 

4 

1 
2 



O 



fi 



of I 



of 4^ 
of 3G 
of^ ofl 
I of i I of A 



8 
If 

lof iij 

I of A 
4 of ^^ 
I<'f4^ 
i of r)G 
I of I of 
f of I of 



9 
2 5 



implc! ones: 
of g. 
of {i. 
of if. 
of h 
of il. 

of 4L 
of 72. 

of I 
of 



1 
t 

5 



I 

1 
6 

7 
8 

6 

t 



5 

.5 



,'5 
I 1 



of 1 1 . 
of n. 



21 of G5 of 13 of 10^ 81 of m of lOi (,f 7 J 



Find the sum of 



III. ADDmOIN OF FRACTIOINS. 
EXERCISE CXXVII. 



1. 

^ • 

3. 
4. 
f). 
6. 
7. 
8. 
9. 
10. 



A, 



IT, IT 



tV, 


fV, 


iV 


1 
IT, 


A, 


t\ 


4 

5, 


3 

4, 


/.r 


i 


A, 


41 


I 


1 

6, 


4 


t, 


tV, 


If 


if, 


H, 


II 


H, 


15 

4 4 , 


H 



f, 5, 9 



1 

T, 

S 
IT, 

2_ 

? 6, 

2 

T, 

.3 

T, 

4 

¥) 

^\, 

M, 
f, 

2 

3^, 



1 

7, 

5 

«, 

5 
6, 

1 1 
T4, 

1 9 

3 

4, 

3 

5, 



3 

"f 

8 
IT 

8 
^S 

H 
5 

t\ 

1 3 

?8 



9, 
4 

4 
TST, 

3 

!^, 

3 

4, 

5 
6, 

-X- 



h I 



2 

T3, 

5 






3 , 

4 

T, 

O 

M 

5, 

T'fT, tI, 
0, 8, 



t\. 

9 
f¥. 

If. 

9 
■3^8. 

t\. 

20 . 

4 

■2T. 

9 
TI- 



ADDITION OP FnAOTIONS. 



91 



HI 



EXERCISE CXXVIII. 



!U1 11 


udi'i. 


nd \l- 


tMliiitc ill 



T than il 
MH'h less 

es: — 
1 



5 

a. 
[9 



Of H 

L' " 2 



S o 



f 71 



i, 


5 


f\, 


A 


A, 


A 


1, 


If 


■f, 


9 
^8 


2 

5» 


iV 


If, 


H 


M, 


A 


i, 


A 


f, 


A 



1. 


Add i 


to i 






< to li 


i to^ 


2, 


iv'M li 


to i 






\ t.) iV 


I to ,', 


8. 


Add ;; 


to A 






S to A 


8 i... H 
8 to 1 J 


4. 


Add g 


t«» 2^ 






1 to 1 


4 to l^ 


T). 


Add 1 


to A 






if to A 


Vf to A 


G. 


Add A 


to A 






A to A 


A to iV 


7. 


Add /, 


to .'^T 






A to A 


A to i\ 


S. 


Add I 


to ,\ 






i to-rV 


} to ,^6 


9. 


Add 1 


to •? 






4 tog 


i to A 


10. 


Add U t<) {3 






n to 11 


Htoll 






EXERCISE 


CXXIX. 




Sini)) 


lify:- 












1. 


l +,^ 


+ 1 


+ 


1. 






2. 


3 +^ 


+ J 


+ 


5 


+ A. 




3. 


2 1 2 


+ 2^« 


+ 


5 


+ A. 




4. 


1 1 4 

8 +9 


+ ^ 


+ 


r, 


+ 1 +u. 




T). 


t + A 


+ A 


+ 


1 

18 


+ 21 +20. 




G. 


t2l +31 


+ 71 


+ 


.)! 


+ C1. 




7. 


7i\ + 3 A 


+ 4.^ 


+ G,^ 


1 +8A +GA. 




8. 


2:1 +3] 


+ 4i 


+ 


.-)^ 


+ 21. 




9. 


11 + ^ 


+ 2A 


+ 


7i 


+ c. 




10. 


3i +9^ 


+ 7A 


+ 


>■> 


+ 42V. 





EXERCISE CXXX. 

1. John spent i of his money on Monday, i of it on Tuesday 
and w of it on Wednesday. What part did he spend altogether? 

2. A fanner has three fields; the first contains 10| acres, the 
second 91 acres, and tlie third 9tij acres. How many acres had 
he in all? 

3. How many pounds of butter are there in four tubs weigh- 
ing respectively 274 lb., 24| lb., 30* lb., and 29A lb. 

4. How man^' tons of coal are there in four loads weighing 
respectively li t.. If t., Ira t. and larr t. 

5. What fraction is that which exceeds S^ by i? 



i:h 







IMAGE EVALUATION 
TEST TARGET (MT-3) 








1.0 !f"- 1^ 



1.25 



S *^ III 



2.2 



I.I 1.*^ 1^ 



1.8 

1.4 nil 1.6 




■y ^ *? />^ 

^'^ %. # 



7 




Photographic 

Sdences 

Corporation 



23 WEST MAIN STREET 

WEBSTER, N.Y. 14580 

(716) 872-4503 



<V 



iV 



<^ 





^^ 



■\ 




C\ 



\ 








o^ 



'% 






92 



ARITHMETIC. 



6. A weighs 172| lb. ; B weighs 5^ lb. more. How much 
does B weigh? 

7. What number is that from which if 4 J be taken the 
remainder will be aff? 

8. One man rode 17ts mi. Another rode 4A mi. farther. 
How far did the second one ride? 

9. A- grocer has ii barrels of molasses. The first contains 
JJ3i gallons, the second 45i gallons, and the third 35| gallons. 
How many gallons are there in the 3 barrels? 

10. On Monday A rode 35f mi., on Tuesday 40^ mi., on 



Wednesday 361 mi. and on Thursday 20 r* mi. 
ride in the four days? 



How far did he 



IV. SUBTRACTION OF FRACTIONS. 



Subtract : 


t^tK« 


;idt CAAAI. 




1. 


i from f 


f from 1 


1 from V. 


2. 


4 from f 


A from ii 


f from |. 


3. 


TIT from f 


A from 1 


f from |. 


4. 


T*i from f 


f from f 1 


i from H- 


5. 


1 fromi: 


1 fromH 


f from M. 


6. 


4 from 1 


1 from^^ 


A from A. 


7. 


A from If 


A from i 


1 from U. 


8. 


U from U 


A from H 


fl from if. 


9. 


U from H 


11 from H 


A from Ih 


10. 


J from 2 


f! from 3 


4 froni 5. 


Simplify 
1. 


._ EXERCISE CXXXII. 

g — i ¥ —I 


1 -i 


2. 


f -1 


A— A 


l-f. 


3. 


l-l 


A-A 


H-ii. 


4. 


j\-j\ 


H-i§ 


u-n. 


0. 


•sPt— /^ 


il-A 


fi-A. 


Find the difference between; 


— 




6. 


A and A 


A and A 


1 andA- 


7. 


-1 and il 


A and A 


li andM. 


8. 


TT and ii 


^h and A 


A and If. 


9. 


U and V2\ 


IS andl? ' 


11 andAV 


10. 


tV and tItt 


41 and U 


A\aiid|I. 



SUBTRACTION OF FRACTIONS. 



93 



ni 



1^ mi., on 
far did he 



I is white, f red, and the rest green. 



How 



What 



EXERCISE CXXXIII. 

1. Henry had I of a dollar and spent I of a dollar, 
much had he left? 

2. Of a pole 
part of it is green? 

3. How much must be added to hi to produce '§? 

4. How much does the sum of i and i exceed the sum of i 
and i? 

5. Subtract the difference between /g and tj from the dilTer- 
ence between ^V and /?. 

6. The sum of two fractions is fj and one of them is H- 
Find the other. 

7. Find the sum of the greatest and least of the fractions 
\hi hri, 1, I, and subtract this sum from the sum of the other 
two fractions. 

8. A traveller went VV of his journey on foot, A by railroad, 
and the remainder on horseback. What part of the journey did 
he go on horseback? 

9. Find the difference between the sum of i and ^ and the 
Slim of -^5 and ^pg. 

10. The sum of three fractions is MS- Two of them are is and 
■i;j. Find the third. 



Simplify: 

1. 
2_ 

3. 
4. 

^ 

;). 
6. 
7. 
8. 
9. 
10. 



EXERCISE CXXXIV. 



II 



9 6 

— Jj~^ 

— iff 



T^ 



S^% -3A 
6tV -2il 
7/4 -41 
19 -4f 

£?1 S 

04¥ 

32U-5lf 
Ml -161 
41/2-171 



r:l 2 



8A -5i*i 


71 2 

<T5 - 


-2 A. 


5i -41 


71 - 


-7tV. 


7A -2/ir 


StIt- 


-2 A. 


8t\ -3A 


7A - 


-2 A. 


4A -11 


m - 


-5f|. 


36 -12i*i 


24 - 


-3M. 


4H -4il 


21A- 


-lOA 


27A-6|i 


mi- 


-7iL 


561 -1711 


48! - 


-161. 


IGA-^h 


26^, 


-^Vs 



EXERCISE CXXXV. 

1. From a barrel of vinegar containing 31i gallons 14| 
gallons were drawn. How much was left? 

2. From a piece of cloth containing 35i yards a merchant 
cut 21 J yards. How much was left? 



94 



ARITHMETIC. 



3. A man staited on a journey of 45 J miles, and travelled 
28S miles. How far had he still to travel? 

4. The sum of two numbers is 56i, and one of the numbers is 
251. What is the other number? 

5. If I have $437i, and pay out $341iV, how much have I 
left? 

6. From a farm containing 1648^ acres, 4J^ acres were sold. 
How many acres remained in the farm? 

7. John's monthly salary is $1661 and his average expendi- 
ture is $971 i. How much does he save each month? 

8. What must be taken from 35i to leave 22|? 

9. The sum of two numbers is 26^^. One of them is 10^. 
Find the other number. 

10. From a barge load of coal consisting of 540i tons 375^ 
tons have been taken. How many tons are still on board the 
barge? 









EXERCISE 


CXXXVI. 


Simplify: — 








1. 


31 


+4i 


-6f • 


81 -71 +U. 


9 

mm • 


51 


-21 


-1 


8 -f +3! -li 


3. 


lA 


-/^ 


-.v 


11 +5i -fl. 


4. 


5^ 


+4t\ 


-4i 


15 -3f -21. 


5. 


f? 


+41 


-! 


m +m -1/t. 


G. 


7\ 


-2f 


+5 -7M 


5oA-4f -n -s^\. 


7. 


2G 


-51 


-61 -2h 


30 -U -fi -h 


8. 


4^ 


-3^ 


+5-/T-2f 


151 -101 +71 -5tV. 


9. 


31 


+41 


-7-^j-hdl 


141 -lOA-41 +II/1 


10. 


3A 


-11 


-U +7A 


8A -211 +41 -8A. 



EXERCISE CXXXVII. 

1. From 144 lb. of sugar there were taken at one time 
171^ lb. and at another 28r^ lb. What quu,ntity remains? 

2. A cask of wine contained 42i gal.; of this 13f gal. 
Y^ere drawn off, and 12 J gal. leaked out. How much remained 
in the cask? 

3. A grocer bought 89i lb. of tea; of this he sold 13i lb. 
to one customer, 9i lb. to a second, and 12f lb. to a third. 
How many pounds had he left? 

4. What number must you add to the sum of 126| and 2401, 
to make 5601? 



MULTIPLICATION AND DIVISION OP FRACTIONS. 



95 



travelled 
umbers is 
ch have I 
were sold. 
5 expeudi- 

sm is lOU. 

tons 375U 
I board the 

h 

If -li 

n 



:K 



4 

S - 

3 

"8 ■ 



-3A. 



:i -5tV. 



one time 
lins? 

]s 13t gal. 
remained 

lold 13i lb. 
Ito a third. 

and 2401, 



5. A man had to walk 97f mi. He walked 30j mi. the first 
day, 33i mi. the second day, and finished the journey the third 
day. How far did he walk the third day? 

6. A drover bought 4 cows for $168i, and after paying 
$341*0 for pasturage, he sold them for $203i. Did he gain or 
lose, and how much? 

7. James had $12?, and Jane as much, lacking $l\i. How 
much money had they together? 

8. Bought a quantity of coal for $140f , and of lumber for 
$456L Sold the coal for $175i, and the lumber for $516i^. How 
much was my whole gain? 

9. A merchant had 3 pieces of cloth, containing, respec- 
tively, 19f yd., 36i yd. and 33f yd. After selling several yards 
from each piece, he found he had left altogether 711 yd. How 
many yards had he sold? 

10. A merchant sold a customer 22i yd. of silk, 3i yd. of 
paper muslin, li yd. of silesia, 5t yd. of cambric, and 5i yd. of 
ruffling. How many yards were sold? 

V. MtLTIPLICATIOIN AND DIVISION OF FRACTIONS. 

EXERCISE CXXXVIII. 



Multiply " 


— 






1. 


h by 3 


f by 4 


i by 6. 


2. 


t\ by 5 


t by 7 


4 by 6. 


3. 


$A by 9 


$41 by 6 


$A by 8. 


4. 


A by 36 


A by 26 


1 by 24. 


5. 


i\ by 32 


rV by 12 


f by 16. 


6. 


f by 24 


hi by 10 


A by 12. 


7. 


TT by 22 


4 by 21 


1 by 36. 


8. 


1 by 27 


A by 35 


i by 27. 


9. 


A by 21 


A by 25 


U by 15. 


10. 


U\ by 20 


4f by 14 


31 by 24. 




EXERCISE CXXXIX. 




Divide :- 


- 






1. 


f by 2 


if by 4 


H by 3. 


2. 


M by 8 


if by 7 


tVt by 12. 


3. 


61 by 3 


201! by 4 


28U by 7. 


4. 


3411 by 17 


27if by 9 


54M by 6. 


5. 


6f by 9 


4f by 10 


15^ by 23. 



I m 



ml 



P 



06 




ARITHMETIC. 




Divide: 


• 






G. 


2f by 5 


61 by 6 


10^ by 5. ^ 


7. 


h hy 3 


3 by 5 


I by 4. 


8. 


^ by 9 


1^ by 6 


A by 5. 


9. 


n by 7 


11 by 9 


5]^ by 9. 


10. 


711 by 8 

1 


84f by 12 

EXERCISE CXL. 


36 A by 7. 


Multiply: — 






1. 


6 byi 


12 byl 


20 b> 1. 


2. 


1 by! 


I hyl 


4 byi 


3. 


1 by! 


1 byf 


1 by 1. 


4. 


f by 4 


t\ by a 


1 by I 


5. 


i byil 


f byf 


f by V. 


6. 


f byV- 


V byl 


1 by V. 


7. 


1 by^ 


M byH 


i by U. 


8. 


if by 1 


n by if 


HI by A. 


9. 


Mby4 


!4 byT%^ 


11 by If. 


10. 


H by 11 


nt by n 

EXERCISE CXLI. 


V- byV. 


Simplify: — 






1. 


4^ x4^ 


51 x5| 


n x7i. 


2. 


51 xf)^ 


6f x6f 


8f x8! 


3. 


61 x6f 


71 x7| 


12|xl2t 


4. 


^ xf xl 


1 xl xlf 


f x^ xH. 


5. 


1| x2|x3| 


3i x? x5l 


3i x4l XtV. 


6. 


21 xMxl 


5i Xt\x3^ 


81 xA .x5i 


7. 


U xlhx^h 


2f X 41x15 


3 x7i x-U. 


8. 


21 x3ix4f 


3i xl xl? 


lAxljVxf. 


9. 


$31 xtjV 


$3ix/2 


925 mi. x|. 


10. 


$37ixir) 


140oz.x2|i 


21 lir.xlL 



EXERCISE CXLII. 

1. Find the cost of 9i yards of cloth at $4i a yard. 

2. When flour costs $6| a barrel, how much will 26f barrels 
cost? 



MULTIPLICATION AND DIVISION OP FRACTIONS. 



97 



by 5. 
by 4. 

by 3. 

by 9. 
rby 7. 



by I. 
by I. 
by I. 
byi 
by 

by 

by II 



5 

8 
5 

i 

111 by 






S^ 



by 
by 



V- 



x7i. 
x8! 

x^ 



xH. 



x4l xiV. 

xrr X'")^- 
x7i xii 
PtxIjVx^- 
If) mi. X 5. 
hr.xla- 



lard, 
ill 261 barrels 



3; Find the cost of 51 dozen eggs at 121 ctH. a dozen. 

4. John walks at the rate of H'i miles an hour, ilow far 
will he go in 2i hourHf 

;'). A piece of clotii contains KJi ydw. Find the cost of i of 
the piece at $',H per yard. 

6. If it takes If bu. of wheat to how an acre, how many 
bimhels will it take to how 7s acrenlf 

7. If a man earnn $\Vih per week, how much will he earn in 
a year of 52 weeks ? 

8. If one horse eats ? bu. of oats in a day, how many 
bushels will 14 horses eat in G days? 

9. A man owning X of 156| acres of land, sold i of I of his 
share. How many acres did he sell if 

10. At $95 per ton, wiiat will be the cost of i of § of a ton of 

hayf 

EXERCISE CXL!II. 

1. A boy spent j of his money and had 96 ct. left. How 
much had he at first? 

2. If I buy ? of an estate for $18000, what should I give for 
the whole of the estate? 

',i. After going 121 miles I have still f o of my journey to go. 
Find the total length of the journey. 

4. Seven -ninths of a post is in the mud and water. There 
are 8i ft. in the air. How long is the post? 

5. A traveller 'finds that 175 miles is A of the distance he 
has to go. How far is his journey? 

6. A man at his death left his wife $12500, which was | of 
c of his estate. What was the value of the estate? 

7. If f of a certain number is 42ro, what will } of l|f of it be? 

8. In a battle a general lost n of his army. He still had 
;{4500 soldiers left. How many soldiers liad he at first? 

9. John has read -^ of a certain V>ook. He still has 112 
]»ages to read. How many pages are there in the book? 

10. A person dying left i of his estate to his wife, rs of it to 
his daughter and the remainder to his son. His son received 
$16400. What was his estate worth? 



Simplify: — 



EXERCISE CXLIV. 



1. 

3. 
4. 



fx(l|+2H 
8x(3-f) 
(4H2|)x2| 
(4^-21) x2A 



7x(6-2^). 

(3J-2f)xl. 

(3i+2i)xU. 






y» ARITHMETIC. 




Simplify: — 




, 


.'). (i + l) of ,«, 




(32^6-5'',) of lA. 


G. (^ + i-i)xl2 




(2^3^-4^x12. 


7. (^-Ul)x24 




12x(2R4j-3i). 


8. i\ of U of Axa2 




1x1 of 4 of A. 


9. (4^-2.1+51) of 4J 




(^>f3-iof |)x2A. 


10. (1 of n+2i of l-?)of 


A 


(31-1 of U) of lA. 



EXERCISE CXLV. 

1. If a train of eai*s runH 22i mi. an hour, how far will it run 
in Si hrs.? 

2. A merchant bou^'ht 500 cords of wood at $2| per cord. 
He sold 75i cords at $4i per cord and the rest at $5. Find his 
gain. 

3. A merchant purchased 150 yards of cloth for $675, and 
sold I of it at a profit of $f per yard, and the remainder at a 
loss of $^ per yard. How much did he gain? 

4. There are 50i bu. of wheat in a bin. How n^uch remains 
after sowing a field of 7^ acres at 2^ bu. per acre? 

5. A bought 319 acres of land at $200 per acre; he then 
sold 250^ acres at $250 per acre, and the remainder at $266J per 
acre. How much did he gain? 

6. From the sum of 3^ and 2i take their difference and 
multiply the remainder by 2f . 

7. What number added to 14|f+?+^+4TSV+lH wiU malte GOT 

8. Three men own a hou.p worth $6250; one owns VV. the 
second ^ of it. What is the value of the share of the third? 

9. A grocer bought 100 barrels of flour at $6| per barrel ; he 
sold 49 barrels at $7i per barrel, and tixe rest at $7i per barrel. 
How much did he gain? 

10. A drover bought 64 sheep at $71 apiece; he then sold 
30 of them at $6^ apiece, and the remainder at $8| apiece. 
Did he gain or lose, and how much? 



ivide : 
1. 


10 by 4 





20by| 


3. 


5 byf 


4. 


12 by tV 


5. 


16 by 3^ 



EXERCISE CXLVI. 

6 by I 
25 by i\ 
8 by I 
25 by i 
25 by 4| 



12byi 
36 by A. 
9 byT*t, 
27 by I. 

•) j. 



3C by -^ 



;t 4 



MULTIPLICATION AND DIVISION OP FRACTIONS. 



99 



Divide:- 


- 








6. 


42 by 6J 


45 by ')l 


7. 


20 by 31 


25 by 61 


8. 


3 by^ 


1 byl 


9. 


! byl 


I by 1*5 


10. 


31 by liV 


21 l)y 41 




EXERCISE CXLVII. 


Simplify 


: — 




1. 


71 - 


-4! 


/. - 


-M 


2. 


i\ - 


4 

-6 


u - 


-II 


3. 


U - 


-fl 


iSS - 


-U 


4. 


11 - 


-41 


8i - 


-12^ 


5. 


iiA- 


-12^ 


s\ - 


-2^ 


6. 


33^ - 


-lOH 


VA - 


-n 


7. 


6i - 


-2i 


n - 


-n 


8. 


121 - 


-31 


4T«r - 


-51 


9. 


71 - 


-41 


51 - 


-7^ 


10. 


18 - 


-2i 


12fT- 


-81 



74 by 61. 
42 l)y 5L 
I byt. 

JTbyli. 

52 by 55. 



J - 



— Afif 



HI 
21 • 
9J 



TTT- 



--301. 



5^ 

181- 

8! 

171 

501 



3. 
4- 



lif 



•Itl 

31. 



";8 



-2J. 



i>S3 
-3 6. 

8*6 . 



EXERCISE CXLViei. 

1. At $* per yard, how many yards of cloth can be bought 
for f.*}U? 

2. A man rode 37i miles in 4i hours. How far did he ride 
in one hour? 

3. A farmer sold 25f acres of land for $072. What was the 
pi'ice per acre? 

4. A vessel sails 464 miles in 26j hours. Find its rate per 

hour. 

5. A miller has 27i bushels of meal which he wishes to put 
into bags, each bag to contain 2f bushels. How many bags 
will be required? 

6. If 3i pounds of beef cost 431 cents, what is the price of a 
pound? 

7. If a man travels at the rate of 271 miles an hour, how 
long will it take him to travel 784i miles? 

8. By what numb'^r must \Q\\ be ruultipliad to produce 1481? 

9. A fivmer sowed 478i bushels of grain on his farm. If he 
sowed 2^ bushels per acre, how many acres did he sow? 



M 



Si 



S; ; 



■I 






100 



AUITHMETIC. 



10. A Mnuitoba faritipr thranlu'd 10127 IuihIu'Is of wheat. 
This WHH ail av<'raKe yield of 127A ))UHlielH jun- aore. How many 
acres liiul he in wheat? 

11. If the cost of carryinpf 'jr)?')^ biisliels of wlieat from 
Winnipeg to Montreal is $31)4.9] , find the rate charged per bushel. 

12. If a man can do a piece of work in 18 days l>y working 
14!j hourH per day, in how many days can he do the same work, 
if he works 8i hours each day f 

l.'l. When 3')! bushels of potatoes cost $28.60, how much 
should be paid for 4i bushels? 

14. Find a number which divided by 3i, the quotient increased 
by li, and the sum multiplied by 7i, the product is 54. 



Simplify: — 



EXERCISE CXLIX. 



1. (r)|+3U-iJ 


(8|-31)-U. 


2. (8i-3i)^U 


4j-(3^-2l). 


3. 7\^{-,^,-2\) 


20- (51-41). 


4. (3-n-(3+i) 


(4i-2!)-(4|4-2!). 


5. (5H4^)-^(.J^-41) 


(2U-18t\)-(2U+18A). 


6. (|_i+l)-.(H^-l) 


3?-.-5f of jV. 


7. 201 x3i of Ty*„+21 


(2Uli)-(3ix5n. 


8. (8lx3Ax2!)-^3l 


(2R3j)xl2^4i. 


9. 1 of? of 2-4^ of 3i 


(4i_3i)x8i^l()0. 


10. 7i^(4l--3l-5i) 


72-i-44-f-04-|-«>3 . 


EXERCISE CL. 


{Simplify: — 




1. hxl-\xl 


i of Kl of I 


2. ixKl-l 


KKi-i 



3. 51 of 8|xll 

4. 5^ of 81-21- of 3^ 

5. HI of l-l of I 

6. 8|-16f+^ of I 

7. f of fUlof IB 

8. 3|-|xl| 

9. (12|-8f) of lA 
10. T^?-lix2A 



51x8.1^21x3^. 
7l-6A-6A-7i. 

f of U of 91-1 of 
3|-i of If. 
12!-8t of lA. 
12!-8fxlf*T. 
A-ll of 2A. 



3f 



GOMPLKX FRACTIONS. 



101 



of wheat. 
How many 



VI. COMPLEX FRACTIOINS. 





EXERCISE 


CLI. 


Simplify 


1 "^^ • 




1. 


1" 


3 
4 

6 * 


2, 


8 

i 


8 

"4 

9 


3. 


2\ 


r)i 




4i 


3i 


4. 






5. 


41-3.^ 


7^-5] 




41+3^ 


7i+oi 


6. 


3l+4i 


31-12 




G^+1,V 


93 5 

-4 — J» 


7. 


1^ of 11 


7h-2} 




11 of i\ 


^ of 3^ 


8. 


2i of 2h 


21 of U 




li of 3| 


5^ of 31 


9. 


n 


16 




li of A of 3| 


t\ of 2A of H 


10. 


(2-U)x2i 


4h of 5l-f2| 




i of Ih 


4^ of r)i-iof 



EXERCISE CLII. 

Simplify: — 

1. (321+71 )-f of t\. 
(5i+3f)-(94-5U. 
(i^V+Uf fx|)-(/ir-iof|+n. 
rV--(/oof H)xiS-.UxU. 

I of 9?^+3g-r8To — Tlor. 

6. 3j-2^x4i-4TV+3TV. 



2. 

3. 
4. 
5. 



'•I 



102 



ARITHMETIC. 



7. U-|-2§x32+U-Ux38. 
G]-5i Gi-r-fji 3 



9. 



( 



i+' 



1 



G' 



+''!)-iixJ5i. 

3 4ft/ «i2 



10. 2|-.^ of lii + ii 

6 + 3 <>t H— bX 86 



EXERCIltE CLIII. 

1. What must be added to |-f ^+7J to make 10? 

2. Subtract the sura of 4j{- and IJi from the difference 
between 151 and .'i§. 

3. Multiply :H+5f Vjy 4,^ of U and divide the product 

by 8-1^. 

4. Bv how ranch does the sum of i+i+i+a+u exceed the 
sum of l+i+A+if^? 

'). The sum of J of 1X2 and f of |X4i of ^ in equal ^.o how 
nnmy times their difference? 

54x 
G. The smaller of two numbers is ^ — - . ; and their difference 

f of 4* 

is . . Find the larger number. 

7. What number divided by 4|— i of Siif+i^ will make the 
quotient 2f ? 

8. The product is 124; the multiplier is 8f. Find the 
multiplicand. 

9. Find the sum, the difference, and the product, of ^j and 
H; also find their quotient, making the greater fraction the 
dividend. 

10. What number multiplied by | of |X3f, will produce ff? 



VII. G.C.IVI. AND LX.M. OF FRACTIOINS. 
EXERCISE CLIV. 

1. Find the G.C.M. and the L.C.M. of A, M and U- 

2. What is the G.C.M. and the L.C.M. of i, ^ and H? 

3. Find the G.C.M. and the L.C.M. of 4, 2f and 2f. 

4. What is the length of the longest measure that can be 
exactly contained in each of the two distances, 18f feet and 57i 
feet? 



G.C.M. AND L.O.M. OF FRACTIONS. 



103 



r difference 



f>. Wlmt aio tlio longest Hectlons of wire fence, of equal 
length, with which I citn enclose a triimgulnr plot whoHO sides 
are respectively 'J'Jjf t'«'«'t, 'M\k f<"et, and !){) fe«'t? I low many 
sections are recpiireil to enclose the n»'l(lf 

(J. How nuiny times do«'s the L.C.M. of Hi, 48 and 5i 
contain the (l.C.M. of these nunihersf 

7. What is the smallest sum of money with wiiich I could 
purchase a numl)er of sheep at I'Ji each, a number of calves at 
$4i each, or a numher of yearlings at .$98 each? How many 
of each could I purchase with this money f 

H. A farmer has H'M buHluds of corn, ()7i bushels of rye, 70| 
busliels of wheat. He wishes to put this grain, withoiit mixing, 
into the smallest numlxM' of bags, each of which shall contain 
the same quantl^iy. Required the quantity each bag will contain 
and the number of bags. 

9. A merchant has three kinds of wine, of the first 1.34} gal- 
lons, of the second 128it gallons, of the third lloi gallons; he 
wishes to ship the same in full casks of equal size; what is the 
least number of casks he can use without mixing the different 
kinds of wine? 

10. A, B, atid C start at the same place and travel round an 
island, A making the circuit in J of a day. B in ^ of a day, and 
C in ^ of a day; in how many days will they meet at the start- 
ing place, and how many times will each have gone round the 
island? 

VIII. DEINOMilNATE FRACTIONS. 

A Denominate Frj'ction is one in which the 
primary unit of the fraction is a denominate number, 
as I oz., f mi., 3 gal. 

EXERCISE CLV. 

Reduce each of the following to lower denominations: — 



1. 


£| 


^\s. 




Is. 


2. 


$1 


n 




$f. 


3. 


It. 


I'lr cwt 


• 


I lb. 


4. 


f mi. 


Ird. 




f yd. 


5. 


f A. 


TT sq. 


rd. 


V'ff sq. yd. 


6. 


1 cd. 


A cu. 


yd. 


^\ cu. ft. 


7. 


Ibu. 


Ipk. 




fgal. 


8. 


8 gal. 


1 qt. 




1 gal. 


9. 


i\ wk. 


A da. 




i% hr. 


10. 


r 


tc. 




6 ° 



I ; 
I. 



' ' HI 



^r^K^/^jzsL^raf— 



104 



ARITHMETIC. 



EXERCISE CLVI. 

Reduce the following: — 

1. 7 mi. 5 id. 1 yd. to incheH; 2 mi. 2 ft. to inches. 

2. 7456 ft. to miles, etc.; 2745 yd. to miles, etc. 

3. 3f mi. to inches; 7| rd. to inches. 

4. 5 A. 7 sq. rd. to scj. inches; 98 sq. vd. 14 h({. yd. to sq. 
inches. 

5. 57896 sq. ft. to acres, etc. ; 100000 sq. ft. to acres, etc. 

6. 2| A. to sq. inchei.; 3ri sq. rd. to sq. inches. 

7. 4i t. to pounds, 2§ cwt. to ounces. 

8. Ti mi. to rd., yd., etc.; i^ A. to sq. rd., sq. yd., etc. 

9. 47212 sq. yd. to acres, etc.; 6912000 sq. in. to acres, etc. 
10. 1 t. of water to gallons; 7000 gal. of water to tons, etc. 



Find 
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 



EXERCISE CLVII. 

the value of 

T^i of $140.76; f of $50,40. 
I of £3 7s. 6d. ; t of £1 8s. 4d. 
I of 5 t. 8 cwt. 6 lb. ; I of 2 t. 15 cwt. 9 lb. 



I of 7 mi. 35 rd. 1 ft. 



^ of 3 mi. 45 rd. 3 yd. ; 
f of 4 A. 50 sq. rd. 3 sq. yd. ; | of 2 A. 100 sq 
I of 3 cd. 120 cu. ft. ; t of 12 cd. 72 cu. ft. 
f of 3 bu. 3 pk. 1 gal. ; | of 2 bu. 2 pk.' 5 qt. 
I of 7 gal. 2 qt. ; ": of 15 gal. 3 qt 



rd. 



f of 1 da. 8 hr. 40 min. 



J of 15" 45' 18"; f of 17° 24' 36". 



1^- of 8 hr. 33 min. 20 sec. 



EXERCISE CLVIII. 

If 1 ft. is the unit, what immber expresses 8 ft.?, 12 ft.?, 
21 ft.? 

If 2 is the unit, what number expresses 8?, 12?, 21? 
What part of 8 is 2? Of 12 is 2? Of 21 is 2? 
What fraction of 8 is 2? Of 12 is 2? Of 21 is 2? 

1. Reduce I lb. to the fraction of a cwt. 

2. What fraction of a pound is |d.? 

3. What part of a bushel is §^ gal.? 

4. Reduce f yd. to the fraction of a rod. 

5. Reduce i in. to the fraction of a rod. 

6. What part of a pint is ufo bu.? 

7. Reduce atho cwt. to the fraction of an ounce. 

8. What fraction of $9f is $7i? 

9. What part of 2 mi. 130 rd. is 1 mi. 30 rd.? 
10. What part of a foot is ir/sBi) mi.? 



APPLICATIONS OF THE xiEVlOUS RULES. 



105 



H(l. yd. to sq. 



in. 20 sec. 



EXERCISE CLIX. 

1. Whftt part of a pound Tro> wt. is 10 oz. 13 dwt. 8 gr. ? 

2. What part of £8 is U s.? 

3. What fraction of a mile 74 rd. 5 yd.? 

4. What part of 3i yards square is 3i sq. yd.? 

5. What part of 5 weeks is 7 da. 23 h. 20 min.? 

6. What fraction of a cubic yard is 7 cu. ft. 8G4 cu. in.? 

7. What part is 26 gal. 2 qt. 1 pt. of 3H gal. ? 

8. Reduce 35 rd. 3 yd. 2 in. to ihe fraction of a mile. 

9. What part of a pound Avoirdupois wt. is 1 lb. Troy wt.? 

10. Reduce 86 sq. rd. 4 yd. 5 ft. 127^3- in. to the fraction of 
an acre. 

EXERCISE CLX. 

V. 91 sq. rd. 7 sq. yd. 5 



sq. ft. 29 aq. in. to sq. 
are equal to 432 lb. 



1. Reduce 5 

inches. 

2. How many pounds Troy weight 
Avoirdupois weight? 

3. If a pint of milk costs 2i ct., how many quarts can be 
bought for $8.45? 

4. If a sheet of paper is 13i in. long and 8J iu. wide, how 
many such sheets will be required to cover an acre? 

5. The circumference of a buggy wheel is 7 ft. 4 in. long. 
How often does it turn in 6 miles? 

6. How many paces 2 ft. 8 in. long are there in 3 miles? 

7. What is the cost of 12 bbl. of vinegar averaging 41 gal. 
3 qt. 1 pt. at 12i ct. per quart? 

8. Find the value of a pile of tanbark 100 ft. long, 39s wide 
and 181 ft. high at $3.20 per cord. 

9. A merchant paid $35 for 8 bbl. of chestnuts averaging 2 
111). 3 pk. 2 qt. per bbl. He sold them at 5^ ct. per pint. Find 
!iis gain. 

10. Find the value of a pile of wood 225 ft. long, 5i ft. high 
and Q'k ft. wide at $4| per cord. 

IX. APPLICATIONS OF THE PREVIOUS RULES. 

EXERCISE CIXI. 

1. If a cubic foot of broken stone weighs 168 lb., find the 
weight of 5 ed. 63i cu. ft. of such stone. 

2. A pile of wood is 168 ft. long, 6 ft. high and 4 ft. wide. 
How many corde are there in it? 

3. What will a pile of stone 240 ft. long, 8 ft. high and 4 ft. 
wide cost at $2.50 per cord? 



II 



\'^ 



106 



ARITHMETIC. 



4. What are 3 bu. of strawberries worth at 2 et. per pint? 

5. A gardener sells 495 crates of berries, each containing a 
bushel, at 2 ct. a pint. How much did he receive for them? 

6. In 1896 how many days were there from Jan. 10th to Oct. 
Drd, inclusive? 

7. How many minutes were there in Jan., Feb. and March, 
1899? 

8. How many more minutes were there in Feb., 1896, than 
in Feb., 1897? 

9. What is the value of a barrel of syrup containing 29 gal. 
li qt. 1 pt. at 9 ct. a pint? 

10. How many poles each 7i ft. long, placed in a straight 
line, will reach 2 mi. 280 rd.? 

EXERCISE CLXII. 

1. Divide 13 cwt. 63 lb. equally among 29 persons. 

2. A pint of water weighs 1 lb. 4 oz. How many pints are 
there m 22 t. 11 cwt. 40 lbs. of water? 

3. If 178 cwt. 61 lb. are divided into 53 equal parts, how 
many ounces are there in each part? 

4. How many tons, cwt., etc., are there in one million 
ounces? 

5. How many parcels each weighing 2 lb. 12 oz. can be made 
from 2 t. 9 cwt. 50 lb. of sugar? 

6. Find the cost of 4 t. 19 cwt. 99 lb. of sugar at 5 ct. a 
])ound. 

7. How many ounces of iron are required to make 32 iron 
bars, each weighing 2 lb. 7 oz.? 

8. I bought 3 cwt. 19 lb. of tea for $127.60, what did I pay 
per lb. for it? 

9. Out of a box containing 3 cwt. 78 lb. of sugar, how many 
2 lb. parcels can be made? 

10. A railway truck weighs 5 t. 3 cwt. On it are placed 97 
iron bars each weighing 3 cwt. 76 lb. Find the total weight in 
pounds of the truck and bars? 

EXERCISE CLXIII. 

1. How many grains in 11 silver medals each weighing 4 oz. 
5 dwt. 6 gr.? 

2. If 7 silver medals each weighing 10 dwt. 13 gr. are melted 
and the silver divided equally among 11 persons, how many 
grains would each have? 

3. In 2468 grains of gold dust, how many ounces are there? 

4. In a silver box weighing 10 oz. 16 dwt., how many grains 
are there? 



APPLICATIONS OF THE PREVIOUS RULES. 



107 



er pint? 
ataining a 
■ them? 
3th to Oct. 

nd March, 

1896, than 

ling 29 gal. 

. a straight 

18. 

[ly pints are 
[ parts, how 
one million 
lean be made 
at 5 et. a 
ake 32 iron 
at did T pay 
r, how many 



placed 97 
tal weight in 



re 



'ighing 4 oz. 

\ are melted 
how many 

Is are there? 
Imany grains 



5. How many grains of gold will be required for 12 orna- 
ments each weighing 1 oz. 18 dwt. 12 gr.? 

6. Reduce 58376 grains to lbs., oz., etc., Troy. 

7. How many forks averaging 2 oz. 9 dwts. each can be 
made from 5 lb. 1 oz. 5 dwt. of silver. 

8. How many lbs. of silver in 270 spoons, each of which 
weighs 1 oz. 13 dwt. 8 grs.l 

9. Express 4040789 grains in lbs. oz. dwt., etc. 

10. A pound Troy contains 5760 grains and a pound Avoirdupois 
7000 grains. Find how many pounds Troy there are in 94 lb. 
8 oz. Avoirdupois. 

EXERCISE CLXIV. 

1. How many inches are there in a mile? 

2. A lake is 112 fathoms in depth; what is its depth in 

inches? 

3. A wheel is 13 ft. 9 in. round. In turning 768 times, how 
many miles does it pass over? 

4. Find the cost of 20 miles of telephone wire at 35 cents a 
lb. supposing a lb. stretches 80 ft.? 

5. Find the cost of 4 miles of barbed wire if 4 feet cost 8c. 

6. What will it cost to survey 25 miles of road at 25 cents 
for every 66 feet? 

7. The distance from London to Harrisburg is 61 miles 224 
rods. How long will it take to walk that distance at 32 rods 
per minute? 

8. How many inches are there in 5 times 4 mi. 319 rd. 5 yd. 
1 ft. 6 in.? 

9. How many more inches are there in 3 times 7 mi. 1759 
yd. 2 ft. 2 in. than in 4 times 3 mi. 319 rods 5 yd. 6 in.? 

10. A boy going to school walks 126720 inches every day. 
How far will he walk in a school year of 220 days? Answer in 
miles, etc. 

EXERCISE CLXV. 

1. At 40 cents a gallon what would be the cost of 5 bbl. 
syrup, each containing 36 gal.? 

2. A man bought a hhd. (63 gals.) of molasses for $18.90 
and sold it at lOe. a pint. How much did he gain? 

3. 1 bought a bushel of chestnuts for $4.80. What will be 
the cost of 13 qts.? 

4. A gardener has 13 bu. 2 pk. 1 gal. 2 qt. of strawberries. 
How many quart baskets will be needed to hold them? 

5. If 376 gal. 3 qt. 1 pt. of milk be divided among 9 charities, 
how many piuts will each receive? 



I ■i 



i; ' 



f if 



108 



AHITHMKTIC. 



6. A man bought 14 bags of beans, each containing 2 Vm. 2 
pk, for $21, and sold them in boxes of 1 bu. 3 pk. eacli, so as 
to neither gain nor lose. Find the price per box. 

7. How many loads of apples of 27 bu. 3 pk. each can be 
bought for $53.28 at 48e. per bushel? 

8. What is the value of 324 bags of beans, raeh containing 2 
bu. and 1 pk. at 70c. a bushel? 

9. A milkman started with 10 gal. of milk. He sold i pt. to 
each of 52 people and a pint to each of 50 others ; how much has 
he left? Ans. in quarts. 

10. Reduce 143 bu. 3 gal. 3 qt. 1 pt. of wheat to pints, and 
find the value at H cents a pint. 

EXERCISE CLXVI. 

1. A farmer travels .!00 miles in 8 days, liow many days will 
it take him to go 4224000 ft.? 

2. A man walked 13G miles in 45 hrs. 20 min., how many 
feet did he go per minute ? 

3. How many times is 195 yd. 1 ft. 8 in. contained in 1 mile? 

4. A train goes 30 miles an hour, how many feet does it go 
l>er second? 

5. A rate of 22 yd. in 5 seconds is equal to what rate per hour? 

6. A tank has 12000 gal. of water in it. How long will it take 
to empty it, if 5 pints are emptied in a minute? 

7. How many days of 10 hrs. each would it take to count 
30,000,000 sovereigns at the rate of 100 per minute? 

8. Find the cost of 3975 lb. bran at $1.44 per cwt. 

9. A farmer paid a laborer $1.75 a day for the month of 
August, what should he get if the month began on Wednesday? 

10. Find the cost of 40 lb. of ice, delivered three times a 
week from April 1st to October Gtli inclusive, at COc. per 
hundred pounds. 

EXERCISE CLXVII. 

1. Find the difference in the cost of 17 bu. of wheat when 
sold at Ic. per lb. or le. per pint. 

2. A pile of 4 foot wood is 64 ft. 
to contain 10 cords? 

3. How many steps each 2 ft. 
take in walking 3| miles? 

4. A farm of 111 acres is divided into fields of 7a. ()4 s<|. r'l. 
How many fields are there? 

5. How far can I walk in 10 hv. 45 min. at the rate of a 
mile in 15 minutes? 

6. How many more hours are there in January than in 
February, 1896? 



long. How high should it l)e 
() in. ill length will a man 



APPLICATIONS OP THE PREVIOUS RULES. 



109 



taiuing - 



how many 



7. How. many paces each 2 ft. 8 in. are there in 2J miles? 

8. Rednce 3 weeks 19 hrs. 2") min. 15 sec. to seconds, and 
lii'S weeks 6 days 19 hrs. 5 min. 45 see. to seconds, and divide 
the larger quantity by the smaller. 

9. The circumference of a wheel is 16 ft. (J in. lon^. How 
often will it turn between London and Hamilton, 76 miles If 

10. A coach wheel 10 ft. 9 in. round, turns 12 times in 10 
seconds, at what rate per hour is the coach going? 

EXERCISE CLXVIII. 

1. Find the weight of a dozen and a half silver spoons each 
weighing 4 oz. 4 dwt. 22 gr. 

2. Add together .£:J7 17s. 4id.. £19 12s. lOid, £18.1 19s. .3d. 
and £52 Os. Hid. and take £93 lv;s. 5d. from the sum. 

3. Multiply 3 cwt. 3 lb. 3 oz. by 69 and subtract the result 
from 11 tons. 

4. A bicyclist travelled 50 miles in 3 hrs. 3 min. 20 sec. 
What was his rate in feet per second? 

5. A train travels 95 miles 1100 yd. in 2 hr. and 50 min. 
How far does it go in 1 minute? 

6. If I walk 350 yd. in 2 min. 40 sec. how long will it take 
me to walk 560 yd.? What distance can 1 walk in 7 min. 28 
sec. at the same rate? 

7. How many yards per minute faster is the rate, 42 miles 
an hour, than the rate 20 yards per second? 

8. How many bags of sugar each holding 235 lb. are there in 
6 t. 6 cwt. 90 lb? 

9. A grocer buys 13 hhd. of sugar weighing 6 t. 8 cwt. 57 
ib. How much did each weigh? 

10. How many trees will be required to plant 27 a. 91 sq. rd. 
22 sq. yd. 2 sq. ft. 36 sq. in., allowing 105 sq. yd. for each 

tree ? 

EXERCISE CLXIX. 

1. How many more inches are there in 3 yd. 1 ft. 6 in. tlian 
in 3 ft. 6 in. 

2. Three men can cut 8 ae. 36 sq. rods in a day, how long 
will it take them to cut 57 ac. 92 sq. rods. 

3. How many days from March 13th, 1898, to July 3l8t, 
1899, both inclusive? 

4. How many miles will a boy walk to plough 6 acres turning 
9 inches of a furrow? 

5. A man bought 3 bu. 3 peeks of nuts at 75e. a peck and 
sold them at 10 cents a quart. How much did he make? 



r <f3 






no 



ARITHMETIC. 



6. A farmer in tlie North- West had 4H(> acres of wliejit, and 
the averaj^e yiehl was 27 bus. 'A pks. G qts. 1 pt! i>er a'.'re. 
What will the whole be worth at GO et. i)er bushel ? 

7. The price of broadcloth at lOs. 8d. per yd, is jCUG 128. 
How many yards are there of it ? 

8. A boy bought a bushel of nuts for $1 and sold them at 5 
ct. a quart. How much did he gain f 

9. If sound travels at 1144 feet per second, how long would 
it take to travel to the moon, a distance of 240500 miles? 

10. If a wheel turns 780 times in going over 1 mi. 1G85 yd. 
What is the length of its circumference? 

EXERCISE CLXX. 

1. What 's the difference in weight between .3 dozen silver 
table spoons weighing 5 lb. 9 o/.. 8 dwt. and as many silver tea 
spoons weighing 1 lb. 9 oz. IG dwt. 18 gr. 

2. How many times is 391 yd. 4 in. cc-ntainbd in 2 mi,? 

3. If a man walk i mile in 5 minutes, how many hours will 
it take him to walk 36 miles at the same rate? 

4. Find the number of days between Sept. 23rd and Jan. 
11th, one of these days included. 

5. A man walks 1 mi. 47 rd. in 20 minutes how long will it 
take him to walk 123 mi. 276 rd. 

6. How many boards each 11 ft. 6 in. long and 10 in. wide 
will be required for the flooring of a room 23 ft. long and 17 ft. 
6 in, wide? 

7. How many turns will a wheel 3 yd. 2 ft, 3 in. round make 
in passing over 198 miles? 

8. How many silver spoons weighing 1 oz. 18 dwt, 12 gr. 
can be made from 23 oz. 2 dwt, of silver? 

9. What is the rate per hour of a horse that travels 18 mi. 
1620 yd. in 3 hr. 4o min.? 

10. Find the cost of 260 lb. of tea at 3s. 3fd. per lb. If 20 
lb. of it be spoiled, how much is gained by selling the remainder 
at 48. lid. per pound? 

EXERCISE CLXXI. 

1. How much oats will it take to seed 87 acres, using 2 bu. 
1 pk. 5 qt. to the acre? 

2. A miller ground 7845 bu. of wheat. How many barrels of 
flour did he obtain, provided each bushel yielded 39 lb. 3^ oz.? 

3. A and B togeth<-r bought a web of silk; A piid for ,\ of 
it and B for the remainder. The difference between their shares 
in 5i yd. What is the share of each? 



APPLICATIONS OF THK PRKVIOUS Kfl.KS. 



Ill 



4. If A travels 24 mi. 198 id. 4 yd. in (5 )ir. 30 min., how far 
will he go in 9 hr. 45 min.? 

5. A field 80 rods long contains 1;') acres, while another field 
of the same width contains 9 acres: wliat is the length of the 
latter field? 

0. A lady bought 15 yd. of velvet i yd. wide. How much silk 
I yd. wide must she buy to line itf 

7. Mrs. Brown wishes to carpet a room 18 ft. long by 15 ft. 
G in. wide, with Brussels carpet I of a yard wide, at $1.25 a 
yard. How much will it cost her? 

8. If 4^ lb. of pepper cost $2.15, what will .30 lb. cost? 

9. If 30iV tons of iron cost $1728, what will 7ii tons cost? 

10. If drk tons of copperas cost $333J, what quantity of 
copperas should be received for $500. 

EXERCISE CLXXII. 

1. If A of a barrel of flour costs $2.25, what will a whole 
barrel cost? 

2. If T^ lb. of a drug costs $2.52, what is the value of ^ of a lb. ? 

3. If 41 tons of coal cost $28, what will 15 tons cost? 

4. When $8 are paid for If yards of broadcloth, how much 
must be given for 8| yards? 

5. Sold 7i^ busLjls of apples for $7.28. What should I 
receive for 19t5 bu.? 

6. How many yards of muslin, at 62i ct. per yard, must be 
given in exchange for 34 bu. of sweet potatoes, at 50c. per 
bushel? 

7 How many pounds of btitter at 18f ct. per pound, should 
be exchanged for 40i yd. of calico at 12i ct. per yard? 

8. If a man works Si hr. a day, he can finish a piece of work 
in 12J days. How many hours per day must he work to com- 
plete it in lOl days? 

9. If ^ of a yard of ribbon cost $|, what will 5| yd. cost? 

10. Paid $7888tt, for 83A acres of land. What sum did I pay 
for each acre, and what would be the cost of 7 acres? 

EXERCISE CLXXIII. 

1. How many parcels each weighing 41 lb. 8 oz. can be made 
up out of goods weighing 1 ton, and what weight will be 
remaining? 

2. How many pounds of sugar at 6i cents a pound will pay 
for 12 dozen eggs at 16S^ cents a dozen? 

3. If a man can drive lOf miles in H hours, how far can he 
drive in 5f hours? 






tA 



112 



AlilTHMKTlf. 



4. How many yards of cambric | yd. wide will it take to line 
14 yards of (;l(;tli li yd. widt*? 

5. After selling? 'H of his sheep to n, drover, and Jt of the 
remainder to hia neififhbor, a farmer has 100 left. How many 
were there in the Hock at first if 

(5. A road to the top of a hill has a rise of A of a foot in 10 
feet. How many feet is the total elevation of the hill, if the 
length of the roud is 2 miles? 

7. From 120 A. of land 32lf A. are soM to one man and J of 
the remainder to another. How many acres are unsold? 

H. A grocer buys 'M lb. of tea at 48 ct. a pound, and '}0 lb. 
at 64 ct. a pound, and having mixed them sells 40 lb. of the 
mixture at oG ct. per pound. At what price per lb. must 
he sell the remainder that he may neither gain nor lose? 

9. A gentleman gave i of his estate to his wife, I of the 
remainder to his oldest son, and f of what then remained to his 
daughter, who received $750; required the whole estate. 

10. A man has 4 lots containing 4| A., 6fB A., 9i A. and lli^ 
A. respectively. He wishes to divide each lot into the largest 
sized building lots possible, each lot to contain the same area. 
How much land will each building lot contain? 



EXERCISE CLXXIV. 

1. A wine merchant bought a pipe of wine (126 gal.) and 
bottled it into an equal number of quart, pint, and half-pint 
bottles. How many bottles of each size had he? 

2. At $6.40 a cord, what is the value of two piles of wood, 
each 4 ft. wide and li yd. high, but the one 2i rd. in length, 
and the other 15i yd.? 

3. From two fields 482 bushels of corn are gathered. The 
first field yields i as much as the second. How many bushels 
does each field yield? 

4. What must be paid for a pile of wood 25 ft. long, 3^ ft. 
high, and 6f ft. wide at $4|^ per cord? 

5. If lOi lb. of milk make a lb. of cheese, find the value at 
9 ct. per lb. of the cheese made from 350 tons of milk. 

6. A cistern 7i ft. long and 5i ft. wide contains 3321 eu. ft. 
What is its depth? How many gallons of water will it hold? 

7. At 12 cents per cubic foot, what will be the cost of a 
block of stone 9 ft. long, 5i ft. wide, and 4 ft. thick? 

8. A father divided a piece of land among his three sons 
thus: he gave 12i acres to the first, I of the whole to the 
second and to the third as much as to the other two together. 
How many acres were in the piece of land? 



APPLICATIONS OF THE PREVIOUS RULES. 



113 



9. A man bequeathed $37000 to his family. He gave i to his 
wife, i to his son, and divided the rest equally among 5 
daughters. How much did each daughter receive f 

10. A young man lost i of his money in betting on races, jt 
of the remainder In stock jobbing, | of what was left by invest- 
ing in foreign bonds, and has now $1750 left. Find the amount 
of his property at first. 



sq. 
was 



rd. were 
divided 



wide, 



EXERCISE CLXXV. 

1. From a tract of land containing 365 A. 90 
sold 110 A. 110 sq. rd., and the remainder 
equally among 5 persons. Find the share of each 

2. In digging a cellar 24 ft. long and 10 ft. wide, 1860 cu. 
ft. of earth were removed; how deep is it? 

3. If a pile of bark 24 ft. 6 in. long, and 4 ft. 6 in, 
contains 9ooi cu. ft., how high is it? 

4. A gentleman sent a silver tray and pitcher, weighing 3 
lbs. 9 oz., to a jeweller, and ordered them to be made into tea 
spoons, each weighing 1 oz. 5 dwt. How many spoons should 
he reefeive? 

5. A man having a piece of land containing 3844 A., divided 
it between his two sons, (r'.ving to the elder 22 A. 60 sq. rd. 
more than to the younger. How many acres did he give to each? 

6. A and B own a farm; A owns -^ of it and B the re- 
mainder. The difference between their shares is 15 A. 68i sq. 
rd. How much is B's share? 

7. The forward wheels of a wagon are 10 ft. 4 in. in circum- 
ference, and the hind wheels 15i ft. How many more times will 
the forward wheels revolve than the hind wheels in running 
from Boston to New York, the distance being 248 miles? 

8. What will be the cost of plastering the walls and ceiling 
of a room 36 ft. long, 26i ft. wide, and 15 ft. high, at 21 cents 
a sq. yd., making no dedtictions? 

9. A man has a piece of it.nd 201 1 rods long and 41 J rods 
wide, which he wishes to lay out into square lots of the greatest 
possible size. How many lots will there be? 

10. A gentleman gave J of his property to his son James; i 
of it to his son William ; ^ of the remainder to his daughter 
Mary; and the balance to his wife, Mary received $2243.26 less 
than James. What was the amount divided, and how much did 
each receive? 



m 






EXERCISE CLXXVI. 

1. A can dig a fi^ild in 5 days. B can dig it in 4. If both 
work together, what part of the field will they dig in one day? 



;« 



114 



ARITH;ilI::TIO. 



2. A can do a piece of work in six days which B can do in 8 
days. Tliey work together at it I'or 2 days. How much of the 
work remains to l>€< done? 

'.i. A can mow a piece of grass in 4 days, and B can do it in 
2 days ; liow long will it take both working together to do it * 

4. A and B together can do a piece of work in 18 days, l>nt 
with the assistance of C they do it in 12 days. In what time 
can C do it by himself? 

5. A and B together can do a job in 7 days, b«it it would 
take A alone 12 days to do it. How long would it take B alone 
to do it? 

6. A and B together can do a piece of work in 20 days. A 
can do it alone in UG days. After A lias worked 3 days alone, 
how long would it take B to ftnish it alone? 

7. Three men can do a piece of work in 4 days; the first can 
do it in 15 days, and the second can do it in 12 days. How long 
will it take the third to do it? 

8. A can do a piece of work in 3 days, B can do it in 4 days, 
and C can do it in 5 days. How long will it take them to do it 
together? 

9. A can mow a field in 10 days, B in 8 days, and C in 5 
days. When working together, how many days will they need? 

10. A can build a wall in 8 days, B in C days, and C in 5 
days. A and B worked together for 1 day, when they were 
joined by C. How many days will they need to complete the 
remainder of the work? 

11. A and B working together can mow a field in 10 days; A 
and C can do the same work in 9 days ; and B and C in 12 days. 
In what time can C do the work alone? 

12. If 4 men or 20 boys can do a piece of work in 12 hours, 
in what time can 3 men and 30 boys do the same work? 

13. If 5 men, 8 women, or 12 boys can do a piece of work in 
20 hours, in what time can 1 man, 2 women and 3 boys do this 
work? 

14. Three men are employed to dig an acre of land. A can 
dig 40 sq. rd. in 6 days, B can dig 60 sq. rd. in 8 days; and C 
can dig the whole in 16 days. If all begin to work together, in 
what time will they dig the acre of land? 

15. A can dig a garden in ')l days; B can dig the same garden 
in 4f days. If they begin to dig together in what time can they 
dig the entire garden? 

16. A can do a piece of work in 6j days; B can do the same 
work in 7i days and C can do it in 8^ days. A works alone at 
the job for 2 days when B begins and the two work together for 
a day. Then C joins them and they all continue until the 
work is done. How long does A work? 



an do in 8 
ueh of the 

an do it in 
to do it? 
S days, i»ut 
I what tiiue 

lit it would 
ike B alone 

20 days. A 
days alone, 

the first can 
, How long 

it in 4 days, 
hem to do it 

, and C in 5 

1 they need? 

and C in o 

\n they were 

loniplete the 

^1 10 days ; A 
in 12 days. 

Jin 12 hours, 

lork? 

le of work in 

jboys do this 

land. A can 
lays; and C 
I together, in 

Isame garden 
Ime can they 

lo the same 
[rks alone at 
[together for 
\e until the 



CHAPTER VII. 



DECIMALS. 



I. DEFIINITIOINS, INOTATIOIN AND INUIVIERATIOIN. 

When the numltcr 10000 is divided by 10, tiiequotient is 1000. 

When 1000 is divided hy 10, the quotient is 100. 

' When 100 is divided by 10, the quotient is 10. 

When 10 is divided by 10, the quotient is 1. 

When 1 is divided by 10, the quotient is ra and ir ritten .1. 

Wiien .1 is divided by 10, the quotient is Too am is written 
.01, etc. 

Such nnin])ers as .1, .01, .001, .34, 5.7, etc., are 
called decimals, or deeiiiial fractions. 

Decimals, or Decimal Fractions are fractions in 
which the unit is divided into 10, 100, 1000, etc., 
equal parts. 

A decimal is expressed by writing the numerator 
of the fraction with a point so placed as to indic^ate 
the order or place of the decimal. 

This i)oint which separates integers from decimals 
is called the Decimal Point. 

When there is a i>art of the nunil^'r to the left of 
the i)oint, this is Cc'Ucd the integral part, and that 
to tiie riglit, the Decimal part, of the given numl)er. 

The following table shows the relation of the various orders 
ov plaees to the right iind left of the unit's place to each other, 
tliiis the order tens is lirst to the left of units, the order tenths 
is iirst to the right of units; the order hundreds is secoml to 
the left of units, the order hundredths is second to the right of 
units, et". 

115 



no 



aimtiimktk;. 



Notation ank Nr.MKitATioN 'I'ami.k. 



i 



o 

r. 

C lu 

O TS 

fQ K 



a 
o 



<■* 



a 
H 



4 

a 

o 
H 



a 

W 



XI 

a 

'/J 

a 
o 

H 



01 



7: 

a 

a 
o 
ja 
H 



a 
a 

W 



]() 9 K 7 () T) 4 ;{ 






a 



^ 



22 - .2 ^ 

a •- ^j a 






I 











ra 












"3 


a 




• 






a 

a 



a 

•/. 

a 





1 




,2 

1— ii 


■/I 

a 


a 


H 

1 

a 


a 

a 





• p-4 

1 

a 


0; 


a 


^ 


0) 


• ^ 


a> 


H 


W 


H 


H 


W 


?^ 


H 



I 

a 
o 






iNTKCiKKS. 



. 1» ;; 4 ;') <) 7 H I) 10 

i 

Decimals. 



EXERCISE CLXXVII. 



Koiul or writ*' in words: — 



1. 


.9 


.45 


.75 


.08. 


2. 


.17.') 


.087 


.006 


.209. 


3. 


'J.OG 


7.001 


10.07 


9.207. 


4. 


.:5875 


.0562 


.0083 


.0006. 


15. 


l.()31 


1.315 


48.007 


87.0006. 


G. 


201.201 


78.567 


100.001 


709.224. 


7. 


612.612 


13.0108 


700.625 


5.6006. 


H. 


10000.001 


1000.0001 


100000.01 


1000000.1. 


9. 


200.2006 


2002.006 


20020.06 


20.02006 


10. 


78965. 4.*{2 


789.65432 


7896.5432 


789654.32. 



EXERCISE CLXXVIII. 

Write in fi^ires: — 

1. Three limidretl siiid twenty-five, and seven tentlis. 

2. Four hundred and sixty-five, and fourteen hundredtlis. 

3. Ninety-three, and seven liundredths. 

4. Two hundred and tiiirteen thousandths. 

5. One tliousand, and six ten-thousandths. 

Thirty-sev^n, and seventy-two thousandths. 

Seven Inindred and eighteen ten-thousandths. 

Two liundred and forty thousand, and four hundred and six 
thousandths. 

9. Fifty-six million, and fifty-six jnillionths. 

10. Seventy million, and seven millionths. 



6. 
( . 

8. 



AnniTION OF DKCIMAL8. 



117 



J 







a 






• 


o 






X 








^4 
















*-• 


• r-* 








tt-4 




■/! 


_o 


1^ 
1 


/ 


xa 


'»— ; 


-fl 


-S 


*j 


• ^4 


01 


■»-> 


•-< 
o 


?^ 




o 




1 


PI 


• •^ 

S 


7 


H 


J) 


10 



VLH. 



.08. 
.209. 
9. '207. 

.000(5. 
87.000(). 
709.224. 
r).()00(). 

1)00000.1. 

20.02006. 
1789654.32. 



Miths. 
lundredtlis. 



tidred and six 



Add togt'tlier: — 



1. 



359.6 
35.964 
520. 
43.7 
.876 
1.01 



II. ADDITIOIN. 
EXERCISE CLXXIX. 

7.04 
3«).475 
90.007 

0.689 
367. 

7.82 



200. 


1.01. 


36.010 


19.00!). 


7.7 


178.6. 


84.09 


6.83. 


785.3677 


20.761. 


6.005 


.84. 



2. 18.79, 147.072, 856.709, 185.8761, 397.05784. 



3. 
4. 



3.584, 387. <), 5.894003, .00397, 8.889. 



6. 
7. 

8. 



8939, 8.939, 89.39, .89.39, .00089.39, 893.9. 
56.6794, 5.76, ..579, 342.1, 34.21, 7000, 9.7646. 
47.21, .946, 154.172, .000457, 17.46, 173, .05409. 
4.71, 3.967, 17.10845, .04075, ().154, 99.876. 
27.16, 47.148, 9, 9.2387, .()047(), .0853, 78. 
9. $47.19, $27.15, $364.10, $.75, $4,085, $65,075. 
.10. $7,009, $7, $871, $.065, $1,005, $21,075, $6,675. 

EXERCISE CLXXX. 

Sini)dify: — 

1. 64 + .78 + 479.543 + 66.8 + 3^5.4876. 

2. 34.084 + .088 -f 96.7854 + 78 + 42.89. 

3. 9.3 + .04 + 8.0067 -f 778.7 + 47.0.393. 

4. .365.84 4- 19.07 + 17.8 + 78 + 584.3671. 

5. 729. + 2.3788 -|- 35.68 + 7806.7 + .379. 

6. 19.7864 + 3987 + .9 + 577.17 -f 93.8 + .48. 

7. 9.7 4- 64.36 + .587 + 97 + .00487 + 54.7. 

8. 76.54 + 3896.0484 -|- 77.3456 + 68 + 78.99. 

9. 87.4785 + 78 -f .84 + 37.84672 + 18.75. 
10. 3698 + 786.4 + 7 + 4.9 + 36.847 -j- .099. 

EXERCISE CLXXXI. 

1. A man lias in one field 27.9 aeres; in another, 45.755 
acres; in a tliird, 135.125; and in a fourth, 73.625. How many 
acres has he in all? 

2. Add together two hundred and nine thousand, and forty-six 
millionths; ninety-eight tliousand two hundred and seven, and 
fifteen ten-thousandths; fifteen, and eight hundredths; and 
forty -nine ten -thousandths. 

3. What is the sum of the following numbers: twenty-five, 
and seven millionths; one hundred and forty-five, and six 
hundred and forty-three thousandths; one hundred and seventy- 
five, and eighty-nine hundredths; seventeen, and three hundred 
and forty-eight hundred-thousandths? 



:m 



118 



ARITHMETIC. 



4. A merchant bought at one time 23.75 yards of cloth; at 
another time, 57.375 yards; and at another, 34.6875 yards. How. 
many yards did he buy in all ? 

5. A farmer sold 2.87-5 tons of fodder; 8.3125 tons of oats; 
5.4.55 tons of hay, and 7.625 tons of clover. How much did he 
sell in all? 

6. Add the following numbers: fifty-nine, and fifty-nine 
thou'andths; twenty-five thousand, and twenty-five ten -thou- 
sandths; five, and five milliouths; two hundred and five, and 
five hundredths. 

7. What is the sum of 304 thousandths, 5103 hundred - 
millionths, 61032 millionths, 413 hundred-thousandths, and 
603 ten -thousandths? 

8. Jones bought 4 loads of hay, weighing 1.475 tons, 2.085 
tons, 1.516 tons, and 1.424 tons, respectively. How many tons 
are there in all? 

9. What is the sum of forty-nine, and one hundred and five 
ten -thousandths; eighty-nine, and one hundred and seven 
thousandths; one hundred and twenty-seven millionths; and 
forty-eight ten-thousandths? J 

10. What is the sum of three, and eightet.'n ten -thousandths; 
one thousand and five, and twenty-three thousand and forty- 
three millionths; eighty-seven, and one hundred and seven 
thousandths ; forty -nine ten -thousandths ; forty -seven thousand, 
and three hundred arid nine hundred-thousandths? 



III. SUBTRACTION OF OECIIVIALS. 
EXERCISE CLXXXII. 



1. 


From 
Take 

From 
Take 

From 
Take 


7.84 
3.67 

39.3 * 
1.6789 

7.6 

2.847 


81.01 

27.08 

5. 

1.678 

3.842 
1.9678 


36.006 
21.783 


76.89* 
7.397. 


2. 


6.1 

1 .99999 


41.7 
21.9767. 


3. 


.0067 
.0009 


7. 
1.345. 



4. From 8, take 2.7689; from (5.5, take 2.378. 

5. From .8, take .347; from ()!), take 7.9684. 
(). From 25, take 12.789; from 17, take .0007. 

7. From 100, take .0001; from 10, take .01. 

8. From 87.1, take 5.6789; from 1, take .87654. 

9. From 74.8, take 37.456; from 5.08, take 1.675. 
10. From 385, take .0076; from 1001, take 7.0006. 



SUBTRACTION OF DECIMALS. 



119 



Simplify: — 


1. 


7— :5.45() 


»>_ 


2.5—1.7859 


:j. 


8.275—5.185 


4. 


70.5— .0375 


5. 


9.008— 4. 75G3 


G. 


10— .0005 


7. 


.75— .075 


8. 


600— 6.r)() 


9. 


4— 3.87G5 


10. 


100—3.145 



17—6.435. 
5.1 — .7^45. 
3— .214. 
17—9.0067. 

1— .0001. 
25—3.675. 
785— .785. 
1— .175. 
3.65—1.19. 
7.89646—6.9. 



EXERCISE CLXXXIII. 

15—2.34 
.36— .0897 
2.0132—1.25 
6.4—3.876 

2— .745 
100—99.875 
735—7.85 
5— .275 
■ 28—2.8795 
5 — .5555 
EXERCISE CLXXXiV. 

1. From seventy -three, take seveiity-three tliousandths. 

2. From twenty-three hundredths, take three hundred and 
seven ten -thousandths. 

3. From three hundred and sixty-five, take forty-seven ten- 
tliousandths. 

4. From seven thousand, and seventeen millionths, take 
.0004125. 

5. From one million, take one millionth. 

6. From eighteen thousandths, take five hundred and nine- 
teen millionths. 

7. From three million, and one millionth, su, tract one tenth. 

8. From one thousandth, subti'act one millionth. 

9. From fifty-three, and ninety thousandths, take ten, and 
three hundred -thousaTuiths. 

10. From seven thousand and seven, subtract seventy-seven, 
and four thousand and seven hundred-thousandths. 



Simplify: — 



EXERCISE CLXXXV. 



1. 25.000315 — .00045 + .2801 — 16 + 21.001. 

2. 8.14 -f 38.124 — .9175 — 16.28 + 46. 

3. 16.945 — 2.994387 — .06735 — .0007 -f .953 + 0.8. 

4. 7.654327 — .3793080 -f 9.06990 — .00999 + .345. 

5. 78 — l(i.45 — 32.08 — 11.709 -f 24.305 -\- 7.09. 

6. 100 -f 1.005 — 41 — 36.008 — 21.07 -f 1.225. 

7. 84 — 7.(59 -f 9.0S9 — 3.425 — .S25 — .006. 

8. 1.6 -f 7.92 -f 6.859 — 3.9999 — 2.5554 — .0(;4. 

9. 75 - 25.8 -f 36.08 — 25.755 -f 42.375 — 21.875. 
10. .008 -j- 10.01 — 3.5876 — 2.8497 -f 7.854 — 2.345. 



li 



120 



ARITMHETIC. 



EXERCISE CLXXXVI. 

1. A farmer owning 957 acres of land sold at one time 
225.7 acres; at another, 175.45 acres; and at another, 327.375 
acres^ How many acres did he still have? 

2. A merchant, having $1000, invested it as follows, viz. : 
$145.75 in calico; $275.56 in shoes; $95.25 in hats; $156,375 
in broadcloths, and the remainder in groceries. How much did 
he invest in groceries? 

3. A is to ti-avel 597 miles in 3 days. The first day he 
travels 196.4 miles, and the second day 201.25 miles. How 
many miles must he travel the third day? 

4. A man received the following sums: $27.40, $68.75, 
$810.47, $381>.59, and $2.20. He paid out the following sums: 
$78.67, $129.72, $119.46, and $3.88. How much had he left? 

5. A man owning 875 acres of land divided it among his 
four sons as follows: to tlie first he gave 213.65 acres; to the 
second, 192.375 acres; to tlie third, 206.625 acres; and to the 
fourth, the remainder. Wliat was the fourth son's share? 

6. In 1897 tlie rainfall in Ontario for six months was as 
follows:— April, 2.52 in.; May, 3.38 in.; June, 2.83 in.; July, 
5.36 in. ; August, 2.62 in. ; and September, .83 in. How much 
did the rainfall during the second three months exceed that 
during the first three? 

7. A gardener sold his cabbages for $212,875 and his 
turnips for $118.33. The cost of raising the cabbages was 
$119.75, and the cost of raising the turnips was $99,875. What 
was his profit on the two crops? 

8. A speculator, having 57436 acres of land, sold at different 
times 536.74 acres, 1756.19 acres, 3678.47 acres, 9572.15 acres, 
7536.59 acres, and 4785.94 acres. How much land had he 
remaining? 

9. From a hogshead of sugar containing 397.25 lb., a grocer 
sold parcels as follows: 110.25 lb., 64.5 lb., 14.25 lb., 29.375 
lb., 39.23 lb., and 16.33 lb. How much was left? 

10. A flagstaff is made up of two parts, the upper part being 
27.84 ft. long, and the lower part 57.86 ft. long. If the lo-er 
part is set 11.97 ft. in the ground, how many feet of the whole 
staff are above tlie ground? 

11. Four men dug a ditch. The first dug .123 of it; the 
second .234 of it; and the third .343 of it. How much of it did 
the fourth man d' jf? 

12. On Monday the mercury of a barometer was 30.356 in. 
high. It fell .017 in. and .15,3 in. during the next two days. 
During the next four it rose .008 in., .027 in., .231 in., and .018 
in. On the seventh day it fell .132 in. Find its height at the 
end of the seventli day. 



MULTIPLICATION OF DECIMALS. 



121 



IV. MULTIPLICATIOIN OF DEC1IV1ALS. 



Multi 

1. 
o 

.3. 
4. 
5. 
G. 
7. 
H. 
J). 
10. 



EXERCISE 

ply:— 

4.8 by 4.2 

3.5 by 3.5 

4.5 by 3.58 
240.5 by .25 

32.7 by 2.35 
G1.76 by .071 
.0009 by .0009 
.0068 by .0062 
7.006 by 4.05 



CLXXXVII. 



5.4 by 5.G 
12.7 by 12.3 
.37 by 4.3 
.45 by .21 
.009 by .07 
.6101 by .061 
.084 by .086 
.0125 by .0125 
75.6 by 75.04 



7.007 by 7.007 



1.0001 by .001 



7.1 by 7.9. 

10.8 by 10.2. 

5.25 by 3.75. 
.27 by .0009. 

12.5 by 12.5. 
.1234 by 1234. 

.073 by .077. 

.075 by .075. 

245 by .245. 
34.56 by .008. 



Simplify: — 



EXERCISE CLXXXVIII. 



1. 72.5 X .006 

2. 37.654 X 13.45 

3. (2.45 + 3.08) X .0024 

4. 3.075 X 80 X .15 

5. .008 X .019 X 25000. 
G. .0525 X 10000 

7. (101 -f 10.1) X 101 

8. 1.0005 X (3.4 + 5.66) 

9. .0003 X .003 X .03 
10. .012 X .0012 X 12000 



8.45 X .008. 

7. 0805 X 5.0006. 

(7 - 1.234) X 5.65. 

895 X .475 X .004. 

123 X 12.3 X 1.23. 

.0927 X 1000. 

(7 — .564) X 8.5. 

7.245 X (75 — 36.45), 

1000 X .0006 X 8. 

64 X .125 X .004. 



EXERCISE CLXXXIX. 

1. Multiply 123.456 by 10; by 100; by 1000. 

2. What is the product of one thousand and twenty-five, 
multiplied by three hundred and twenty-seven ten-thousandths? 

3. Multiply one hundred and fifty-three thousandths by one 
hundred and twenty-nine millionths. 

4. Multiply five thousandths by seventy-three hundredths. 

5. Multiply three hundred and fifty-six thousandths by one 
hundred and forty- five ten-thousandths. 

6. Multiply 4.5 by 10; by 100; by 1000; by 10000. 

7. Multiply eiprht hundred and forty-two thousandths by five 
hundred thousand. 

8. Multiply'one hundred and seven thousnnd, and fifteen ten- 
thousandths by one hundred and seven ten-thousandths. 



M 



1>)0 



AKITHMETIC. 



9. Multiply twenty- five ten-thousamlths by two hundred and 
seventy- five, and fourteen hundredths. 

10. Multiply thirty-four millionths l»y twenty-six ten-mil-' 
lionths. 

EXERCISE CXC. 

1. If a nnm can walk 27.25 miles in a day, how far can he 
walk in 7.;') days at the same rate? 

2. A cubic foot of water weighs 02.5 pounds. Whsit will be 
the weight of 7.25 cubic feet? 

:J. What is the profit on one million yards of cotton cloth at 
$0,007 per yard? 

4. How many solid feet are there in a pile of wood 7.3 
feet long, 5.7 feet wide, and G.5 feet high? 

5. A roller 4.15 feet in circumference makes 208.4 revolu- 
tions in passing from one end of a field to another. Find the 
length of tha field. 

G. A is .875 times as old as C, and C is 1.08 times as old 
us B. B is 25. How old is A? 

7. If one cubic inch of pure water weighs 252.458 grains 
Avoirdupois, how many grains will 1728 cubic inches, or one 
cubic foot, weigh? 

8. A and B start from the same place at the same time, and 
travel in opposite directions, A travelling at the rate of 22b 
miles per day, and B at the rate of 24.04 miles per day. How 
far apart will tliey be at the end of 12.45 days? 

9. From a cistern containing 27G5 gallons, 56.25 barrels, of 
31.5 gal. each, are drawn off. How many gallons remain? 

10. A man made a journey as follows: He travelled 7.75 
hours by rail at the rate of 22.75 miles an hour, 9.875 hours by 
stage at the rate of G.75 miles an hour, and 11.75 hours on foot 
at the rate of 4.G2 miles an hour. What was the length of the 
jourf^iy? 

V. DIVISION OF DECIMALS. 

EXERCISE CXCI. 



ivid 


e: — 






1. 


.8 by 2 


8 by .2 


2.5 by .05. 


2. 


12 bv .06 


124 by .31 


.09 by .003. 


3. 


.08 by 5 


.9 by .12 


1 by .125. 


4. 


.51 by .015 


.005 by .020 


.375 by .025. 


5. 


.008 by .04 


.12 by .0000 


.004 by 2.5. 


G. 


155 by .0025 


.00025 by 25 


25 by .30025. 


7. 


272.G3G by 6.37 


281.8585 by 3.85 


9.6188 by 3.40. 


8. 


40.1975 by 54.35 


.014274 by .001 


345.15 by .075. 


9. 


3.0 by .00000 


75 by 10000 


4.30 by 10000. 


10. 


216.32 by .00512 


5058 by .00i23 


4.110 by .0075. 



DIVISION OF DECIMALS. 



123 



iidred and 
ten-mil- 

fav can J»6 

tiat will be 

on cloth fit 

wood 7.IJ 

iA revolu- 
Find the 

iraes as old 

1.458 grains 
has, or one 

le time, and 
rate of 22| 
day. How 

1 barrels, of 
eraain? 
ivelled 7.75 
75 hours by 
Durs on foot 
ngth of the 



Simplify: — 
1. 01.04 



EXERCISE CXCII. 



by .05. 
by .003. 
by .125. 
by .025. 
by 2.5. 
by .)0625. 
by 3.46. 
by .075. 
by 10000. 
by .0075. 



3. 
4. 
5. 
G. 
7. 
8. 
9. 
10. 



(JO. 25 H- 3.125. 

.0045 -:- 225. 

5.007 — 375. 

154.28 ^ .0004. 

(28 + 11.75) -^ 1.25. 

1.2 X .7 ^ 12.5. 

100 X 4.0125 -r .004. 

(7.89 — 3.0111) ^ .015. 

12"— (.832 — .757). 

11.25 X 11.25 ^ 937.5. 



4.30 
9005 — .049 
327.6 -r 0.25 
10 — .0004 

(0.05 + 3.75 — .0048) -> .4 
.06 X .08 -H 3.2 
8 ^ .025 X .01 
12 -^ (.015025 + .040875) 
(.06 + .006 — .00000) ^ .06 
3.225 — .75 X .01 

EXERCISE CXCIII. 

1. Divide one hundred and forty-seven, and eight hundred 
and twenty-eight thousandths by nine, and seven tenths. 

2. What number must be multiplied by .0017 to give 595? 

3. By what must .7847 be divided to give 1.9 for quotient? 

4. Divide seventy-five thousand eight hundred and one by 
two thousand two hundred and ninety-seven ten-thousandths. 

5. What is the quotient when 10.9536 is divided by 1000 
times .4564? 

6. Divide three hundred and twenty-three tiiousand seven 
hundred and sixty-five by five millionths. 

7. Divide 123.45 by 10; by 10( ; by 1000; by 10000. 

8. What is the sum of the quotients of 24 by 9.6, of 42.75 
by 11.4, and of 17.85 by 4.2? 

9. The product of three numbers is 2.94294. Two of these 
are .21 and .11. Find the third number. 

10. Divide seven, and five tenths by one hundred; by one 
thousand; by ten thousand. 

EXERCISE CXCIV. 

1. If 25 men build 154.125 rods of fence in a day, how 
niueh does each man build? 

2. There are 16.5 feet in one rod, and 5280 feet in a mile. 
How many rods are there in a mile? 

3. How many bushels of clover seed at $6.25 a bushel will 
Itay for 25 barrels flour at $10.5 per barrel? 

4. A man has 324 bushels of apples which he wishes to init 
into barrels containing 2.25 bushels each. How many ) ."Is 
will be required? 

5. Tlere are 31.5 gallons in a barrel. How many barrels 
can be tilled from 2756.25 gallons? 



■i 



124 



ARITHMETIC. 



6. A speculator bonglit 78.2') acres of land for $9781.25, 
and sold it so as to gain $3.50 an acre. How much did he get 
per acre? 

7. A man bought a farm containing 64.5 acres for $177.'1.75. 
How much did he pay per acre? 

8. Twenty -five hundredths of a farm cost $3000. Find the 
cost of .9 of it. 

9. If 20.5 acres of land produce 322.875 bushels of wheat, 
what is the yield per acre? 

10. If a train goes at the rate of 24.75 miles per hour, how 
long will it be in going 128,7 miles? 

VI. REDUCTION OF DECIMALS. 



EXERCISE CXCV. 

Reduce the following decimals to vulgar fractions in 
lowest terms: — 



their 



1. 


.35 


.48 


.25 


.125. 


2. 


.625 


.75 


.375 


.64. 


3. 


.016 


.225 


.875 


.035. 


4. 


.275 


.575 


.0375 


.005. 


5. 


.068 


.024 


.175 


.0175. 


6. 


.99 


.021 


.123 


.003. 


7. 


2.75 


4.76 


7.45 


5.. 36. 


8. 


3.25 


9.75 


12.725 


5.064. 


9. 


6.0125 


16.075 


7.875 


11.625. 


10. 


5.3125 


2.1875 


7.9375 


9.6875. 



EXERCISE CXCVI. 

Reduce the following vulgar fractions to decimals: — 



1. 


i 


o 


5 
8 


8. 


t\ 


4. 


h 


5. 


A 


C. 


1 8 
TJ5 


7. 


4^\ 


8. 


i%z 


9. 


T5 


10. 


1 31 
625 



3 
11 

40 

q89 
o 1 1 



H 

SI 

40 

1 1 1 

nil 
«J4 

711 

441 

15 25 



3 

tV. 

1 3 
Iff. 

1 8 

33 

4 (J- 

2 1 1 

73 9 
'40- 

8/5. 

311 
625- 



APPLICATIONS OF PREVIOUS HULKS. 



126 



EXERCISE CXCVII. 

Expiess each of the foUowiiif? as oonipound iiuinlior.s: — 



1. 


£.79002.') 


2. 


.83125 cwt. 


3. 


.787") mi. 


4. 


.907") A. 


n. 


.9370 on. yd 


G. 


.875 bu. 


7. 


.875 gal. 


8. 


.495 da. 


9. 


.975° 


10. 


.0125 fathom. 



£.705025 
.08745 t. 
.2525 mi. 
.881 25 A. 
7.875 ed. 
2.375 bu. 
5.175 ^'al. 
7.875 wk. 
2.8475" 
17.875 rra. 

EXERCISE CXCVIIi. 



£1.809375. 
3.8975 t. 
21.30875 mi. 
13.4375 A. 
0.75 cu. yd. 
5.475 bu. 
7.75 gal. 
9.95 wk. 
17.3875°. 
7.75 gro. 



FiX])ro'ss oMoh of the following as a dofimal of its highest 
deuominatiou: — 



1. £1 10s. Od. 

2. 9 t. 17 cwt. 8 lb. 

3. 7 mi. 35 rd. 2 yd. 2 ft. 3 in. 

4. 9 A. 48 sq. rd. 

5. 7 cd. 112 cu. *t. 
0. 7 bu. 3 pk. 2 qt. 

7. 27 gal. 3 qt. 1 pt. 

8. 3da. 13hr. 24min.3Gsec. 

9. 3'^ 52' 39" 

10. 5 nn. 17 qr. 18 sheets. 



£7 13s. 7.1d. 

5 t. 14 cwt. 7i lb. 

Gmi.28rd.2yd. 1 ft. 11.04 in. 

7A.45sq.rd.8sq.yd.4.23sq.ft. 

7 en. yd. 18 cu. ft. 972 cu. in. 

5 bu. 3 pk. 4 qt. 1 pt. 

14 gal. 1 qt. 1 pt. 

2 wk. 5 da. 9 lir. 4G niin. 48 sec. 

17° 7' 25.5". 

24 grs. 9 do 55. 



VII. APPLICATIONS OF PREVIOUS RULES. 
EXERCISE CXCIX. 

1. What will l>e the cost of filling in a street GOO ft. long 
Mild (55 ft. wide, averaging 4i ft. below grade, at $.52 a cubic 
yard? 

2. Goliath of Gath was 6i cubits high. What was his 
luiglit in feet, the cubit being 1 ft. 7. 108 in.? 

3. What will be the cost of the wood that fills a shed 20 ft. 
long, 10 ft. wide, and 8 ft. high, at $4.75 a cord? 

4. Which will contain more — a box 5.5 inches long, 4 iiichcs 
\\idc, and 4.25 inches deep, or one 0.5 inches long, 4.5 inches 
\\i<t(', and 3.5 inches deep? 

5. How much gold may be obtained from a ton of quart/; 
'uck, if it yieWs .0010 of its weight in gold? 



126 



ARITHMETIC. 



G. At ()7i «'ents per eu. yd., what will be the cost of iligging 
a cellar 15.5 ft. long, 12 ft. wide, aud 5 ft. 4 in, deep? 

7. How many yards of carpeting 1 yard wide will b« required 
to cover a tloor 33.5 ft. long aud I22i ft. wide? 

8 What is the cost of slating a roof 52 ft. lU in. long, each 
side being 20 ft. wide^ at $15.25 per square, a scpiare being 

100 sq. ft.? 

9 If 1 cu ft. of water weighs 1000 oz., what will be the 
weight of the' water iu a cistern 8.5 ft. long, U ft. 3 in. wide, 
and 3 ft. 9 in. deep? 

10 At $13.60 per square, what will be the cost of tinning 
both" sides of a roof 36 ft. 6 in. in length, and each side 18 ft. 
9 in. in width, a square being 100 sq. ft.? 

EXERCISE CC. 

1. If 11.8 A. of land cost $236, what will 20.7 A, cost at 
the same rate? 

2. Find the cost of 8725 ft. of boards at $12.50 per 
thousand? 

3. A drover bought sheep at $3.37i a head, and sold them 
at $3.87i a head, and gained $37.50 by the transactions. How 
many sheep did he buy? 

4. What is the cost of 24 ewt. 87 lb. of sugar at $6.50 per 
hundredweight? 

5. The contents of a chest of tea weighing 87.5 pounds are 
made up into an equal number of 1 pound, i pound, and i 
pound packages. How many packages are there of each kind? 

6. What would 7| bales of cotton cost, each bale weighing 
537.5 pounds, at $0.11 J a pound? 

7. Boys in playing hare and hound run 3.875 miles. The 
hares drop a piece of paper every 5.5 feet on the average. 
How many pieces do they drop? 

8. A merchant sold 4 pieces of matting, each containing 
35.5 yards, at $0,375 per yard. How much money did he 
receive ? 

9. Divide $47.10 among 6 men and 11 youths, giving a youth 
0.525 of a man's share. What is each man's share? 

10, The great pyvitmid of Clieops measures 763.4 feet on eacli 
side of its base, which is square. How many acres does it 
cover? 

EXERCISE CCI. 

1. Bought land at $62.50 an acre, and sold it again at $75 
an acre, thereby making $846,875. How nuiny acres vvei'( 
bought ? 

2. If .875 of a man's age is 35 years, what will .7 of his 
age l.>e? 



APPLICATIONS OF PREVIOUS RULES. 



127 



i ve(iuued 

long, each 
tare being 

nil be the 
1 in. wide, 

of tinning 
side 18 ft. 



A. cost at 

$12.50 per 

d sold them 
tioiis. How 

at $6.50 i»ev 

pounds are 
[ound, and i 
f each kind? 
|ale weighing 

miles. The 
the average. 

Ih oontaininp; 
}oney did he 

iving a youth 

foet on each 
lucres docs it 



afi;ain at $7.> 
ly acres wert 

LiU .7 of his 



;{. If .75 of a ton of steel rails is worth $7i!, wluit is the 
value of 275.875 tons? 

4. Divide 1(5. .'1-4 into two parts, so that one i)art may be 
1.50 larfrer than the other. 

5. A ujan spent .875 of his money and has $1.29 left. How 
much had he at first? 

G. Bought G7.75 acres of land at $62.50 an acre, and hoUI 
the lot for $5081.25. Was there a gain or loss? How much was 
gained or lost on the whole, and how much an acre? 

7. Divide $133.26 between A and B so that A may have 
$18.48 cents more than B. 

8. What number is that which, being diminished by 2.75, 
the remainder, multiplied by 4.6, and the product, increased 
by 6.75, gives 70? 

9. How many cu. ft. of water will pass under a bridge every 
12 min. if the stream is 125.125 ft. wide and 4.8 ft. deep, and 
flows at the rate of 2.5 mi. per hour? 

10. Two men who are 17.82 miles apart start at the same 
time to walk towurds each other, one at the rate of 3.27 mi. 
per hr. and the other at the rate of 3.48 mi. per hr. How i 
will each walk before they meet? 

EXERCISE ecu. 

1. What is the price of 20 joists, 10 ft. long, 6 in. wide, and 
2 in. thick, at $25 per M. ? 

2. What is the cost of 576 fence boards 16 ft. long and 9 in. 
wide, at $14 per M. ? 

3. During a week the barometer stood as follows: — On 3 
days at 29.46 in., on 2 days at 30.05 in., on the other two days 
at 29.48 in. and 30.85 in. What was the average for the week? 

4. In walking 3.6 mi. a girl took 7040 steps. What was the 
average length of her step? 

5. Find the average of 2.6, 2.37, 3.025, 2.973, and 0.516. 

6. Find the G.C.M. and L.C.M. of 2.25, 3.375 and 2.8125. 

7. How many boxes 4.5 ft. by 3.25 ft. by 2.875 ft., outside 
measurement, can be stored in a room 52 ft. by 36 ft. by 345 ft. ? 

8. If a block of English oak 3i ft. long, 2 ft. l)road, and 1.75 
ft. thick, weighs 710.5 lb., find the weight of a cu. ft. of 
English oak. 

9. What will be the cost of painting the walls of a room, at 
$.30 per sq. yd. the length being 19 ft. lOi in., the breadth 16 
ft. 1* in., and the height 10.25 ft.? 

10. A merchant fails in business and his assets pay $.425 on 
the dollar. How much does a creditor receive to whom he owes 
$453,60? 



. -i 



I Tr 



128 



AKITHMKTIC. 



EXERCISE CCIII. 

1. Fiml llin sum of tlic su?n, <lilT«n'<'ii(M<, mid lu'odiid of 
seven, iiiul t\vouty-tiv«5 Imiulredths iiiul tlirco, uud eif^hty-foiii' 
ImiidiMMlths. 

'J, Find tho sum of the sum, dilferunco, jn'oduct, and two 
quotients of l.G and 4. 

I{. -.5 tiincH the sum of two nnmhers is 35.25 and one is 2.8 
more than the other. Find the numbers. 

4. Two ni<Mi toj^etlier eliopped 50.75 cords of wood and one 
cliopped 1.45 cords more than the other. How much did each 
ciiop? 

5. Two men are 120.25 miles apart. They walk straij^ht 
towards each other and when they meet one has gone 7.75 mi. 
less than the other. How far has eaeli gone? 

G. If a merehant deposits !)!;i75. 50 in a bank at onetime, ami 
$487.75 at another, how much will remain after he has with- 
drawn $17().;{7 and $340.83? 

7. Bought 1 ])arrel of flour at $8.50; 3 })ushels of corn at 
$.505 a busliel; 24.5 jmunds of sugar at 8.ic. a pound; 3 gallons 
of molasses at 37ie. a gallon; 2 pounds of tea at 624c. a 
])ound; pounds of cotfee at 35e. a pound ; 15 pouiuls of rice 
at 8c. a pound; and 4 pounds of butter at 22c a pound. What 
was the cost of the whole? 

8. A guinea is 21 shillings. Reduce 7i guineas to the 
decinuil of £10. 

9. A stick of square timbor is 17.5 in. wide by 13.5 in. 
thick. What length must be cut off to contain 7 cu. ft.? 

10. What must be the length of a plot of ground, its breadth 
being 70.23 yd., to contain 232.848 sq. rd.? 

11. Divide $302.50 among A, B, and C so that A may receive 
1.5 times us much hh the otiier two together, and B, 1.75 times 
as much as C. Find the share of each. 

12. In sinking a shaft it is found that .375 of it passes through 
earth, .075 of it tlirough shale, and the remainder through 
solid rock. The shule is 90 ft. deep. How much of the shaft 
is in the solid rock? 

13. A stick of square timber 32.5 ft. long, 2.5 ft. wide, and 
1.125 ft. thick, weighs 4387.5 pouiuls. Another stick of the same 



kind of timl)er is 21.75 ft. 



long, 



1.875 ft. wide, and 1.25 ft. 



thick. How much does <he second stick wiMgh? 

14. A piece of work can l)e done by A in 17.5 days; by B in 
22.5 days; and l»y (' in 15.75 days. If A works alone at it for 
5.5 days and is then joined by B and C, how long mus^ the 
three work together to finish the remainder? 



M 



CHAPTER VIII. 



PERCEINTAGE. 

The expression Per Cent. (L.itiii per ceiitiiin) 
nnnuia for, or hij tlic Inindnd. 

A Rate Per Cent, denotes u eerluin mmiber of 
liuiidredths, as G per cent, denotes 1 0,7 or .00; 4 per 

eent. denotes liyOr .0075. 

Tlie symbol " „ is used for the phrase per cent. 



EXERCISE CCIV. 

Express the following as hundredths: — 

1. -)% 7% 10% 1.-)% 

'2. 7i% (U% 12i% 20% 

Express the following deeimuls in percentage: — 

;{. .05 .07 .1 .17 

4. .055 .0725 .105 .125 



27%. 
50 % . 



.1725. 



Express the following — (1) iis decimals, and (2) as common 
fractions in their lowest terms: — 



O. '070 



5% 



8% 
lGf% 



# 10% 

37J% 



12.i% 

75% 



G. 1U% 

Express as hundredths and also in percentage 



20%, 

87^%. 



I 



t\ 



S. 3 



i 



i 



4 

8 . 



Express the following as fractions in their lowest terms: — 

9. 4% 40% 80% 15% :{0%. 

10. •m% Gi% Si% 5§% G2i%. 

r29 



PI 



KJO 



ARITHMETIC. 



Kiihl IIh' following: 
I. :\'/ro\'^HM 
li. 4'/f> (tf lOOiicros. 
i't^^fi <»r 'J.')!) words 
U)% of ")()() Itoys 
20% ofsUl";')!) 
I7r of 200 men. 
2)i% of $2(500 
n.'.T^'of 270yil. 

U)''r of $7.M 



;{. 

4. 

T). 
(>. 
7. 

s. 

!). 
10. 



EXERCISE CCV. 

r)%of!»!ioo 

H%of 2r)0 A. 
C)'/t' of "mO vvonlH 



100'? (if 79 



io7'> of !)<:{r>o 

2r)%or7r>0 mi. 
•i'^ of 400 yd. 
12.i% of 400 11. 
X]k'/r of 7r)0 slu'cp. 

2')7f of lOiiO mt-y. 
S7i% of lG()4yil. 



7% of !fir»oo. 

U>7 of 75 A. 

(i'V of !)00 COWH. 

10% of I'tOyiirds. 

7.')% of 00 JM-IIH. 

r^% of .1(200. 

H,^%of<)GOnu'U. 

('))}% of 4r)0co\vs. 
;57i % of r)7GI»ooks. 
22^ % of .1!720U. 



EXERCISE CCVI. 

Find thf rjitc ix'r cent, equal to t'lich of the following: — 



1 . $5 IMT !i«2r) 

2. 1 hr. per 10 lir. 

Wliat per eeut Jh: — 

3. 8 of IG? 

4. 3 ft. of GO ft.? 
i). 240 lb. of 1 ton? 
G. 24 da. of 480 da. ? 



$8 i)er !i!80 

5 lb. per 1 cwt. 



$1;') per $G0. 
$G0 per .$480. 



20nii.of 4.')0mi.? 
880 ft. of :i mi.? 
$<)G of $1920? 
5 qt. of 10 gal.1 



$.") of $40? 
7 mi. of 100 mi.? 
84 men of 1200 men? 
50 men of 80 men? 

Find the difference between the following: — 

7. 'M7o of $100 and f of $100; G0% of 200 A. and J of 20f) A. 

8. t of 80 lb. and 50 % of 80 lb. ; I of 80 gal. and 80 % of 80 gal. 

Find the sum of the following: — 

9. $40 and 5% of .$40 $100 and 7% of $100. 

10. $G0 and 50% of $G0 50 mi. and 10% of 50 mi. 

EXERCISE CCVII. 

1. A f.irmer having 1200 sheep lo.st 37% of them. How 
many did he lose? 

2. A lawyer collected $2575 for a merchant, charging 4% for 
liis services; what was his charge? 

3. A ship loaded with 1875 bales of cotton was overtaken by a 
storm, and the sailors threw overboard 12 per cent, of the 
cotton; how many bales were lost? 

4. In a warehouse 1920 boxes of tobacco were stored; the 
warehouse haviiig taken fire, 15% of the tobacco was burned. 
How many boxes were burned? 



PKRPF.NTAOK. 



VM 



f). A iniin'M inoniuc is (I'lSOO ii y«'ur, (if wliit'li \iv piiys 1)1% 
for lioiiso rent. Whiit. r«'iit iloos Ik* pay f 

(5. A iiiiiii owns 'J I'lirms. Tli«' first contuiiis .'H!0 A. iiii*l tli«' 
ikiiiiImt (tl" iicrcs in tin- second is l.'td'f of tlif ininilx-r of iicrcs 
in tin* lirst. Find the nnniltcr in tlic st'cond farm. 

7. If copjHT ort' yields {]% of pure metal, how many jto.in.'s 
of copper will lie obtained from I t. of ore* 

S. A l>on^'ht ;{*J() acres of land, and sold (ilii"/ of it. JJow 
many acres did he sell? 

!». In an orchard of 900 trees, '.V.\h% are peach trees. How 
niiiny peach trees are there in th.* orchard? 

10. A nnm havin<; 11250 bu. of wheat, sold 'Sf/r of it. How 
mnch did he sell 1 

EXERCISE CCVIII. 

I. A man has an income of .$4000; he spends {>'>% of it. 
How much does he save? 

'2. A lionse post .fOTOO and 20% of the money is ])aid at nnee. 
How much still remains unpaid? 

'A. \ man has a farm of 200 acres. He sells 40% of it in 
viliaj^e lots. How much has he left? 

4. A man bouf?ht a farm for $;{000. How much must he sell 
it for to fi;ain 12i% on his outlay? 

r>. A speculator invested !i!3r),400 in stocks and lost 168^% of 
his investment. How much had he left? 

(). A shepherd luid 5,800 sheep b>it lost 15% of them in a 
snow siorin. How many had he left? 

7. In a seliool 420 pupils are enrolled, 45% of v/hom are 
tioys. How many girls are enrolled? 

5. The population of a certain city is 18775. What will it be 
ill one year from this time if it jrains 8% ? 

i>. If 5% is deducted from a bill of $755, how much will pay 

the bill? 

10. A farmer having a flock of 1200 sheep lost 27% of them, 
Wliiir per cent, of them, and how many sheep, had he left? 

EXERCISE CCIX. 

1. A cask contained 42 gallons of vinegar, and 14 gallons 
leaked out. What per cent, was left? 

2. In an orchard of 4000 trees, 80 died. What per cent, 
if'tnained? 

;{. In a school of 50 j)upils, 10 are absent. What per cent. 
are ]»resent? 

4. A merchant bouglit shoes at $2 a pair, and sold them at 
f'> a pair. What per cent, of the cost did he gainf 



^Ul 



132 



ARITHMETIC. 



f). A mnii bouglit a hoisc for Jt^'J-lf) mikI soM liini l"<>i' $ll!)4. 
VVIiiit per cent, of llio cost tlitl lie f,';iiii.' 

(i. ir ;i niercluint houj:;lit tc:i at .")(» ct. per Ih. and sold it at 
44 ct. pw lb., wliat is his loss ]»('!• cent. .' 

7. A workman's wages arc reduced from ^lOawi-ck to fj<7..1(l. 
Find the per cent, of decrease. 

H. A collector cliarged t^2').i)2 for collecting ^',^24. What rate 
percent, did he charge? 

9. A man's income is $840 a year and his expenses .toCO. 
What per cent, of his income does he save? 

10. A and B engage in partnership. A invests ifoGOO and U 
$8400. What per cent, of the capital does each invest? 

EXERCISE CCX. 

1. The aver.age attendance in a school was 5(5; this is 80% 
of the nnmher enrolled. How many were enrolled? 

2. A bookkeeper spends ^WO per year, which is 24% of his 
salary. Required his salary. 

3. I have bought two ]»uilding lots. For the one I paid $.300, 
which was GO per cent, of what I paid for the other. What 
did I pay for the latter ? 

4. A young farmer owns J520 acres of land, which is 40% of 
the land his father owns. How mucli has the father* 

5. A man had 24 sheep killed ])y dogs, which was 5^% of 
his flock. How many siieep had he at lii'st? 

C. A gentlennm pays $49;") for the rent of a hon^;e, which is 
at the rate of 11 per cent, of the vahie of the house. What is 
the value of the house? 

7. A schoolboy in one week reiid 450 lines of Latin, which 
was 75% of the number in tiie book. How many lines had he 
still to read? 

8. A clerk spent 00% of his salary for board, 20% of it for 
clothes, 11% for books, and saved $117. What was his salary? 

9. A wool grower sold 3150 head of sheep, and had 30% of 
his original flock left. How many sheep had he at first? 

10. The number of pnpils belonging to a certain school is 48(5, 
which is 8% more than belonged a year ago. How many 
belonged to the school a year ago? 

EXERCISE CCXI. 

1. A grain dealer had 7000 busliels of grain; 17% was oats, 
30% wheat, and the rest l»arley. How much barley had he? 

2. A man bought a horse for $85 and sold him foi' $90.10. 
What per cent, did he gain? 



PERCENTAGE. 



133 



:?. Increase $450 by H% of itself, and decrease $450 l)y S'fr 
(>r ilselt', and find the difference between tlie I'esults. 

4. Find tliu dill'ereuco between 40 ^fc of $12200 and (JO'r of 
$ir)(H). 

5. A farm contains IJilO acres; 15% of it cost $'J<S pei- acre, 
2i)'''r' cost $;{5 per acre, and tlie rest $40 per acre. \Vliat was 
the total cost? 

G. A f?rocer sells 128% more j^ranulated than loaf su^ar. Ho 
sells 38275 lb. of loaf sugar in the year. How much granulated 
sugar does he sell in a year? 

7. A music dealer bought ?> pianos at $250 each. He sold 
one at a gain of 'AQ7o, another at a gain of 40%, and the thir<i 
at a loss of 20%. What was his net gain? 

8. A drover sold cows and sheep for $9180. Ho received for 
his sh"ep 70% of what he got for his cows. What did he get 
for the cows? 

i). A young man having received a fortune deposited 80% of 
it in a bank. He afterwards drew 20% of his deposit, and then 
had $57(50 in the bank. What was his entire fortune? 

10. I sold my farm for $5000 and made 25%. What per cent. 
should I have gained, or lost, if I had sold it for $3500 1 

EXERCISE CCXII. 

1. How many rods are there in 8i% of 121 miles? 

2, What ^•um of money, increased by 8]t% of itself, will 
ii mount to $403? 

',',. What is the quantity 71% of which is 12 ounces? 

4. A train which runs 45 miles per hour has its rate increased 
by G;i%. How far will it then run per hour? 

5. A library consists of English and classical books. The 
imniber of English books is 2135, which is 7Gi% of the whole 
niinilier of books. How many books does the library contain? 

(). In a r(\giment of 9G0 men of English, Scotch, and Irish 
(liscent, 40% of the whole are Irish, and3G8^%are Scotch. How 
ninny are of English descent? 

7. The sum of two numbers is 3901 and one of them is 71% 
more than the other. Find the numbers. 

S. A nuin owning 75% of a foundry sold 40% of his share to 
"lie man and 33^% of the foundry to another. What per cent. 
<it' llii' foundry did he still own? 

!). Tlif population of a city in 1891 was 15048, being 41% 
I'loie tnan in 1881. What would have been the population in 
I'^Ol, if there had been a decrease of 4i%? 

10. If water expands 10% when it becomes ice, by what per 
cent, does ice contract when it b(;comi'S Wiiter? 



' ';! 



CHAPTER IX. 



APPLICATIONS OF PERCENTAGE. 

I. TRADE DISCOUNT. 

,. Discount is a sum deducted from the face of a 
bill, debt or note. 

Trade or Commercial Discount is a sum deduc^ted 
from the catalogue or list i)rices of goods. 

The terms Catalogue Price, List Price, Gross 

Price and Invoice Price all denote the same thing, 
viz., the price entered in the catalogue of the goods. 

The Net Price is the List Price diminished by the 
discount. 

An Invoice is a bill of goods purchased at one 
time. 

EXERCISE CCXIII. 

1. Find the discount off the following bills: — 
Invoice price $i')Q, discount 2')%. 
Invoice price $570, discount 37i % . 

2. Find the net price of goods bought as follows: — 
Invoice i)rice $'SG'), discount off 20%. 

Invoice price $756, discount off 33i%. 

3. The discount off a bill is $27 ; the rate of discount is 25%. 
Find the bill. 

4. The rate of discount is l(}i% and the discount is $17.50. 
Find the list price of the goods. 

5. The discount off a bill of goads is $45; the rate of dis- 
count is 20%. Find the net price of the goods. 

6. The rate of discount being 33i% and the discount being 
$75, find the net price of the goods. 

7. Find the rate of discount on goods bought as follows: — 
Invoice price $;)G0, discount allowed $1(!.20. 

Invoice price $420, discount allowed $157.50. 

8. Tlu^ net price of goods is $270. The rate of discount 
being 25%, lind the list price. 

i;i4 



TRADE DISCOUNT. 



135 



is(h1 at one 



tt> of discount 



9. A doalor paid fpG20 for goods at 22^% off. Find tlio list 
]»ri('(' of the goods. 

10. I am eliarged $2.r)0 for a book, wliicli the bool\seller says 
is '.iVI^'/o less tliau it cost liim. Find tlie cost. 

EXERCISE .CCXIV. 

1. Find tlio net price of goods bouglit as follows: — 

Invoice price $^75, discount off 20% and 10%. 
Invoice price $800, discount off 25% and 10%. 
Invoice price $800, discount off 20%, 10% and r)%. 
Invoice price $1640, discount off 25%, 10% and 5%. 

2. What is the net cost to the purchaser of hardware 
invoiced at $815 and subject to a discount of 20%, 10% and 5% ? 

15. A's list price for pocket-knives is $9 per dozen, 20% anil 
')% off. B's list price is $9.50 per dozen, 25% and 10% off. 
How much will be saved by ordering 24 dozen knives from B 
rjitlier than from A? 

4. At what price must goods l)e marked to sell for $2.72 
after allowing 15% discount? 

5. At what price are goods listed that sell for $18 after 
allowing 20 and 10 off? 

f). If goods cost $3.60, what must be the invoice price to 
allow discounts of 25%, 20% and 10%? 

7. At what price must goods which cost $216 be listed to 
give 25% gain after allowing 25, 20 and 10 oft'? 

S, At what price must goods which cost .$1.52 be listed to 
f.ave 121% gain after deducting discounts of 20%, 10% and 5%? 

9. What single discount is equivalent to a discount of 25% 

ami 10%? 

10. What single discount is equivalent to 25%, 20% and 
10% off? 

tXERCISE CCXV. 

1 . What is the difference on a bill of $425 between a 
discount of 50% and a discount of 30% and 20%? 

2. A bookseller wishes to mark a book wliich cost $2.00 that 
he may allow a discount of 25% and still make a profit of 20%. 
What must be the marked i)rice? 

.'{. What direct discount is equivalent to a discount of 20% 

and 10%? 

4. A bookseller buys at a discount of 20%, 10% and 5% off, 
and sells at list prices. What per cent, profit does he make? 

5. The selling price of an article was $25 when the rate of 
^'aiii was 25%. Find its cost pricef 

• i. It' $1.40 is gained by selling goods at 25% altove cost, 
liiid what selling price would make t)u^ rate of gain 35%. 



i. 'J 



136 



ARITHMETIC. 



7. An invoioo wns $fiK), trsulc dlsooujit 20 ami f) off. Find 
tli(^ cost ol' tlic j;()»>«ls. 

S. A dciilci' Ixtu^lii !i l>()<»k, list prico $1 .00, iit n discount of 
2i)'/tJ, itiid iit'terwiii'ds sells tlio book jit $1.00. VVh.'it ]>('i' cent, 
docs lie j^iiin? 

9. What is tlic not amount of a bill for $720, discounts 
being 2'), 10 and ") off? 

10. A man jmrchasos goods, list prico $080, discounts being 
'S:ik%, Vl}.% and I07r. Find llic not amount of the bill; also, 
a single discount e(iuivalent to these three. 

II. PROFIT AND LOSS. 

Profit and Loss, as a ooinmcrci.'il toi-m, donotes 
the ^i\u\ or loss ill business tniusac^tioiis. 

Profit is tlie amount l)y wliieli the sellin<^ pi'iee 
exceeds the cost price. 

Loss is the amount by wliicli tlie selling; price falls 
short of the cost price. 

The Rate of profit or loss is usually expressed as 
a certain i)erceutage of the cost pric(\ 

EXERCISE CCXVI. 

1. Find the i)rofit or the loss on the following: — 

Cost $0, selling i)rice $8; cost $15, selling price $2^. 
Cost $115, soiling price $113.50; cost $75.50, selling price, 

$77. 

2. Find the gain or the loss per cent, on the following: — 

Cost $G, selling price $8; cost $80, selling price $125. 
Cost $7.50, selling price $9; cost $100, selling price $95. 

3. Find the profit or the loss in the following: — 

Cost $100, gain 10"^ ; cost $500, loss 8%. 
Cost $G5, gain 8% ; cost $450, gain 33^%. 

4. Find the selling price iu the following:- - 

Cost $40, gain 7i% ; cost $80., loss 6i%. 
Cost $120, loss 15%; cost $75, gain 33^*^. 

Find the cost price iu the following: — 

8elling price $110, gain \0% ; selling price $210, gain 5%. 
Selling price $40, loss 33i% ; selling price $84, gain l(Sl7o . 
Helling price $05, gain 8;^% ; selling price $72, loss 25%. 
Find the cost in the folloAvinji:: — 



5. 



Profit $3, gaiTi 10%; profit $8, gain 5%, 
Jjoss $5, loss 20% ; loss $50, loss 8%. 



PROFIT AND LOSS. 



la? 



r» off. Find 

discount of 
lilt pel' et'iit. 

:(), discovmtS 

counts behif? 
Hi bill; also, 

■m, (lonotes 

(T price falls 
expressed us 



X)Y 



ice $2r>. 



selling ])net', 

bllowing:— 
price $125. 
ug price $1)5. 



I<210, gain 5^c. 

U, gainlG^^o. 

r2, loss 25':^. 



I':'! 

I 
■I 



7. A iloek of slieep increases from 88 to 110 in a year. What 
is tlie gain per cent.? 

H. Bought books for $420, and sold them for $357. Find 
my loss per cent. 

[). If Mr. Jones buys a farm for $3875, and sells it for $3720, 
wiuit per cent, does he losef 

10. If I buy i)aper at $3.50 a ream, and sell it at 25c. a 
(juire, what is the gain per cent.? 

EXERCISE CCXVil. 

1. A merchant sold cloth which cost $1.75 per yard so as to 
gain H%. Find the selling iirice. 

2. Goods which cost $735 ,vere sold at 20% gain. Find the 
selling price. 

3. At what price must goods be sold to lose 12%, if they 
cost $-13.50. 

4. Bought a house for $3500, expended $750 in repairing it, 
iuitl then sold it so as to lose 15% on the whole cost. What 
did I receive for it? 

5. Sold goods at a loss of 20%, an actual loss of $59.50. 
What was the selling price? 

0. Find the selling price of goods by which there is a loss of 
2'r and an actual loss of $55.50. 

7. A farmer bought 35 A. of land for $1750, and sold it at 
20% gain. How much did he get per acre? 

8. Mr. Smith bought a house for $5000 and spent $400 more 
for repairs. He sold it at 15% gain on the whole cost. What 
was his profit? 

9. A quantity of wheat whieli cost 72 ct. per bu. Wfis sold 
lit a loss of 20%; the total loss was $1290. How many 
Imshels were there? 

10, A grocer sold potatoes for $10.10, gaining 15%. If he 
had sold them for $18.20, how much would he have made above 
the cost price? 

EXERCISE CCXVIII. 

1. A set of jewelry was sold for $140 at a gain of 25%. 
What did the set cost? 

2. A ]>roduco deahn- sold a sliipinciit of wlu^it at a loss of 
'^'r", realizing as the net proceeds $S170. What was the cost!? 

•>. A miM'cliant sold rye at 15% gain. His profit was $2(5.70. 
How much did he receive for the ry»!? 

4. A man gained 24% by selling land for $lit5 more than lu) 
jniid for it, liow much Uiti he receive for the laud? 



4 



138 



AHITHMKTIC. 



'). TiMi COWS were sold foi- $()!)(), at a ^i\\u of 15^. Fov how 
mticli per lufiul, oil tlie iivernge, should tliey have Im'cii sod to 

6. A merchant lost 25'^ by selling flour at $0 i)er barrel. 
If he had sold it at $9 per barrel, what would have been tlie 
gain per cent. ? 

7. 1 sold a liorse for $240 and lost 20%. For what should I 
have sold him to have gained 10%? 

8. A building lot was sold for $1840, at an advance of 15% on 
its cost. What would have }»een the gain per cent, if it had 
been sold for $2240? 

D. I bought a lot of goods for 1;")% below market price, and 
sold them for 15% above market i)rice. What per cent, did I 
clear? 

10. Sold my carriage at 30 per cent, gain, and with the 
money bought another, which I sold for $182, and lost 12i per 
cent. How much did each carriage cost me? 

III. COMMISSIOIN. 

Cominission is the compensation received by an 
agent for transacting (pertain kinds of business. It is 
generallj^ reckoned at a rate per cent, on the money 
involved. 

The agent is variously known as Commission 
Merchant, Broi<er, Collector, Factor, &c. 

In selling, the Commission is reckoned oh the 
money received by the agent. 

In buying, the Commission is reckoned on the 
money paid by the agent. 



EXERCISE CCXIX. 

Find the commission on the following: — 

1. $450 at 4% $300 at 2*% 
$1200 at 4A% $5700 at 3g % 

Find the commission on the followiiig: — 

2. $2500 at i% $044^ at i% 
$3000 at li% $4800 a" 5% 

3. An agent received a consignmeui of flour, .vliich ho sold 
for $3750. What was his commission at H%? 

4. My agent in Chicago has purcliased whert for me to the 
amount of $7728. What is his commission at 14 per cent. ? 



$575 at 4J%. 
$1875 at 4^%. 

$3000 at i%. 

$8400 at i%. 



)r what should I 



)ned on the 



COSIMISSION. 

i;. Find the rate of oo '^**^ ^^^ i^e cVjJ,; *^, ^"^' ^'^eeived 

,-, ,^: ;^" '-^Sent sold 'no vd'^nJ''^^ '^''''^- 

l"^' "Ot proceeds flic™ ""vli;- "f/^' "' 25 at. pe,. Ih „. . 

4 Find t, '""'=™"»'»sionf ^ *° "«' <>«■■'«■ *2334.5o: 
.."-io,, U2i'i STJS: """•"' ^"-i' -ere sold when the com 

EXtRCISE CCXXI. 




m 



140 



AKITIIMETIC. 



12. A Hour nn'ivluiiit rcniltM to lils aj^riit in ('hiciif^o $;J71)(i, for 
tlu' imrcliiisc of j^ijiiu, iiftc^r dediu'tiiij^ the eomiiiissioii at 4"r , 
How imu'li will tliu Hf^«Mit exptMul for his einployci-, and what will 
l>o the coininiHsionlf 

J{. A miller sent liis Montreal apont $9270 to }>e invested in 
flour, after deductinj* liis eonnnission of ii'/r . What was the 
conuuission? 

4. Hent to my apjent in Boston .$:?8Lir) to l)o invested in 
French prints at $.15 per yard, after deducting? his commission 
of '2 % . How many yards shall I receive ? 

5. An agent received $2040 to be invested in sugar at .'Ji ct. 
l>er pound, after deducting his commission of 2%. How many 
pounds did he buy? 

(5. What weight of wool at 40 et. a lb. can he bought for 
$1722 by my agent, after deducting his commission of 5% ? 

7. I sent $2G7H to my agent to invest in calico at 5 ct. per 
yard after deducting his commission at 3%. How many yards 
did I receive? 

8. A si)eculator received $:{290, as the net jiroceeds of a sale, 
after allowing a commission of 6%. What was the value of the 
property? 

9. A hiwyer collected 75% of a debt of $1200, and charged 
5% commission on the sura collected. What did the creditor 
receive ? 

10. I sent a quantity of dry goods into the country to be sold 
at auction, on commission of v% . What amount of goods must 
be sold that my agent may buy produce with the net proceeds, 
to the value of $3500, after retaining his purchase commission 
of 4%1 

IV. IINSURAINCE. 

Insurance is n contract wliercby one jmrty, in 
consideration of a certain snm, g-uarantees another 
party aj?ainst loss by fire or accident. 

The Premium is the sum paid for the insurance. 
It is always a certain percentage of the sum insured. 

The Policy is the written contract, j?iven by the 
insurer to the insured. 

EXERCISE CCXKII. 

Find the premium on the following: — 

1. $ 850 at 1% $1200 at f% $ 900 at 1%. 

$1500 at ?.% $3200 at f% 

ijiOOOO ?it .70% ijio^OO ut .80% 



T-. ("-i 



$8000 at .75 
$G(iOO at .()Oii% 



Vf) , 



INSURANCE. 



141 



;j7<U), for 
1 at 4'^. 
what will 

^.est('«l in 
was tlio 

vestcfl in 
)unnissi(m 

V at 3i <'t- 
How many 

l)0uslit for 
f 5%? 
vt 5 et. poi" 
many yavdsJ 

Is of a sale, 
ralue of the 

md charged 
the creditor 
1 

to he sold 
jroods must 
, proceeds, 
commission 



party, in 
another 



insnrance. 
11 iiisnred. 
/en by the 



)0 at S '^r . 
«)() at .75 % . 
loo at .U0^%. 



2. Kind tlie cost of insurin<? ]>ropt'rty wortli linOOO at },% , 
if i of the vahu' is insured. 

;{. A insured his house for 1 y(Mir for $8000 at the rate of 
i%, and his furniture for sfHOOO at tlie rate of 1%. W'iuit was 
the total |>reniiuni? 

4. A cotton factory worth $25000, and tlie machinery and 
stock wortli ifltoOOO, are insured for -i their value, at i%. What 
is the premium? 

5. A cotton factory and its machinery, valued at $75000, are 
insured at ,-"; per cent. What is the yearly premiuT»'? and if it 
should be destroyed, what loss would the insurance company 
sustain? 

G. What will be the cost of insuring 4000 bu. of wheat worth 
75 ct. a bushel, at i% ? 

7. The lioyal Insurance Company took a risk of $16000, for 
a premium of $280. What was the rate of insurance? 

8. A company charges $20.25 for $2700 insurance. What is 
the rate charged? 

9. I have goods worth $37560, which I insure for i of their 
value, paying $262.92. What is the rate? 

10. The sum of $280 was i»aid for the insurance at i of its . 
value of a storehouse worth $40000. What was the rate 
ciiarged? 

EXERCISE CCXXIII. 

1. At 1^%, how much insurance can be effected upon a store 
for $128? 

2. For what sum was a house insured, if the premium paid 
was $24 and the rate of insurance ^ % ? 

3. A company charged $225 for insuring property at l^% 
premium. What was the value of the policy? 

4. A man pays $87.50 for the insurance of house at |%, and 
$50 for the insurance of furniture at li%. If both are 
destroyed by fire, hosv much will he receive? 

5. Find the cost of insuring ^ of the value of 6000 bbl. of 
Hour worth $9.60 a barrel, the insurance being reckoned at |%. 

6. A vessel and cargo, valued at $35000, are insured at f per 
cent. Now, Tf this vessel should be destroyed, what will be the 
actual loss to the insurance company? 

7. I insure a factory for one year, at -ro%, for i of its value. 
'J'lie premium is $270. How much is the factory worth? 

8. I buy a house for $8000, and get it insured for f of its 
value, at S-%. If the house is burned, what is my loss? What 
is the loss of the insurers? 






142 



AUITIIMKTIC. 



9. All insiinmco compiiiiy, Iiaviii;^ taken ii i-isk of $20000 nt 
1%, rciiiHured ♦SdOO ut ^'.o with iiiiotlici' (•((inpaiiy, :iihl .f(J()(l() 
at 'i% with iiiKtthi-r. it' no loss ofcms, wimt docs tlic first 
company ^'i'" ' 

10, A lmii«liiif< wortii $1,10000 is insured in three eonipjiiiies; 
in tlie lirst for ^UwOOO, in tlie second for $;jr>000, iind in the tiiird 
for $40000. For what is eaeii company liable in case of damaj,'e 
to the extent of $10000 f 

V. TAXES. 

A Tax is ti sum of niouey levied on the i)ersoii, 
property or income of iudividiuils for piiblie i)in'poses. 

Taxes on property or income tire nn^koiied at Ji 
certain rate per cent, of tlie assessed vtiliie of the 
property or income, or at Ji certtiin number of mills 
on the dollar. 

Taxes are of two kinds: — Direct Taxes jind 
Indirect Taxes. 

Direct Taxes are levied by the Province, Town- 
ship, Town, or City. 

Indirect Taxes are called Duties and nre levied by 
the Dominion. 

Customs Duties are levied on articles imported 
from other countries. 

Excise is a duty on articles manufac^tured in tlie 
country itself. 

Duties are either Ad Valorem or Specific. 

An Ad Valorem Duty is reckoned at a certain rate 
l)er cent, of the cost of the goods in the country from 
which they have been imported. 

A Specific Duty is a fixed sum levied on the 
quantity of goods without regard to their y.ost. 

EXERCISE CCXXIV. 

1. Find the tax on $4500 at 12 mills on the dollar. 

12. Find the tax on property assessed at $7r)00 at 2%. 

3. Tlie law exempts $700 of income from being taxed. 
What does A, whose salary is $12000, pay when the rate is 15 
mills on the dollar? 



TAXES. 



143 



lilt' thinl 



^ person, 
purposes. 

)1UhI «it Jl 

ue ot tlio 
f of luiUt^ 

axes and 

ice, Towii- 
e levied by 
s imported 
Hved ill tlie 

fic. 

'ertain rate 
luutry f I'om 

ied ou tlie 
Icost. 



liar. 
lat 2%. 

Ibeing taxed. 
Ihe rate is 1^^ 



4. Kind tlio duty (mi fiiriiitiiir, the invoice prifo ol' which is 
$l7.")n, :it :i()%. 

.'». A hMi'dwan* nicnditiiit iniports «'uth'ry to thi- vahic of 
$1:17'). What duty must he pay at :U)'i i 

(». What is the duty (»n a case of sardines couXaiMiu^ 410 
boxes at 5 et. per box? 

7. Kind the duty on KOO Ih. of snfjjar oaiuly worth r» et. i)er 
Ih., the speeifie duty lieinj,' i et. i>er Ih. and the ad valon-iu 
duty [iiS % . 

H. What is the rate of taxation, wlien property assessed for 
$'J7r)() pays $:{H.r)() tax? 

9. Wiuit is the rate of taxation, wlien .+ 1120 is the tax upon 
$U<)00? 

10. Find the rate of taxation, wlien $'J8 is the tax on $1(500. 

EXERCISE CC\XV. 

1. Wliat is the assessed "■itlue of pro])ertv on whieh the tax 
is $:U.r)0 at lli mills on the dollar? 

2. The rate is 16J mills on the dollar. A's income tax is 
$29.70. What is A's income, $700 of it being exempt? 

15. The expense of buildinj? a public bridfjje was $17(58, which 
was defrayed by a tax upon the proi)erty of th.^ town. Tiie 
rate of taxation was 3i mills on one dollar. What was the 
valuation of the property? 

4. The duty upon stockings is 35%. What is the invoice 
cost of stockings upon which $35.56 duty is paid? 

5. What is the invoice cost of goods upon which .$025 duty 
is paid, if the duty is reckoned at 25%? 

6. If a tax of $12350 is to be raised, and the collector 
receives 5% for collecting the taxes, what sum must be levied? 

7. What sura must be assessed in order to raise a net amount 
of $.5501.50, and pay the commission for collecting at 2%? 

8. In a certain section a scho ilhouse is to be built at an 
expense of $9600, to be defrayed by a tax upon property valued 
at $153(5000. What shall be the rate of taxation? 

9. In a school section, a tax of $375 is levied for the 
sn])port of schools. What is A's tax on a valuation of $4000, 
the entire valuation of the district being $00000? 

10. A town is to be taxed $23200 on an assessed valuation of 
$2900000. What is A's tax ou au assessed valuation of 
$14275? 



[rl 



"l^Bi 



144 



AltlTllMRTlC. 



VI. SIMPLE INTEREST. 

Interest is imuicv p<'ii<l tor llic iisr of iiHUH-y. 

Ttie Principal is the smn lor Ihr iis«> of wliicii 
interest is paid. 

The Amount is tlic sum of tlii> Principjil mikI 
Interest. 

The Rate of Interest is tlie rate per cent, of 
tlie principal allowed for its use for one year. 

Interest, is either Simple or Compound. 

Simple Interest is tlie sum <'liarji:ed foi* the use 
of the IM'ineipal oidy. 

Compound Interest is intei*est re(!koued on the 
principal and mIso on tlu' aeerue(l interest as it falls 
dut^ from period to period. 

EXERCISE CCXXVI. 

1. Find till! iiitert'st on the following: — 

$m) at 6% for I yr. if^'JOO at 4% for 1 yr. 

$ir)() iit 4% for () nio. ^'AH) at ;')% for ;{ mo. 

IIJ.'jU iit (5% for 4 mo. ^■i')0 ut 4% for (J mo. 

t>. What will l>e the interest on $;U)0 for 5 mo. at G%? 

15. Tf !fi;5r)0() Itorrowed money is re]>aid in 7'A (lays, how much 
interest should he paid, money being worth HVr ^ 

4. Find the simple interest on $4800 for 1 yr. 5 mo. at !S% . 

n. Find the interest on ^'2i){) for G mo. at 8% . 

(I. What is the interest on i^HO'.i for J}') days at tho rate of 7% 
per annum? 

7. Find tlie interest on $S7() for 10") days at G%. 

8. Find the interest on .$17512 from June '.i to Oct. IG at (>% . 

9. What interest is due on $584 from March 7 to August li) 
at 5%.? 

10. Find the interest on $131.40 from Sept. 5, 1899, to March 
7, 1900, at 7'^r. 

EXERCISE CCXXVII. 

Find the amount of the following: — 

Principal, Kate. Time. 

1. $ 8712 G % 10 mo. 

2. $ 9412 G % 15 mo. 

3. $]S9(i 7 % 17 mo. 



8IM1'I-K INTKKKST. 



115 



[Mil i>»»(l 
.('lit. of 

the ^^^^ 

i\ (n\ the 
IS it fulls 



)r W mo. 
)v () nio. 

, how mxich 

mo . at T) /f • 

rate of l^c 



[t. IG Jit (•)%• 

Ito August 19 

[99, to March 



Ime. 
mo. 
mo. 
mo. 



4. 

n. 
0. 
7. 

8. 



$511 

$408.80 

$17'J8 

$(iO 



7 ^ .liiiH- 'J to Off. 1:.. 

5 ^r April I, 1851!), to .hiii. 1^1, liMlO. 

7 rf .hily ;{, 18!»!», t(. F«l.. !{, 1!)00. 
(5K^ 1 yr. 'J 1110. 

8 'ir 1 VI'. '.] nu). 



<>. J. Ay<T li:iM I). How's note Cor !f!l8'jr.. «liit«'(l Dec. L'S), 
181M); \lmt in the iimoiint Oct. !», I'XIO, iit (J per cent.* 

10. I*. K'vc's his iiot«', Aii^rnst (itii, IS!)!>, lor .flOiC), interest iifc 
7^'r; he piiys tlic note iiiid interest May 17lh, I'.MMl, how niucli 
did he pav? 

EXERCIS^E CCXXVIII. 

What is th(» rate jtei' cent, wiieii 

1. The interest on $4'yO for 1 y. is ^'27'! 

12. The interest on .f!>.")0 for 1() nio. is $88ji ? 

;{. Tiie interest on !f!:i80 for 1 yr. 4 nio. is $'J2.80? 

4. The interest on Mil for 75 da. is ^^71 

5. $480 amounts to l-llO in 1 yr. f 

(5. .$()00 amounts to $()i;{.75 in 5 nio.f 

7. $ll(i8 amounts to .$in»5.()0 in II.") da.? 

8. The amount of $1022 for 2(50 days is $10.')4.7r.? 

9. The interest on $80:{ from June 10 to Dec. 2 is $2;{.K»? 
10. The amount of $87(3 from April 10 to Dee. 1 is $!)0!j.84? 

EXERCISE CCXXIX. 

Find the time in wliich 

1. Tiie interest on .$45(5 at (]% will be $27.:}(i. 

2. The interest on $540 at 4J% will be .$:{(5.45. 
:i. The interest on $840 at G% will l»e $(5:5.45. 

4. The interest on $1.')00 at 7% will lie $4:5.75. 

5. The amount of $1(500 at 5i% will be $l()(i(5. 
G. The amount of $750 at 7% will lie $785. 

7. The amount of $2920 at M% will be $2901.40. 

8. Tlie interest is ill,, of the jirincipal at 4.1 Cir. 

9. The amount of $7:53.(55 will be $751.74 at 0^. 

10. A j.rincipal of $i:514, loaned May 12, 1S99, at 5.]^^;, will 
amount to $1328.85. 

EXERCISE CCXXX. 

Find the prineii)al that 

1. I'roduces $24.:;0 interest in 1 yr. at 4.?'^. 

2. i'rodiices $;;!». :;o interest in I yr. mo. at 4%. 
:5. Produces $21.25 interest in G mo. at 5%. 



m 



-" I IV 



146 ARITHMETIC. 

4. Produces $22.50 interest in 1 yr. ;it tii%. 

f). Produces $.56 interest in 1 yr. 4 mo. at ^%. 

6. Produces $22.50 interest in 8 mo. at 4i%. 

7. Produces $12.96 inte-est in 90 da. at 6%. 

8. Produces $56.25 interest in 225 da. at o%. 

9. Produces $6.48 interest at 6% from June 5 to Dec. 2. 
10. Produces $lu5 interest at 7i% from April 15 to Oct. 7. 

EXERCISE CCXXXI. 

Find the pvineipal that 

1. Amouiits to $265 in 1 yr. at 0%. 

2. Aruounts to $496 in 1 yr. 4 mo. at 5%. 
Amounts to $596.70 in 1 yr. 6 mo. at 7%. 
Amounts to $595.40 in 8 mo. ut 6%. 
Amounts to $li{91.50 in 1 yr. 1 mo. at 5%. 
Amounts to $424.83 in 9 mo. at 5i%. 
Amounts to $796| in 1 yr. '.i mo. at 5%. 
Amounts to $1782.60 in 85 da. at 7i%. 

9. Amcant> to $3735.50 from June 3 to Dee. 10 at 4i%. 
10 Amounts to $3338.50 from April 17 to Dec. 3 at 6i%. 



3. 
4. 
5. 
6. 
7. 
8. 



Vli. COMPOUND INTEREST. 

EXERCISE CCXXXII. 

Find the compound interest and the amount of 

1 . $800 at 5 ^ , compounded annually, for 3 yr. 

2. $2500 at G% , com])ounded annually, for 3 yr. 

3. $1250 at 4'~r, compounded lialf-yearly, for 18 mo. 

4. $8000 at '}9h, compounded iinnually, for 4 yr. 

5. $10000 at 12%, comi)Ounded quarterly, for 1 yr. 

Find the jcineipal which will ])roduce 

6. $648.90 interest at 6%,' compounded annually, for 2 yr. 

7. $151.32 interest at 5%, compounded annually, 'or 3 yr. 

8. $927.27 interest at 6'!^: , j-ompounded half-yearly, for 18 mo. 

9. How much j^i'cater is the cf)mpound inicrcst on $1200 foi' 
2 yr. Jit 6'^f ,. conipounded yeiirly, tlian the sini])le interest for 
the same tinu'? 

10. ilov niiich juri'ciitcr is the coinpouinl interest on $SO00 for 
2 yr. ill, lO'/i, coiniiouiidctl half-yc;ti'Iy, thiin the simple interest 
for the same time .' 



BANK DISCOUNT. 



147 



Dec. 2. 
to Oct. 7. 



at 4*^0. 
3 at 6i%. 



18 mo. 
a*. 



fov 2 yv. 

'or '^ yv. 
irly, forlHi'if»- 
u ;„ $1200 for 
ilo interest lor 

it on i^«'"^'^ *''^'; 

V,uil»»« interest 



Vm. BANK DISCOUNT. 

Bank Discount is the charge made by a bank for 
advaiudng the payment of a note not due. It is equal 
to tlie simple interest on the face value of the note, 
for the time between the date of buying the note and 
iho. time it falls due. The banker deducts the dis- 
count from the face value of the note and pays the 
balance, which is called the Proceeds of the Note. 

A Promissory Note is a promise in writing, made 
by one person to another, to pay on demand, or at a 
designated time, a specified sum of money. 

The Maker of the Note is the person who signs 
the note. 

The Payee is the person to whom, or to whose 
order, the note is made payable. 

The Holder is the person who has legal possession 
of the note. 

The Face of the Note is the sum for which it is given. 

The Maturity of a note is the time at which it 
becomes legally due. 

Days of Grace are three days whi(^h elapse from the 
time specified in tlu^ note for its payment until it is 
legally due. The time that elaj^es between the day of 
discounting the note and the day of maturity, called 
the term of discount, includes the days of grace. 

A Negotiable Note is one which is made payable 
1<) bearer, or to the order. of the payee. It can be 
sold to another. If payable to bearer, no endorsement 
is necessary. If i)ayable to the order of the payee, it 
must be endorsed by him before being disi)osed of. 

The Payee endorses the note by writing his name 
across the back of the note. 



PROMISSORY NOTE. 



$;{oo. 



Toronto, Uay 18, 1900. 



Sixty (lays aftoi' date I promise to ])ay Xicliolas Walsli, 



or 



(irdcf, iJilJOO, value received. 



John Biuck. 



Tliere arc three parties to a draft: — 
The Drawer, the person who makes the di-ai't, — 
the person who ordei'S the m(Mi(^y to be paid. 



1- - 



148 



ARITHMETIC. 



The Payee, the person in wliose favor it is drawn. 
The Drawee, the person on whom it is (h'Hwn. 
If the draft is ae(;ei)ted, the Drawee l)eeoines the 
Acceptor. 

DRAFT. 

$100. Toronto, Jan. ]5tli, 1900. 

Ten (liiyH aftoi- sif^ht i)ay to the order of James Mills the sum 
of one hundred dollars for value received, and charj^e the same 
to the amount of 

Thomas Lovkll. 
To John Smith, Esq., 

Merchani;, London. 

In the above draft, Thomas Lovell is the drawer; John 
Smith, Esq., is the drawee; and James Mills is the payee^ 

EXERCISE CCXXXill. 

1. Draw a note due in 3 months with interest at 0% per 
ann., (1) payable to John Smith or bearer, (2) payable to John 
Smith or order, (3) payable to John Smith. 

2. Draw a note payable on demand. 

3. Write a note for the following: — Face $250; time 3 mo.; 
interest 4% per ann.; maker James Jones; payee Thomas 
Harris. 

4. Write a note payable at a bank for the following: — Face 
$.")(); time 3 mo.; interest 5% per ann.; maker Thomas Jones, 
payee Wm. Meadows. 

5. W^iat is the cost of a sight draft in Montreal for $750, at 
i% premium? 

6. What is the face of a draft which can be purchased for 
$1500, at 1 % premium? 

7. Suppose that Porter & Jones of Montreal, owe you $350. 
Write out a sight draft on them for that sum in favor of the 
Bank of Commerce. 

EXERCISE CCXXXIV. 

Find (1) the day of maturity, (2) the term of discount, and 
(3) the proceeds of the following: — 

Date of Note. Face of Note. 

$657 

$803 

$182.50 

$5021 

$511 

$) 1(5.80 



1. 


April 


17, 


1899 


2. 


Oct. 


20, 


1899 


3. 


Sept. 


15, 


1899 


4. 


May 


11, 


1899 


5. 


Aug. 


23, 


1899 


(1. 


June 


20, 


1899 



Time. 


Discounted. 


Kate. 


3 mo. 


May 1 


8 %. 


4 mo. 


Dec. 15 


7 %. 


(5 mo. 


Dec. 28 


•5 %. 


4 nio. 


.Inly 31 


G %. 


!>() dii. 


Oct. 25 


r^}<%. 


(iO da. 


-lune 28 


7li%. 



• 



STOCKS AND Dl VI DKNDS, 



149 



(Iniwu. 
wu. 
iiies the 

», 1900. 
s the sum 
tho siuno 

LiOVKLIi. 



ver; John 

at f)'"/" P*^i' 
ble to John 



\me 3 nio. ; 
ree Thomas 

ins:— Faee 
Hiias Jones, 

[for !i;7r)0, at 

Liehased for 



■(> yon $350. 
It'avor of tUt! 



tsconiit, and 

Imtetl. Kate. 

1, S '>. 

15 7 ^'■. 

'>S '5 % • 

31 %. 

25 5i'^. 

oy 7 i % , 



7. Find the face of a note wliieli will realize !f31K.50 when 
diseonnted 4 mo. Iti^fore maturity at (5%. 

K. Mr. Jones lias a })iil for $5(58.80 to pay. He f^ives iiis 
note for 3 mo. whieh discounted at 5% on the day of inaiUiii^ just 
l>rodiKM*s tliis sum. Find the fae(* of the note. 

9. Find tlio proeec'ds of the following notes: — 

$19()L'i'*,A,. Toronto, July 1>G, 1899. 

Four months after date I promise to j)ay to the order of 
James (Jillis one thousand nine hundr<Ml and sixty-two hA, 
dollars at tin* Ontario Bank, for value received. 

Discounted Aug. 'J(5, at 7%. John Dkmaukst. 

10. 
.HIOOGiV... Winnipeg, April 19, 1899. 

Nin(^ty days after date we promise t' pay to the ord(M' of 
Kiii}^ & bodge one thousand and sixty-six iVo dollars at the 
])oiiiinion Harik, for value received. (!ask & Sons. 

Discounted May 8, at G%. 

IX. STOCKS AND DIVIDENDS. 

An Incorporated Company is n iiurn})(a" of per- 
sons einpovvered by law to act as a sin^lo individual. 

Stock is the eapitnl of an incorporated company 
or the money borrowed ))y a government. 

A Share is one of tlie (Hjnal i)arts into which 
sl(M'k is divided. Sometimes the share is $200, or 
$100, or $r)0, etc. Any sum may be agreed upon. 
When the i)rice is quoted it is always on the })asis 
of $100 of stock. 

A Certificate of Stock is a statement showing 
that th(^ party therein named owns a certain numl)er 
of shares of the capital. 

The Par Value of sto(;k is the value nanKul on Ihe 
face of the certificate. 

The IVIarket Value of stock at any time is what 
it can be bought or sold for at that time. 

Stock is at a Premium, or Above Par, when Hk; 

mai'ket valu(^ is greater than the i)ai' value. It is at a 
Discount, or Below Par, when tin; mai'ket value is 
l<'ss tliau the par value. 



^4i 



a; 



150 



ARITHMETIC. 



Dividends jire the profits from tli<^ ))usiTiess oi' 
compaiiies distributed from time to time amoiijif the 
stockliolders as percentages upon the par value of the 
stock. 

A Bond is an obligation to pay a um of money 
at a certain time with interest at a fixea rate at stated 
l)eriods. 

EXERCISE CCXXXV. 

Find the value of the following: — 

1. $7000 stock in the 4 per cents, at 103. 

2. $r^'>00 Bank of Ontario stock at 130. 

3. $4850 Bank of Commerce stock at 145. 

4. $650 Standard Bank stock at 192. 

5. $3400 scock at 78 i. 

No. of shares. 

6. 25 shares Imperial Bank 

7. 45 shares Bank of Commerce 

8. 75 shares Dominion Bank 

9. 40 shares Bank of Montreal 
10. 20 shares Ontario Bank 

EXERCISE CCXXXVI. 

How much stock can be bought with 

1. $588 in the 3 per cents, at 84? 

2. $5300 in Imperial Bank stock at 212? 

3. $3220 in C.P.R. stock at 92? 

4. $5733 in Toronto Railway stock at 102s? 

5. $5500 in War Engle stock at 250? 
How many shares of stock can be bought as follows?— 

Sum invested. Per value of share. Sellinj; prictj 



Par value. 
$100 

$50 


Sel 


ing price 
190. 

145. 


$50 




260. 


$200 




255. 


$100 




130. 



6. 
7. 
8. 
9. 
10. 



$650 

$5200 

$576 

$588 

$900 



$100 

$200 

$50 

$25 

$40 



130 
260 
192 

84 
150 



EXERCISE CCXXXVII. 

VVhiit incotiic is made from investing as follows: — 

1. $5200 ill stock at 130, pjiyiiig 5"!^ diviileiid? 

2. $5390 in stock at 2694, paying 12% dividend:' 



STOCKS AND DIVIDENDS. 



151 



3. $3600 in stock ut 144, paying 8% (livi«l«'iidF 

4. $1350 in stock ut 135, payiiif? lOTi dividend? 

5. $28(53 in stock at 102i, paying' 4% dividend? 
What rate of interest is made by investing? as follows: — 

(5. In British America stock at 125, paying 7% dividend? 

7. In Dominion liank stock at 270, payiiifjj 12% dividend? 

8. In London Pjiectric stock at 120, paying? (>% dividend? 
1). In Traders Bank ^^tock at 112i, paying 6% dividend? 

EXERCISE CCXXXVIII. 
What sni. nust })c invested to produce an income of 

1. $350 from stock at 130, paying a 5% dividend? 

2. $550 from stock at 242, paying a 10% dividend? 

3. $500 from stock at 141f, paying a 7% dividend? 

4. $720 from stock at 173, paying an 8% dividend? 

5. $660 from stock at 104i, paying a 6% dividend? 

How many sliares of stocl< must l)e bouglit to j>r()duce tiie 
following incomes: — 

Par value of stock. Dividend. 
50 12%? 

400 20%? 

40 10%? 

50 6%.? 

EXERCISE CCXXXIX. 

1. I received $880 from a 5i per cent, dividend. How much 
stock do I own? 

2. I receive $279 as my share of a 4J% dividend. How 
iiKiiiy shares^ at $50 each, do I own? 

3. A lady receives $1200 dividend at 7%. 'Required th(* 
uinouiit of stock she owns and the number of shares, valued at 
$25 each. 

4. A owns 85 shares of ruili-oad stock, at $100 a share, attd 
receives a dividend of $080. What was tiie rate of dividend ? 

5. Find tiie rate of dividend ]»aid l)y a railroad when a 
holder of 240 shares, at $100 a share, receives $1722. 

(). Mr. .Tones owns 25 sliares, .'it $50 a share, and receives a 
li;ilf-yearly dividend of $43.75. What was the half-y(^arly rale? 

7. A has 40 shares, $50 each, of stock in a bank, wliicii 
ilfclares a dividend of 5%. What is A's dividend? 

8. How much income will be obtained iinnually by investing 
■f^iMO in (;% bonds, selling at HI)? 

!•. Find the sum refjuired tor :in iMV«'stnient in a 4% stock, 
;il !>.S.i, to produce iin income of $200 a year. 





Income 


0. 


$360 


7. 


$5600 


8. 


$880 


•J. 


$1500 



\i ■ '?■?■■ 



152 



ARITHMETIC. 



EXERCISE CCXL. 

1. If money is worth 7%, whut ouglit a stock tlmt regularly 
pays S% a year to sell for? 

2, What must be the price of a T)^ stock in order that a 
buyer may receive G% on his investment? 

n. IMoney l»ein,<? worth 41^, what ought to l»e paid for stock 
that regularly pays 12% per annum ? 

4. If an H% stock is wortli ]')0, what rate of interest will a 
purchaser receive on his money ? 

5. How much stock must be sold at V2'.i, brokerage i, to 
produce $2949? 

6. What must l)e paid for 40 shares of stock $25 a sliare, 
selling at 142i, brokerage!? 

7. How many shai'es of stock, $50 a share, at 72|, i% 
brokerage being paid, can be bought for $1825? 

8. What sum must be invested in 6 per cent, gas stock, at 
84, to produce an annual income of $2100? 

9. The security being equal, which is the better investment 
— 5 per cent, stock at 125, or 4i per cent, stock at 115? 

10. A owns $5000 stock, which pays a dividend of 7%. How 
much must B invest in a stock which pays 6i% dividend so 
that his income may be $50 more than A's? 

X. EQUATION OF PAYMENTS. 

Equation of Payments is the process of fiiuliiij? 
the time at which several debts due at different tiiiK^s 
may be paid without k)ss of i?iterest to either the 
debtor or the creditor. 

The Equated Time is the time at whicli the 
several debts may be caiK^elled by one payment. 

EXERCISE CCXLI. 

1. The interest on $100 for 10 days is equal to the interest 
on what sum for 1 day? for 2 days? for 5 days? 

2. The interest on. $250 for 12 days is equal to the interest 
on what sum for 1 day? for 2 days? tor 3 days? for 5 days? for 
8 days? for 10 days? 

3. A loaned me $000 for 10 days. For how long should I 
allow him the use of $;J75? of $1200? of $1500? of $3000? 

4. T borrowed from P> $200 for 4 months, $300 for G montlis, 
and $400 for 7 months. How long should I lend him $1800 to 
repiiy the favor? 

5. T .7we to A $500, |>;iyjil>Ie in (! moiitlis. and $400, due in 
15 mouiUs. When may 1 pay the whole in one payment ? 



EQUATION OF PAYMENTS. 



168 



Ito the interest 



n. I owe to B $80, due in 2 da. ; $60, due in 8 da. ; $40, due 
in lOda. ; and $100, due i;i 12 da. Find tiie c'(Hiated time of 
imynieut. 

7. A del>t of $200 is due in (50 da.: $r)0 is paid 12 d.-i. 
Ix'foi'o it is due, and $1(M) is paid 24 da. before it is due. When 
should the balance be paid? 

8. A man bon{?ht a farm on .Ian. 1st, 1900, and is to pay 
$(500 casli, $000 in 2 mo., $800 in 6 mo., and $1000 in 12 mo. 
Find the equated time of payment. 

0. On Jan. 1st, 1900, a man jijave 3 notes, the first for 
$r)0(), ])ayable in IJO days; the second for $400, payable in 
()(] days; the third for $G00, payable in 90 days. What was 
the average term of credit? 



< ( 



4 
o 






l\ i|!400, due in 



EXERCISE CCXLII. 

1. Find the averaj?e term of credit for the following l)ills: — 

(a) $100 due in 2 mo. (/>; $100 due in 1 mo. (c) $700 due in .') mo. 
;K)0 " 4 " 200 " 2 " IJaO 

200 " 7 " 300 " 3 " 550 

400 " 8 " 400 " 4 " 400 

2. A grocer buys $400 worth of goods at 90 days, at the end 
of 00 days he pays $200. Find when the balance should be 
paid. 

3. If I buy goods for $3200 and agree to pay 1 in 3 months 
and tlie rest in 5 months, but afterwards decide to pay all iu 
one sum. When should I pay it? 

4. A note for $800 is to be paid as follows:— i at once, I in 6 
months, and the balance in 8 months. When could it all be 
piiid together? 

5. What is the average date for paying three Vjills due as 
follows:— March 31st $400, April 30 $300, May 30th $200? 

G. On Jan. 25th, 1899, a grocer sold goods for $1340, i 
l>!iyable in 90 days; i in 120 days, and the balance in 150 days. 
Wiuit was the equated date of payment? 

7. I bought goods for $600; i to be paid at once, } in 4 
months, and ts in 6 months. At what time may the whole be 

\KiuU 

H. A owes a sum of money, of which ^ is payable at 30 days, 
■■ at GO days, and the rest at 90 days. What is the equated time 
tor the payment of the whole? 

9. A man purchased real estate, and agreed to pay i of the 
jivife in 3 months, i in 8 months, and the remainder in 1 
year. W^ishing to cancel the whole obligation at a single pay- 
ment, liow long shall this payment be deferred? 






<n 



m 



!il 



1 



CHAPTER X, 



PARTNERSHIP. 

Partnership is tlie association of two or more 
persons in business, witli an agreement to share the 
profits and losses. 

Partners are tlie persons associated in business. 

The Association is called a Company, a Firm, or a 
House. 

The Capital or Stocic is the money or property 
invested in the business. 

'< EXERCISE CCXLIII. 

1. B and C gain in business $1050. B's stock was $1500 
and C's $2000. What share of the gain should each get? 

2. A and B are partners. A furnished $840, and B $1030 
capital. Find the share of each of $432 profit. 

3. A and B agreed to do a work for $260. A worl<ed 27 
days and B 25 days. How should the money be divided? 

4. A, B and C rent a pasture field for $275. A puts in 17 
horses, B 26 horses, and C 12 '"orses. What share of the. rent 
should each pay? 

5. A, B and C engage in business. A puts in $3600, B 
$1700, and C $4800, and they gain $2424. What share of the 
gain should each get? 

6. A and B engage in business with a capital of $6000. At 
the end of the year, ,i. gets $208 and B $272 gain. What was 
the capital of each? 

7. A, B and C enter into partnership. A puts in $2325, 
B $3250, and C $4625.. A gets $465 for his share of the gain. 
What should B and C receive respectively? 

8. The capital of a firm consists of $40000, of which A 
contributes $14000, B $17000, and C the rest. Divide $5000 
profits among them in proportion to the capital of each. 

9. A, B, C and D form a partnership. The capital of each 
is $4500, $2300, $1900, and $1100 respectively. They lose $1568. 
What is A's share of the loss? 

10. Divide $9282 among A, B, C and D, giving A 10% more 
than B, B 10% more than C, and C 10% more than D. 

154 



or property 






Partnership. 

EXE.7CISE CCXLIV. 



155 



7 weeks 'Vi^n^ i'"'" '^ P»«tiJre for .*4/) * 

, -•• A and B take ., . '"'*''''^ 

i"'-^ *7;io, be divided ' '" ^'^>'«- ^ovv .iji'.r*" f"/ 10 

cows (or mo. How ,.?. , ' • ^' ^" cow, w •, "°- ^ Pi'ls in 
"o i B ^Jt.^'"™." Partnership. T^ ?'"-■'' "">■' 

^- A and B form n * °" 

"-rtidJ^f »«»« »o-. °^iv? ?S "L1o"'^'h*?S 

.Ii.l B joi;;" '• ""«' """"y months befJ^e'C: ' ■•«<'™1 """ 

9. A and R f >''■'"■ * 

«'"<» and B $mT " P»rt"erahip for „ y,„, , ^ ^,. 



CHAPTER XI. 



IINVOLUTIOIN AND EVOLUTION. 

I. INVOLUTION. 

A Power of n iniuilx'i* is tlic product <>l)taiiio(l ])y 
taking the imnilM'r a number of times us a factor. 

Involution is \\w proct^ss of raisinj? a iiiurioer to a 
power. 

Tlie Index or Exponent of a power is a Hjfun; 
placed at tlie ri^lit and a little above the iminher to 
show how many times it is used as a factor; thus, 5", 
2 is the exponent. 

The Square of a number is the product obtained 
])y using tlie number twice as a faetor. 

The Cube of a number is the product obtained 
by using the number three times as a fac^tor. 

4 X 4 = 4** = IG, or, tlie'Jnd power, ors(niiU'('(jt'4. 
4X4X4 = 4*^ = ()4, or, the 3rd power, or cul)e of 4. 
4X4X4X4 = 4* = 256, or, the 4th power of 4. 
4X4X4X4X4 = 4"^ = 1024, or, the nth power of 4. 

EXERCISE CCXLV. 

Write tlie following as powers nvl find their vjilues: — 



1. 2X2X2 

2. r)X5X5 

.•J. ixixi 

4. 2iX2i 

5. .IX.IX.I 

C. .12X.12X.12 



2X2X2X2 
5xr>XoX5 

ix*x*x* 
;jix3ix:{i 

.03X.03X.0:{ 
.15X.15X.15 



;}x3x:jx;5x3. 

5xr)X 5X5X5. 

6 /\ u /N 6 '^ n /^ r. • 

4iX4iX4iXv^. 

.05X.05X.05X.05. 

2.5X2.5X2.5X2.5. 



"Write the factors of the following powers and find their pro- 
ducts: — 
7. 2^ 3* 4^ 



8. 


ar- 


(f)^ 


(i)^ 


9. 


i.'^V 


(.05)- 


(.001)'' 


10. 


(2i)« 


iuy 


(5i)*. 



156 



INVOLUTION AND EVOLUTION. 



157 



bXERCISE CCXLVI. 

.S(|uiir«' llir following iiumber.s: — 



for. 
r.bt'i" to a 

i\imbt'V f<> 

thus, r>-, 

t obtuiiuHl 

t obtained 

rs(iu!in'of4. 
or cube of 4. 

i: 4. 

f 4. 



Is : — 

l5X5X'>. 

:X4*X'.*. 

iooX.OoX.O'). 
.5X2.5X2.5. 

Ind their pvo- 

|3 
,5/ 

.001)'. 

:5i)*. 



1. 19 


45 


86 


93. 


2. 101 


504 


906 


708. 


3. 75.G 


40.8 


97.5 


7.96. 


4. * 


♦ 


i 


A. 


5. 4i 


7h 


9i 


V2L 


ibe the following 


numbers : — 






G. 9 


19 


41 


91. 


7. 101 


110 


506 


909. 


8. 30.5 


4.55 


78.4 


6.97. 


9. 1 


A 


H 


\t. 


10. 2i 


5i 


31 


71 



EXERCISE CCXLVII. 

Kiiise the following numbers to the powers indicated: — 



1. 9^ 




5=' 




25^ 


l6^ 


2. (.09)'' 




(.ir 


y 


(2.5)« 


(.33)3. 


3. (t)« 




(1) 


I 


(2i)» 


(3i)^ 


Find the value of 












4. 452 


24 


? 




88* 


(If)". 


5. S'-'XS" 


7* 


X7'* 




12''X12'^ 


(i)''x(^)^ 


0. 12'' -^12'* 


a* 


-H-' 




J23^2'' 


9^-3^ 


7. 10^-5' 


(2 


5)«- 


■{.IV 


i^y^av 


(3.5)«^(.5)» 



S. What power of )i number is the product of the first power, 
the second power, and the third powerf 

9. If the fifth power of two be multiplied by the third power 
of two, find the resulting number. 

10. What power is the square of the cube of the fourth 
power? 

11. Of what number is 7009 one of the two equal factors? 

12. Of what number is 5050 one of the three equal factors? 

13. Find the number of which one of its four equal factors 
is .002. 

14. Show that 3G'' = 2*X3^ 

15. A field is 48 rods long and 32 rods wide. Fiud the area 
of a square with an equal perimeter, 



168 



AUITliMETIO. 



II. SQUARE ROOT. 

The Square Root of a numbot' is oik; of its two 
equal tactors, tlms G is the s(nuir(i root of 36. 

The stiimn; root of a nuniljcn- is iiidif^attnl by th« 
radical sujn J, or by tlie fra(!tion A written above and 
to the right of tlie number. 

EXERCISE CCXLVIII. 

Find the square root of the following: — 



1. 


SI 


i) 


i:{G9 


8. 


iimi 


4. 


U 


5. 


ni\ 


6. 


.01 


7. 


.061009 



121 

:ji;{6 

98596 

.0025 
.001225 



144 

4096 
655:36 



684 I 

1 2 r 

.0009 

.oo:i;u54 



225. 

6561. 

277729. 
1 a 2 6 

5411. 

T H (t a • 

.0S41. 

.0256. 



Find the value of the following 

8. (144)^ (A)^ 
Find the following: — 



I 



Ki) ^ \^2a) V81 '^ V 1 Off 



9. v/9.3025 i/. 010404 /. 326041 >/. 0000316969. 

Find correct to 3 decimal places the square root of 
10. 5 .5 .9 .009. 

EXERCISE CCXLIX. 

1. Find the two equal factors of 240100. 

2. What number must be multiplied by itself to produce 
2450,Vff. 

3. Resolve 10252804 into two equal factors. 

4. The area of a square lawn is 576 sq. yd. What is the 
length of one side? 

5. Tlie area of a square is 40 acres. Find tho length of one 
of the sides in yards. 

6. How many rods long must the side of a square field be to 
contain 250 acres? 

7. Find the side of a square equal in area to a rectangle 
whose sides are 544 ft. and 136 ft. 

8. What will it cost to fence a square farm coritainiug 160 
(icres at 25 ct, per vo^i 



OUBK KOOT. 



ir>j» 



f its two 

iO. 

id by tli« 

ibove aiul 



225. 

()')()!. 

277729. 

1 2 'J 5 

6 4 1V 

T 6 » »^. 
10 rt & • 

.0841. 
.02r)(5. 



JW^'J 



19B 



)000:U69(i9. 

)f 

.009. 

[if to produce 

What is the 

length of OIK- 

lare field be to 

^0 a rectaiigh' 

hontainiug lO^J 



!>. Tin- i«lo of 11 H»|U!ir<> licld is !Mi rods Ion;;. l-'iinl lli«t 
Iciij^th of i\w si(l(* of II sciuarc (Muitiiiiiiii^ 2i tiiiifs jih iiiiicli. 

10. A s<|iiare lnwii contuin.s ll(i(J4 sq. yd. What will it rost 
to fciK'e it at $.7 > per yd. If 

EXERCISE ecu 

1. A nMtaii>?)iIar KardiMi contains IS7r> h(|. yd., and it is '.i 
tiiiics as long as it is widi^ Find its length and width. 

2. A rectanjfUJMr pird<<n contains 2 acres, atid it is ;') times 
as long as it is wi(h». Find its Icnj^tli and width in yiirds. 

3. A s(iuaro yiird is divided into 57(5 ecjuiil squares. Find 
tlio length of a side of each. 

4. A field is 12 rd. sqiuire. How lotig is the side of another 
square field containing 1 s<j. rd. more than twice th«» first? 

5. Find the number of rails, each 12 ft. lon^, re(|uired to 
Itnild a straight fence 6 rails high round a s(iiiare lOA. field, 
allowing the rails to overlap 1 ft. f 

(). The rroii of a square field is 122i acres. A rectjtngiiliir 
Held containing the same area is 4 times as long as it is wide. 
Find the number of rods in the h-ngtii of this field. 

7. llaw many yards of fencing are required to enclose a 
sfpiare farm containing 832A. 105 n(\. rd. ? 

H. A square bin has a capacity of 1800 cu. ft. and is 8 ft. 
deep. What is its length? 

9. The side of a square field it; 171 yd. loiif; and of another 
square fiold 140 yd. long. Find the length of the side of a 
s<|. field as large as both together. 

10. The i)erimeter of one square is 3840 yd. and .)f another (i()88 
yd. Find the perimeter of a square equal in area to both of 
them. 

III. CUBE ROOT. 

The Cube Root of a iiii]ri])er is one of its three 

equal factors; thus, 4 is tho cube root i;f 64. 

T\u' cube root of a number is indicat(!(l by f, or 
)ty file fraction ^ written abov(i and to tlie rij^lit of 
tile numl)er. 

EXERCISE ecu. 

Resolve the following nnnibers into prime factors, and from 
these find their cube roots: — 



1. 


216 


512 


729 


1728. 


«) 


3375 


4096 


5832 


93«1. 


3. 


15625 


13824 


21952 


35937. 


4, 


42871^ 


T17649 


166370 


175616, 



1(50 



AUITIIMKTId. 



Extnu't llio (MiVx' ro(»t of tlu^ follnwlu'': 



f). 


4in;j 


G. 


14,SS77 


7. 


io:j():u)1 


S. 


3 4 :i 
"2 1 y 1 


9. 


.001 



rji(i7 

2or);j79 

];5()7();}i 

7 ',' 
T) « f) 

.0001210 



24:}8!> 

:5007():! 

4S'j()Soa 

£ 7 4 4 

1 1 r> 1 ti 
ir)GO.S9(5 



Find tlio ciihc) root corrc'ct to 'A (liM'iiuul pliicos of 
10. .8 .08 .008 



jjOCm:}. 
3r)7911. 

G7;")1"J()9. 

1 .'i .•! 1 

f> a :n 9 • 

47832.147, 



CXERCISE CCLII. 

Find the followint^: — 

1. f'lilG'JS f .Oir)G25 fl.8G08G7 f I012.0480G4. 

2. (92G1)^ (8i:W0^ (373i¥5)'' (480it;l)^ 

3. Tiu' product of tluvo oqnul fii- 'ors is ,3980.977. Find 
the factors. 

4. Uequirod i\)e rnKn'ru-r of squnro feet in ono faee of a 
cubical bloelt wliose contents ai-e 40r)224 cu. ft. 

5. What is the entire snrftice of a cube whose cnl>ieal 
coiitents are 912(573 (Mil)ie ft.? 

G. A cubical cistern liolds 4913 cu. ft. JIow deep is it? 

7. The edf?es of a rectanfjjnhir solid are IGO iii., 2;") in., and 
54 in. respectively. Find the edj^e of a cube of the same 
volume. 

8. The contents of a cube arc 97.33G cu. in. Find the ed^e 
' of a cube that contains 8 times as niucli. 

9. A rectanf^ular l)loc]i of stone with a square end is 8 times 
as long as it is wide and contains 27 cu. ft. Find its length. 

10. The contents of two cul)es are respectively 53;')9.37o and 
5.3r)937i') cu. in. Find the dilference between the lengths of 
their edges. 

11. Find the total lengtli of the edges of a cube containing 
5005)5 cu. inches. 

12. What nnist be the edg(^ of a cubical bin that shall contain 
as many bushels as a bin 10 ft. 5 in. long, 5 ft. 4 in. wide, 
and 2 ft. 3 in. deep ? 

13. Tile product of tliicc numbci's is 2304. The second is 
twice the first and the third is one-third of the second. Find 
the first inimlter. 

14. A rectangular room "ont.i" -< 13;'<24 cu. ft. Its width is H 
of its length and its lieiglil is h .' il:; width. Find its length. 



:.o(»r)3. 

3r)7'.)U. 

G7r)ii:()'J- 

1 ;{ :( 1 
5 « :t 1 • 

47832.147. 



CHAPTER XIL 



/1012.0480G4. 

480itS)^. 
80.977. Find 

ono faee of a 

whoHo cul)ical 

idccp is it? 
u., 2') in., and 
of tho same 

Find the od}?e 

end is 8 times 
Id itH lenj?tli. 
]y MiVJ.:^.") and 

tiie lengths ot 

lube containing 

lit sliall contain 
ft. 4 in. wide, 

Tlic second i^ 
second. Fi»"' 

Its widtii is H 
hiid its length. 



MENSURATIOIN. 

A Triangle is a plane figure Ijounded by thivv, 
straight lines. 

An Equilateral Triangle is one whieh has its three 
sides equal to one another. 

An isosceles Triaiigie is one whieh has two sides 
('((ual to eaeh other. 

A Right Angled Triangle is one which has a 
riglit angle. 

The Hypothenuse is the side of a right angled 
triangle, whieh is opposite to the right angle. 

The Base and the Perpendicular of a right 
angled triangle are the sides that (contain the right 
angle!. 

A Quadrilateral is a i)lane figure Ixmnded ))y four 
.<iruiglit lines. 

A Parallelogram is a qnadi-i lateral, the opposite 
sides of whieh are i)arallel. 

A trapezoid is a quadrilateral with oidy two 
sides ]){irallel. 

A Rhombus is a (piadrilateral whieh has its four 
sides ('(pud to one another. 

A Trapezium is a (quadrilateral, whicdi has none of 
its sid(\s i)arallel. 

A Circle is a plane figure bounded l)y a enrved 
line ealhul the circumference, every point of whi(di 
is equally distant from a point within called the 
centre. 

The Diameter of a (urcle is a straiglit line i)}issing 
thi'ough the centre and t(!rniinated Ixjth ways l)y 
the cinnunference. 

161 






I 



162 



ARITHMETIC. 



The Radius ot n ciivle is a straiglit line drawn 
from the (tcMitre to the eircumfereiice, 

A Right Cylinder is a solid, bounded by two 
(eir(;ulai*) plane faees and a eui'ved faee, every part 
of whieh is the same distanee from a straiglit line 
joining the eentres ot the plane faees. 

A Right Pyramid is a solid, bounded by a plane 
fa(;e enelosed by three or more straight lines, called 
the bfi^e, and as many triangular plane faees as the 
base has sides. 

A Right Cone is a solid, bounded by a circular 
l)lane faee, (tailed the base, and a cnirved face tapering 
from the circumference of the base to a point. 

A Sphere is a solid, bounded by a curved face, 
every i)art of which is equally distant from a i)oint 
within it called the centre. 

EXERCISE CCLIII. 

1. Find the area of a square whose side is 39 yd. 

2. How many square feet are there in the surface of a table 
7 ft. 8 in. long and 3 ft. 10 in. wide? 

3. A rectangular grass plot 25 yd. by 20 yd. has a gravel 
walk 4 ft. wide round it. Find the area of the gravel walk. 

4. The sides of a rectangular field are 525 ft. and 84 ft. 
Find the side of a square of the same area. 

5. A rectangular field contains .78 A. It is 3 ch. 25 1. long. 
Find its width. 

6. Find the area of each of the pai'allelograms, one of whose 
sides and the perpendicular distance between it and the opposite 
side are respectively as follows: — 

(a) Side 17 in., perpendicular 131 in. 

{h) Side 3 ch., perpendicular 1 ch. 80 1. 

(c) Side 3 yd. 1 ft., perpendicular 2 ft. 8 in. 

7. The parallel sides of a trapezoid are 48 in. and 56 in. 
long respectively, and the perpendicular distance between them 
is li ft. Express the area in sq. ft. 

8. The base of a parallelogram is 75 rods long, and it con- 
tains 7i acres. Find its width. 

y. The area of a square field is 40 A. Find it? side. 

10. A grass plot in the form of a parallelogram is 125 ft. 
long and ;$G ft. wide. Find the cost of levelling and sodding it 
at 10 ct. per sq. yd. 



MENSURATION. 



163 



drawn 

by two 
ivy part 
gilt line 

a plane 
;s, called 
iS as the 

I ciroAilar 
! tapering 
it. 

rved f'lce, 

II a point 



1. 

je of a table 

lias a gravel 
.vel walk. 
. and 84 ft. 

|i. 25 1. long- 

)ne of whose 
the opposite 



, and 56 in. 
between them 

and it con- 

pide. 

im is r2r> ft 

liul sodding it 



EXERCISE CCLIV. 

1. Draw figures repi-esenting the following triangles, and 
find the area of eacli, the base and perpendicular upon tlio btcx 
from the opposite angle being rospectivoly : — 

{a) 24 ft. and 15 ft. G in. 

(h) 21 yd. 1 ft. 10 in. and li yd. 10 in. 

((0 2750 1. and 380 1. 

(d) 20 ch. and 365 1. 

2. The area of a triangle is 875 sq. in. Tlie length of 1!i(? 
perpendicular from an angle to the opposite side is 3;' !ii. 
Find the length of this side. 

3. The arc^a of a triangle is 34 sq. ft. 63 sq. in.; its base is 
14 It. G in. Find the perpendicular from the opposite angle 
upon the base. 

4. A triangular field contains 1 a. 24 sq. per. The per- 
]i<'ndi('ular from an angle to the side opposite it is 4 rd. long, 
llow long is this side? 

5. A 3 C D is a ti'apezium. The diagonal, AC, is 100 ft. 
long. The perpendiculars, frini 1) and B ujon AC, are 30 ft. 
and 56 ft. respectively. Find the area of the trapezium. 

6. In 5, if the diagonal is 65 yd. and tlie two perpendiculars 
27i yd. and 38i yd., find the area. 

7. The longest diagonal of a quadrilateral is 49 yd. and the 
perpendiculars let fall on it from the remaining angles are 
9 ft. 6 in. and 13 ft. 10 in. Find the area. 

8. Draw the trapezoid A B C D, AB and CD being the 
]i;irallel sides and being 48 yd. and 56 yd. long respectively. 
The perpendicular distance botv/een them is 10 yd. 2 ft. Find 
tlie area of the trapezoid. 

9. The parallel sides of a trapezoid are 19 ft, and 23 ft., and 
the altitude is 9| ft. Find the area. 

10. The area of a trapezoid is 1155 sq. ft. One of the parallel 
sides is 84 ft. long and it is 16i ft. wide. Find the length of 
the other parallel side. 

EXERCISE CCLV. 

Note. — In the following examples tt = 3t. 

1 . Find the circumference of circles wliose diameters are 
] 1 in. ; 1 ft. 9 in. ; 3 ft. 6 in. ; 5 yd. 1 ft. 4 in. ; 7 yd. 2 ft. 4 in. ; 
4 ch. 76 1. 

2. Find the diameter of circles whose circumferences are 



5 eh. 39 1.; 4 rd. ; 12 rd. 



1 ft. 10 in.; 4 ft. 7 in.; 20 yd. 6 in.; 
i ft. 10 in. 

3. A boy can walk round a circle in 1 hr. 17 min. At the 
same rate, how long will he take to walk along the diameter? 



164 



ARITHMETIC. 



4. Two bicycles liiive wliools 2 ft. 11 in. and .T ft. G in. in 
diameter respectively. If they start from the same i>lace, and 
each wheel lias made 1000 revolutions, liow far will one lie 
ahead of the other f 

i). A coach wheel turns .330 times in travellinj? one mile. 
Find the diameter of the wheel. 

6. A locomotive is moving at the rate of (50 miles per hour. 
The diameter of the driving wheel is 4 ft. How many times 
does it turn in a second? 

7. The radius of a circle is 8 ft. Find the perimeter of the 
semicircle. 

8. To enclose a circular garden, there are required 5L*8 yd. 
of wire fencing. How long is the radius of the garden f 

9. The diagonal of a square is 4 ft. 1 in. Find the circum- 
ference of a circle circumscribed about the square. 

10. The radius of a circle is 5 ft. 3 in. Find the length of 
an arc of 20^: of 30' ; of 50°; of 60°; of 100°; and of 110^ 

EXERCISE CCLVI. 

1. Find the area of each of the following circles : — 

Diameter, 35 in. ; 42 in. ; 70 in. ; 84 in. ; 105 in. 
Circumference, 44 in. ; 06 in. ; 77 in. ; 110 in. ; 308 ft. 
Radius, 7 in. ; 3i ft. ; 4 ft. 8 in. ; 5 ft. 3 in. ; 21 c!'.ains. 

2. How many square yards of oilcloth will be required to 
cover a circular floor 17 ft. 6 in. across? 

3. Find the circumference of a circle whose area is 3.85 
acres. 

4. The radius of a circle is 84 inches. Find the radius of 
another circle of half the area. 

5. Two circles, the radius of each being 7 in., are placed on 
the surface of a circle whose radius is 14 in. Find the number 
of square inches not covered. 

6. A cow tethered can feed over 2i acx*es of ground. How 
long is the rope by which she is tied? 

7. A circular field contains exactly one acre. Find the lengtli 
of the fence which encloses it. 

8. Find the number of grass sods, each 15 in. by 12 in., 
that will cover a circular piece of ground 21 ft. in diameter. 

9. A circle 18 in. in radius has one 34 in. in diameter 
inscribed within it. Find the area of the part of the largf 
circle without the smaller one. 

10. Find the cost of making a path 7 ft. wide round ;i 
circular pond whose perimeter is 352 yd. at $1 per sq. yd. 



MENSURATION. 



165 



EXERCISE CCLVII. 

1 . b'iiul the hypotl;eiiuso of oucli of tlio following right aiiglfd 
trituigloH whose base uud perpendicular are respectively :- 
(«) i:i ft., 84 ft. (c) 1032 ft., 574 ft. 

{b) 408 ft., 500 ft. ((0 598 ft., 300 ft. 



perpendicular and hypothenuse are respectively:— 

(a) 40 yd., 530 yd. . (c) 117 ft., 125 ft. 

(b) 1450 ft., 1900 ft. {(l) 270 yd., 300 yd. 



2. Find the bases of the following rigiit angled triangles 
whose 

3. Find the perpendicula- of the following right angled 
triangles whose base and hypothenuse are respectively:— 

{a) 050 ft., 794 ft. (c) 50 yd., 394 yd. 

{b) 240 ft., 818 ft. {(I) 272 ft., 353 ft. 

4. A boy is 21 mi. due south from his home; he travels 20 
mi. due west. How far is he then from homef 

5. A ladder is 37 ft. long and leans against a building with 
its foot 12 ft. from the wall. How far from the ground will its 
top rest against the wall? 

0. A garden ■ the form of a rectangle is 210 ft. long and 
170 ft. wide. How far is it from any corner to the one 
diagonally opposite it? 

7. How far is it from the diagonally opposite corners of a 
cube 12 in. long? 

8. How far is it from the diagonally opposite ©orners of a 
box 8 ft. long, 6 ft. wide and 5 ft. deep? 

9. A ladder 26 ft. long stands upright against a wall. How 
far must the bottom of It be pulled out so as to lower the top 
2 ft.? 

10. Find the cost of fencing a field in the form of a right 
iingled triangle, its base being 105 yd. and the perpendicular 
208 yd. long at 10 ct. per yd. 

EXERCISE CCLVIII. 

1. Find the volumes of the cubes whose dimensions are as 
follows: ik in. ; 3i in. ; 2 ft. 5 in. ; 1 yd. 1 ft. 1 in. 

2. Find the surface of each cube in the last example. 

3. A rectangular log is 18 ft. long, 18 in. broad, and 14 in. 
thick, find — (1) its volume, (2) its surface. 

4. A block of marble is 10 ft. long, 5 ft. 3 in. broad, and 
'-i ft. thick. Find — (1) its volume, (2) its surface. 

5. The surface of a cube is 2400 sq. in. Find— (1) the 
Ifiigtli of its side, (2) its volume. 

(). How much will it cost to excavate the basement of a 
sclionihouse 27 ft. long, 20 ft. wide and 8i ft. deep at 25 et. 
l»er eu. yd. 



iT-T" 



166 



ARITHMETIC. 



7. From the log, in examjde 'S, 2i eu. ft. are cut off. What 
h^igth of log is left? v 

S. A room 11 ft. high is half as long again as it is wide, and 
its cubical space is 47G8i eu. ft. Find its length and breadth. 

9. A gallon contains 277.274 cu. in. Find the length of a 
cubical box that holds 10 bushels. 

10. A cubic foot of water weighs 1000 oz. and a gallon 10 lbs. 
How many gallons are there in a rectangular cistern 6 ft. long, 
5i ft. wide, and 8 ft. deep. 

EXERCISE CCLIX. 

1 ■ Find the volume of each of the cylinders whose length 
and diameter are respectively: — 

(a) 8 ft. and 14 in. (c) 10 ft. and 7 ft. 

(6) 12 ft. and 3 ft. G in. {(I) 20 ft. and 2 ft. 11 in. 

2. Find the area of the curved surface of each of the 
cylinders in example 1. 

'.\. A well is 15 ft. deep and its diameter is 3 ft. (5 in. How 
many eu. yd. of earth were taken out in digging it? 

4. A circular slmft is 90 ft. deep and 3 ft. in diameter. 
Find the cost of sinking it at $2.80 per cu. yd. 

5. Find the total surface of the cylinders in example 1. 

6. How much curved heating surface is there in a steam 
pipe 1 in. in diameter and 350 ft. longf 

7. A pillar 21 ft. high and 18 in. in diameter, supporting a 
building, is to be decorated at 25 et. per sq. ft. Find the cost. 

8. A cylinder contains 11 cu. ft. and is 14 ft. long. Find 
its diameter. 

9. It costs $11.88 to paint the curved surface of a pillar 18 
ft. high at 63 et. per sq. yd. Find its diameter. 

10. Find the number of eu. ft. of iron in a water pipe 12 ft. 
long and 2 ft. 6 in. in diameter, the iron being 2 in. thick. 

EXERCISE CCLX. 

1. A square pyramid is 16 ft. high, and each side of the 
base is 4 ft. 6 iui long. Find its volume. 

2. A triangular pyramid is 12 in. high, and the sides of the 
base are 29 in., 52 in. and 69 in. Find its volume. 

3. The slant height of a cone is 10 ft., and the circumference 
of the base is 15 ft. Find the area of the curved surface. 

4. A cone is 3i ft. in diameter. Its slant height is 6 ft. 
Find the area of the lateral surface. 

5. The slant height of a conical spire is 45 ft. The circum- 
ference at the base is 30 ft. Find the cost of painting it at 
45 ct. per sq. yd. 



MISCELLANEOUS EXERCISES. 



167 



G. Find tlio volnmo of a cone 35 in. in diameter at the base 
and GO in. in hcij^ht, 

7. A cone is 48 ft. lii^li; its volume is 138G en. ft. Find — 
(I) the area of the basts (2) the eircuniference of the l)ase. 

8. JTow many yards of canvas 4 yd. wide will be required 
for a eonieal tent L51 ft. in diameter ami 15 ft. high? 

9. Wliat is the volume of the largest possible cone, cut out 
of a cubical block whose edge is 7 ft. 

10. 'I'he radius of the base of a cone whose height is 5 ft. is 
11 in. Find the slant 1; eight. 

EXERCISE CCLXI. 

1. Find the surface of each sphere of the following 
dimensions: — {a) Kadius, '^i in.; (h) diameter, 3^ in.; (c) 
circumference, 44 in. ; {d} circumference, 88 in. 

2. What will it cost to gild a globe 28 in. in radius iit 3G ct. 
per sq. ft.f 

3. The surface of a sphere contains 24G4 sq. ft. Find its 
radius. 

4. The surface of a sphere contains 5544 sq. ft. Find its 
circumference. 

.^». Find the volume of each sphere of the following 
dimensions: — (a) Radius, Gin.; (6) radius, 12 in.; (c) diameter, 
14 in. ; {(I) circumference, 22 in. 

G. Find the volume of a sphere whose surface is 1386 sq. ft. 

7. A cubical block of wood 3 ft. long is formed into the 
largest globe possible. How much wood is cut away? 

8. A solid metal sphere G in. in diameter is melted and 
formed without loss into a cylinder 3 in. in radius. How long 
is tlie cylinder? 

9. A solid metal sphere 12 in. in diameter is melted and 
formed without loss into shot i in. in diameter. How many 
siiot are there? 

10. How many balls i in. in diameter can be made from a 
cubic block of lead 5i in. long? 

IMISCELLAINEOUS EXERCISES. 
EXERCISE CCLXII. 

1. Each equal side of an isosceles triangle measures twice 
as much as the base. If the base is 48 ft. long, find the altitude. 

2. Find the base of a triangle whose area is 5280 sq. yd. and 
lieiglit 120 yd. 

3. The perimeter of an isosceles triangle is 153 yd. and each 
"f tlie equal sides is f of the 3rd. Find (1) the base, (2) the 

iiiea. 



lOfl 



AniTIIMRTir, 



4. Twfi siilcs of ii Iriiiiifrlc iin> 'J IS It. tiiid 241 ft. loup nnd 
tli*> iMTiit'iidK iiliii' from tli(> iiii'lii«l<Mi tiii^lo upon tlir llrtl sitlo 'in 
I'JO ft. I'MikI tli<> :tni si(l«>. 

5. Tlic top of a poi<> ih ln'ok(<n olT hikI striUcs tlio ^roiiiid 15 
ft. from the foot «^ tlu' polo. V'wul i\w wliolo loii>;tli of tlu' polo 
supposing ♦' • bi'Oi\( II j>ioco to l»o ;{!► ft. 

(5. Kiml ,>r< .)f iiii otpiihitoral triimj^lo whoso wido is 10 ft. 

7. A stici ft. 1. .i^r pliicod upi-i^ lit in Ww ground is found 
to Piist )i sluidow 4 ft, ' ni. lon^. V> hut is the hoi^ht of a polo 
tlnit casts a shadow IJH it. lonj^if 

8. A foot jtath fjoos alonj; two adjaoont sid<^s of a I'ocfiinjjio. 
Ono sido is llMiyd. and tho otiutr 147 yd. lonR. Find tho savinj^ 
in distan('(« by f^oiii^ iilon^ Uw dia^oiuil instt^ad of tlio sidos. 

9. Tho pt»riinotoi' of a s((U!iro is 748 in. and of anolhoi' is '.VM't 
in. Find tiio poriniotor of anothor o(|inil in area to tlit othor 
two. 

10. There are two rootanf?ular fields of (^qual iirea. Tho 
adjacent sides of one are 1)45 yd. and IU44 yd. lonj;. Tho lonj^or 
side of tiie othor is 1KJ4 yd. lonj^. Find tln^ shorter sido. 

EXERCISE CCLXIII. 

1. How long is tho edge of a cube whose surfjico is 11094 
sq.ft.? 

2. A triangular field contains one acre. A ])eri)endicular 
drawn from one corner to the side opposite measures 40 yd. 
Find this side.' 

3. The volume of a cube is 37 cu. ft. 64 en. in. Find the cost 
of painting it at 33^ ct. i)er sq. ft. 

4. A has two circular plots of ground 100 ft. and 20 ft. in 
diameter, respectively. How many times is one as large as the 
other? 

5. What must be the circumference of a circular lake which 
shall contain nr part as nnich surface as a circular lake I'M 
miles in circiimference? 

6. What is the distance through the opposite corners of a 
square yard? . 

7. Find the perimeter of a rectangular plot of land whose 
length is 2i times its width, if it contains Oi acres. 

8. A ladder 20 ft. long reaches to the top of a wall when the 
foot is 13 ft. from the wall. How much does the ladder project 
above the wall, when its foot is 5 ft. from the wall. 

9. If a c. ft. of marble weighs 2.71(5 times as much as a en. 
ft. of water. Find the weight of a rectangular block of marble 
9i ft. by 2^ ft. by 2 ft. (A cu. foot of water weighs 1000 oz.) 

10. The sides of a triangular field are 350 yd., 440 yd. and 
750 yd. in length. It rents for $31.50 per annum. Find the 
rent V^^' Jicre. 



MISCELLANEOUS EXERCISES. 



169 



EXERCISL CCLXIV. 



Kind tli(^ li'ii^tli 



!. Tli(f pfrinu'lcr of ii H(ttni(Mr<;lo is 'Mi ft. 
of tlio (litiiiiotiM*. 

'J. VViiioli will carry tin* liirKOKt lunoniit of water two '.i in. 
tikt or ono 4 in. tile, the speed hc/mf? the same in each ease? 

',]. Find the diamet<M' of a eirele ecjual in area to a rectanj^ht 
whose sides are K)4 ft. by Kl ft. 

4. A cireular pond Hli ft. in diameter has a walk 4 ft. wide 
round it. Find the area of the walk. 

5. A tower \i'H ft. hij;h stands in the middle of • stream 144 
ft. widen How lon{» is tlie distance from the she t' the foot 
of the llaj,' staff upon the top of the tower. 

(5. Find the ar(^a of a trapezoid whose parall. . nidis are 178 
ft. and 14(5 ft. and the perpendicular distance between them 

sri ft. 

7. Find the area of a pond whose circumference is 204 ft. 

H. A H (! 1) is a quadrilatcu-al figure. AB 400 ft. lon^,', liC 
'J0:{ ft., CI) '.im ft., DA 195 ft. The anf^ios at A and C are 
rif^ht aufjfles. Draw tlui figure and find its area. 

9. A trapezium is dividcMi into two triangles by a diagonal 
40 ft. long. The difference in length of the perpendiculars 
from the opposite angles on tlio diagonal is 7 ft. Find the 
difference in area of the triangles? 

10. The differetu'o between the circumference and the 
diameter of a circle is 45 in. Find the area of the circle. 

EXERCISE CCLXV. 

1. ABCI) is a trapezoid. AD and BC are the parallel sides 
and are '.V2 ft. and 40 ft. long, respectively. AB is 16 ft. long 
and (M) 18 ft. BA and CD are produced to meet in E. Find 
th(^ length of EB and EG respectively. 

2. Find the aroa of a quadrilateral field wlioso diagonal is 40 
rods and the perpendiculars on this diagonal from the opposite 
angles 14 rods and 2U rods, resi)ectively. 

.'J. Find the aroa of a trapezium whose diagonal is 108 ft. long, 
one perpendicular on the diagonal from the opposite angle 
being 42 ft. long, the other, 50 ft. long. 

4. The area of a circle is 44 sq. ft. Find the difference 
between the areas of the circumscribed and inscribed squares. 

T). The side of a square field is 40 rods long. Find the 
li'nii,tii of the side of a square field that contains (I) 4 times as 
nuu-h land; (2) 9 times as much; {[i) 5 times as much. 

0. The perimeter of a rectangle is 104 in. and the difference 
in length of the two adjacent sides is 22 in. Find the area of 
the rectangle, 



170 



AKITIIMKTIO. 



7. The Idisc (»r ii friiiiigic is 07 ft. long iiiul i\w <lifT«<rriK'«> in 
loii^tli of llm oilier two sidcH is li ft. TIk' (listiiiico Itctwt'cn tlio 
middle of the Imse mid tin- perdciidiciiliir let full from the v«'i*ti- 
cal allele on Ihe base is ."Ji fl. Find (1) the other sides of the 
triangle, (2) the length of the perpeiidieiihii'. 

H. The lieight of a tower on a river bunk is ir)4 ft. Tie 
length of a line from the top of the tower to tin' opposite bank 
is 170 ft. Find the breadth ol' the stream. 

t). Find the surfaces of the cubes whosi* contents are 1)201 cii. 
in. ttud IDGH.'] e. in. respectively. 

10. A man has a circular lawn 75 ft. in diameter. What is the 
length of a string that as radius would des<'ribe a circle contaiu- 
iug 9 times as much ground.' 

EXERCISE CCLXVI. 

1. A circular garden contains 24(5400 s((. ft. A pole ])lnced 
in the centre of tlie garden is broken and the top just reaches 
the odge of the garden. Find the heiglit of the piece still 
standing, tlu^ length of the broken part being 287 feet. 

2. A cylinder is 14 ft. long and 7 ft. in diameter. Find (1) 
the area of the curved surface and (2) the area of the entire 
surface. 

3. What is the length of a stone wall that will enclose an 
acre of land in the form of a circle'/ 

4. How many men can stand on an acre of laud allowing 12 
sq. ft. to each? 

5. What length of wire without loss of metal may be drawn 
from a globe 6 in. in diameter, the diameter of the wire being 
iTo of an in.? 

6. The area of a rectangular field is 5 acres and the fence 
that encloses it is 120 rods lung. Find the length of the sides 
of the field. 

7. A stick of square timber 24 ft. long contains 90 e. ft. 
What must have been the diameter of the tree from which it 
was hewn? 

8. A square tank holding 4500 gal. of water is 5 ft. deep. 
Find its length. 

9. What is the cost of lining a water-cistern .'5 ft. long, 2 ft. 
deep and 2 ft. in. l)road, with sheet lead of 10 l)>. per square 
foot at $9.00 per cwt., there l)eing no lid. 

10. What is the cost of painting a t'onical spire whose slant 
height is 120 ft. and circumference at the base GO ft., at 8 c. 
per sq. yd.? 

EXERCISE CCLXVII. 

1. Three squares contain respectively 36, 04, and 576 sq. ft. 
Find the length of a side of that square which Juih tin jirop: 
pqual to four times their sum, 



MI8(;KIiLANE()UH KXKRCISEH. 



171 



[•net! in 
i>en the 
,. v»'i'ti- 
I (it the 

t. Tie 
tv bank 

!)201 en. 

lilt is the 
contiiin- 



,le placed 
,t rcachrrt 
»iuce Htill 

Find (1) 
the entire 

snelose an 

llowinj; 12 

be drawn 
^vire being 

the fence 
the sides 

[s 90 c. ft. 
which it 

a ft. deep. 

lon^^ 2 ft. 
I per square 

Lvhose shmt 
|ft., at 8 c. 

57G eq. ft. 



2. What in llie h-iiRth of a perin'tHlicuhir I<'t fall from any 
nnj,'le of an equilateral triangle to its opposite side when this 
siile is 12 yd. louj^? 

.'5. How many elmins are there in the side of a field in the 
torm of an (>(piilateral trianj^le, containing; 24 acres? 

4. The len>,'th of a rectangle is 12 chains. What is its 
In-eadth to contain 4 acres? 

f). The sides of a i-ectangle are 77 yd. and ;i2 yd. What is 
the diameter of a circle of ecpial areaf 

(i. The liase and perpt^jidicular of a right angled triangle are 
44 ft. and (>'.i ft. respectively. Find the diameter of u circle of 
equal area. 

7. The l)a«e and i)erpendicular of a right angled triangle are 
respectively, IIOH ft. and 87") ft. long. Find the diameter of a 
circle equal in area to the triangle. 

8. The side of a square is 15 ft. long. What is the length of 
the diameter of the circumscribed circle? 

9. The length of a stick of timber is 24 ft. ; its breadth is 3 
ft. and its thickness 2 ft. 9 in. Find the area of the entire 
surface. 

10. Find the volume of a cylinder 21 inches i i diameter and 
20 ft. in length. 

EXERCISE CCLXVIII. 

1. Find the area of the surface of a sphere lii ft. in 
diameter. 

2. The side of a cubical box is 20 in. long. Find the 
length of its diagonal. 

;$. The volume of a cube is 4096 cu. in. Find the length of 
its diagonal. 

4. A room 18 ft. high is quarter as long sigain as it is wide and 
its cubical contents are 20250 cu. ft. Find its length and 
breadth. 

5. Find the weight of a metal disc 7 ft. in diameter, and li 
ft. thick, if a cubic foot of this metal weighs 371 lb. 

6. How many planks each 13i ft. long and lOi in. wide will 
cover a platform 54 yd. long and 21 yd. wide? 

7. A cii'cular plate- of lead 2 in. in thickness and 8 in. in 
diameter is converted without loss into spherical shot each of 
.05 in. in radius. How many shot does it make? 

8. If a cube of lead the edge of which is 1 in. long weighs 9 
oz., find the weight of a cube of lead whose edge is 3 in. long. 

9. A solid sphere of iron 12 in. in diameter is melted and 
cast into a hollow cylinder 7 in. in radius, Hovv long is the 
cylinder, the iron being 2 in. thick. 

10. A sphere 5 in, in diameter weighs 75 oz. Find the 
weight of a sphere 4 in. in diameter iP^^i^ ^^ paaterial 2b% 
heavier than the other, 



CHAPTER XIII. 



THE METRIC SYSTEM OF WEIGHTS AIND MEASURES. 

The Metric System of Wciglits and Measures is 
])ase(l upon the deeimal m'n\v of notation. 

It is used in seientifie treatises, aiul lias heen 
adoi)ted ))y most of tlie nations of p]uroi>e 
and South America. 



Its advantages are: — 

(I) It is easily applied. All the opera- 
tions are the same as in simple numbers. 

^ (2) It does away with Reduijtion, Addi- 
2 tion, Subtraction, Multiplication and Divi- 
I sion of Compound Numbers. 

I (3) Its general introduction would 
g greatly facilitate commerce and exchange, 

II giving all nations a universal system of 
g weights and measures. 

I The fundamental Unit is the Metre, 
rt From this all the other units of the 

1 system are derived, hence the namc^ IVIetrlc 
7 System. 

2 The principal units of the system are as 
I follows: — 

I The unit of Length is the Metre, which 
^ is 39.37 inches. 

The unit of Capacity is the Litre, which 
is .2201 gallons. 

The unit of Weight is the Gram, which 
is 15.43 grains. 

The unit of Surface is the Are, which 
is J19.6 so. yd. 

173 



01 



^ 




9 : 

01 L 

Q - 

^^ I 

« : 

Cl - 

T^ - 


CO 

1 C4 



THE METRIC BY8TEM. 



173 



\SUBES. 

liis 1h'<'^^ 



lio opt-va- 

ion, A(Wi- 
and Divi- 

(^^i would 
cxcluinKf, 
svsteiu of 



Tli(< Metri<; Syslcni is entirely (UmmiiihI. The siib- 
iniiltiples siiid multiples of the unit tin; denoted l>y 
the t'oliowinj^ prefixes : — 



Milli = .001 

Ceiiti = .01 

Deci = .1 

Deka = 10. ^timew, 

Heeto = 100. 

Kilo = 1000. 

Myria = 10000.' 



a metre. 

a litre. 
1 a gram. 
[liix aru. 



LINEAR MEASURE. 

10 millimetres (mm.) = 1 centimetre 
10 ceiitimetreH (cm.) = 1 decimetre 
10 decimetreH (dm.) = 1 metre 
10 metres (m.) = 1 dekametre 

10 dekametres (Dm.) = 1 hectometre 
10 hectometres (Hm.) = 1 kilometre 
10 kilometres (Km.) = 1 myriametre 

Note. — 1 metre = 39^ in. nearly; 70 yd. = G4 metres nearly. 
1 kilometre = 1 100yd. nearly ; 8 km. = 5 mi. nearly. 



.01 


metre. 


.1 




1. 




10. 




100. 




1000. 




10000. 





48.3 mm., 
(1) as centimetres, (2) as decimetres. 



EXERCISE CCLXIX. 

1. Read the following:— 37.5 m. ; 12.7 cm. 
7.H05 Dm. ; 9.7 dm. 

2. Express 4560 mm. 
(;{) as metres. 

3. Express 1.87 Dm. — (1) as metres, (2) as millimetres, (3) 
IIS centimetres. 

4. Simplify .789 m. + 78.9 cm. + 7856 mm. + 1897 km. 

5. Simplify .845 Km. — 6457 cm.; 6.59 cm. — 54.87mm. 

6. Simplify 768.4 cm. X 12; 3.7896 dm. X 789.5. 

7. A ]>ook is 3.2 cm. thick. If the average thickness of the 
leaves is 05 mm., find the number of leaves in the book. 

8. Tilt 'Ircumference of a wheel is 6.3 m. in length. How 
often will such a wheel turn in going 173.88 Km.? 

1>. Find the cost of 27.84 m. of cloth at $2.75 per metre. 

10. The Mont Ceuis tunnel is about 12.22 Km. long. How 
iimny miles is this? 

H. Find the cost of building a railroad 37 Km. 47 m. long at 
*irtOOO a kilometre. 

12. How often will a bicycle wheel 225 cm. in circumference 
turn in going from Toronto to Hamilton a distance of 63 Km.? 



174 



ARITHMETIC. 



SQUARE OR SURFACE MEASURE. 

100 sq. millimetres (sq. mm.)- 1 sq. eeiitiiii(>tie=^ .OOdl sq. metre. 

100 sq. centimetres (sq. cm.) 1 sq. decimetre == .01 

100 sq. decimetres (sq. dm. )--l sq. metre =- 1. " - 1 centare. 

100 .sq. metres (sq. m.) 1 sq. dekiiiiietre 100. " =--1 are. 

100 sq. dekametres (sq. Dm.)- 1 .sq. liectometre - 10000. "=1 hectare. 

100 sq. hectometres (sq. Hm.) -=1 sq. kilometre =1000000. 

NoTK.— The -ML, ceutiire juid hectare are used only in land 
measure. 

The are is slightly less than 4 sq. rods. 

The hectare is slightly less than I2i acres. 

EXERCISE CCLXX. 

1. Convert 287G345 sq. m. into hectares. 

2. How many arts are there in 3.7850 sq. Km.? 

3. Write 5.7536 sq. ni. as sq. centimetres; as sq. millimetres. 

4. How many sq. metres are there in 2.34' 7 sq. Km.? 

5. How many sq. centimetres are there in .0542 sq. m.? 

6. Write as one quantity in sq. metres 3 sq. Km. + 3 sq. 
Hm. -■}- 3 sq. Dm. -f 3 sq, m. 

7. How many ares are there in a rectangle 200 metres long 
and 50 metres wide? 

8. How many sq. metres are tliere in a rectangular floor 
0.8 m. long and 4.8 m. wide? 

9. What will be the cost of 5 sq. m. of sheet tin at 5 mills 
a sq. decimetre? 

10, How many bricks, each 20 em. long and 10 em. wide, 
will be required to pave a sidewalk 3.3 m. wide and 1.7 Km. 
long? 

MEASURES OF CAPACITY. 

1000 cu. millimetres (c. mm.)=--l ci. centimetre = .000001 cu. metre. 

1000 cii. centimetres (c. cm. )=-l cu. decimetre = .001 " =1 litre. 

1000 cu. decimetres (c. dm.)=l cu. metre =1. " =1 stere. 

Note. — In measuring wood a cul)ic metre, called a stere 
(st.), is used; 3-0 steres = 1 "ord nearly. 

In measuring liquids the cubic decimetre, called a litre. In 
used. 

In measuring grains, fruits, etc., the hectolitre is r.sed. 

The numeral preiixes are used with the litre af with tln' 
metre. 

EXERCISE C'JLXXI. 

1. How many steres of wood are there in a p'ie 29 m. long, 
1.25 m. wide, and 2 m. high? 

2. What will 17.3 HI. of Wiieat cost at $0 25 a dekalitre? 






'^HE METRIC SVSTEM. 



only in land 



10 cm. wide, 
and 1.7 Km. 



ed a litre, is 



175 



.01 
.1 



, '^- 'f^W J.lfUlv )it,.,.w .,„ ., ^' 

'"ll.-"' i- .i m!'*l„" j"'i "•■; ''l«t will „„ ti,, ,.„,. „f ,. . 

JO deei^^rams 1]?/) Z J ^^««iS''fim = 

JO grams ^A^/ ^ .J ff^'fim :^ j 

.NOTR.--A cubic cenfilT ^'^'^^'^'am == ,000. 

1 - am - L,| ^,,.,^j,^g 

AJ<.,„,.„,„ = ,, ,, ^,„,',>;',;« «™-= 1 o... Avoi... ,.e„W.. 

K'UO kilograms ^ 22 evvt - w 

A "tre of water weig],, l" 7uL ""'' ^' "^^*"« to". 

A eiibie metrfl nC . ^^^'ogram. 

metie of water weighs looo 1-n 

J- Write 5 Kg .^ j^''^''''*^^ CCLXXII. 

4. Express oT-7" ' "'^ ^^"t'>''am?s.^'' ^ «^nt,grams and 5 
. ''■ ^^'^lat is thetl ^'""''' «« f'entigrams 

,^;ram.? ''*''*^^««o«tof .67225Kg of o. • 

^- ''^ "l"'"" at G2,l et. per 



ffJ'fun. 



^!v*C^ 



17G 



ARITHMETIC. 



1). (Jivo llic w»'if,'lit ill milli<j:riuiis of a pill wlion n, mass 
wcij^liiiij^ 21.7 K- '^ iiiiiclc into 70 pills. 

10. Wliiit decinuil is ;") K- '^ <'K- <**^ <>"<' l<iloj?riim? 



EXERCISE CCLXXIII. 

Write* tlio following: — 

1. {a) Write 7 dekametres, 2 decimetres and f) centimetres 
as nieti-es. 

{h) Write H hectolitres, 8 litres and 7 decilitres as litres. 

((') Write If) ares, 9 declares and 8 milliares as ares. 

(d) Write 27 kilograms, ',i decigrams and 7 centigrams as 
grams. 

2. Mercury weighs 115. f) times as much as water. Find the 
weight of 44 litres of mercury. 

;j. Marble weighs 2.7 times as much as water. Find the 
WH'ight of a rectangular block of marble 2.5 m. long, 1.75 m. 
wide, and 4 m. thick. 

4. If silver weighs 10.5 times as much as water, how many 
coins, each weighing 5 grams, can be coined from a cubic 
decimetre of silver? 

5. If alcohol is 80% as heavy as water, find the weight of 
485 com. of alcohol. 

0. How many steres of wood are there in a pile 50 m. long, 
1.1 m. wide, and 2 m. high? 

7. What is the ])rofit on 75 hectolitres of potatoes, l)ought 
at 7 francs a hectolitre, and retailed at 1 franc a dekalitre? 

8. How many hectolitres of apples, at $1.25 a hectolitre, 
should be given for 5 dekasteres 5 steres of wood at 75 ct. per 
stere ? 

9. A druggist having .75 Kg. of quinine 'makes up 500 pills 
containing 2 decigrams of quinine each. How many grams ho,s 
he left? 

10. A farmer, having 4 hectometres of wire fence, uses a 
portion of it to enclose a field 50 metres square. How many 
metres has he left? 

11. What will be 'the profit on 10 g. of calomel, bought for 
50 ct., if sold in powders of 5 dg. at 5 et. each. 

12. A train runs 47.5 Km. per hour. How many miles does 
it go in 6 hr. 24 rnin. 

i;5. How often can a cup, holding 3 ci., be filled from a- 
vessel containing 14.:?1 1. of water? 

14. How many rolls of wall pjiper, 10 m. long and .5 m 
wide, are needed to paper the walls of a room, 6.3 m. long, 4.2 
m. wide and 3.2 m. high? 



lien a mass 



centimetres 



r. Find the 



CHAPTER XIV. 



^'SCELLANE^ EXERCISES 
»• CfRCULATrNO DECIMALS 

Recurring Decimals. '"^'"'*^' Circulatinq o, 

A Terminating Decimal 

- '-t I.mited number ornH^^^^^^^ ^^^'^'^^ ^'^^'^'"cls 

i>*'"'^ as .375, .()()24 ^^''''"^^ ^^•^>"' the DeoimaJ 

A Circulating Decimal , 

''«'"''^n or set of tinn^, /• "' ^" ^^'^^^^'^^ ^h. su,m. 
same order as ^n'7'7 ' ''''^^^'^^I'dUy reeurs in 

,.,.TheRepete„d.«.,,„,eor.,;,«^„.,.,_,„,.,^,_ 

.^Circulating DeclmaU . ' ■-•^*'** 

M.xed arc„?atl^g'7?eclmals""""'' " "' ^-^^ ,..,„ 

'^""'l'"'e tho foil • ^•'^^'*^'SE CCLXXIV. 



1. 



J 

3" 

4 

Si 






fl 



H r, 
Ti r. 



*. 






^\^!'f^ 



178 



AKITIIMETIC. 


5 

7 


^r 


^ 


t\ 


iV 


n 


S 1 
22 


S6 

2 8 


AV 


14T 


■1V4 


^VST 


4 r, i» 
6 


111 


DOT 
14U 8 


.Vt 



o 4 

'>. 1 

4. i\ 

5. I 

6. 11 

7. H 

8. If 

y. 84 

10. 2 88 

EXERCISE CCLXXV. 

Reducn the followiuK to vulgar t'nietions hi their lowest terms:— 

1. ' 



1 
1 J. 

1 
T 1 • 

1 .{ 
1 4. 

1 1 
"44f • 

29 

Tift. 

8 
21 . 

8 9 1 

"17 7 (r . 

2 7 7 
"I37ff. 



.5 .17 .;i6 

2. .018 .627 .OOU 

3. .054 .'h'-i .1376 

4. .945 .423 .78;i 

5. .9801 .923076 .142857 

6. .954 .527 .3si 

7. .7852 .103G .01(59 

8. .G59(') .00()75 .24376 

9. .7954 AWAh 2.297 

10. 4.00(i 5.o6() 7.00(5 

EXERCISE CCLXXVI. 

Simplify the following: — 

1. .23 + .234 + .2345 + 5.7 + .12345. 

2. .1(5 + .792 + .21431 + S)iS + .5(5. 

3. 25.12;i — 15.(53; l9.io7 — 5.043. 

4. .574 — .2rx; .574 — .25. 

5. .754 + .213 — .(5S47 + .45()i — .00(5. 
G. .(53 X 2.5; 2.15 X 3.204. 

7. .1(5 X .72; .75 X .75 X .75. 

S. .339 - .72; .SI — 2.3. 

i). 2.7;!<5 — 4.3; 51. SI — 5.18. 

1<>. 4.37 X .27 —2.18; .154 — 2 X 11.25. 



.210. 

.144. 

.296. 

.261. 

.285714. 

.24390, 

.01315. 

.3857142. 

7.675. 



Ta O 



7. 






«« jrVVv^ <": 



CIRCULATINO DEC^IMALS. 



179 



At terms: — 



)714. 

m. 

6. 
)7142. 

75. 
|7. 



EXERCISE CCLXXVII. 

1. The product of .9, .19 and a third factor is 2.1. Find 
the third factor. 

2. What must be multiplied by .809523 to produce .liif 

3. Without dividiufif, .vrite the decimals equivalent to rooryt 

7 1 7L 7.1 7 1 _Xl_ 7_1_- 

UUU) OUO) UOd> WIMIOJ UOOO) llttUU* 

4. What two numbers are those the sum of which is 
.l!)-i and the greater exceeds the less by .128? 

"). Without dividing, state what kind of decimal each of the 
following are e<iuivalent to: — I, ^, n, ^, -i\, v, A, T. 

G. Simplify .(5518 -^ .140 X .225 + 5 — .15. 

7. Simplify .7 of £3 + .2i of 5s. + .:!(') of lid. 

8. Simplify .38 of 9 t. + .144 of 37 lb. — .45 of 3cwt. 74 lb. 

9. Simplify .375 of 16 mi. + .40 of 198 rd. + .35 of 4^ yd. 
10. How many tons, cwt., etc., are there fn .375 of 185 t. ? 

EXERCISE CCLXXVIII. 

1. Describe the vulgar fractions whose equivalent decimals 
are finite. 

2. Why do I, 1, ro, "/o> ¥u, iso and fi i)roduce finite decimals? 

3. How many figures will there he in the decimals equivalent 
to ixij s, :T2? and airo. 

4. Why do §, ^, n and ;\^ produce infinite decimals? 

C-,. How many figures will thcic lie in the non-re|)eating 
part of the decimals, equivalent to §, j|, jij, H> and ^ff? 

(). Whether is 7.45()48 more accurately represented by 
7.450 or by 7.457? 

7. Show that .005 X .005 X .04 X .04 = .0002 X .0002. 

8. Show how a numl»er may be multiplied or divided by 10, 
100, 1000, etc., by merely shifting the decimal point. 

9. Su]»pose unity represents .0015, what decimal will 
represent .0002? 

EXERCISE CCLXXIX. 

1. A father, dying, left .518 of his property to the elder of 

his two sons, and .518 of the rest to his younger, and the 
n'Uiiiinder to his wife. The older son received $1900 more than 
the y(,nnger. What did the elder son receive? 

'.'. A reservoir is 03, ;j ft. long and 48.5 ft. wide. How many 
•'ultf ft it of water must be ]iumped out of it to make the 
uider sink 3 it.? 



180 



ARITHMETIC. 



;j. Divide $G54.50 amonp A, B and C in proportion to the 
numbers 1.3, 2.5, and 2.7. 

4. A man, after spending .4 of his money, found that .6 of 
the remainder was $40. How much had he at first? 

5. Multiply the sum of 1.5, .6 and .75 by the difference 
between .26 and .15, and divide the product by 43.5. 

6. A man on a journey goes .6 of it by train, .18 of it by 

street ear and walks the remaining distance in 1.6 hours at the 
rate of 3 miles an hour. How far is the distance? 

7. The area of a square field is 72.9 acres. How long will 
A require to walk around it at the rate of 3.3 miles per hour? 

8. A grocer buys tea at 30c. ; twice as much at 33.3c. ; and 

three times as ranch at 36. 6e. per lb. He mixes the three kinds 
tojijuther and sells the mixture at 40c. per lb. Find his gain 
p( r cent.? 

9. Subtract .08 from .08 and divide the remainder by .625. 



II. PROBLEMS RELATIING TO WORK DONE. 
EXERCISE CCLXXX. 

1 . If A and B cnn do a woik in f of a day, and B alone can 
do it in 2i days, how much more does A do than B in 1 day? 

2. A can do a work in i day; B can do it in i day and C in 
i day. How long will it take if all begin working together to 
do the entire work? 

3. A can do a work in 4i days; B can do it in 3^ days. 
Wi^h the help of C the work can be done in li days. In what 
time can C do the work? 

4. A's working power is t of B's working power. How long 
would A take to do what B dtfes in 12i days? 

5. B liikes I of the time that A takes to do a work. What 
fraction of B's working power is A's working power? 

6. A and B take 18 days to do a work, A doing twice as 
much as B. In what time could each do the work by himself? 

7. .V, B, and C can do 5 of a work in 3i days, A doing half 
as mucli as B and twice as much as C. In what time could 
each do the woi'c by himself? 

8. If 10 men can do a work in 15 days, how soon after cora- 
meticing v.mst 4 additional men be employed so that the work, 
may bo done in 12 days? 



CLOCK PROBLEMS. 



181 



9. A can do a work in 27 days, and B in 15 days. A works 
at it alone for 12 days; B then works alone for 5 days; then C 
finishes the work alone in 4 days. In what time could € do the 
whole work by himself? 

10. If 5 men or IG boys cau do a piece of work in 15 hours, 
in what time could 3 men and 48 boys do the work ? 

11. If the times taken by A, B, and C to do a work are as 1, 
2, and 3; and tof^ether they cau do the work in 20 days, in 
what time could each do it by himself? 

12. A does ^ of a piece of work in 12 days. He then calls in 
B, and they finish the work in li days. How long would B 
take to do the whole work l>y himself? 

13. A and B can together do a work in 14 hr. 56 min. A 
alone can do it in 28 hr. In what time could B alone do it? 

14. A can do a work in 3| hr., B in 2i hr., and C in 3i hr. 
In what time will it be finished by the three, if B begin i hour 
after A, and C 22i miu. after B? 

15. If 2 liorses do the same work as 3 mules, how many 
horses along with 7 mules will be required to draw 9i tons the 
same distance in the same time that G horses and 5 mules cau 
draw 7 tons? 

16. A can do a work in 12 days ; B can do it in 15 days and C 
in 10 d.iys. They all begin to work together but A stops 2 days 
and B 1 j days before C who finishes the work. How long does 
each one work? 

17. A can do a piece of work in 7i hr. ; B can do it in 8i hr. 
If tliey do it together and the work is worth $2.10, what sum 
ouulit each to receive? 



III. CLOCK PROBLEMS. 
EXERCISE CCLXXXI. 

1. The hands of clock are together. In what ti' *o will they 
be 11 minute -spaces apart? 22 minute-spaces apart? 27i 
minute - spaces apart ? 

2. The minute-hand is 16i miiuite-spaces behind the hour- 
hand. When will they be together? 

3. At what time between 3 and 4 o'clock are the hands of a 
watch together? 

4. Find the first time after 6 o'clock tliut the hands of a 
clock are at riglit angles. 

5. The hands of a clock are opposite each other at 6 o'clock. 
At what time will they l)e togetluM* for the first time? 

6. Find the first time after 5 o'clock that the luinds of a 
clock vviU be 3 minute -spaces apart. 



182 



ARITHMETIC. 



7. Fiiul the times between 6 and 7 o'clock wlien the linnds 
of u watch are 8 minute-spaces apart. 

8. Find the time after 8 o'clock when the hands of a clock 
are («) together; [h) at right angles; (c) opposite each other. 

9. Find the times Lotween 9 and 12 o'clock when the hands 
of a watch are together. 

10. Find the first time after 5 o'clock that the hands of a 
watch are equally distant from the figure five. 

EXERCISE CCLXXXII. 

1. Find the first time after 4 o'clock that the hands of a 
watch are 48° opiri. 

2. Tlie hands of a watch are 18° ajjart for the second time 
after 3 o'clock. Find the time. 

3. Find the first time after 6 o'clock that the minute-hand 
is midway between the hour-hand and the figure six. 

4. Two clocks are together at 12 o'clock. One loses 8 sec. 
and the other gains 7 sec. in 24 hours. \Vh('U will one be half 
an hour ahead of the other and what time will each show? 

5. Two clocks are together and show correct time at noon. 
One loses 5 see. and the other 7 sec. in 12 lir. When will one 
be 5 minutes faster than the other? 

6. A clock loses 5 sec. in 24 min. At 9 p.m. on ^Monday 
it is 17 min. fast. When will it show cori-ect time? 

7. A watch set accurately at 12 o'clock indicates 5 min. to 5 
at 5 o'clock. What is the exact time when the watch indicates 
5 o'clock. 

8. One clock gains 2 min. in 12 hr., and another loses 2 
min. in 24 hr. Tliey are set right at noon on Friday. What is 
the time indicated by each clock when one appears to have 
gained 8.i minutes on the other? 

9. A clock which was 1.4 min. fast at quarter to 11 p.m. on 
May 2, was 8 min. too slow at 9 a.m. on May 7. When was it 
exactly right? 

10. A watch showing correct time at noon on Tuesday gains 
3 min. 40 sec. in 24 hr. What is the correct time on Saturday 
evening when it is 10 o'clock by the watch. 

IV. PROBLEIVIS IINVOLVIfNO VELOCITY. 
EXERCISE CCLXXXIII. 

1 . How many feet per second is equal to a rate of 30 miles 
l)er hour? 

2. ITow many miles per hour is equal to a rate of 50 ft. per 
second? 



THE SUM AND DIFFKRENCE OK TWO NUMBERS. 



183 



3. A train 22 rods lonp' i)aHS08 a post in 11 socondH. At 
wliat ratt< per hour is it moviiif?? 

4. How loiif^ will a train GO yd. in length, moving .'JO miles 
per hour take to pass another 50 yd. long standing on a sidingf 

5. A railway train moving at the rate of 49 miles {»er hour 
goes 7 miles while a coach goes 2 miles. How long will it 
require the coach to go ;{.36 miles? 

6. A is walking 4 miles an hour, and B, who is 4 miles ahojid 
of him, is walking 3i miles an hour in the same direction as A. 
How long will it be before A overtakes B? 

7. A starts from Sarnia to walk to London, u distance of GO 
miles. At the same time B starts from Londoti to walk to 
Sarnia. If A goes 4J miles per hour and B ',ii miles per hour, 
how far from Sarnia will they meet? 

8. In a mile race A can beat B >)y 80 yd. and C by 87 yd. 
By how much can B beat C in a mile race? 

9. In a mile race A can beat B ])y 22 yd. and B can beat C 
by 11 yd. How many yards start can A give C that there may 
be a dead heat? 

10. If the hands of a clook coincide every G5 minutes, how 
unich does the clock gain or luse in a day? 

V. PROBLEMS IINVOLVIINO THE SUM AND DIFFERENCE 

OF TWO NUMBERS. 
EXERCISE CCLXXXIV. 

1. The sura of two numbers is .'565; their difference is 83. 
Find the numbers. 

2. A man rows at the rate of 7 miles per hour down a 
stream which flows at the rate of li miles per hour. Find his 
rate of rowing against the current. 

3. A man can row 8 miles down stream in 2 hours, but he 
takes 3 liours to row back to the starting point. Find the rate 
of the stream. 

4. If a man rows 10 miles in 21 hours against a stream, the 
rate of \ylnch is U miles per hour, how long will he be in 
rowing 3 J miles down the stream? 

3. A man rows 15 miles down stream in 21 hours and up in 
4 hours. Find his rate of rowing in still water. 

G. A can row a distance down stream in 15 minutes and the 
same distance up i,i 20 minutes. Wliat is the distance, the 
rate ot the stream being 1 mile per hour? 

"• A man rows on the still water of a canal one mile in 15 
|iiin. Tie then reaches the river and rows down stream U miles 
"I the next 15 min. How long will he take to return to the 
starting-point? 



!!' 



184 



ARITHMETIC. 



H. IIow far can a man who rows 4 miles per hour in still 
water row up strenm, which Hows nt the rate of 2 miles per 
hour, so that he may be 2 hours before he returns to the Vioat- 
house? 

9. A crew can row down a stream a eertain distanee in 2 
hours and back the same distanee in .1 hours. Comi)are the 
rate of rowing in still water with the rate of the stream. 

10. If A can row (ii^ miles in 2h hours against a strenm flow- 
ing H miles an hour, how long will it take him to row 12 miles 
with the current? 

EXERCISE CCLXXXV. 

1. A skated G miles at the rate of 10 miles an hour with the 
wind and returned against it in 50 minutes. Find tli»' rjito of 
the wind i)er hour. 

2. Two trains moving on parallel traeks in opposite direc-' 
tions, and respectively 110 yd. and 8s yd. long, pass each other 
in ;') sec, and, when moving in the same direction, the faster 
l)asses the other in 45 see. Find their rates in miles per hour. 

',]. A train 110 yd. long, moving i mile a minute, meets 
another on a parallel tiack, moving 40 ft. per see. and passes it 
in 8 sec. Find the lengtii of the second train. 

4. If telegraph poles are 88 yd. apart, and one is observed 
to pass the window of n r.-iilway car every 4 sec, at what rate 
pc hour is the train moving? 

5. An express train going 57 miles an hour passes a station 
5i min. after a freight, going 38 miles an hour. When will the 
express overtake the freight? 

6. A train going 30 miles an hour passes a man walking in 
the same direction at 3 miles per hour in 10 sec. Find the 
length of the train. 

7. The whole time taken by a train 150 yd. long in crossing 
a bridge at the rate of 25 mi. per hour was 20 sec Find the 
length of the bridge. 

8. If a train 88 vd. long overtakes a person walking at the 
rate of 4 miles per hour and passes him in 10 sec, what is the 
rate of the train in miles per hour? 

9. If a train 110 yd. long meets a person walking on the 
railway at the rate of 5 miles per hour, and passes him in 8 
sec, what is the rate of the train in miles per hour? 

10. A train 352 ft. long overtakes a man going in the same 
direction at 4 mi. per hour and ])asses him in 15 sec Shortly 
after it passes a man walking in the opposite direction in 9 
sec. At what rate per hour is the second man walking? 

11. A train 88 yd. long takes 10 sec to cross a bridge 44 yd. 
long. At this rate, how many hours will it take the train to 
go 180 miles? 



REVIEW EXERCISES FOR THIRD CLASS. 



185 



'< 



; 






VI. REVIEW EXERCISES FOR THIRD CLASS. 
EXtRCISE CCLXXXVI. 

1. Two pieces of elotli of the wjuno length cost $r);{.G4 iiml 
!}!(J9.lL!, respectively. Tlu* price of the hist was !)!i.4y u yiucl. 
What wjis the price of second per yard? 

2. Three l)iif,'s couttiiued 025 nuts. The first bag contained 25 
more than the other two together; and the second contained 5U 
more than the third bag. How many nuts are there in each 
bag? 

3. A man living on $700 a year for 6 years finds that he is 
exceeding his income and then lives on $500 a year for 4 years 
and finds he is just out of debt. What was his income? 

4. How often can £3 17s. lOid. be subtracted from £288 4s. 
lid., and what is the last remainder? 

5. A boy had the same num])er of five, ten, and twenty-five- 
cent pieces, and had $6.80 in all. How many pieces of each 
kind had the boy? 

<). Find the largest number that will divide '{65, 540, and 
1140, leaving as remainders 20, 17, and 13, respectively. 

7. A, B and C have JC53 Os. 8d. among them. B and C have 
£40 2s. 8d. ; A and C have £29 10s. How much has C? 

8. How many l)oards 15 ft. long will build a straight fence, 
(i boards high, around a field 120 rods long and 30 rods wide? 

9. A man ploughs a furrow 8 in. wide the whole length of a 
field in 6 minutes. How many hours will be required to plough 
a ridge 16 ft. wide? 

10. A farmer's wife sold 8 pairs of ducks at 75 ct. a pair and 

13 pairs of chickens at 50 ct. a pair and received payment in 

•sugar at 16 lb. for 1 dollar. How many pounds did she receive? 

EXERCISE CCLXXXVII. 

1. Into a veetangular cistern, the bottom of which is 8'ft. by 
6 ft., water is pouring at the I'ate of 500 gal. per hour. How 
long will it take to fill the cisl rn to a depth of 4 ft.? 

2. Divide $25.75 among 10 men, 8 women, and 7 boys, giving 
each man 50 ct. and each woman 25 ct. more than each boy. 

3. A agrees to trade apples at $2.50 per bbl. for cloth at 
$1.75 per yard. What is the least numbers of barrels that can 
be exchanged for an integral number of yards? 

4. The quotient is 7469; the divisor is 728, and the remainder 
is 19. If the dividend remains unchanged what divisor would 
give as quotient 5320 and remainder 411? 

5. A and B ran a race. B had a start of 20 yd., but A ran 



3 yd. while B ran 2 yd. and won by 5 yd. 
the race? 



Find the length of 



<^. 



^^'^'5* 

o /*>.^. 




IMAGE EVALUATION 
TEST TARGET (MT-3) 




1.0 



I.I 



1^121 12.5 

^ Ufi 11 2.0 



1.8 







L25 1 M, 


1.6 




^ 


6" - 




► 



v^ 



7: 







Photographic 

Sciences 
Corporation 



23 WEST MAIN STREET 

WEBSTER, N.Y. 14580 

(716) 873-4503 




^ .<. 







Ili 



186 



ARITHMETIC. 



U. If 30 men do a piece of work in 24 diiys working 10 hours 
a day, in bow many days would 25 men do the sunie piece of 
work, working 9 hours a day? 

7. The hind wheel of a wagon is 12 ft. in circumfereneo and 
turns 7480 times in going from one village to another. How 
many miles are the two villages apart if 

8. A man bought 120 A. of land for $7800. He sold 30 A., 
gaining $10 per A. and 45 A. at a loss of $15 per A. At what 
price per A. must he sell the rest to gain $300 in the whole 
transaction if 

9. A farmer sold 250 animals (sheep and pigs) for $1720. 
He received $8 for each sheep and $6 for each pig. How many 
were there of each If 

10. The cost of 5 coats and 4 vests is $33.25, each coat 
costing $1.25 more than a vest. Find the cost of a dozen coats. 

EXERCISE CCLXXXVIII. 

1. A bankrupt paid $2.50 out of $4 on one-half his debts and 
$2 out of $4 on the other half. Altogether he paid away $7200. 
How much did he owe? 

2. A man buys 128 gal. of wine at $1.70 per gal. How 
much water must be added to gain $33.40 on the outlay by 
selling the mixture at $1 per gallon? 

3. A farmer sells 9 horses and 7 cows for $1200 and 6 horses 
and 13 cows for the same sum. Find the price of 3 horses and 
8 cows at the same price. 

4. A person bought 475 apples at 5 for 6 ct. and another lot 
at 8 for 5 ct. He paid altogether $10.20. How many of the 
latter kind did he buy? 

5. A divided a field 40 rods lon^j .md 24 rods wide into lots, 
each 165 ft. long and 66 ft. wide and sold all for $1800. Whnt 
price did A get for each lot? 

6. A grocer bought 60 chests of tea weighing 40 lb. each for 
£280 and sold it at 3s. 6d. per lb. How much did he gain? 

7. What is the value of a pile of cord wood 60 ft. long, 8 ft. 
wide and 8 ft. hi^h at $3.25 per cord? 

8. Find the greatest unit of time by means of which 23 hr. 
2 min. 36 sec. and 46 hr. 8 min. 55 sec. can both be expressed 
as integers. 

9. Divide $1078 among John, Thomas, and Henry, so that 
John has 5 times as much as Thomas, and Thomas 8 times as 
much as Henry. 

10. A farmer planted 60 rows of corn. Each row had 240 
hills and 5. hills produced one quart. The crop was sold for 
$50.40. What was the price per bushel? 



REVIEW EXERCISES FOR FOURTH CLASS. 



187 



EXERCISE CCLXXXIX. 

1. Find the cost of o.irpetinf? a room 18 ft. loiij? iiml 13 ft. G 
in. wide with carpet 2 ft. 3 in. wide at 75 et. a yard. 

2. How much rope will it take to tie a box in the ordinary 
way, tlie box beinj? 4 ft. by 3 ft. 2 in. by 2 ft. 8 in., allowing? 1 
ft. G in. for the knot if 

3. The average height of four boys is 4 ft. 7 in.; but if 
the height of two others be considered, the average height of 
the six will be 4 ft. 5 in. Find the average height of the other 
two. 

4. If 5 lemons are worth 4 oranges, and 2 oranges are worth 
3 apples, find the price of 15 lemons when apples are worth 10 
ct. per doz. 

5. Find the smallest number of rails of equal length that can 
be used without cutting to make a straight fence 6 rails high 
around a rectangular lot 1089 ft. long and 1375 ft. wide. 

G. The product of four consecutive numbers is 212520. Find 
the uumbers. 

7. On counting out the marbles in a bag by 3 at a time, or 
by 4 at a time, or by 5 at a time there are always 2 over; but 
on counting them 7 at a time there are none remaining. Find 
the least number of marbles there could be in the bag. 

8. At 25 et. per sq. yd. find the cost of painting a close 
board fence G ft. high round a rectangular lot 40 yd. long and 
20 yd. wide. 

9. How many shingles 4 in. wide and 4 in. exposed to the 
weather would be required for a roof 35 ft. by 25 ft. ? 

10. A bale of hay is 3 ft. long, 2 ft. wide, and 18 in. thick. 
A car 33 ft. long, 8 ft. wide, andG ft. high requires 2G400 lb. 
to fill it. Find the weight of one bale? 



VII. REVIEW EXERCISES FOR FOURTH CLASS. 
EXERCISE CCXC. 

1. A farmer bought two farms of 130 A. each for $19500. 
What was the cost of an acre of each, if 2 A. in one are worth 
3 A. in the other? 

2. In going to town the front wheel of a carriage makes 2G4 
turns moi^ than the hind one. If the former is 10 ft. and the 
latter 12 ft. in circumference, how far does the carriage go? 

3. A laborer is to receive 95 ct. and his board each day he 
works, and pay 45 et. for each day he is idle, to pay for his 
board. At the end of 100 working days he receives $7G.80. 
How many days did he work? 



188 



ARITHMETIC. 



4. Wliieli is tlie pjreater cost and by how much: — feiieiiig a 
lot 40 Y(l. long and 30 yd. wide at 1.') ct. a foot or liuildint? a 
wall< round it 4i ft. wide at 29 et. i)er sq. yd.? 

5. A water tanlt without a lid, IG ft. 6 in. long, 7 ft. 6 in. 
wide, and 7 ft. deep, is lined with zinc weigliing 8 lb. to tlie 
square yard. Find the cost of the zinc at $4.90 per cwt. 

6. Four-fifths of a merchant's goods were destroyed by fire; 
I of the rest were injured. He sold the injured goods at 1 cost 
for $840 and the uninjured for $300. There being no insurance, 
find his loss by the fire. 

7. A sum of money in 5 yr. at a certain rate per cent, 
simple imprest amounts to $1131 and to $1339.80 in 9 yr. Find 
the sum and the rate per cent. 

8. A goldsmith manufactured 2 lb. 3 dwt. 8 gr. of gold into 
rings, each containing 9 dwt. 16 gr. He sold them for $8.75 
each. How much did he gain, gold being worth $18 per oz. ? 

9. If 150 men can do a work in 40 days, how soon after 
ccmmeneing the work must 60 additional men be employed so 
that the work may be done in 34 days? 

EXERCISE CCXCI. 

1. A legacy of $4500 is left to three persons in the propor- 
tion of 2, 3, and 4. What should each receive after deducting 
the legacy duty of 10 % ? 

2. A man paid $2580 for 85 head (horses and cattle) , there 
being t^i Jis many horses as cattle, and the cattle cost $8 less per 
head than the horses. Find the cost of a horse. 

3. A farmer sold a load of barley, weighing 3024 lb., when 
barley was 46 ct. a bushel. In weighing the ,?rain, the dealer 
made a mistake and took it as rye, and paid 55 ct. a bushel. 
How much did the farmer gain or lose by the mistake? 

4. A county map is drawn on a scale of 2 in. to the mile 
and covers a surface 4 ft. by 2i ft. How many acres are there 
in the county? 

5. A rectangular field whose length is to its width as 4 to 3 
contains 10 A. 268 sq. rd. Find its dimensions. 

6. A bookseller sold a book 16% below cost. Had he 
received 50 ct. more for it, his gain would have been 4%. 
Find the cost of the book. 

7. A stone wall, under a building 24 ft. longer than wide, 
contains 8550 eu. ft. This wall is 10 ft. high and 2i ft. thick. 
Find the dimensions of the building. 

8. A father gave his son $128.50. This was 66|%'of what 
^he father had left. How much money had the father at first? 

9. The amount of a note for 1 yr. 9 mo. at 6% simple 
interest was $391.17. What was the principal? 



( I 



REVIEW EXERCISES FOR FOURTH CLASS. 



189 



10. A farmer agreed to pny his hired man 8 sheep and $180 
for one year's work. The man quit work at the end of 7 mo., 
receiving the sheep and $80 as a fair settlement. Find the 
value of each sheep. 

EXERCISE CCXCII. 

1. A and B earn $4.02 in 7 days; A and C, $7 in 10 days; 
and B and C, $8.36 in 11 days. How much did each earn per day? 

2. A hare is 80 leaps before a hound, and takes 4 leaps while 
the hound takes 2, but 2 of the hound's leaps equal 5 of the 
hare's. How many leaps will the hound take to catch the hare? 

3. A sells goods to B at a gain of 12%, and B sells the same 
goods to C at a gain of 15%. C paid $3155.60 for the goods. 
What did the goods cost A? 

4. Find the time a train 184 yd. long, running 21 mi. per 
hour, will take to pass another on a parallel track 135 yd. long, 
going in the same direction at the rate of 16 mi. per hour. 

5. A hor-^e and lot are together worth $4750. Twice the 
value of the house is equal to 17 times the value of the lot. 
Find the value of the lot. 

6. If a grain dealer by selling 416 bu. of oats for $277i 
loses 10%, at what rate per bu. should he have sold the oats to 
gain 8%? 

7. A man mowing gi-ass travelled 4 mi. per hour. In 72 
min. he cut 2i-,- A. What width did the machine cut? 

8. I bought .2000 lb. of sugar, part at 7 et. and part at 10 
ct. per lb. Had I bought all at 8 et. per lb., it would have 
cost $13 less than it did. How many pounds of each kind did 
I buy? 

9. The area of a rectangular field whose breadth is i of its 
length is 15376 sq. yd. Find its dimensions. 

10. A hall 60 ft. long is to be carpeted. It is found that by 
stretching the carpet lengthwise any one of 4 pieces — f yd., 
1 yd., li yd. and li yd. wide respectively — will exactly fit the 
hall without cutting anything from th« width of the carpet. 
Find the cost of carpeting the hall with the narrowest piece at 
$1.10 per yard. 

EXERCISE CCXCIII. 

1. A train going 30 mi. an hour passes a man going in the 
same direction at 3 mi. an hour in 10 sec. How long is the 
train? 

2. A and B enter into partnership. A puts in $4900 rnd B 
$1400. B receives 6% of all the profits for management. The 
rest is divided in proportion to the capital invested. What is 
A's share of $450 profit? 



I 



190 



ARITHMETIC. 



3. In a long division example the dividend is 1768479, and 
the successive remainders from the first to the last are 127, 180, 
166, 28. Find the divisor and the quotient. 

4. What is the prime cost of a yard of clotli, if selling it at 
1% gain brings $1 more than selling it at 11% loss? 

5. Twenty-five animals (cows and calves) cost $427.75, but, 
if the number of cows and calves is reversed, they would cost 
$303.50. A calf being worth $5.75, find the cost of a cow. 

6. A and B rr . a two mile race; A wins. If B had run one- 
third faster, he would have won by 22 yd. Compare their rates 
of running. 

7. A can dig 36 post-holes in a day; B, 32; and C, 30. 
What is the smallest number of post-holes that will furnish an 
exact number of days' labor for each working alone, for any 
two, or for all three working together? 

8. A, B and C together invest $4860 in wheat. A invests 
twice as much as B, and C invests twice as much as A and B 
together. They gain 40% on their investment. What is each 
person's share of the gain? 

9. If my income of $1150 is reduced by taxation to $1063.76, 
what is the income of another who has $1554 left after paying 
his taxes? 

10. A sold two city lots at the same price. On one he gained 
20% and on the other he lost 20%. He lost $30 by the transac- 
tion. Find the cost of each lot. 

VIII. REVIEW EXERCISES FOR FIFTH CLASS. 
EXERCISE CCXCIV. 

1. What is the least number by which 2016 must be multi- 
plied to become a perfect cube? What will be the cube root of 
this cube? 

2. Divide $1650 into two parts such that the simple interest 
on one of them, at 4i% for 3 yr., would be equal to that on 
tae other for 2i yr. at 5 % . 

3. A man bought a horse and sold him at 10% loss. If he 
had received $45 more for it, he would have gained 12i%. 
What did the horse cost? 

. -,. ... (.201- .102)'^ 

4. Simplify ^201)^'- (102)^" 

5. A marked goods at an advance of 40%, but in selling 
them a false b.alauce was used, by means of which he gave 14 
oz. to the pound. His total gain being $240, find the cost of 
the goods. 



REVIEW EXERCISES FOR FIFTH CLASS. 



191 



6. The amount of a sum for a certain time at 8% is $336, 
and at 7i % for the same time it is $330. Find the sum and 
the time. 

7. A solid sphere of iron 12 in. in diameter is melted and 
oast into a hollow cylinder 6i in. in radius and 8 in. long. Find 
the thickness of the iron in the cylinder. 

8. A hare takes 4 leaps to 3 of a greyhound; but 2 of the 
hound's are equivalent to 3 of the hare's. The hare has a start 
of .'iO of its own leaps. How many leaps must the hound take 
to catch the hare? 

9. A clock loses at the rate of 8i see. per hour when the 
fire is alight and gains at the rate of 5r5 sec. per hour when 
the fire is not burning. Upon the whole it neither gains nor 
loses each day. How long in the 24 hours is the fire burning? 

10. A walks a distance at a certain rat'*. If he had walked 
1 mi. per hour faster, his time would have been f of what it 
was. If he had walked 1 mi. per hour slower, he would have 
taken 4 hours longer than he did. Find the distance. 

EXERCISE CCXCV. 

1. A man buys wine at $3.20 per gallon; 20% leaks away. 
At what price per gallon must he sell the remainder to make 
20% on the outlay? 

2. A's income is derived from the proceeds of $227.5 at a 
certain rate per cent, and $2700 at 1% more than the former 
rate. His total income being $425, find the rates. 

3. A grocer has two kinds of tea. By selling the first kind 
at 45 ct. a pound, he gains 25%, and by selling the second at 
42 et. per pound he gains 40%. If he mixes them in equal 
quantities and sells the mixture at 43i ct. per pound, find his 
gain per cent. 

4. A shipment of wheat was insured at 2#% to cover three- 
fourths of its value. The premium was $44.07. The wheat 
being worth 80 ct. per bushel, find the number of bushels there 
were in the shipment. 

5. In a constituency having 3200 voters, A received 23 votes 
for every 25 votes received by B, and was defeated by 124 votes. 
How many did not vote? 

6. How fast is a locomotive going when the small wheel, 
which is 4 ft. in diameter, makes 180 revolutions per minute 
more than the large wheel, which is 7 ft. in diameter? 

7. Ten men can do a work in a certain time, but 7 men 
would require the same time and 7 days more to do the same 
work. How long did it take the ten men to do it? 






.1' 
it' 



192 



ARITHMETIC. 



8. There is a j?ras8 plot in the form of a ciicle 145 yd. in 
rrjIiiiH and a carriage drive round the outside of it 4 yd. wide, 
llnvv many cu. yd. of gravel will be required to cover the drive 
to the depth of 8 inches? 

9. A can do a piece of work in 10 days; B, in 12 days; and 
(% in 15 days. They all begin to work together, but C stops 
2 days and B li days before the work is finished. A finishes 
the work. How long does he work? 

10. Divide $2699.10 among A, B, C and D, so that A may 
have 12% more than B; B, lOVo more than C; and C, 5% more 
than D. 

EXERCISE CCXCVI. 

1. A farmer raised 3105 bu. of oats in 2 years. He had 30% 
more the first year than the second year. How many more 
bushels had he the first than the second year? 

2. The breadth of a room is half as much again as the 
height, and the length is twice the height. It costs $33.60 to 
paint the walls at 30 ct. per sq. yd. Find the dimensions of 
t''t-» room. 

.".. Iron weighs 7.112 times as much as water. How many 
i" = ft. are there in a ton of iron? 

4. A person holding $5000 of 5% stock and $7600 of 6% 
stock sold the first at 110 and the second at 115, and re-invested 
the proceeds in 4*% stock at 89. Find the gain or loss in his 
income? 

5. How many oranges must a boy buy and sell to make a 
profit of $12, if le buys at the rate of 5 for 3 et. and sells at 
the rate of 4 for 3 ct. ? 

6. The price cif gold is £3 17s. lOid. per oz. A compound 
of gold and silver, weighing 18 lb., is worth £637 78.; but if 
the proportions r^re reversed, it would be worth £259 Is. Find 
the value of silver per oz. and the proportion of gold and silver. 

7. A drover bought sheep at a certain price per head. He 
sold I at a gain of 20%, n,- at a gain of 15% and the rest at a 
loss of 10%, and gained, on the whole $217. How much did he 
pay for the sheep? 

8. A rows 30 mi. and back in 12 hours, and he finds he can 
row 5 mi. with -e stream in the same time as 3 mi. against it. 
Find the rate ot the stream. 

9. If the time past 3 p.m. is to the time past 1 a.m. as 4 to 
1, find the time. 

10. The sides of a rectangle are in proportion of 5 to 6, and 
it contains I A. Find the cost of painting a close board fence 
6 ft. high around it at 45 ct. per sq. yd. 



RRVIKW KXKR(MSK8 FOR FIFTH CLASS. 



193 



5 yd. in 
d. wide. 
;he drive 



ays; aud 
; stops 
k. ftuishes 



it A may 
5% more 



B had 30% 
lany more 

lin as the 
A, $33.60 to 
aensions of 

How many 

7600 o£ 6% 
re -invested 

loss in his 

to make a 
md sells at 

compound 

7s. ; but if 

l9 Is. Find 

and silver. 

head. He 

\\e rest at a 

luch did he 

Ifinds he can 
against it. 

la.m. as 4 to 

5 to 6, and 
Iboard fence 



EXERCISE CCXCVII. 

1. Find the area of ii sciiiuro inscribed in a circle 48 ft. in 
diameter. 

2. Tlie n«'t proceeds of the sain of 1000 tons of hay at $20 a 
ton after deducting !t!875 for freiglit, etc., were $18325. What 
rate of commission was charged? 

3. From a cask of wine one-fourth is drawn off, and the cfi' '< 
is filled up with wat« r: one-fourth of the mixture is then dra 
off, and tlie cask again lilled up with water; after this process 
has been repeated four times altogether, what fraction of the 
original quantity of wine will be left in the cask? 

4. A wall whose height is i of its length, and whose thick- 
ness is i of its height, co.itains 625630/4 eu. in. Find its 
thickness. 

5. Express as a vulgar fraction, and also as a decimal, the 
difference between 25.135 X 13a-T and 61.375 X b^. 

6. Calculate the ratio between the values of gold and silver, 
if from 2 lb. of standard gold are coined 89 guineas, and from 
1 lb. of standard silver GO shillings, y-i of standard gold being 
alloy, and A of standard silver. 

7. A grocer bought 1500 lb. of tea and sold 300 lb. at 45 et. 
a pound, making 12i% profit. Find the price at which he 
must sell the remainder per pound to gain 20% on his outlay. 

8. A merchant bought 240 yd. of silk. He sold i of it at 
2')% gain; i of it at 20% gain; rnd tlie remainder at 15% loss, 
and received $800 in all. How much did the silk cost him per 
yard ? 

9. How mtich less will it cost to fence a square field of 40 
acres than a rectangular one of the same size, 90 rods long, at 81 
ct. a rod? 

10. By selling $1000 of 3 per cent, stock at 95 and reinvesting 
the proceeds I increase my income $10 a year. If the dividend 
on the new investment is at the rate of 8%, what is the price 
of the stock? 

EXERCISE CCXCVIII. 

1. A rectangulsr field contains 27 A. 48 \\q. rd., and 13 times 
its length is equal to 21 times. its breadth. How many rods of 
fencing will be required to enclose it? 

2. A buys $18300 of 3% stock at 75 and pays for it with 
money loaned at 8% per annum. At the end of a year he sells 
out and his gain is $122. At what price did he sell the stock? 

3. A bought cloth at 20 ct. and the same quantity at 30 ct. 
per yard. He sold all at the same price per yard so as to gain 
as much per cent, on tlie one kind as he lost on the other kind. 
Find the selling price and the total gain or loss per cent. 



194 



ARITHMETIC. 



4. The area of the two larger walls of a room is 810 sq. ft.; 
of the two smaller, 024 sq. it.; and of the floor, 884 sq. ft. 
Find the dimensions of the room. 

5. The road between A and B, distant 15 miles, poes over a 
hill whose summit is 15 miles from A. Two men set ont at the 
same time from A and B, the former going 4 miles per hour up 
hill and 5i down, the latter 3i uj) and 4i down. IIow far will 
tile slower have to go when the faster reaches B? 

0. A pond A. in area is frozen over to a dej>th in. If a 
cubic fcot of water weighs 1000 oz. and ice is nt »^ heavy as 
water, find how many tons of ice there are on the pond. 

7. A man bought 03 sheep. He sold J of them at 15% gain; 
y of them at 50% gain; and the rest at 25% loss. His total 
gain was $15.40. How much did he pay for the sheep? 

8. A's present age is to B's as 9 is to 5, and 23 years ago 
the proportion was 10 to 3. Find the present age of each. 

9. If gold can be beaten out so thin that a grain will form a 
leaf of 50 sq. in., how many of these leaves will be required to 
make up the thickness of a sheet of paper, the weight of a cu. 
ft. of gold being 1215 lb. and 400 sheets of paper being 1 in. 
thick? 

10. If 5 men, 4 women, and 3 boys can complete a piece of 
work in 150 days, what time would it take 9 men, 15 women 
and 18 boys to do twice as much, the parts done by each in the 
same time being as 3, 2, and 1, respectively. 

EXERCISE CCXCIX. 

1. The perimeter of a serai'jireular flower-bed is 00 ft. How 
many plants will it contain, allowing 1 sq. ft. to each plant? 

2. A sold a farm to B at 15% Joss; B sold it to C at 10% 
loss; and C sold it to D for $3786.75 at 10% gain. -How much 
did the farm cost A? 

3. A can row 4i miles an hour in still water and he finds he 
can row a distance down stream in one-third of the time he can 
row back again. Find the rate of the stream per hour. 

4. How much tea at 48 et. a pound must be mixed with tea 
at 60 ct. a pound to form a mixture of 180 lb. in which the 
value of the different teas will be equal? 

5. A grocer buys coffee at $34 per ewt. 
per ewt. He mixes them in proportion of 5 
lb. of coffee and sells the mixture to gain i of the cost. 
much does he charge i)er pound? 

6. A town levied a tax for a bridge which cost $2520. 
Allowing 4% for the cost of collection, wliat sum wa^j levied? 



and chicory at $10 
lb. of chicory to 7 
How 



REVIKW EXERCISES FOB FIFTH CLASS. 



195 



) sq. ft. ; 
4 sq. ft. 

es over n 
ut at the 

V hoiiv up 

V fur will 

in. If a 
, heavy as 
id. 

].f>% gain; 
His total 
p? 

yoawi ago 
each. 

will form a 
required to 
lit of a cu. 
being 1 iu. 



a piece of 

15 women 

each in the 



60 ft. How 
eh plant? 

,0 C at 10% 
•How much 

. he finds he 
time he can 
_our. 
xed with tea 
u which the 

liicory at $10 

chicory to 7 

cost. How 

eost $2520. 
;a,.i levied? 



7. A merchant's debts amonntrd to $5000. Ono-lialf of liis 
stock was sold at '.i\i7c discount and tin* rest at 12i% discount. 
His creditors received G2i% of what was owing them. Find the 
value of the goods. 

8. White cedar weiglis 20 lb. to the cu. foot, while a cu. ft. 
of water weighs (iiii 11). A kind of iron is 7.492 times as heavy 
as water. Wliat thickness of iron will be of the same weight as 
a 9 in. plank of white cedar, their lengths being equal? 

9. A cube contains n.']90025 en. in. Find to four places of 
decimals the differeiice between the lengths of the edge and of 
the diagonal. 

10. Two men formed a partnership. A put in $10000, and B 
$10000. They lost $2080 and their capitals were reduced 
accordingly. They then took in (! as partner .ith $18000. 
They gained $4716. How much should each receive? 

EXERCISE CCC. 

1. A merchant mixes wine at $'i a dozen with wine at $3.60 
a dozen. He sells the mixture at $4.32 a dozen at a gain of 
26%. In what proportions are the two kinds mixed? 

2. It is between 4 and 5 and the hands of a watch form with 
a line joining their extremities an isosceles triangle, each of 
whose angles at the base is half the third angle. What is the 
time? 

3. I bought an article and sold it at a loss of 20%. If the 
cost had been 10% less and the selling price $13 more, I would 
have gained 25%. Find the cost. 

4. The expense of carpeting a room was $45. If the breadth 
were 1 yd. less the cost would be $36. Find the breadth. 

5. Seven pounds of tea being mixed with 4 lb. of a better 
quality the mixture is worth 88 ct. per pound. What is the 
value of each kind, the difference of values being 22 et. per 
pound? 

6. I buy two houses for $5850 and sell one at a loss of 8% 
and the other at a gain of 10% and neither gain nor lose on the 
whole transaction. How much did each house eost? 

7. The sides of two squares are 2321 ft. and 23i ft. 
respectively. Find the side of a square whose area is equal to 
the sum of the areas of the other two squares. 

8. If 175 men and 240 boys do in 1330 days the same 
amount of work as 603 men nnd 1005 boys in 350 days, compare 
the average daily work done by each man with that done by 
each boy. 



ill 



190 



AUITIIMKTIC. 



!>, Ill tin* ('«'iitrt» of n room 121 ft. sqmirc, thero is ii sqiiiire 
<'iir|»«*t. 'V\w rt'Ht of the fIor>r is covon'd with oil-cloth. The 
oirpct mill thf oil-clotli post rcspcctivM'Iy $-.40 and IMi ct. p«'r 
H(|. .v<l. ; and tln' wliolf cost of carpet iiiul oil-cloth is .fJtO.CiO. 
FimI the width of the oil -cloth. 

10. Tliicc nicrchaiits enter into partnership. I'he fii-st, A, 
jmts in $W\{) for (5 months; the second, li, a certain snm for 12 
months; and the third, (', ff<)40 for ii certain time when the 
accounts vver* settled. A leceived .$1200 for his stock and 
j.roHt, H $2400 for his, and C $1040 for his. What was H's 
Htock and (''s time? 

EXERCISE CCCI. 

1. If tlie telcfjraph poles at the side of a railway are GO yd. 
apart, what fraction of the true speed will the error bo in 
rt'ckoninj; the speed of the train to be twice as many miles ptr 
hour as the train passes poles per minute. 

2. A and B f?o to nnirket and biiy tofjfether 80 lb. of meat at 
10 ct. per lb. A takes HO lb. and B the rest. Upon examin- 
ation, they a{?ree that A's meat is worth i ct. per lb. more than 
B's. How nnich must each pay for the meat. 

;{. A merchant borrowed $1300 at .3^% and at the same time 
$1790 at ^i7r and j)aid both loans when the sum of ])rincipal 
and interest was $3202.50. How long did he keep the money? 

4. Two circular gold plates each 1 in. thick and (5 in. and 8 
in. in diameter, respectively, are melted and formed into one 
j)iate also 1 in. thick. Find its diameter. 

5. A merchant sold 400 yd. of cloth, 
it he gained 10% and r>% on the remainder. 
S% gain, he would have made $21 more. 
l)er yard. 

C. Find the cost price of 3 per cent, stocks, so that if $3(5000 
be invested, the income may be $1140 after paying an income 
tax of 5 ct. on the dollar. 

7. If James can do S^ of a work in 8 hr. and John can do f 
of the remainder in 2 hr. and Charles can finish it in 40 
minutes. * What time would all take working together? 

8. A piece of metal weighing 1410 lb. has been formed by 
compounding three metals in quantities which, by measure, are 
as 5, 3, 2; but the weights of equal volumes of them would be 
as 7, 11, 13. What weiglitof each of the component metals has 
been used? 

9. Divide $5600 into 4 parts, sucli that the respective 
interests on the 1st at 2^ per cent, for 4 months, the 2nd at 3 
per cent, for 4 months, the 3rd at 4 per cent, for 5 months, and 
the 4th at 5 per cent, for G months may be the .same. 



On one -fourth of 

Had he sold it at 

Find the cost price 



REVIKW KXKRCI8ER FOR FIFTH 0LA8S. 



197 



HOtiare 
» ct. |»»'r 



first, A, 
11 for VI 
rhim the 
:()('k imd 

was H'H 



ro GO yd. 
•or bo iu 
miles ptr 

f meat at 
II examin- 
more tlian 

same time 
f principal 
he money? 

■) in. and 8 
into one 

-fonrth of 
sold it at 
cost price 



it 



it $:U)000 
an income 



n can do I 
it in 40 
f? 

formed by 
easuve, are 
1^ ^^•ould be 
; metals has 

respective 
llie 2nd at 3 
iionths, and 



10. In a niih' rjH'c, A starts at U70 paccH of 48 inohes ])er 
minute, and li 'MO paces of 44 inclies per minute. After 4 
minut«'s, H (|uickeiiM his pace to II'JO. Siipposiiifi; A eontinueH 
at his (irij^iniil rate. VVIiich wins, l»y how much, and in what 
time? 

EXERCISE CCCII. 

1. I'Mnd the dilTerence between the areii of u triaiif^N' wliose 
sides are IDI ft., -0 ft. and 44 ft., respectively, aiul that of an 
e(iuilate.'al triangle of the same perimeter. 

2. Divide $;r)GO among A, B, (', and 1), giving A 'M% of 
D's sinire; C, '.M% of A's share; and B as much as A and C 
toj^ether. 

:j. A sold a lot which cost $1875 and gained Gi% of the 
selling price. He sold another which cost $1200 at H% gain on 
the cost price. His whole gain was $221. Find the selling 
price of each. 

4. A farmer holds two mortgages for $14000 and $34000 
rt;spec(ively, which bring in $2000 interest each year. 'V\w 
rate on the latter is i% higher than that on the former. Find 
the rates. 

ii A buys tea at '){)c. per pound and the same quantity of a 
l»etter quality. He mixes them and selfs the mixture at GGc. 
l)er pound and thus gains 20% on his outlay. Find the price 
of the second kind of tea. 

G. After a certain number of men had been employed on a 
piece of work 24 days and had half finished it, IG men more 
were set on and the remaining half was completed in 16 days. 
How many men were employed at first? 

7. A sets out to walk to a town at 3 miles an hour; B on a 
hicycle sets out with him at 12 miles an hour. On reaching the 
town B rests half an hour, and after riding 40 minutes on the 
return journey meets A. How far is the town distant from the 
starting point? 

8. A banker increased his capital 10% per annum and in 4 
years, the interest for one year at 4% on the capital he then 
had was $3GG0.25. Find his original capital. 

9. The minute-hand of a town clock is 9 feet long. Find 
the time after twelve when its extremity has moved over 11 ft. 
on the dial. 

10. If $5 be allowed as discount off a bill of $125 for a certain 
time, what should be the discount if the bill had twice as long 
to run, (1) at simple interest, (2) at compound interest? 



ANSWERS. 



10 



5. 
10 



10 

4. 

9. 

4. 
9. 

4. 

9. 



10 

5. 
9. 

6. 

G. 



Ex. IX. 1. 49 et. S. $47. 3. 209 bu. 4. 87 mi. 5. 124 mi. 
945769. 7. 969 yd. 8. 1367 mi. 9. 786. 10. 1668 pages. 

Ex. XIV. 1. 303. 2. 354 A. 3. 272 marMes. 4. 158 mi. 
$7353. 6. 1273 animals. 7. 885 trees. 6. MCXVII. .9.46391. 
. 226. 

Ex. XV. 1. 40 marbles. ^. $45. 3. 870 pages. 4. 300 mi. 
1000 et. G. $1900. 7. $270. S. 98 et. 9. 208 mi. i^. $7856. 

Ex. XVI. 1. 9054. 2. $9000. 5. 814 baskets. 4. 106 ft. 
170 ct. 6. $129. 7. 144 et. 8. 500 ct. 5. 160 A. 
. 90 sheep ; $389. 

Ex. XVII. 1. $999:! . 2. $350. 3. 197795. 4. $52948276. 
3617 sheep. 6. 510 mi. 7. $100. ^. $120. 9. 195 et. 
. 3666. 

Ex. XVIII. 1. 76 mi. 2. 1159620. 3. $45000. • 
1171460 oranges. 5. $3811. 6. 78. 7. $31839. ^. $12085. 
$33820. 10. $33020. 

Ex. XIX. 1. 1990977. 2. 72720, 147720. 3. $18565. 

154 yd. 5. 31136. 6. 131 et. 7. 365 days. 5. 12413. 

1832. 10. $140900. 

Ex. XXI. I.Ul cows. ;?. 40 chickens. 5. $23. 

113 pages. 5. 272 gal. 6. $150. 7. 254bbl. ,5. 1232 sheep. 

433 A. 10. $1200. 

Ex. XXVII. 1. 74. 2. 286032. 3. 6319267. 4. 32299. 
676. 6. 2714. 7. 526084. 8. 2578. 9. 6667315. 10. 141998. 

Ex. XXVIII. ^. 89 sheep. ^.$257. 5. $468. '^. 24168 bu. 
$1779. 6. $2168. 7. $49. .9. 1432 mi. 9. 162482. 
. 158677 cows. 

Ex. XXIX. i. $807. ^.39 marbles. 5. 13999 men. 4. $.3816. 
351636 min. 6. 439 pages. 7. $21506957, 8. 6300836 ft. 
117993. 10. 83849884 lb. 

Ex. XXX. 1. 27 ct. 2. 288. 3. $11993. 4. $35. 5. 1642. 
89 yr. 7. 983 yr. .?. 3688 it. f^. 1325 votes. iO. 3969356. 

Ex. XXXI. Z. 45. ^.$198. '?. 215bu. 4. $3250. 5. $32. 
$107950, 7. $7178. 8. 5mi.,13V7'1. 9. 225 mi, 10. 2210. 
Ex. XXXII. i. $245. 2.1950. 3. Ut7 A. 4. 45 yr., 38 yr. 
Loss, $2410. 6. Jas. 31, Jno. 26. 7. 4o A. 8. 70 da. 
18 marbles. 10. 211V 1, 14896, 18691. 

198 



ANSWERS. 



199 



Ex. XXXIII. 1. 6746. 2. 129G8. 5. 1606. 4. 2658225. 
5. 6529. 6. 925358. 7. 2534. 8. 73699. 9. 2155. i^A 8453. 
i/. 23718. 12. 74128. 

Ex. XXXIX. 1. 1200 mi. ^. $195625. 3. 607488 oz. 
4. 1632000 mi. 6. 63168 et. 6. 702 trees. 7. 2920 mi. 
8. 95424 hills. 9. $130455. 10. 75087 lemons. 

Ex. XL. 1. 1530000 ct. 2. 32076 yd. 3. 2368 nails. 

4. 62640 mi. 6. 171216 ia. 6. 383600 ct. 7. 482040 ct. 

8. $204000. 9. 525600 min. 10. 5285484 papers. 

Ex. XLI. 1. 43050. 2. $2241190. 3. $5. 4. 553 ct. 

5. $516. 6'. Gain, $32. 7. 94720 ct. *. 2472 ct. 9. 1037 mi. 
i^. Loss, $83. 

Ex.XLII. i. 172484. ^.233189. 5.1062347. 4.67419143. 
5. 15403465. 6. 2016978981. 7. 1123193115. 8. 63096033. 

9. 50700. 10. 14254. 

Ex. XLIII. 1. 55986805. 2. 1516. 3. 62985. 4. 9989001. 
5. 7051253. 6. $30613. 7. 57415 ct. 8. 15725910 A. 
9. 703 stocks, 8436 sheaves. 10. 99693084. 

Ex. XLVII. 1. 16, 28, 44, 88 yd. 2. $121. 3. $75. 

4. 329 bbl. 5. 142 lb. 6. 524 lb. 7. 15065 lb. 8. 532 pk. 

9. $7625. iO. 379 t. 

Ex. XLVIII. 7. 480 mi. ^. 1760 yd. 5. $13. 4. 13 hr. 

5. 30 ct. 6. $32. 7. 57 persons. *. 362 mi. 
U. 11625000 mi. a min. 10. 5642 pence. 

Ex.LII. i. 6540. ^.391525. 5.489673. 4.150287. 5.481. 
6'. 4798. 7. 61. 8. 378. 9. 9605. 10. 228689. 

Ex. Llll. 1. 134 da. 2. $2003. 5. 2640. 4. 29603 lb. 
5. $658. 6. 160sq. rd. 7. 327 mi. *. 275 persons. 9.168 1b. 

10. 9 da. 

Ex. LIV. 1. 179 mi. 2. 96934 yd. 5. 19 mi. 4. 64 bu. 

5. 51 bu. 6. 245 bu. 7. 144. 5. 75 c. yd. 9. 207 bbl. 
^<?. 704 cd. 

Ex. LV. 1. 119. 2. 910. 5. 83. 4. 1331424. 5. 45. C. 27. 
7. 14839. .?. 811. 9. 41. iO. 23849. 

Ex. LVI. 7.7469. ^.23. 5.631229. 4.323603. 5.150321. 
0. 66. 7. 245. ,?. 119025. 9. 767561. 20. 336. 

Ex. LVII. 1. 840 steps. 2. 14668. 5. 2380277. 4. 1249. 
5. 962556. 6. 179538. 7. 253440 in. ,S. 20063110804. . 

9. 35643910. 10. 40160 ct. 

Ex. LVIII. 1. 91132497. 2. $288. 3. 1145348. 4. 6029. 
5, 30595. 6. 815. 7. 99368. .9. $254. i^. 1420799. 10. 224(1 ct. 

Ex. LIX. 1. $336. ^. 18 et. 3. $5 each. 4. 2632 ct. 
5. 200 ct. 6. $50. 7. $1620. 5. 485 sheep. 9. 11657397. 

10. 8 yr. 



-v^ 



illl 



200 



AKITHMKTIC. 



6'. 

C. 

6. 

4. 
8. 



6. 

5. 
10 

5. 

9. 



Ex. LX. 

960 et. 



1. 2552, 
7. 72 et. 



2. 18480 et. 
8, $4800. !K 



S. 95 et. 4. 42. 
113. i<^. 203. 



5. 10624. 



Ex. LXI. i. 27 ct. 2. 10 ct. .■?. 21 mi. 4. $51. 5. $150. 
30 yd. 7. 21 dresses. 8. 1728 bu. 9. 11 br. ^6*. 579000 lb. 

Ex. LXII. i. 21da. ^. 95da. 5. 20 da. ^. 27 da. 5. 18da. 
15 men. 7. 45 men. 8. 6 men. 0. 240 men. lU. 225 men. 

Ex. LXMI. 1. 16, 20. 2. 20, 30. 3. 39 bu., 46 bu. 



42 yd., 58 yd. 5. 44, 50. 6. 12 yr., 15 yr. 
Ill votes, 129 votes. 5. 67 mi., 90 mi. lU 
Ex. LXIV. 1. 8458. 2. 181357. 3. $3570. 
$16. 6. 240 ct. 7. $6. *. $135. 9. 170. 

Ex. LXV. 1. 33148. ^. 5607 ct. 3. 10 ct. 
21450 et. 7. 19 gal. ^. $170. 9. 2046 et. 

Ex. LXVI. 1. 120 pieces. ^. 159 pieces. 
1800 ct. G. 11 stacks. 7. 302304 ct. ^. 
17 hats. 

Ex. LXVII. 1. 36405 bu. 2, 202878 ct. 
Gain, $161. 6'. 38400 lb. 7. 5355 ct. 
36 1b. 10. 1953. 
Ex. LXVIII. 1. 1580712. 



7. 19, 28. 
192, 195. 

4. 264 mi. 
10. $46836. 

4. 17. 5. 47 ct. 
10. $468. 

5. 9 et. 4. 21. 
500 A. 9. 60 bu. 



3. 23 lb. 4. $2028. 
8. 4860 et., 90 et. 



2. 148 mi. 5. $2277. 4. 1862 et. 
5. $2688. 6. 150 boys. 7. $31104. 5. 86 A., $42. 9. 132 head. 
10. 114 mi. 

Ex. LXXIII. 1. £83 12s. 9d. ; £74 18s. lid.; £810 2s. 

2. 74 cwt. 64 lb. 3oz. ; 127 t. ewt. 72 lb. ; 56 1. 1 ewt. 281b. 3 oz. 

3. 82 yd. 1 ft. 9 in. ; 18 yd. 2 ft. 4 in. ; 58 yd. ft. 9 in. 

4. 16 bu. 2 pk. 6 qt. ; 32 bu. 3 pk. 5 qt. 1 pt. ; 133 gal. 2 qt. 1 pt. 

5. 38 gal. 3 qt. ; 32 da. 18 hr. 51 min. 56 sec. ; 7 wk. 4 da. 2 hr. 

45 min. 3o sec. 
£3 3s. 9d.: £19 9s. 3d.; 4 cwt. 22 lb. 10 oz. 



6. 
7. 
S. 
9. 



10 t. 15 cwt. 63 lb. ; 3 yd. 1 ft. 5 in. ; 47 yd. 1 ft. 3 

8 bu. 3 pk. 6 qt. ; 2 qt. 1 pt. 
41 see. ; 1 wk. 5 da. 7 hr. 14 min. 



yd. 18 e. ft. 1483 c. 



in.; 51 e. yd 



in. 

45 see. ; 
2 e. ft. 



28 bu. 1 pk. 7 qt. ; 
2 da. 18 hr. 8 min. 

6° 50' 39". 
10. 30° 53' 49"; 31 c. 

1488 e. in. 

Ex. LXXIV. 1. £66 9s. 2d. ; £454 14s. ; 136 ewt. 67 lb. 1 oz. 

2. 61- 1. 13 ewt. 31 lb. 8 oz. ; 211 yd. 2 ft. ; 967 yd. ft. 3 in. 

3. 23 bu. pk. 1 qt. 1 pt. ; 95 bu. 3 pk. 2 qt. ; 34 gal. qt. 1 pt. 

4. 187 gal. 2 qt.; I.i9 da. 11 hr. 33min. ; 46 da. 13 hr. 34 min. 56 sec. 

5. 123° 53' 39"; 422° 17' 20"; 86 c. yd. 22 e. ft. 967 e. in. 

6. £20 98. 5d. ; £5 3s. lid. ; 7 ewt. 85 lb. 14 oz. 

7. 2 t. 10 cwt. 64 lb. 9 oz. ; 12 yd. 1 ft. 11 in. ; 9 yd. ft. 11 in. 

8. 4 bu. 3 pk. 6 qt. 1 pt. ; 8bu. Opk. 1 gal. 1 qt. ; 15 gal. 2qt. Ipt. 
.9. 4 gal. 1 qt. 1 pt. ; 164 hr. 26 min. 24 see.; 187 da. 21 hr. 

55 min. 57 see. 
10. 19° 15' 42"; 125° 9' 24"; 19 e. yd. 22 e. ft. 969 e. in. 



ANSWERS. 



201 



Ex. LXXV. 1. 13; 32. 2. 400; 35. 3. 49; 42. 4. 77; 720. 
.5. 325; 64. 6, 1856; 375. 7. 90; 35. 8. 2880; 156. 

.'>. 78; 1680. 10. 1120; 303. 

Ex. LXXVI. i. 4 ft. 8 in. ;g. 504pt. 5. 744hr. 4. 131,36oz. 
5. £116 168. 3d. 6. £54 13s. 4d. 7. 11 ft. 6 in. ; 6 ft. 6 in. 
S. 107° 40' 38". 9, 353. 10. $529.20. 

Ex. LAXVII. i. $27. 2. 1301. 5. $104. 4. 3080 yd. 
5. $164475. 6. 342 min. 7. 37 lb. 14 oz. ,S. 15 t. 9. 3000 gal. 
10. $551760. 

Ex. LXXVIII. i. 45t. ^. 60 spoons. 5.108. -^.15 pages. 
5. 42 mi. 60 rd. 6. £110 10s. 7. £9 78. 6d. .S. $54.92. 9. 60 yd. 
iO. 15 ct. 

Ex. LXXIX. 1. 95 gal. 2 qt. 1 pt. ;g. 12 gal. 2 qt. 1 pt. 
S. 278 bu. 36 lb. 4. 23 bu. 13 lb. 5. 5 min. 15 see. past 8. 
6'. 4 lb. 4 oz. 16 dwt. 7. £3 17s. lO^d. 8. 288 lb. 9. $2919. 
26*. 15 lb. 

Ex. LXXX. 1. $44.70. 2. $153. 5. $8778.50. 4. $134.09. 
5. $297.45. 6. $153.27. 7. $17.81. ^. $49.97. 9. $2.56. 
i(?. $58.95. 

Ex. LXXXI. 1. $290. ^. $2.79. S. $7.25. 4. $311.48. 
.5. $221.81. 6. $5.32. 7. $21.80. 8. $42.70. 5. $13.94. 
iO. $71.91. 11. $13.54. 

Ex. LXXXII. 1. 10 in. ; 14 in. ; 22 in. ; 16 in. 2. 56 ft. 

-:?. $45. 4. 250 boards* 5. $3.40. 6. $700. 7. $256. 
S. 14080 yd. 5. $1440. 10. 120 ft., 40 ft. 

Ex. LXXXIII. 1. 1224 sq. ft.; 1216 sq. ft.; 5616 sq. ft. 
^. 9 A. ; 10 A. ; 15 A. ; 42 A. ; 15 A. ; 19 A. S. 18 sq. ft. 

4. 11 sq. yd. 5. 2304 sq. yd. 6. 200 sq. yd. 7. 112 sq. in. 
8. 1056 sq. ft. 9. 2000 sq. ft. 10. 24 sq. ft. 

Ex. LXXXIV. 1. 18 ft. 2. 54 ft. S. 40 rd. 4. $290. 
0. $150. 6. 500. 7. 72 ft. 8. $940. i>. 360 ft. 10. $660. 

Ex. LXXXV. 1. 40 yd. ,?. 60 yd. S. 32 yd. 4. 70 yd. 

5. 196 yd. C. $57.60. ' 7. $13. 8. $130. y. $24. if. $12.60. 

Ex. LXXXVI. ?. 6; 9. ^.8. .?. 16. ^.8. 5.10. 6.72 yd. 
/'.48 yd. .§.$58.80. r>. $88. iC. $110. 

Ex. LXXXVII. 7. 80 sq. yd. 2. 168 sq. yd. S. 224 sq. yd. 

4. $9.12. 5. $40.02. 6. 82 sq. yd. ; 91 sq. yd. ' 7. $23.60 ; $26.20. 
<V. $21; $23. 9. $:59; $41 ..'50. if. $70.20; $76.14. 

Ex. LXXXVIII. 1. 160 yd. 2. 288 yd. .^. 448 yd. 4. 96 yd. 

J. 348 yd. C. 82 yd. 7.396 yd. 5.144 yd. .^>. $5.85. if . $16.25. 

Ex. LXXXIX. 1. 9 ft. ; 24 ft. ; 24 ft. ; 24 ft. ; 40 ft. ; 24 ft. ; 

12 ft. 2. 3300 ft. S. 4200 ft. 4. 2220 ft. 5. 7680 ft. 
6'. 768 ft. 7. 1650 ft. 8, 10000 ft. 9, $300, 10. $540. 



202 



ARITHMETIC. 



Ex. XC. 1. 2880 c. ft. 2. 210 c. ft. 3. 60 c. yd. 

4. 210 c. yd. 5. 4032 lb. 6. $40.50. 7. 13600 c. yd. v 

8. 109 e. yd. 1 c. ft. 9. 2376 c. ft. 10. $1380. 

Ex. XCI. 1. 30 cd. 2. 63 ed. 3. 30 cd. 4. $84. 6. $216. 
6'. $75.25. 7. 80 ft. ,S. 5 ft. D. 8 ft. id?. 224 ft. 

Ex. XCII. 1. 7 ft. 2. 11 ft. S. 24 ft. 4. 3 ft. 6. 112 ft. 

6. 18144. 7. 192 ft. «. 40 ft. 9. 30 in. 10. 17 ft. 

Ex. XCIII. 1. 32 ft. ^. $40.25. 3. $1080. 4. 1120 lb. 

5. 32 t. 6. 48 t. 7. 1760 c. yd. 8. $792. 9. $1440. i<?. $72. 

Ex. XCIV. 1. $32.64. 2. 220 yd. 5. 3600 sods. 4. 3 ft. 
5. 90 c. ft. 6. 33 mi. 7. 15 ft. 5. 9 ft. 9. 36 8q.yd. 10. 5 ft. 

Ex. XCV. 1. $17; $23. 2. 19 yd.; 30 yd. 3. 36; 48. 

4. $48.75; $50.25. 5. $27000; $23000. r>. $215; $160. 

7. $425; $371. 8. 271 mi.; 237 mi. 9. yu5; 361. 
iO. $4500; $1250. 

EX.XCVI. 7. $5120; $1280. ^. 2064 bu. ; 2311 bu. 5. $2726. 
4. 361 yd.; 242 yd. 5. 297; 315. 6. 462; 534. 
7. 24 ed. 39 e. ft. : 27 cd. 89 c. ft. 8. 9 A. 115 rd. ; 10 A. 45 id. 

9. 4 mi. 275 rd. 10. 1 t. 8 ewt. ; 2 t. 

Ex. XCVII. 1. 30; 90. 2. 254; 508. 3. 23 yd.; 92 yd. 

4. $2450; $9800. 5. $75; $168. 6. $145; 462. 7. $3450; $10500. 

5. 30 rd.; 90 rd. 9. $126. 10. 1240; 3737. 

Ex. XCVIII. 1. $36; $48. ^. 60 bu. oats; 150 bu. peas. 
3. 17. 4. $7800; $11700. 5. 275; 330. 6. $20; $40; $60. 
7. 30; 45; 75. 8. 6. 9. $420; $140; $560. 

10. $10940; $3020; $2450. 

Ex. XCIX. 1. $8; $10; $13. 2. 170 lb.; 152 lb.; 134 lb. 

3. 150 yd. ; 125 yd. ; 169 yd. 4. 2400 lb. ; 2200 lb. ; 1800 lb. 

5. 127 lb.; 100 lb.; 175 lb. 6. 60 mi. ; 25 mi.; 40 mi. 

7. 81 rd. ; 45 rd. ; 123 rd. 8. 256; 378; 452. 9. $450; $531 ; $612. 
10. 180 bu. ; 233 bu. ; 160 bu. 11. 32 et. 

12. 87 red, 94 blue, 105 white. 

Ex. C. 1. 1975. 2. 3683. 3. 184019. 4. 7, 10, 9. 5. 14, 11. 

6. 43, 16. 7. 14 lb. 8. 48 yr. 9. $119. 10. $7095. 

Ex. CI. 1. 6.59 lb. 13 oz. 2. 256 mi. 160 rds. 3. $204.75. 

4. $17.82. 5. 35 ewt. 25 lb. 6. 12 lb. 9 oz. 7. 33 mi. 96 rd. 

8. 45. 9. $75. iO. 24 lb. 10 oz. 

Ex. Cll. i. qj32. ;?. 7 ct. ,?. 15 carats. 4. 40 ct. 5. 6 et. 

6. 200 bu. at 75 ct., 300 bu. at 70 ct. 7. 4 ft. 3 in. 8. 139 lb. 

9. Is. 7d. 10. 4s. 9d. 

Ex. cm. i. 272 lb., 2448 lb. ;g. $570940. 5. 2oz. 4. 35et. 
5. 22 yr. 6. $25. 7. 7 ct. 8. •*6 ct. 5. $6.60. 10. 12 carats. 



ii 



A17SWERS. 



203 



[. 6. $216. 

5. 112 ft. 

1120 lb. 

:0. 10. $72. 

. 4. 3 ft. 
yd. 10. 5 ft. 

16 ; 48. 
L60. 

bu. 5. $2726. 
; 10A.45rd. 

. ; 92 yd. 
3450; $10500. 

bu. peas. 
0; $60. 



lb. ; 134 lb. 
.. ; 1800 lb. 

mi. 
i; $531; $612. 



9. 5. 14, 11. 

3. $204.75. 
mi. 96 rd. 

et. 5. 6 ct. 
8. 139 lb. 

loz. 4. 35 ct. 

10. 12 carats. 



Ex. CIV. 1. 2, 2, 3; 2, 2, 2, 7; 2, 2, 3, 7; 2, 3, 5. 

;?. 2, 2, 7, 7; 3, 7, 11; 2, 2, 3, 3, 7; 2, 2, 2, 2, 2, 2, 2, 3. 

S. 2, 2, 3, 73; 2, 2, 3, 79; 2, 2, 263; 3, 353. 

i. 3, 5, 73; 3, 7, 53; 7, 7, 23; 2, 2, 17, 17. 

5. 2, 601; 2, 607; 2, 3, 7, 29; 5, 311. 6. 797, 821. 7. 1187. 

^. 2543, 2521. 9. 2273, 2339, 2417. 10. 3119. 

Ex. CV. 7. 2, 5; 5, 7. ^. 3, 7; 11, 13. 5. 7, 17; 2, 2, 3. 
4. 2, 2; 2, 2, 3, 3, 3. 5. 2, 2; 5. ^. 30; 25; 275; 193; 443. 
0. 2, 3, 5; 3, 5, 7; 5, 7, 11; 7, 11, 13; 11, 17, 19. 

Ex. CVI. 1. 180. 2. 5. 5. 6. 4. 120. 5. 4. 6. 1008. 
7. 2400. ^. 900 bu. 9. 75 yd. iO. 40 da. 

Ex, evil. 1. 14; 16; 13. 2. 35; 46; 42. 3. 72; 32; 4. 

4. 9; 16; 7. 5. 25; 42; 42. C. 9; 4; 73. 7. 73; 32; 11. 

5. 9; 8; 13. 9. 32; 110; 14. iO. 91; 143; 323. 

Ex. CVIII. 1. 14 ft. 2. 17 in. 3. 15. 4. 7 ft. 5. 2 ft. 3 in. 

G. 13 ft. 7. 63 bu. 8. $1, $2, $5, $10, or $50. 9. $124. 
10. 26880 rails. 

Ex. CIX. i. 18; 7; 251. 2. 107, 311, 103. 3. 52, Prime, 601. 
4. 31, 947, 233. 5. Prime, 47, 811. 6. 8, 616, 884. 

7. 1188, 13, 13. 8. 46, 21, 9. 9. 897, 1323, 1429. 10. 315, 19. 

Ex. ex. 1. 105; 3, 5, 7, 15, 21, 35, 105. 2. 2 da. 5 hr. 
3. 1 mi. 37 yd. 4. 3 gal. 5. 117. 6. 29. 7. 25. 5. 19 men. 

9. 7 oz. iO. 126. 

Ex. eXI. 1. 24; 120; 120. 2. 75; 600; 720. , 
3. 315; 2652; 3705. 4. 360; 1260; 504. 5. 576; 600; 27720. 

6. 1260; 8415; 16546530. 7. 10890; 17160; 205205. 

8. 14280; 166320; 22770. 9. 1190595; 27945372; 885989. 

10. 12018233514; 110250; 620310. 

Ex. eXII. 1. 120. 2. 360. 3. 85085. 4. 6435. 5. 48. 
6. 143. 7. 1526. 8. 90. 9. 120 ft. iO. 60 gal. 

Ex. eXIII. 1. $20. '2. 141 lb. 5. 94 lb. 4. 30. 5. 30 mi. 
6.365. 7.62,122,182. 5.600 bu. 9.13,14,15,16. i<?. 1008000 gr. 



51 



r). 

7. 
8. 
9. 
10 

s. 

5. 
7. 
.9. 



Ex. CXV. 1. f; V-; V; V- -2- V; l 

V;-V-; ff; %¥. 4. V; V; ¥; ^F 

4JLQ . 508.23 3.S2T3 /? 8449. 4 41 8 






30 



^. 



^9. 4^^ 



TT : -ff-; T5"; i^T- n. --^s- 

519L. 68861. 36449. 19126 
13 33 1. 44 3 99. 5.9881. 1.60689 
1.102 2. 71041. 18 3 821. 101001 
.2 8 114 1. 49880 3. 288161. 110 8 61 



> 



46664 . 



84 80 



Ex. exvii. i. 



oi. 






7,1!; 5; 51*4; 5A. 4. 9A; 
5fA; 4iAA; 6,¥,-; 13f:^. 6 



34 ; 2. 



(9 17. oB , 






^- 16M: 33i§; .35^. 

4,^^a„-; 260|i; 16-3¥3 ;. 1-,W:< 



20h-§; 9f|f; Sfltf ; 342^2^^. 8. 334^3; lOOrg-; lOeVy ; lO^^u 
'>'^M; 45f gal.; 53f da. 50* lb 



10. 7M mi. ; 24f? cd. ; 2lH yd. ; 63^ oz. 



204 



ARITHMETIC. 



Ex. CXVIII. 1. $4i. 2. 92i bu. 3. 4i mi. i. 16.V lb 
6. 321* bu. 6. Latter by ij^ lb. 7. li in.; 7 lb.; 25 oz. 
S. 7i gal. y. 20 ft. ; 16 ft. 10.. $19.75. 

Ex. CXXII. i. i; I; f; i. ^. 

A; /s; I. 4. J; l;il; i^. 



3. 
0. 
&. 
10. 

2. 
3. 
4. 

5. 
6. 
7. 
8. 
9. 



6 . 

iVr; 






i; /s; I 

AV; 11; 

I; " 



^1; 



i; I; 

4. J; 

5 3 9 

8jir; ij. 

13. 829 
gCr; T33T 



A; 



3 . 

6» 



'y 8.89. 

' • 9 ; jt; 



i^. 



A; 



H; 



5. 

841 . 

68T; 



1 . 4 

s; 1 
1 . 
3; 



e; 

II. 

6 fi 3 9 
T29 6 5. 



V, 



63 
13 «. 



i. 



Ex. CXXIV. 

12 6 2 4 3 6_ . 

TSO", TS^T, T60 > 

8 4 2 3 3, 

liii lir, T¥4> 

2 16 14 1 8 0, 

2 5 3» 8Jf3» ^5? 



8 0^ 

6 2, 
]8 8ff, 

J 8 
TTf, 
39 . 



15 



"A; 



Tg 
110 1 1 

9 0-, f f , I 



42 

¥8, 



3 6. 

■98» 



8 



A2 

600 

64 

84 

Tffff, 

^/l 22 
10. ^9, 



4P 



fl, fl, !l, II; il, H-, h, -It 

" 102 

HI, 

Hi Mi 



If. 



86 

18 10 

3 0_ 14 
— TTT? 



4*0.. 8 8_ 
10 8 19 2 



66 . log. 
TffF; T?o, 

rrff, rrs, yrs" 

6. 3 .120 198. 3 2 4. 
99, ff9 , ¥9"; 4 5(r, 



f3 
ITT, ¥^¥, 



10 
TUTT, 

tVtt, 

1 2 1 
626 



96 
TSTF. 
1 32 
Tff"8, 

84 

39 

3150 
¥30". 



9 



Ex. CXXV. 



i^. 



I; 



3 
ro 



i; h 






5. 1: 2; 

13.1 li.3 

It; i2r«. 



"30' 

d. 



36 



1 4> 



13 



«? 



91 25. 



29'-^ 



23f. 
ft A. 5. 



6. 



6. 



4' 



mi. 

/. •T2 0. <*• 35» 
iZ Q 71 

30- ^' S1)0« 



9. 



114/2- gal. 






8. t\' 

Ex. CXX^^I. .?. h ; 

Ex. CXXVII. 4. 2; 1; 2. 

7. IH; li^.; 2A< 
^0. im;2A^o; iS-t^ 

Ex. CCXIX. l.\\l. i 
6. 24t. 7. 35i^. ,?. 17^0. 

Ex. CXXX. 1 
6. 178/„. 7. f.}. 

Ex. CXXXIII. 

& 'T kl. O 

5 4' ' • 1 2 O • O 

Ex. CXXXIV. 

"2 8 , UjjHU. 

14f; 23 ,i,; 20,^, 
9. 17f|; m?-, 31M. i<? 

Ex. CXXXV. /. m gal. i?. 13f yd. 

5. $95f^-. (;. l.>9^i}A. 7. $68f. .?. 13,\. 

Ex. CXXXVI. 1. U; lA. 2. 3i; SH. 

4. 6; 9/s. 5. 4|; 5^1. 6. 1-|?; 34§. 7. 

«. 2H; 7i^9. 9^ 10; llA. i<9. 8^; in^. 

Ex. CXXXVII. i. 97M lb. ^. 16i gal. 

6. 33i miles. 6. Gained $la%. 7. $23j. 
iO. 37M yd. 






iO. 



6. 



288, 1024. 
1^9, 2r2. 



2.> 



O 119, oli. . ol-^£ 

y. T»?; •isi; ^440. 



1 73 4 

1 S 36 • * • 

10. 26i§. 
llll^ lb 



*3B0» ^' 



O li!7 



73 

20- 



'8 , 
jlB 



•Jl 1 



•'1 3« 



59 
200' 

7 
^)» 



23 

60 



. 4. 

10. 132i mi 
5 



11 



5.H 



too- 



f; 1 



4 ^^3- • 4. ft . 4 
*• «>17 , ti 1 ? '^i 



3' 



7. 1 



48 . 
5 39 , 

OQ '-3 . 



5. 

133 



21 



14 , 



17 
144- 



13 . 10^5^1 

84 » i"l 40 

10-A_. 

1-143 , 

6 



13 ^-A 



Ol 7 . 12 63. 

-2T, 1288' 

^. 2G*-i; 2011 ; 



lOy^. 



T5- 



16i" 



.9. 



«4 mi. 

6 

Yb- 

a IQl. 
<5 • I 1 O 1 

111; 27H 



4. -m. 



\'^n. lO.lQii} 



4i. 



3. 54 lb. 



5. 



$94H. 



4. 

9. 



193H. 
18i vd. 



ANSWERS. 



205 



i- lb. 
oz. 



6 3, 



h- 



2i?t 



40» 



8, 1024. 



5. -jSTbo- 



7 3 
|«-< i 2 O • 

\2i mi 
foo* 






5.i 



11 



?oM; iOt^. 

4. 30ft. 
:?0. 164s}t. 

|4i. 



4. 193H- 
9. 18i yd. 



4. 

H. 

3. 
0. 
9. 



.«.. . 1 1 . 1,1 

1 > ■'■To > T'f' 



Ex. CXL. i. 4; 9; 8. 2. tI; ^r; M. 5. |t; H; M- 

m-, i%. 6. A; f ; 4i. 6. ^; Gl; 5f. 7. -h: I; H. 

i'. 8; f; n. 10. h T%; 35. 

Ex. CXLI, 1. l»Oi; 30fV; 5GA. ^. 30*: 42^; 72H. 
42^; 5(iA; 15ttU. 4. i; t^; A. 5. 15; l(i*; 9*. 
U; 11; 20. 7. U; 195; 16i. 5. 31i; 2A; 1. 
$1^; $i; i>55 mi. 10. $558; 324 oz. ; 3 hi*. 

Ex. CXLII. 1. $39i^. 2. $159lt. ^. 71|c. 4. 8i mi. 
$13i. 6. 12k^ bu. 7. $1733i. ^. 36 bu. 9. 47 A. i<?. $4. 

Ex. CXLIII. 1. $1.68. 2. $30000. 5. 85 mi. 4. 37^^ ft. 
385 mi. 6'. $105000. 7. 257|. .S. 39100 men. 9. 210 pages. 
$65600. 

Ex. CXI IV. 1. 21; 24i. 2. 18; U. 3. 17ir; 7. 
4. 3^1 U. 5. ,J\; 3^ G. 7; 20. 7. 10; 40. 8. 2f; tV. 
y. 3i4; i. ic^. 1; 2i^. 

Exc CXLV. 1. 1851 mi. 2. $1012. 5. 59|. 4. 32H bu. 



10 



5. $170861. G. 10. 7, 



37 im- 



^. $3125. 9. $43i. iO. Gain, $12. 



Ex. CXLVI. 1. 14, 16, 15. 2. 36, 55, 44. 3. 8f, 14|, 24f. 
4. 171. 31i, 30f. 5. 4f, 5.^4, 6^. C. 6||, 1^%, llf}. 
7. 5i 4, 7i. .Sf. la-o, laS, it- 9. ih, 2i, If. ^ 3, i, U. 



Ex. CXLVI I. 7.11; 

TT> 



111 <? 1 1 IB. S. y 1 1 11 1 a 



2if, 12. 4. 



^. 231, 16. 9. 



h 



^' 5) »■, T" i'" ii> It* k). G. 3i8» It, l54» 7. 2i, 6, 8. 
^. 31, h, 3i. 5. 1|§, t, 2. ii^. 7f, A, 5i. 

Ex. CXLVIIi. .*. 37* yd. 2. 8| mi. .9. $26i. 4 
5. 10 bags. G. 12i et. 7. 28| hr. 8. 8M. 9. 217i A. 
10. 370i A. ii. 15i ct. 12. 32 da. 13. $3.60. i4. 20. 

Ex. CXLIX. 1. 7^, 4. :^. 3J, 3f 

r ol 2.5 /I 5. 4>a6 w jl _S,_ 

•-'• "T, aaa. o. 7, -sT. /• *1i> ii5» 

Ex. CL. 1. 1^, 3i 

i^' H(H «4« 'J' 10) *jT« 

Ex. CLI. 7. 5f, i. 2. n, U. 

/; 11 3 /; 1 14. /y 9I .jA o 

Ex. CLII. /. 144§. 2. 2. 5. 



17f mi. 



2H. 
1 1 

6 O > 1 « • 



2. 3i, 30. 3. 54, 66J. 4. 6, 
7. i, 5i. ,?. lOA, f. 9. 5H, *. 



IB. 



1 ra> li. •^^ 2 1 » 3 



13 



7 -1 



7. 15i. V?. 43 1^ 

Ex. CLIII. 

7. 101. ,?. U. 9 

Ex. CLIV. 7. 



9. h. 



\h. 



9. 11, 40. ' 10. 4, 
I. 5. 7i. C. 4x^„. 



2. 



1 11 

i. TJ. 



^. 



10. 

4. 



-36 • 



lUi. 1» 



6 

r3 



3B ; 

30 fj 

T3» >* 



4. 

5. 6H. 

2 1 6 J •- iB 

7_ . 21 
T3i5 > 



4, ^0. 5. 2. 

10. f. 

4^5 ; 60. 



e. 35. 



4. 2h ft. 



5. 5tft.; 19. G. 60. 7. $112i. 8. 3S bu., 51 bags. 9. 59. 
10. 6| da; A, 10 times; B, 15 times; C, 8 times. 

Ex. CLV. 1. 16s., 3M., 4id. 2. 87i et., 80 ct., 75 ct. 

3. 17 cwt. 50 lb., 7 lb. 8 oz., 14 oz. 

4. 213 rd. 1 yd. 2 ft. 6 in., 3 yd. 2 in., 2 ft. 6 in, 

5. 128 sq. rd., 22 sq. yd., 2 sq. ft. 117 sq. in. 



y"' 




2Qe 



ARITHMKTIC. 



6. 96 e. ft,, 11 e. ft., 432 c. in., r)04 c. in. 

7. 2 pk. 1 gal., 1 K'll- H qt., 'A (jt. if. 3 qt. 1 pt., li pt., 3i- qt. 
.'/. 4 da. 21 hr. 'Mi niin., 7 lir., 2.') min. 10. 40, 288 , 16'' 40". 

Ex. CLVI. 1. 444.')4() in., 12(5744 in. 
^. 1 mi. i:{l rd. 4 yd. 2 it. G in., 1 mi. 179 rd. 1 ft. 6 in. 
3. 237600 in. luuOi in. 4. 31637628 aq. in., 3860136 sq. in. 
5. 1 A. 52 Hq. rd. 19 sq. yd. 8 sq. ft., 2 A. 47 sq. rd. 9 sq. yd. 

3 sq. ft. 36 »q. in. 
6'. 16727040 sq. in., 131868 .sq. in. 7. 9600 lb., 3800 oz. 

8. 14") rd. 2 yd. 1 ft. 6 in., 93 sq. yd., 10 sq. vd. 108 sq. in. 

!). 9 A. 120 sq. rd. 22 sq. yd., 1 A. 16 sq. rd. 9 sq. yd., 3 sq. ft. 
10. 200 gul., 35 t. 

Ex. CLVII. /. ,$82.11, $28.80. ;?. £1 Hs. 3id., £1 2s. 8d. 

3. 3 t. 12 ewt. 4 lb., 1 t. 11 cvt. 48 \h. 

4. 2 mi. 197 rd. 5 yd. 9 in., 2 mi. 270 rd. 4^ in. 

5. 1 A. 135 rd. 22 yd. 8 ft. 51 in., 2 A. 16 rd. 

a. 2 ed.59eu.ft., 10 ed. 60<?.ft. 7. 3 bu. ^gjil., 2 bu. pk. 4 qt. 
8. 5 gal.,, 13 gal. 1 pt. 9. 23 lu-. 20 min., 5 hr. 26 min. 40 see. 
10. W 30' 12", 14" 30' 30". 

Ex. CLVIII. 1. tItt owt. 2. &A-S. 3. iV Ini. 
i. 



A i'<^. •^. liir i"<l. 
A. 10. { ft. 


0. 1 1>I. 


7. i oz. .S. U. 


Ex. CLIX. 1. ^ 11). 
iW. 6. A on. yd. 


2. lb. 

/-. lit. 


.7. m iiii. 4. T*J 

c'v. I mi. .'y. ^^^ 



557561. 
10. $300. 

$3.84. 
i>. $21.51. 



5. 

10. i\ A. 

Ex. CLX. 1. 34940585. 2. 525 lb. 3. 169 qt. 4 

5. 4320. 6. 5940. 7. $251.25. 8. $1837.J. i>. $44.20. 

Ex. CLXI. 1. 118188 lb. 3. 31 i cd. -■?. $150. 4 
5. $633.60. 6. 267 d. 7. 129600 min. ,?. 1440 min. 
10. 2024 poleo. 

Ex.CLXII. i. 471b. ^. 36112 pt. 5. 5392oz. 4. 31t.5ewt. 
5.1800. 6'. $499.95. 7. 1248oz. A'. 40et. 5.189. id>. 467721b. 

Ex. CLXIII. ^. 22506 gr. 5. 161 gr. S.ohho?.. 4. 5184gr. 
/J. 11088 gr. C. 10 D). 1 oz. 12 dwt. 8 gr. 7. 25. 8. 37i lb. 
y. 701 lb. 6 oz. 6 dwt. 5 gr. 10. 114|| lb. 

Ex. CLXIV. 1. 63360 in. 2. 8064 in. 3. 2 ml. 4. $462. 
5. $428.40. 6. $500. 7. 10 hr. 17 min. 8. 1584000 in. 
0. 506898 in. 10. 440 mi. 

Ex. CLXV. ?. $72. .?. $31..50. ,?. $1.95. ^. 438 baskets. 
5. 335pt. 6. $1.05. 7.4. .S'. $510.30. .9. 2 qt. iO. $13T.74i. 

Ex. CLXVI. 1. 32 da. 2. 264 ft. 5. 9. 4. 44 ft. 5. 9 mi. 

G. 320 hr. 7. 500 da. cV. $57.24. .9. $47.25. 10. $19.44. 

Ex. CLXVII. 1. 68 et. 5. 5 ft. 3. 8184. ^. 15. 5. 43 mi. 
G. 48 hr. 7. 4620 paces. 8. 43. .9. 24320. 70. 8f| mi. 



VNSWERS. 



2U7 



pt., 3i- qt. 
16'Uo". 



i in. 
sq. in. 
. 1) sq. yil. 

oz. 

< sq. in. 

I., 3 sq.ft. 

;i 28. 8d. 



i.0pk.4qt. 
[iiin. 40 sec. 

bu. 

4. T5' 
144 

4. 55756^ 
0. ^6*. $300. 

4. $3.84. 
. iy. $21. ni. 

31t.5ewt. 
JO. 467721b. 

4. 5184 gr. 
h*?. 37i lb. 

4. $462. 
in. 

basliets. 
to. $137,741. 
It. 5. 9 mi. 

519.44. 

5. 43 mi. 
1 4 mi' 



4. 6(5 mi. 



9. .■?. 12 hr. 



Ex. CLXVIII. 1. 6 lb. 4 oz. H dwt. 12 gr. 2. £200. 
5. 10 cwt. 80 lb. 1 oz. 4. 24 ft. J. 990 yd. 
6'. 4 min. 16 sec; 980 yd. 7. 32 yd. *. 54. 9. 989 1b. 70. 1271. 

Ex. CLXIX. 1. 84 in. ;.^ 7 da. 5. 506 da. 
5. 75 ct. 6. $8050.50. 7. 49| yd. ,y. 60 et. 
!K 12 da. 20 hr. 20 min. 10. 4 yd, 1 ft. -i in. 

Ex. CLXX. 1. 3 lb. 11 oz. 11 dwt. 6 g. i 

4. 110 da. 5. 36 hr. 6\ 42. 7. 92928. ,!;. 12 spoons. .9. 5/a mi. 
iO. £43 Is. 3d. ; £6 8s. 9d. 

Ex. CLXXI. /. 209 bii. 1 pit. 3 qt. S. 1569 bbl. 

3. A, 131 yd.; R, 19i vd. 4. 36 mi. 298 rd. 1 ft. 6 in. 

5. 48 rd. 6. 8f yd. 7. $62. ,?. $13.50. 9. $432. iO. Hi t. 

Ex. CLXXI I. ./.s-7.50. iJ. $1.76. 5. $96. -^ $49. 5. $19.12. 

6. 27i yd. /". 27 lb. 8. 1.0 hr. 9. $8. 92 J. 10. $94.40, $660.80. 
Ex. CLXXIII. /. 48, 8 lb. 2. 32 lb. 3. 42 mi. 4. 24 yd. 

5. 450sheep. 6.176ft. 7. 58|A. ^. 60ct. .9. $12000. 10. U A. 

Ex. CLXXIV. /. 288. 2.$:]H. 5. 160| bu., 32U bu. -^. $20J. 

5. $6000. 6. 8i ft,., 2079U gal. 7. $23.76. ^.100 A. 9. $4070. 
10. $0250. 

Ex. CLXXV. /. 50 A. 156 rd. 2. 7 ft. 9 in. 3. 8f ft. 

4. 3 doz. .5. 181iJ A., 203^5 A. 6. 38 A. 91i rd. 7. 42240. 

^. :-!;6C.01. .9. 396 lots. iO. $13459.56; Jamr*' $3364.89; William, 
S»}4486.52; daughter, $1121.63; wife, $4486.52. 

Ex.CLXXVI. 7. all. ^. -i\. 5. l^da. 4. 36da. 5. 16^ da. 

6. 41ida. 7. 10 da. 8. Uf da. 0. 2h da. 10. l|f da. 11. 21^ da. 
12. £J hr. 13. 28f hr. 7-^. 6^,^ da. 75. 2^ da. 16. 3^ da. 

Ex. CLXXXI. 1. 282.405 A. 5. 307222.086446. 

3. 363.536487. 4. 115.8125 yd. 5. 24.2675 t. 6. 25269.111505. 

7. .42951303. 8. 6.5 t. .9. 138.122427. 10. 48095.139833. 

Ex. CLXXXIV. 1. 72.927. 2. .1993. 3. 364.9953. 

4. 6999.9996045. 5. 999999.999999. 6. .017481. 
7.2999999.900001. .?. .000999. .9.43.08997. 70.6929.95993. 

Ex. CLXXXV. 7. .30.280965. 2. 75.0665. 3. 15.635563. 
4. 16.()799884. 5. 49.1.56. d. 4.152. 7. 81.143. 8. 9.7597. 
.9. 80.025. 10. 9.0897. 

Ex. CLXXXVI. 7. 228.475 A. ^. $.327,065. 3. 199.35 mi. 
^.$963.68. 5. 262.35 A. 6. .08 in. 7. $111.58. 5. 29569.92 A. 
9. 123.325 lb. 10. 73.73 ft. 77. .3. 12. 30.338 in. 

Ex. CLXXXVIII. 7. .435; .0676. ^. 506.4463; 35.4367519. 
-'?. .013272: 32.5779. 4. 36.9; 1.7005. 5. 3.8; 1860.867. 

6. 525; 92.;. 7. 11221.1; 54.706. 5. 9.06453; 279.29475. 
9. .000000027; 4.8. 70. .1728; .032. 

Ex. CLXXXIX. 7. 12.34.i56, 12.345.6, 12.3456. 2. 33.5175. 
3. .000019737. 4. .00.365. 5. 005162. G. 45; 450; 4.500; 45000. 

7. 421000. 8. 1144.90001605. 9. .68785. 70. .0000000000884. 




208 



AKITHMETIC. 



4. 
.V. 

6. 
8. 

4. 

9. 



3. 
4. 

6. 

G. 
7. 
8. 

!). 
10 

3. 



9. 

4. 

8. 



6. 
8. 

5. 
10 

4. 
7. 
11 



9. 



Ex. CXC. J. 204.375 mi. il. 4'y'.i A'2') lb. 3. $7000. 
270.40.) ft. 5. H64.H() ft. 6. 23. (52.') yr. 7. 4:{(}247.424 ^r. 
r)yO.U28 mi. 9. 993.12;') gal. JO. 2y7.2r)37r). 

Ex. CXCIII. /. ir>.24. ;.\ 3r)0000. 3. .413. 4. 330000. 
.024. 6'. 647r)3(;t)0000. 7. 12.34r), 1.234.^), .12345, .012345. 
10.5. 9. 127.4. 10. .075, .0075, .00075. 

Ex. CXCIV. /. (5.165 nl. 2. 320 rd. 3. 42 bu. 

144 bbl. 5. 87.5 bbl. 0. $128.50. 7. $27.5. 8. $10800. 
15.75 bu. 10. 5.2 hr. 

Ex. CXCVII. /. I.^s. 9fd.; 15h. 3|(1.; £1 16s. 2id. 
83 lb. 4 oz. ; 1 cwt. 74 lb. 14.4 oz. ; 3 t. 17 cvvt. 95 lb. 
252 rd.; 80 rd. 4 yd. 1.2 ft.; 21 mi. 118 rd. 

145 sq. rd. 6 sq. yd. 64.8 sq. in. ; 141 sq. rd. ; 13 A. 70 sq. id. 
25 eii. ft. 540 eu. in.; 7d. 112 cu. ft.; 9 eu. yd. 20 cu. ft. 

432 cu. in. 
3 i>k. 1 gal.; 2 bu. 1 pk. 1 gal.; 5 bu. 1 pk. 1 gal. 3.2 qt. 
3 qt. 1 pt. ; 5 gal. 1.4 pt. ; 7 gal. 3 qt. 
11 hr. 52 min. 48 sec. ; 7 wk. 6 da. 3 hr. ; 9 wk. 6 da. 15 hr. 

36 min. 
58' .30"; 2" 5C' 51"; 17° 23' 15". 
. 3 ft. 9 in. ; 17 rra. 17 qr. 12 sh. ; 7 gro. 9 doz. 

Ex. CXCVIII. 1. £1..')25, £7.68125. 2. 9.854 t., 5.70375 t. 
7.1109375 mi., 6.089 mi. 4. 9.3 A., 7.283 A. 
7.875 cd., 7.0875 cu. yd. 6. 7.8125 l.u., 5.890625 bu. 
27.875 gal., 14.375 gal. 8. 3.55875 da., 2.7725 wk. 
3.8775% 17.12375°. 10. 5.8875 rm., 24.75 grs. 

Ex. CXCIX. 1. $.3380. 2. 10.3826 ft. 3. $59,375. 

The latter, 8.875 cu. in. 5. 3.2 lb. G. $24.80. 7. 83.75 yd. 

$322.28. 9. 199218.75 oz. 10. $186.15. 

Ex. CC. 1. $414. 2. $109.0625. 3. 75 sheep. 4. $161.6.')5. 
50. 6'. $492.01875. 7.3720. A\ $53.25. 9. $i. i6^. 13.378A. 

Ex. CCI. 1. 67.75 A. 2. 28 vr. 3. $26484. 4. 7.39, 8.95. 
$10.32. 6'. Gain, $846,875, $12.50. 7. A., $75.87; B., $57.39. 
16.5. 9. 1585584 cu. ft. 10. 8.6328 mi., 9.1872 mi. 

Ex. ecu. 1. $5. 2. $96,768. 3. 29.83 in. 4. 2.7 ft. 
2.2968. 6. .5625, 33.75. 7. 15360. 8. 58 lb. 9. $24.60. 
. $192.78. 

Ex. CCIII. 1. 42.34. 2. 17.3. 3. 8.45, 5.65. 

26.1 cd.. 24.65 ed. 5. 64 mi., 56.25 mi. 6. $340.05. 

$18.8325. S. .7875. 9. 4 ft. 3.2 in. 10. 92.4 vd. 

, $181.50, $77, $44. i^. 660 ft. ^5. 2446.875 lb. i4. 4A da. 

Ex. CCVII. 1. 444 sheep. 2. $103. 3. 225 bales. 
288 boxes. 5. $216. G. 480 A. 7. 120 lb. 8. 200 A. 
300. 10. 30 bu. 



ANSWERS. 



209 



td. 
)5lb. 






\. 70 sq. 
. 20 cu. 


1(1 
ft 


1. 3.2 


qt. 




da. 


1;-) 


hi 



Ex. CCVIII. /. $1400. 2. $77(50. S. 120 A. 4. $:j:175. 

6. $29500. 6. 4930 sheep. 7. 231 girls. 8. 20277. U. $717.25. 
lU. 73%, 876 sheep. 

Ex. CCIX. /. 061%. 2. 98%. S. 80%. 4. 50%. 
5. '20%. 0. 12%. 7. 25%. H. 8%. y. 33i%. 
10. 40%, 60%. 

Ex. CCX. 1. 70. ;^. $2500. 5. $500. 4. 800 A. 
5. 450 sheep. 6'. $4500. 7. 150 Hues. ^. $1300. 
9. 4500 sheep. i(>. 450 pupils. 

Ex. CCXI. /. 3290 bu. .^6%. 5. $72. ^.$20. 
5. $12932.50. 6'. 48992 lb. 7. $125. H. $5400. U. $9000. 
2(^. Lost, 12i%. 

Ex. CCXII. 1. 330 rd. 2. $372. 5. 10 lb. 4. 48 mi. 
5. 2800 books. 6'. 224 men. 7. 1880, 2021. 8. 11|%. 
f^. 13752. 10. 9A%. 

Ex. CCXIIl. 7. $112.50; $216. 2. $292: $504. 
5. $108. 4. $105. 5. $180. 6. $150 7. 4i%;374%. 
^. $360. 9. $800. i6^. $3.75. 

Ex. CCXIV. 1. $270, $540, $547.20, $1051.65. 2. $557.46. 

3. $10.26. 4. $3.20. 5. $25. 6". $6g. 7. $500. 5. $2.50. 

9. 32i%. iO. 46%. 

Ex. CCXV. 1. $25.50. ^. $3.20. ,?. 28%. 4. 46.19%. 
5. $20. 6. $7.56. 7. $850. .!?. $33i%. 9. $461.70. 

10. $357, 47i%. 

Ex. CCXVI. 7. 25%. «. 15%. 9. 4%. iO. 42f. 

Ex. CCXVII. 1. $1.89. ^. $926.10. 3. $.38.28. 

4. $3612.50. 5. $238. 6. $2719.50. 7. $60. 8. $900. 

5. 9000 bu. 10. $4.20. 

Ex. CCXVIII. 1. $112. ;g. $8600. 5. $204.70. 4. $1007.50. 
5. $75. 6. 12*%. 7. $330. .^. 40%. 9. 35^. 
i<?. $160, $208. 

Ex. CCXIX. 3. $168.75. 4. $115.92. 5. $12.50. (. $19.38. 

7. $13.50. .?. 3%. 5. U%. iO. 3|%. 

Ex. CCXX. /. 3%. 2. 2\%. 3. 3*%. 4. $14400. 

5. $8400. 6. $2592.80. 7. 84ct. 5. $7200, $216. 9. 156 members. 
10. $3264. 

Ex. CCXXI. 1. $150. ^. $3650, $146. 3. $270. 
•^. 25000 yd. 5. 6000 lb. 6. 4100 lb. 7. 52000 yd. 8. $3500. 
». $897.75. iO. $4000. 

Ex. CCXXII. 2. $80. 3. $66.25. 4. $225. 5. $675, $74325. 

6. $22.50. 7. 11%. 8. %%. 9. i%. 10. |%. 

Ex. CCXXIII. 1. $16000. ;^. $3000. 3. $20000. 
i/. $14000. 6. $420. 6. $34737. .50. 7. $40000. 

8. $2040, $5960. y. $75. 10. $2500, $3500, $4000. 



210 



AKITHMETIU. 



Ex. CCXXIV. /. i|i.'>4. 2. $150. .?. |19.r>0. /. !fir)23. 

5. $tjr)2.50. a. $22. 7. $1H. J^. 14 milln. 'J. 12i mills. 
i^>. 17 J inlllH. 

Ex. CCXXV. /. $2800. ;-'. $2500. .i. $.544000. 4. $101. fiO. 

6. $".)00. a. $13000. 7. $5075. 8. 6i inillH. U. $25. 
10. $114.20. 

Ex. CCXXVI. 1. $0, $8, $.'{, $7, $7, $9. 2. $9. ./. $50. 
4. $:i40. 6. $10. 6'. $5.39. 7. $15.12. 8. $38.88. 
f>. $13.20. 10. $4.0110. 

Ex. CCXXVII. /. $915.00. ii. $1012.05. 3. $2084.02. 

4. $074.01. 6. $531.65. 6'. $425,050. 7. $1859.04. 8. $66. 
0. $1910.20. 10. $1154.04. 

Ex. CCXXVIII. l.(S%. 2.1%. 3.H%. 4.61%. 
6. Oi%. 6. 5i%. 7. 7i%. 8. 4i%. 0. 6%. iO. 6%. 

Ex. CCXXIX. i. 1 yr. 2. li yr. .?. li yr. 4. 5 mo. 
6. 9 mo. 6*. 8 mo. 7. 115 da. *. li yr. 9. 150 da. 
10. 75 da. 

Ex. CCXXX. 1. $540. i2. $055. 5. $850. 4. $360. 

5. $840. 6. $750. 7. $876. *. $1825. 0. $219. 26?. $2920. 

Ex. CCXXXI. /. $2.50. 2. $405. 3. $540. 4. $572.50. 

6. $1320. 6. $408. 7. $750. 8. $1742. f>. $.3050. 10. $.3212, 

Ex. CCXXXII. i. $126.10, $920.10. 2. $477.54, $2977.54. 

5. $70.51, $1320.51. 4. $1724.05, $9724.05. 6. $112.55.09. 

6. $5250. 7. $900. 8. $10000. 0. $4.32. 10. $124.05. 

Ex. CCXXXIil. 5. $751,875. 6. $1485.15. 

Ex. CCXXXIV. 1. $645.48. 2. $792.22. S. $180..50. 
4. $.5579.42. 5. $508.69. 6. $115.48. 7. $325. 8. $570. 
9. $1920.70. 10. $1053.77. 

Ex. CCXXXV. 1. $7828. 2. $6760. S. $7032.50. 

4. $1248. 5. $2669. 6. $4750. 7. $3262.50. 8. $9750. 
9. $20400. 10. $2,600. 

Ex. CCXXXVI. 1. $700. ;g. $2500. .9. $3500. 4. $.5600. 

5. $2200. 6. 5. 7. 10. /?. 6. 9. 28. /fl. 15. 

Ex. CCXXXVII. 1. $200. ;2. $240. 3. $200. 4. $100. 
5. $112. 6. 5^%. 7. 4^%. ^. 5%. 5. 5i%. 

Ex. CCXXXVIII. 1. $9100. «. $13310. 3. $11340. 
4. $15570. 5. $11495. C. 60. 7. 70. 8. 220. 9. 500. 

Ex. CCXXXIX. 1. $10000. ;?. 124. 3. $18000; 720. 

4. %%. 6. 1%. 6. 3i%. 7. $100. *. $540. 9. $4925. 

Ex. CCXL. 2. lUf. ;2. 83i. 5. 20Gf. 4. 5*%. 

5. $2400. C. $1420i. 7. 50. 5. $29400. 9. 5%. 2^;. !!;)!00, 

Ex. CCXLI. 4. 3 inc. 5. 10 mo. C. 8 da. 
7. 60 days after the debt is due. 8. 6 mo. 9. 02 du. 



ANSWERS. 



211 



^2i. 

i, $101.60. 
15. 

.h $56. 



184.02. 
8. $66. 

. 6%. 

5 mo. 
da. 

JS360. 

iO. $2920. 

$572.50. 
10. $:J212, 

p4, $2977.54. 
2.55.09. 
24.05. 



80.. 50. 
?. $576. 

50. 
;9750. 

4. $.5600. 

U. $100. 
I340. 

I. 500. 

720. 
|$4925. 

10. t'WOQ. 



Ex. CCXLII. 1. 6 mo., 3 mo., 4 mo. 2. 120 da. S. 4 mo. 

4. 5 mo. 5. Ap. 23. 6. Il2i dii. 7. 3* mo. ,y. 70 da. 
0, H mo. 

Ex. CCXLIII. 1. B, $450; A, $600. 2. A, $189; B, $243. 

3. A, $135; B, $125. 4. A, $85; B, $130; C, $60. 

5. A. $864; B, $408; C, $1152. 0. A, $2600; B, $3400. 
7. B, $650; V, $925. ^. A, $1750; B, $2125; C, $1125. 
!). $720. /^. A, $2662; B, $2420; C, $2200; D, $2000. 

Ex. CCXUV. 1. A, $17.50; B, $22.50. 

5. A, $285; B, $150. ^- A, $25; B, $21; C, $54. 

4. A, $75; B, $175; C, $330. 5. Equally. 

6. A, $2200; B, $3000. 7. A, $1225; B. $875; C, $1050. 
*. 4 mo. 9. $1480. /^. A, $8445.94; B, $4054.05. 

It. $1800. 12. C, $16051^; 1), $1544^^; K, $1050. 

Ex. CCXLVII. 7. 80; 15625; .512; 343. 8. 6th. .9. 256. 
10. 24th. 11. 49126081. 13. 128787625000. 
13. .000000000016. 15. 10 A. 

Ex. CCXLVIII. 9. 3.05; .102; .571; .00563. 
W. 2.236; .707; .948; .094. 

Ex. CCXLIX. 1. 400. 2. 49j. S. 3202. ^. 24 yd. 

5. 440 yd. 6. 200 rd. 7. 272 ft. 8. $160. .9. 144 id. 

10. $324. 

Ex. CCL. 1. 75 vd., 25 yd. e. 220 yd., 44 yd. .9. H in. 
•/. 17 rd. 5. 1440 mils. 6. 280 rd. 7. 8030 yd. S. 15 ft. 
.'>. 221 yd. 10. 7712 yd. 

Ex. ecu. 9. .1; .06; 11.6; 36.3. 10. .928; .4308; .2; 1.709. 

Ex. CCLII. 3. 35.3. 4. 5476 sq. ft. 5. 564.")4 sq. ft. 
0. 17 ft. 7. 60 in. cV. 9.2 in. 9. 12 ft. ^^. 15.75 in. 

11. 37 ft. 12. 5 ft. i5. 12. 14. 36 ft. 

Ex. CCLIII. 1. 1521 sq. yd. ^. 29 sq. ft. 56 sq. in. 
3. 1144 sq. ft. 4. 210 ft. 5. 2 ch. 40 1. 
6". {(i) 229i sq. in. (/>) .54 A. (c) 20| sq. ft. 7. 5A' sq. ft. 
5. 16 rd. 9. 80 rd. 10. $50. 

Ex. CCLIV. i. {a) 186 sq. ft. (^) 318^ sq. ft. (c) 5-A A. 

id) 7A A. 
i?. 50 in. 3. 57 in. 4. 92 rd. 5. 4300 sq. ft. G. 2145 sq. yd. 

7. 1715 sq. ft. 8. .5541 sq. yd. .9. 203 sq. ft. 10. 56 ft. 

Ex. CCLV. 1. 44 in.; 66 in.; 11 ft.; 51* ft.; 73i ft.; 
14 eh. 961. 
2. 7 in.; 17i in.; 19J ft.; 1 ch. 7U 1.; 7 vd.; 21 vd. 7 in. 
^>. 24i min. 4. Ill rd. 1 ft. 10 in. 5. 5 ft. G. 72. 7. 4lf ft. 

8. 84 yd. 9. 12 ft. 10 in. 

10. 22 in.; 33 in.; 55 in.; 06 in.; 110 in.; 121 in. 



212 



ARITHMETIC. 



Ex. CCLVI. 1. 9()2i Hq, in.; 138(5 sq. in.; 3850 sq. in. 

5544 sq. in.; 8(502^ sq. in.; 154 sq. in.; 346i sq. in. 

471f sq. in.; J)62i sq. in.; 7546 sq. ft.; 154 sq. in. 

38i sq. ft. ; G8^ sq. ft. ; 861 sq. ft. ; 1386 sq. eh. 
2. 26M sq. yd. 3. 88 rd. 4. 59.4 in. 5. 308 sq. in. 
6. 62.04 yd. 7. 246.66 yd. cS'. 277.^:. U. 110 sq. in. 10. $838^ 

Ex. CCLVII. 1. («, 85; (/>) 650; (f) 1730; {d) 698. 
2. (a) 528; (/>) 1230; (c) 44; (r/) 144. 

5. (a) 456; (/>) 782; (c) 390; (<0 225. 4. 29 mi. 5. 35 ft. 
6.274 ft. 7. 20.7J^in. ,?. 11.18 ft. .9.10 ft. i^>. $54.60. 

Ex. CCLVISI. 1. 9H eu. in.; 34fi cii. in.; 14 cu. ft.; 197 
cu. in.; 68 cu. ft.; 145 cu. iu. 
2. 121i sq. in.; 63| sq. in.; 35a-4 sq. ft.; lOOA sq. ft. 
S. 311 cu. ft.; 99^ sq. ft. 4. 131i eu. ft.; 18U sq. ft. 
5. 20 in.; 4^f eu. ft. 6'. $41i. 7. 16| ft. 8. 25i ft.; 17 ft. 
9. 28.09 in. 10. 1650 gul. 

Ex. CCLIX. 1. {a) 8f eu. ft.; (ft) 115i eu. ft.; (c) 385 cu. 
ft.;. ((0 13311 cu. ft. 2. {a) 29* sq. ft.; (/>) 132 sq. ft.; 
(c) 220 sq. ft.; (^0 183* sq. ft. 

5. 5f^ cu. yd. 4. $66. 5. {a) 31^ sq. ft.; (6) 15U sq. ft.; 

(c) 297 sq. ft. ; {d) 196 sq. ft. 101 sq. in. 

6. 91^ sq.ft.. 7. $24.75. <f^. 1 ft. .9.1yd. i^. 14|cu.ft. 



Ex. CCLX. 1. 108 eu. ft. 



2760 eu. in. 3. 75 sq. ft. 



:>. 89^ eu. ft. 



4. 33 sq. ft. 5. $33.75. 6. 19250 cu. in. 
7. (1) 861 sq. ft.; (2) 33 ft. 8. 89.51 yd. 
10. 61 in. 

Ex. CCLXI. i. (a) 154 sq. in. (/>) 38i sq. in. (c) 616 sq. in. 
id) 2464 sq. iu. 
2. $24.64. ^. 14 ft. 4. 132 ft. 

5. (a) 905|eu. iu. {b) 3620teu. in. (c) 1437ieu. in. (d) 179lreu. in. 
C. 4851 cu. ft. 7. 14f eu. ft. 8. 4 in. 5. 110592. 10. 2541. 

Ex. CCLXII. J?. 92.9 ft. 2. 88 yd. 3. 68 yd.; 867 sq. yd. 

4. 391 ft. 5. 75 ft. 6. 43.3 sq. ft. 7. 32 ft. 8. 98 yd. 
9. 820 in. 10. 1120 yd. 

Ex. CCLXI 1 1. 1. 43 ft. ,?. 242 yd. 3. 

5. M mi. 6. 4.24 ft. 7. 140 rd. 8. 4 ft. 
i(^. $3.30. 

Ex. CCLXIV. 1. U ft. 2. 3 in. tiles. 
4. 704 sq. ft. 5. 170 ft. 6'. 14175 sq. ft. 



$22f. 4. 25. 
9. 8063i lb. 

3. 126 ft. 

7. 5544 sq. ft. 



8. 79194 sq. ft. 9. 140 sq. ft. 10. 3461 sq. in. 

/. 80 ft. 90 ft. 2. 5 A. 3. 8232 sq. ft. 
89.44 rd. 0. 1560 sq. in. 



Ex. CCLXV. 

4. 28 sq. ft. 5 

7. 65 ft., 68 ft.; 60 ft 

10. 1121 ft. 



80 rd.; 120 rd. 



8. 72 ft. 9. 2646 S(i. in.; 4376 sq. in. 



sq. in-; 
H sq. in.; 
4 sq. ill-; 
h. 

'lO. $838 J. 
198. 

5. 35 ft. 
$54.60. 

-u. ft.; 197 

ft. 
ft. 
ft. ; 17 ft. 

(c) 385 cu. 
132 sq. ft. ; 

L51i sq. ft. ; 

lieu. ft. 
rS sq. ft. 

oil. ft. 



;) 616 sq. 


in. 


I) 179"ncn 
. 10. 2 


. in 
541 


; 867 sq. 
98 yd. 


yd 


4. 25. 

3i lb. 





ft. 

sq. ft. 

sq. ft. 
|)0 sq. in. 
4376 sq. in. 



ANSWERS. 213 

Ex. CCLXVI. 1. 63 ft. 2. 308 sq. ft. ; 385 sq. ft. 
S. 246.66 yd. 4. 3630 men. 5. 4800 ft. 6". 40 rd. 20 rd. 
7. 2.18 ft. 8. 12 ft. 9. $28.32. 10. $32. 

Ex. CCLXVII. 1. 52 ft. 2. 10.39 yd. S. 23.54 ch. 

4. 'ih eh. 5. 56 yd. 6'. 42 ft. 7. 414.12 ft. 8. 21.213 ft. 

5. 292i sq. ft. 10. 48i c. ft. 



1. 38i sq. ft. 2. 34.64 in. 5. 27.71 in, 
5. 1925 lb. 6'. 864. 7. 192000 shot. 



Ex. CCLXVIII. 

4. 37i It. ; 30 ft. 
8. 243 doz. a. 12 in. i^. 48 oz. 

Ex. CCLXIX. ;g. (1) 456 cm., (2) 45.60 dm., (3) 4,560 ni. 
,9. (!) 18.7 m., (2) 18700 mm., (3) 1870 cm. 4. 1897009.434 ni. 

5. 780.43 m. ; 11.03 mm. 6. 92.208 m. ; 299.18892 m. 

7. 640 leaves. 8. 27600 times. 9. $76.56. 10. 7.6375 m'. 

11, $555705. 12. 28000 times. 

Ex. CCLXX. 1. 287.6.345 hectares. 2. 37856 ares. 
3. 57536 sq. cm. ; 5753600 sq. mm. 4. 2341700 sq. m. 
5. 542 sq. em. 6. 3030303 sq. m. 7. 112 ares. 

8. 32.64 sq. m. 9. $2.50. 10. 280500 bricks. 

Ex. CCLXXI. 1. 72.5 st. 2. $432.50. 3. 25800 1. 
^. 23.375 c. m. 5. 2.604 m. G. 1.40 c. m. 7. 30 em. 
8. 300 HI. 9. $275.31. 10. 8 ct. 

Ex. CCLXXII. 1. 5037 j?. ; 503.7 Dj?. ;?. 3075 mg. ; 30.75 (Ijr. 
5. 8070006.5 eg. 4. 2.756 Kg. ; 275600 eg. 5. 7.28 1. 6. $750. 
7. 264.6 Kg. 8. $420.15625. 9. 310 mg. 10. .00504. 

Ex. CCLXXIII. 1. (a) 70.25 m. (6) 808.7 1. (c) 15.908 a. 
((0 27000.37 g. 
2. 594 Kg. 5, 47250 Kg. 4. 2100 coins. 5. 388 g. «. 110 st. 
7. 225 francs. 5. 33 HI. 9. 650 g. /^. 200 m. 11. 50 ct. 

12. 190 mi. iJ. 477 times. 14. 13.44 rolls. 

Ex. CCLXXIV. 1. .3, .45, .96, .765. 

2. .4, .142857, .285714, .42857i. 

3. .571428, .714285, .857142, .076923. 

4. .230769, .384615, .692307, .63. 5. .83, .583, .9318, .9287514. 
6'. .9428571, .954, .89285714, .15990. 

7. .7083, .4196428571, .54861, .164772. 

.S'. .44230769, .72li53846, .1392045, .3809523. 

.'>. .20238095, .8270, .14076.5, .505067'* 

10. .170138, .686789772, .35267857142, .20145. 



214 



ARITHMETIC. 



1 1 16 

1 n , 3r, TIT, 1 1 1 



Ex. CCLXXV. i . § , H , T I , f 1 . ^ 

o2 1810 8 ^35 47 S9 89 

«3- 3T> 5T, i?, ?7. 4. ]JT, Til, 5T, 111 

r9»1218 /J81198110 

5. TIFT, TI, T, T. O. 8 2, 36, tz, 4 1. 

^ 583 61 14 41 o 89 1 389 81 

7- Tffff, 360", ^25, SffOTT. o. 44, T4g, iJSff, '10. 

o 36 43 Oil 735 7/1 /|1- f^l 72 r;5 

^- 44, "SSff, -^Jf, 'IT- -tl'- "ITSO, JT63, '353^, «^1S. 

Ex. CCLXXVI. i. 0.60244. 2. 2.3060941229258. 
3. 9.4H69; 14.0636727. 4. .32457; .32147. 5. .73231777. 

6. 1.590; 6.893. 7. 339; .429. 8. .4675; .350649. 
D. 63; 10. 10. .54175; 7.805. 

Ex. CCLXXVII. 1. 10.5. i?. .42. 4. .161; .03. 
6. 33.142857.7, £2 Os. 8|. 6'. 3 t. 8 cwt. 35.3 lb. 
9. 6 mi. 92 rd. 1.6 yd. 10. 69 t. 888.8 lb. 

Ex. CCLXXVIII. 6. 7.456. 9. 13. 

Ex. CCLXXIX. 1. $3780. S. 9215 cii. ft. 

3. $132, $247.50, $275. 4. $100. 5. .0078125. 

6. 33 mi. 7. .405 hr. 8. W-A'^n. 9. .00129. 

Ex. CCLXXX. 1. A. 2. h dii. S. 3* da. •^. 14.7 da. 
5. L 6. A 27 da., B. 54 da. 7. A 19^ da., B 9|da., C 39ida. 

8. 4i da; 9. 18 da. 10. 4i hr. 

11. A 361 da.; B 73i da.; C 110 da. 13. 15 da. IS. 32 hr. 
i4. li hr. ^5. 8 horses. 16. A 3A da.; B 3^^ da.; C 5h da. 
17. A $1.10; B $1. 

Ex. CCLXXXI. 1. 12imn.; 24.min. ; 30 min. ^. 18 min. 
3. 16ri min. past 3. 4. Wrx min. past 6. 
5. 32 1\ min. past 6. 6. 24 min. past 6. 

7. 24 min. past 6 and 41n- min. past 6. 

.9. (a)43i^i min. past 8, (?>)27A min. past 8, (c) lOi? min. past 8. 

9. 49n min. past 9; 541*1 min. past 10; 12 o'clock. 

10. 23 ra min. past 5. • 

Ex. CCLXXXII. 1. 13A- min. past 4. 2. 19fi- min. past 3. 
3. 3I2-3 min. past 3. 4. 120 da. ; 44 min. past 11 ; 14 min. pnst 12. 
5. 75 da. 6. 36 min. past 6 a.m., Friday. 7. 5A min. past 5. 

8. 5i min. past 9 p.m. on Tnesday, and 57i min. past 8 p.m. 

9. 3 p.m.. May 3. 10. 43MH- min. past 9 p.m. 



Ex. CCLXXXIII. 

5. 14 min. 24 see. 
10. Gains 10/.,% min. 

Ex. CCLXXXIV. 



1. 44 ft. S. 34 A- mi. 3. 22h 4. 
0. 8 lir. 7. 33: mi. 8. 7h yd. 9. 



i'l sec. 



t J M ~ 



5. 41 mi. 0, 



nil. 



/. 224. 141. 2. 4 mi. ,1. J mi. ^. i hr. 
7. 45 iiiiii. 6'. 3 mi. .V. 5tol. tO. '2k hr. 



ANSWERS. 



215 



1 1 6 

riT, T 1 1 



n 5 



1777. 



14.7 da. 

.,C 39^ilii. 

3. 32 hr. 
; C oh dii. 

2. 18 mill. 



mill, past 8. 



lin. past '.5. 

nil. pjist 12. 
|min. past 5. 
ist 8 p.m. 

4. 7i sec. 



li. 4. i liv, 
to. 2i hr, 



Ex. CCLXXXV. 1. l! mi. 3. 45 mi., 36 mi. 3. 114 yd. 

4. 45 mi. 5. 11 min. 6. 396 ft. 7. 94^ yd. .?. 22 mi. 
9. 23i mi. 10. G'i mi. ii. 6| hr. 

Ex. CCLXXXVI. 1. $1.92. 3. 325, 175, 125. 5. $620. 
4. 74; 3s. 8jd. 5. 17. 6. 23. 7. £16 6s. ,S. 1980. 
9. 2 hr. 24 min. it*. 200 lb. 

Ex. CCLXXXVII. 1. 144 min. 2. Men, $12.50; women, $8; 
boys,$5.25. 5. 7bbl. /. 1022. 5.75yd. 6'. 32da. 7. 17 mi. 
8. $80. 9. 110 sheep, 140 pigs. 10. $51. 

Ex. CCLXXXVIII. 1. $12800. 3. 123 gal. 5. $672. 
4. 720 apples. 5. $75. 6. £140. 7. $97.50. 8. 223 sec. 
•O. John, $880; Thomas, $176; Henry, $22. 10. 56 et. 

Ex. CCLXXX!X. /. $27. 3. 26 ft. 6 in. 3. 4 ft. 1 in. 

4. 15 ct. 5. 2C88 rails. 6. 20, 21, 22, 23. 7. 182. 5. $60. 
,9. 7875 shingles. 10. 150 lb. 

Ex.CCXC. i. $90,$60. 2.3m\. 5. 87 da. 4. Latter, 51 ct. 

5. $20.0246. 6'. $8460. 7. $870, 6%. ,?. $2.50. 5. 19 da. 

Ex. CCXCI. 1. $900, $1350, $1800. 2. $36. 3. Gain, 72 ct. 
^.230400 A. 5. 49.90 rd, 37.43 rd. 6. $2.50. 7. 100 ft. by 76 ft. 
8. $321.25. 9. $354. 10. $7.50. 

Ex. CCXCII. 1. A, 30 ct. ; B, 36 ct. ; C, 40 et. 2. 160 leaps. 
•S. $2450. 4. vm see. 5. $500. 6. 80c. 7. U yd. 
8. 900 lb. at 7 ct. ; 1100 at 10 ct. 9. 248 yd., 62 yd. 10. $440. 

Ex. CCXCIII. /. .396 ft. 2. $329. 3. Divisor, 547; Qiiot., 3233. 
4. $4J-. .5. $23.50. 6'. A's rate is to B's as 79 to 60. 
7. 409036320 post-holes. 8. A, $432; B, 216; C, $1296. 
0. $1680. 10. $300; $450. 

Ex. CCXCIV. 1. 294; 84. 2. $900, $750. 3. $200. 4. ,^,?, . 
•5. $400. 6. $240, 5yr. 7. 2i in. ,?. 300 leaps. 9.9hv. 10. 2imi. 

Ex. CCXCV. 1. $4.80. 2. 8%, 9%. 3. 31^-%. 
4. 3060,^j bn. 5. 224. 6. 60 mi. per hr. 7. 16j da. 



10. A, $776.16; B, $693; C, $630; 



8. 813i cu. yd. 9. 4fo da. 
D, $600. 

Ex. CCXCVI. 1. 405 bu. 2. 24 ft. by 18 ft. by 12 ft. 

.?. 4.5eii.ft. 4. Gain, $14. 5. 8000 oranges. 
6. 5Jts. ; 56 oz. gold; 160 oz. silver. 7. $2480. 
5 U mi. per hv. 9. 20 min. past 4 a.m. 10. $217.80. 

Ex.CCXCVII. /. 1152 sq.ft. :?. 4%. 3. -i^^. ^.14.625 in. 

5. I?; 675. G. 14.288 to 1. 7. 48jct. <S'. $3i. i?. $1.80. 10. 190. 

Ex. CCXCVIII. i. 272 rd. 2. 111. 3. 24 ct. ; loss, A% . 
4. Length, .34 ft.; width, 26 ft.; height, 12 ft. 5. 4^ mi. 

6. 3G75§ t. 7. $441. 8. 63 yr. ; 35 yr. 9. 567 leaves. 10. 104 da. 



216 



ARITHMETIC. 



Ex. CCXCIX. /. 213 plants. ;2. $4500. 3.2imi. 4.1001b. 
5. 28 ct. 6. $2625. 7. $4000. 

8. .384 In. (Note, their length and width being equal.) 

9. 164.7114 in. 10. A, $1035; B, $1656; C, $2025. 

Ex. CCC. 1. 2 to 5. 2. 13tV niin. past 4, or 30 min. past 4. 

3. $40. 4. 5 yd. 3. $1.02, 80 ct. 6". $3250; $2600. 7. 233H ft. 

8. 3 to 2. f?. 2i ft. iO. $1600; 15 mo. 

Ex. CCCI. 1. A-. 2. A, $2,901; B, $5.09f. 3. 10 mo. 

4. 10 in. 5. $3. 6.90. 7. 3 hr. ,?. 5251b., 4951b., 3901b. 

9. $2100, $1750, $1050, $700. 10. B, by 50 yd. in 4i min. 

Ex. CCCII. 1. 141.4 sq. ft. 2. A, $600; B, $780; C, $180; 
D, $2000. 5. $2000; $1296. 4. 4%;4i%. 5. 60et. 6. 32 men. 
7. 15i mi. 8. $62500. 9. 11 J min. past 12. 10. $9r3 ; $9|. 



The End. 




4. 1001b. 



a.) 



min. past 4. 
7. 233H ft. 

10 mo. 
, 390 lb. 
I min. 

; C, $180; 

6. 32 men. 
>r3-; $9^.