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MENTAL ARITHMETIC,
BY
J. A. McLELLAN, M.A., LL.D.,
Inspector of Iliyh Schools, Ontario,
PART I.
FUNDAMENTAL EULES, FRACTIONS,
ANALYSIS.
18 78.
ADAM MILLER & CO., Toronto.
RoBKRT Miller, Montreal', J. Lanolais, Quebec; Bucklky k Allrn,
Halifax, N. S. ; J. k A. McMillan, St. John, N B, ; Urrwrr Bros.,
Charlottetv%on, P. E. I.
C(l\ /^^
Entered according to the Act of Partiamcnt of Canada, in tbe year ono
thousand eij^ht hundred and gevcnty-eight, hy Adam Millkr & Co.,
in the office of the Minister of Agr culture.
PREFACE.
Mental Arithmetic is not intended to superfsede written
arithmetic, but should rather be its constant auxiliary.
Without proper mental training, the pupil becomes ac-
customed to depend almost entirely on rules and for-
mulae — not capable of interpretino; the latter, and entirely
in the dark as to the reasons of tlie former. The long
and barren reign of rule and routine is due to the fact
that rational methods in teaching the Logic of the
Public School have been too generally ignored — that
Menial Arithmetic, which, by easy steps, leads the pupil
into an intelligent possession of principles, and renders
him expert and logical it) their application, has hitherto
held an utterly insignificant place in school-room work.
Given a slate, a pencil, a rule, and a salutary dread of
coming trouble, and a pupil was supposed to be seized of
all the elements necessary to make him a first-rate arith-
metician. But better methods have begun to prevail ;
and the improvement in teaching written arithmetic
which has taken place during the past few years has only
to be supplemented by systematic mental training, in
order to reach the highest results of the study of the
same. This is recognized bv the various educational
authorities throughout the Dominion. Most of them
have, it is believed, made it imperative that their teachers
shall have a thorough training in Mental Arithmetic,
and prove by actual examination, their knowledge of
rational methods as well as their ability to teach them.
PREFACE.
In a very short tinle the wisdom of this course will be
seen, not only in increased proficiency in mathematical
science, but in consequently increased intelligence and
power in mastering other subjects.
It is hoped that this work, undertaken at urgent re-
quest of many teachers and inspectors, will be found
useful in suggesting the methods and affording the
materials for thorough and systematic mental training.
No formal rules nor definitions have been given — these
can be given by the teacher when the pu})il has been led by
easy inductions to a clear comprehension of th(f ideas and
principles they involve. A great variety of type ques-
tions on the fundamtntal rules, fractions, and analysis,
has bfien given ; and the teacher can multiply at pleasure
questions corresponding to the various types.
The Second Part, most of which is already written,
will contain illustrations of condse methods of computa-
tion, ratio, and proportional parts, a full treatment of all
the rules that come under the gen* a*al head of percentage,
and a large collection of xamination papers for mental
solution, affording examples of every variety of question
likely to be met with in ordinary written arithmetic.
HINTS TO TEACHERS.
1. Use natural objects (numeral frame, etc.) to give
first notions of numbers. First, teach carefully the ana-
lysis of elementary numbers (with their notation) up to
nine inclusive — so as to give clear notions of addition,
subtraction, multiplication and division.
2. In addition etc., let the pupil have plenty of drill
in small numbers, till he thoroughly comprehends the ele-
mentary processes. Types of easy questions are given in
the book — let similarly easy questions be framed by the
teacher, and by the pupils for mutual drill.
3. Give many practical questions, so that ultimately
when a problem is prepared the pupil will be able^o
know in an instant which of the fundamental niles, or
what combination of them, is to be applied in the solu-
tion.
4. Always proceed from the known to the unknown.
The pupil learns subtraction from his knowledge of
addition^ etc., etc. : knowing that 4 + 3 = 7, he knows
that 7 — 3 = 4, and that 7 — 4 = 3; knowing that
4 X 3 = 12, he knows that 12 contains 4, 3 times, and
3, 4 times, etc. *
5. In the '* simple rules," prepare the way for fractions ;
make young scholars familiar with factors, multiples,
measures. The pupil having become thoroughly familiar
by proper training in the simple rules, with the notion of
division into equal parts, and with the language expres-
HINTS TO TSACHBBS.
sing such division, will find but little difficulty in the
whole subject of fractions.
6. In general, pupils should not Ije permitted to use a
text-book during recitation — ^young pupils need no book ;
those who have advanced to division, analysis, etc., will
do better to prepare assigned lessons, and at the same
time, should have additional questions proposed corres-
ponding to the given types.
7. In addition to daily oral work, there should he/re-
queiit written examinations ; the pupils are furnished
with pencils and small slips of paper ; they are directed
to turn to certain questions, to write down on their slips
the numbers of these questions, and are then allowed a
given time to solve them mentally, using the pencil only
to write, opposite its number, the answer they have found
for any question.
8. The pupil should commence mental arithmetic
wlien he enters school, and should continue it so long as
it is thought necessai-y that arithmetic should be one of
his studies.
ti
7
\
Section 1
Section 2
Section 8
Section 4
Section 5
Section 6
Section 7
CONTENTS.
Chap. I. — Simple Eules.
rA«a.
o
«a* ••• ••• ••• ••• *** *** *** *** ***
IS
«a ••• ••• ■•• #•• ••• ••• ••• ••• •• *W
26
••• ••• ••• ••• ••• ••• ••• ••• ••• "•• **
88
»«• ••• •*• ••• ••• ••• •••
• • • • «
••• ••• ••• ••• ••• ••• ••• ••• ••• ••• ^KV
47
Chap. II. — Fractions.
Section 1
Section 2 ...
Section 3
Section 4 ...
Section 5
■ •• ••• ••• ••• l*« ••• a«* •»•
• • • « • •
• • • I • •
• • • • •
• • • •
■« «•• •»• ••• •••
• •• ••■ ••• ••• ••• ••*
50
• • • • • • «M*
... 62
67
77
Chap. III. — Reduction and Compound Rules.
Section 1
Section 2
Section 3
■ • • • •
• • • • • •
••• ••• ■•• ••■
85
• •• ■•• ••• ••• ••• WO
90
■ •• ••• ««• •••
Chap. IV. — Questions for Examination.
Questions wb. Examination •• 103
CHAPTER I.
FUNDAMENTAL RULES.
Section I.— Addition,
ExA^liES. 1.
1. Charlie had 2 cents, and he found 1 cent : how many
liad he then 1
Ans. — 2 cents and 1 cent are 3 cents.
2. John has 2 dollars, and his father gives him 3 : how
many has he now ]
8. Harry had 2 marbles, and Charlie gave him 6 : how
many had he then 1
4. Mary had 9 pins, and found 2 : how many had she
then?
5. Sarah paid 3 cents for a pen, and 8 cents for a
holder : how much did she pay for both 1
6. In a class are 9 boys and 5 girls : how many are
there in all 1
7' Mary paid 7 dollara for a dress, and 4 dollars for
a bonnet : how much did she pay for both 1
8. Harry shot 5 pigeons, and Willie 7 : how many did
both shoot 1
9. How many are 2 and 1 ? 1 and 2 ? 2 and 2 1 2
and 3 ] 3 and 2? 2 and 41 4 and 2 1 2 and 5 ? 6
and 2 ? 2 and 61 6 and 21 2 and 71 7 and 2 1 2
and 8 1 8 and 2 1 2 and 9 1 9 and 2 1 2 pence and
9 pence 1 2 days and 9 days 1
10. How many are 3 and 21 2 and 3 1 3 and 3 1 3
2
10
MENTAL ARITUMETIC.
and 4 ? 4 and 3 1 3 and 5 ? 6 and 3 1 3 and 6 1 6
and 3 1 3 and 7 1 7 dollars and 3 dollars ? 3 hours
and 8 hours 1 8 tons and 3 tons ? 3 tons and 9 tons 1 9
thousand and 3 thousand ]
11. How many are 4 and 3 ? 3 and 4 ? 4 and 41 4
and 5 ? 5 and 4 ? 4 men and 6 men 1 6 boys and 4
boys 1 4 yards and 7 yards ? 7 inches and 4 inches ? 4
tons and 8 tons ? 8 tons and 4 tons 1 4 hundred and 9
hundred 1 9 hundred and 4 hundred 1
12. A man Wid 9 dollars for a coat and 5 dollars for
a vest : \vhat did both cost him 1
13. James si)ends 6 cents in apples and 9 cents in
oranges : how much does he spend in all 1
14. A V*oy found 8 eggs in one nest and 9 in another :
how many eggs did he fiTid 1
15. Willie caught 9 lobsters in the forenoon and 9 iu
the afternoon : how many did he catch in all 1
16. How many are 6 cents and 8 cents 1 6 dollars and
8 dollars 1 6 dimes and 8 dimes ? G shillings and 8 shil-
lings 'i 6 pence and 8 pence ? 8 farthings and 6 farth-
ings? 8 pears and 6 pears ? 8 tenths and G tenths ? 8
thirds and 6 thirds 'i
17. How many are 5 and 414 and 515 and 515 and
G 1 6 and 5 1 5 and 7 1 7 and 5 1 5 and 8 1 8 and
51 5 months and 9 months 1 9 tens and 5 tens 1
18. How many are 6 and 51 5 and G1 G and G 1
G and 7 1 7 and G 1 6 and 8 1 8 and G 1 G and 9 1 9
and G 1
Ifl. How many are 7 and G 1 G and 7 1 7 and 7 1
7 farthings and 8 farthings 1 8 drams and 7 drams 1 7
graiins and 9 grains 1 9 grains and 7 grains 1
20. How many are 8 and 7 1 7 and 8 1 8 tuxd 8 1 8
by
ADDITION.
11
and 9 1 9 and 8 1 9 fourths and 8 fourths ? 8 tenths
and 9 tenths 1
21. How many are 9 and 6 ? 6 and 9 1 9 and 7 1 7
and 9 1 9 and 8 I 8 and 91 9 and 9 1 9 thousand and
8 thousand.
22. How many are 10 and 21 10 and 31 10 and
41 10 and 61 10 and 61 10 and 7 1 10 and 81 10
and 9 1 10 and 10 1
23- A man travelled 9 miles by coach and 10 miles
by rail : how far did he travel in all 1
24. John caught 7 haddock and Edward 4 more than
John : how many did both catch 1
26. How many are 11 and 31 13 and 31 16 and
31 22 and 31 24 and 3 1 12 and 51 16 and 51 18
and 51 21 and 5 1
EXAMPLF-S. — 2.
1. Hov/ many are 11 and 81 13 and 81 14 and 8?
18and81 19and81 21and81 llandOl 12and91
13 and 91 15 and 9 1 17 and 9 1 19 and 9 1 21 and 9 1
2. How many arc 2 and 21 2 and 12 1 2 and 22 1 2
and 32 1 2 and 42 1 2 and 52 1 2 and 62 ? 2 and 72 1
2 and 82 1 2 and 92 1 $2 and $92 1 2 pence and 92
l)cnce 1 2 tens and 92 tens 1
3. How many arc 3 an«l 3 1 3 and 131 3 and 23 1 3
anaC31 3 and 431 3 and 531 3 and 631 3 and 731 3
and 83 1 3 and 93 1 96 and 4 1
4. How many arc 4 and 4 1 4 and 14 ? 4 and 24 1 4
and 341 4 and 441 4 and 541 4 and 64 1 4 and 741 4
and 841 4 and 94 1 98 and 2 1
g. How many avc 5 and 5 1 5 and 151 5 and 25 1 5
12
MENTAL ARITHMETIC.
. I
and 35 ? 5 and 45 ? 5 and 55 1 5 and 65 1 5 cents and
75 cents ] 5 pence and 85 pence ] $5 and $95 ] 6 tens
and 05 tens?
6. Susan p&id 7 cents for needles, 10 cents for thread,
and 9 cents for pins : how much did she spend ?
7. A. farmer paid 9 dollars for a harrow, and 19 dol-
lars for a plough : how much did he pay for both 1
8. George buys 9 marbles at one time, 6 at another,
and 12 at another : how many does he buy in all 1
9. A farmer sold 8 bushels of jats, 9 bushels of peas,
and 9 bushels of rye : how many bushels in all did he
sein
10. The head of a fish is inches long, the tail 9 inches,
and the body 1 2 inches : find the length of the fish.
11. Harvey pays 5 dollars for a pair of boots, 17 dol-
lars for a suit of clothes, and 4 dollars for a hat : what
does he pay in all 1
12. A man had 95 dollars in a savings bank, and de-
posited 6 dollars more : how much money had he then in
banki
13. How many are 6 and 6 1 6 and 161 6 and 26 1
6 and 36 1 6 and 46 1 6 and 56 1 6 and 66 ] £Q and
£76 ? 6 and 86 1 $6 and $96 1
14. How many are 7 and 7 1 7 and 17,1 7 and 27 1
7 and 37 1 7 and 47 1 7 and 57 1 7 and 67 1 7 and
771 7 and 871 7 and 971
15. How many are ft and 81 8 and 18 1 8 and 28 1
8 and 38 1 8 and 48 1 8 and 58 1 8 and 6S 1 8 and
781 8 and 881 8 and 981
16. How many are 9 and 91 9 and 19 1 9 and 29 1
9 and 39 1 9 and 49 1 9 and 59 1 9 and 69 1 9 cents
and 79 cental 9 farthings and 89 farthings 1 $9 and
|99 1 9 tons and 99 tens,
ADDITION.
18
17. How many are 10 an<l 11? 10 and 21 1 10 and
31 'i 10 and ill 10 and 51 ? 10 and 61 1 10 and 71 1 10
and Sn 10 and 91] 10 hundred and 91 hundred 1
IG tentlis and 91 tenths 1
18. How many are 10 and 13 1 10 and 22 1 10 and
3?; 10 and 421 10 and 52? 10 and 62? 10 and
72 *? 10 and 82-? 10 and 92 *?
19. I used 8 rolls of paper for a bed room, and 28 for
a pallor : how many did I use for the two rooms 1
20. A farmer has 7 acres in for(;st and 67 acres
cleared : how many acres has he in alH
21. Herman's grandfather was 73 years old 8 years
ago : how old is he now t
22. A man travelled 9 miles by stage and 89 by rail :
how far did he travel 1
23. A carter pail 10 dollars for a cart and 92 dollars
for a hoi'se : how much did he pay for both 1
24. Jsiiio p^id 5 cents for ink, 7 cents for pens, and
92 cents for an arithmetic : how much did she pay out 1
25. •Tohn gave his brother 5 cents, his sister 6 cents,
and hal 19 cents left : h w much had he at first]
26. liichard had 9 marbles, and Harry and Thomas
had together 79 marbles : how many had all three 1
Examples. — 3.
1. TTow many are 10 and 4 1 10 and 141 10 and 24 1
10 and 341 10 and 44 1 10 and 54 1 10 and 64 1 10
and 741 10 and 841 10 and 94 1
2. How many are 11 and 31 11 and 231 11 and
331 11 and 431 11 and 531 11 and 631 11 and 73 1
11 cents and 83 cents 1 $U and $93 1
8. How many are 1 1 and 41 11 and 141 11 and 24 1
u
MENTAL ARITHMETIC.
1 1
Hli
11 and 341 11 and 441 11 and 641 11 and 641 11
and 74 1 11 minutes and 84 minutes 1 11 hours and 94
hours 1
4. How many are 1 ) and 5 1 10 and 15 1 10 and 25 1
10 and 35 1 10 and 45 1 10 and 55 1 10 and 65 1 10
and 75 1 10 guineas and 85 guineas 1 £10 and £95 ?
5. How many are 11 and 51 11 and 15 1 11 and 25 'i
11 and 351 11 and 451 11 and 551 11 and 651 11
seconds and 75 seconds 1 11 francs and 85 francs 1 11
crowns and 95 crowns 1 11 fourths and 95 fourths 1
6. How many are 3 and 8 1 3 and 181 3 and 28 ?
3 and 38 1 3 and 48 1 3 and 58 1 3 and 68 1 3 and
781 3 j^allous and 88 gallons 1 3 pints and 98 pints 1
3 tens and 98 tens 1
7. How many are 8 and 41 8 and 141 8 and 241
8 and 34 ? 8 and 44 1 8 and 54 1 8 and 64 1 8 an<l
74 1 8 and 84 1 8 and 94 1 8 tenths and 94 tenths 1
94 twelfths and 8 twelfths 1
8. How many are 7 and 7 1 7 and 171 7 and 27 1
7 and 37 1 7 and 47 1 7 and 57 1 7 and 67 1 7 and
77 ? 7 and 87 1 7 and 97 1
10
30
50
9. How niauy are $8 and $01 8 shillings and
shillings 1
1
lounds 1
8 pence and 26 pence? 8 pounds and
8 ounces and 46 ounces 1 8 yards and
yards 1 8 miles and 36 miles 1 8 hours and 76 hours 1
8 days and 86 days 1 8 years and 96 years 1
10. How many are 11 and 71 8 and 9 1 10 and 9 1
7 and 141 6 and 121 9 and 15 1 11 and 18 1 15 and
121
11. How many are 14 and 131 16 and 141 21 and
121 24 and 13 i 25 and 151 27 and 131 23 and 171
12. How many are 29 and 111 30 and 20 1 34 and
15 1 32 and 18 1
M
ADDITION.
15
13. Find the result of 8+2+5 + 74-9 + 6+4-f-7 1
Oi 3+4+2 + 7+8+5+9+3+6+? How many are
8+9+3+6+7+5+4? Add 1, 2, 3, 4, 5, 6, 7, 8, 9.
14. How many are 7 inches and 4 inches'? 4 miles
and 7 miles ? 7 pounds and 4 pounds ? 4 ounces and 7
ounces 1 4 tons and 7 tons 1 7 hundreds and 4 hun-
dreds ] 5 tens and 4 tens 1 4 tens and 5 tens ] 7 tens
and 8 tens'?
16. Find the sum of 40 and 50. ^
Ans. — 40 is 4 tens, 50 is 5 tens ; therefore 50
and 40 are 9 tens, or 90.
16. Paid 20 dollars for a cart, and 70 dollars for a
horse : what did I pay for both 1
17. Peter gave away 20 marbles, and had 80 left :
how many had he at first "?
18. Eliza paid 30 cents for a pen case, and 50 centc
for a geography : what sum did both cost Ikm?
19. A farmer sold 20 bushels of turnips, 30 of barley,
and 50 of wheat : how many bushels iu all did he sell i
20. What is the sum of 26 and 37 'I
Ans. — 26 is 2 tons and 6 units ; 37 is 3 tens and
7 units ; 2 tens and 3 tens are 5 tens ; and 6
units and 7 units are 13 units, or 1 ten and 3
units ; which, added to 5 tens make 6 tens and
3 units, or 63.
21. What is the sum of 33+441 35 + 15? 36+121
40 + 361 40+291 44+201 48+^21 45 + 351
22. 4 + 8+6 + 2 + 7 + 12 + 10+9 are how many 1
23 15 + 12+6+18+4+10+24 + 16 + 12 are how
many 1
24. 22 + 23+11 + 10+16x2+28+12+16 are how
many 1
16
MENTAL ARITHMRTia
EXAMPL?:S. — 4.
1. Jane has 13 pins in one cushion, and 27 in another
how many has she in both ]
2. Alfred .^ave 8 pears to WilU;:ni, 12 to Charles, 9 tc
James, and had 11 l(ft : h.)w many had he ai liratl
8. A Woman paid 18 cents for a pound Df cht;«3e, 82
cents for a pound of tea, and IT/ cents for nutmegs; how
much did sle spt nd in all?
4- From Halifax to Shiibonnondie fhe distance is 41
luihis, and from Shubenacadio t > Truro the distnnoe is
19 miles : findtho distance from Halifax to Tiuro.
6. A fijroccr paid 47 dollars for coi'n iii'.al, arid 75 dol-
lars for flour : what did both coyt him 1
6 A farmer has 12 acroo in oats, 17 in rye, and 27
in wheat ; ho'v mtmy acres in t/;am ha3 ho?
7- A fisherman caught 13 coJ wn D-Tonday, 28 on Tues-
day, and 59 on We Imsday : how many did iio ca^-ch in
the three d;iYs'i
8. 734- 17 + 3 -.- 7 4-10 are hr.w many 'i
9. Willie gave 57 cents to ''A^ sisti r, and had 6i> cents
left : how many had he at first?
10- Brampton is 28 miles west of Trronto, and Bow-
manvillo 43 miles cast : find the distance between
Brampton and Bowman villo,
11. A man bei.'an busin»^ss with 28 thousand dollars,
and in 10 vcait) cleared 68 thousand dollars: how much
was In- th«*n worth ]
12. A man bought a cow f r 25 dollars, a calf for 5
dollars, 3 lambs for 8 dollars, and a pig for 2 dollars:
what did he pay for all 'i?
13. A horj^e is worth 85 dollars, and a waggon 35
dollars ; what is the value of both 1
ADDITION.
17
14. Lucy bought a bonnet for 3 dollars, a silk dress
for 111 dollars, and a shawl for 29 dollars: what did she
pay for all]
15- Thore are 31 days in January and 28 in February :
how many days in both ?
16. An orchard contains 15 cherry-trees, 37 plum-
trees, and 45 apple-trees : how many trees are in the
orchard 1
17. A lady bought some tape for 10 cents, some pins
for 18 cents, and a pair of scissors for 30 cents : how
much did she pay for all ]
18. A merchant bought a horse, saddle and bridle;
for the horse he gave 75 dollars, for the saddle 25 dollars,
and 7 dollars for the bridle : what did they all cost him 1
19. From Toronto to Wliitby is 20 miles, and from
Whitby to Fort Hope is 33 miles : what is the distance
from Toronto to Port Hope 1
20. Bath is 18 miles from Kingston and 36 miles from
Belleville : how far from Kingston to Belleville i
21. Cobourg is 72 miles fioiu Toronto and 103 miles
froi)i Kingston : how ftir from Toronto to Kingston ?
22. From Montreal to Cornwall is C8 miles and from
Cornwall to Kingston is 105 miles: what is the distance
from Montreal to Kingston]
23. Oshawa is 33 miles from Toronto and 300 miles
from Montreal : what is the distance from Montreal to
Toronto ]
24. John hoes 19 rows of potatoes, James 31 rows,
and William 48 rows : how many rows do tliey all hoe ?
25. A grocer mixes 3 pounds of tea worth 12 shillings^
with 4 pounds worth 2u shillings : how many pounds are
there in the mixture ]
18
MENTAL ARITHMETIC.
26. A person sells 6 apples for 1 2 cents, and 9 others
for 15 cents ; how many ap})les does he sell, and wha*
does he get for them ?
27. James and Robert had equal amounts of money in
the morning ; during the day, James lost 6 dollars and
Robert gained 9 dollars. In the evening, who had the
larger amount, and how much larger 1
28. A father divi.led a certain numbor of oranges be-
tween his wife, 2 sons and 3 daughters. He gave to
the youngest son 5, to his wife 7, and the rest he divided
equally between his three daughters and oldest son. The
eldest son's share was 5 more that his mother's. How
many oranges were divided 1
29. A father divide I a certain number of apples
between his three sons; to the first he gave 11, to the
second 4 more than the first, and the third 7 more tlian
the second : how many apples had he ]
Section II.— Subtraction.
Examples. — 5.
1. John had 3 cents and gave his brother 1 : how many
had he left?
Ans. — The (Uiforence between 3 (that is 1-f-l-f^)
and 1 is 2, therefore ho had 2 left.
2. A boy had 5 apples and gave away 3 : how many
had he left 1
8. Jennie had 8 needles and lost 5 : how many had
she remaining ?
4' Rufus canght 9 trout and gave Charles 3 : how
many had he left?
SUBTRACTION.
19
6. How many are 3 and 21 2 from 5 ? 3 from 5 1
6* How many are 5 and 4 ? 4 from 9 ? 5 from 9 1
7. How many are 6 and 3 ? 3 fiom 9? 6 from 9 ?
8. How many are 6 and f) 1 5 from 111 6 from 1 H
9. How many are 4 ai)d 71 4 from 111 7 from 11?
10. How many are 4 and 10 ? 4 from 14 ? 10 from
141 ^ .
ll.~How many are 8 and 5 1 5 from 13? 3 from 13 ?
12. How many are 5 and 9 ? ;> from 14? 9 from 1 4 ?
13. How many are 7 and 10? 7 from 17? 10 from
17?
14- I paid 15 cents for oranges and 9 cents for ap-
ples : how much more di<l the oranges cost than the ap-
ples?
15- I had 17 dollars, and paid 12 dollars for two barrels
of flour : how much had I left ?
16. Jane is 16 years old: how old was she 7 years
ago?
17- How many are 4 from 12? 4 fi-om 13? 4 from
14 ? 4 from 15 ? 4 from 16 ? 4 from IS? 4 from 20 ?
4 from 24 ?
18. How many are 5 from 12? 5 from 14 ? 5 from
15 ? 5 from 17? 5 from 20 ? 5 from 22 ? 5 from 24 ?
19. James has 20 marbles and sells 6 of them : how
many has he left ?
20- Bought a cart for 24 dollars and sold it for 17
lollars : how much did I lose ?
21. Bought a cow for 28 dollars and sold it for 40
dollars : find my gain ?
22. How many are 12—^1 15 — 9? 19 — 91
16 — 6? 14 — 4? 25-5? 30-7? 27-7? Id
_6? 14 — 81
20
MENTAL ARITHMETIC.
ill
28. How many are 15 — 3? 24 — 41 16 — 51
17—81 19 — 91 29—81 34 — 31 35—61 50
_8 1 57 — 61
24. How many are 59 — 5 1 53 — 71 15 — 101
36 — 161 25 — 121 20 — 141 30 — 121 29 — 101
39 — 20 1
26. How many are 24-f 2 — 3 1 19-f 5 — 6 1 30-}-
45—121 374-13—151 45-^15-101 40-|-l-|-3
— 59
26. Howmany are 40-t 1-1-3— 51 37-|-3-}-10— 8 1
25-|-15-f-5 — 91
27. Begin with 67 and count back to 3, by sultract-
ing 4 successively.
28. Begin with 50 and count back to C, by subtract-
ing 2 ; thus 5'\ 48, 46, &c.
29* What number must be put with 6 to make 91 4
to make 101 7 to make 131 18 to make 40 1
80. The sum of two numbers is 27, one of them is 13 :
what is the other 1
Examples. — 6.
1. Charlie had 25 cents; he spent 9 cents for a top
and 3 cents for a string : how much had he leftl
2. Isabella is 19 years old and Ida 11 years : find the
difference of their ages.
8' How many is 6 from 131 6 from 151 6 from 161
6 from 19 1 6 from 22 1 6 from 25 1 6 from 27 1 6
tens from 27 tens 1
4. How many is 7 from 13? 7 from 161 7 from
17 1 7 from 19 1 7 from 21 1 7 from 22 1 7 from 26 1
7 from 271 7 from 29 1 7 hundred from 29 hundred 1
5. How many is 11—81 16 — 81 24—81
SUBTRACTION.
21
25—81 27 — 81 29 — 81 3—8? 30 tens — 8
tensi
6. How many is 15 — 91 18 — 91 21 — 9?
22—91 24 — 91 27 — 91 $30— $91 £32 — £91
35 cents — 9 cents 1
7. A man earns 45 dollars a month, he saves 9 d - llai*s
a month : how much does he spend 1
8. From a pile of wood containing 30 cords, a teamster
di'aws 13 cords : hew many cords remained 1
9- A man having 36 dollars, paid 20 dollars for a
coat : how much had he left 1
10- Count by fours from 4 to 58, and from 58 back
to 4.
11. How many is 19 — 101 21 — 101 23 — 101
£28 — £101 $30 — $101 35—101 40 — 101
50 — 10 1
12. How many is 11 — 111
17—111 20 — 111 22 — 111
13. How many is 16—121
24 — 121 28 — 121 30—121
13-
23
19-
40
111
-11?
121
-121
15—111
25 — 111
21 — 121
47 — 121
14- How many is 7 cents — 4 cents 1 7 shillings — 6
shillings 1 7 dollars — 6 dollars 1 7 pounds — 4 pounds 1
7 hundred — 4 hundred 1 7 tens — 4 tens 1 7 tenths —
4 tenths 1
15. How many is 60— 101 36 — 101 47 — 101
31 — 101 27 — 10? 60—20? 60—30? 70 — 201
70_r,o] 80—401 80—601 75 — 301 87 — 501
40 pence — 25 pence? 70 shillings — 40 shillings 1
16. What number must be added to the sum of 4 and
5 to make 121
17. What sum must be added to the sum of 3, 6, 9,
15 to make 40 ?
IS -l
i:
Ift'
u 11
Ml
22
MENTAL AKITHMETIC.
18. The sum of three uunibers is 67, the less num-
ber is 12, and the greater is 14 more than the less:
what is the other 1
19. 4_|-3_2-f.9 — 3+6 — 5-j-3--2-f7 — 9-1-4 — 1 +
8 — 3 is how many 1
20. 9-1-3—84-7—5+4—3+11 — 9+7 — 2+13 —
9+12 — 13+17 — 3 is how manyl
21. From the sum of 9, 6, and 6, subtract the differ-
ence between 11 and 17.
22- What number must be added to the sum of 4, 7,
and 5, diminished by the difference betweei* 9 and 6 to
make 20 1
23- Subtract the sum of 9, 6, 8, 7, 4, from the sum of
5, 3, 11, 2, 13, 7, and 12.
24. The sum of two numbers is 63, the greater is 49 :
what is the less 1
25. What number taken from 29 will leave 18 1
26. The sum (»f three numbers is 34 ; the first is 13,
and the second is 4 less than the first, find the third
number.
27. By how much does the sum of 12 and 9 exceed
the difference 1
28. The minuend is 62 and^the difference is 43;. Find
the subtrahend.
29. 4+5+6+7 — 2 — 3 — 5+9—6+3 — 1+9 —
7+6 — 2+5 — 4+13 — 11+16 — 6+9 — 7+21 — 11
is how many 'i
80. From 18 tens subtract 5 tensi Find the result
of 17 hundred — 10 hundred. 28 fifths— 18 fifths.
23 fiftieths— 10 fiftieths.
SUBTRACTION.
33
Examples. — 7.
I
1. John had 10 cents ; he gave 2 cents for a pencil,
and 4 cents for an orange : how many cents had he
leftl
2. William had 25 cents, and buys a penknife for 16
cents, and a pencil for 6 cents : how much has he left ?
3- James had 40 cents, and paid 12 cents for a
whistle, and 25 cents for a knife : how much had he left )
4- A school-boy paid 56 cents for a geography ; 30
cents for an arithmetic : how much more did he pay for
the geography than the arithmetic 1
5. A drover bought 40 sheep of three farmers; he
bought 8 of the first ; and 16 of the second : how many
did ho buy of the third 1
6- Jane had 9 oranges ; her mother gave her 7 more,
and her father enough to make 40 : how many did her
father give her "?
7. A man travelled 5 miles before breakfast, 19 miles
between breakfast and dinner, and then went back 12
miles : how far was he then from the place of starting 1
8. Mr. Jones owes his grocer, baker, and butcher 50
dollars; he owes his baker 27 dollai's, and his gwJcer 16
dollars : how much d es he owe his butcher 1
9. James goes up 3 steps of a ladiler that has 24
steps, then down 2, then up 5, then down 4, then up 7>
then down 3, then down 1, then up 9 : what stop from
the top and bottom does he stand upon 1
10. If a nian who has $44 earns $27 more, and then
spends $43, how much has he left 1
11. A certain boat has a crew of 18 men, and 79 pas-
is* 1
«1
r
;AH
sengers
if 59 leave, how many are left aboard 1
24
MENTAL ARlTHMEi'IC.
12. A and B start from two places, 96 miles apart,
and travel tows^jrd each other. The first day, A goes 48
miles, and B 27: how luany miles are they then apart 1
How far is A from B's starting place 'I How far is B
from A's starting place 1
13- Two men bought a horse, the one jmys 75 d liars,
and the other 29 dollars less : how many dollars did both
payl
14- From Toronto to Thornliill is 1 2 miles, from Thorn-
hill to Richmon 1-hill is 5 miles : how far from Richmond-
hill to Aurora, the distance from Aurora to Toront'-
being 31 miles'?
15. John bought a watch for IT* dollars, and a chain
for 9 dollars. He sold them both for 29 dollars : how
much did ho gain ]
16. William and James start from the same point ani
travel in the same direction, the one at the rate of 13
miles, and the other at the rate of 7 miles : how fur ii\mvi
will thev be ?
17. On January 7th, how many days yet remain in the
month 1
18. Mary was born years before Ann; Mary is 21
years old : how old is Ann ?
19. How many is 90 — 50 1
Ans. — 90 is 9 tens, and 50, 5 tens, 9 tens -- 5 tens
are 4 tens, or 40.
20. How many is 75 — 25 ? 92 — GO 1 vS7 — 40 ]
98 — 70? G7 — 42] 84 — 43] 90 — 3G] 80—55/
21. How many is 75 — 37 ?
jifis^ — 75 is G0-[-15 and 37 is 3 -}-7, therefore the
diflerence is 60— 30 -f- 15 — 7, which is 30+8
or 38 or 75 — 3c is 45, and 45 -^ 7 is 38.
SUBTRACTION.
25
22- How many is 46 -
89_74'? 43 — 28] 52
35 ? 57 — 38 ] 39 — 19 1
-271 67 — 391 84 — 651
23. To the number 10, add 10 and subtract 5, add 6
and subtract 10, add 12 and subtract 6, add 6 and sub-
tract 12, add 20 and subtract 10, add 20 and subtract 10,
and give the result.
24. There are 65 schohirs in a .school, and 30 of them
are girls : how many boys are there 1
25- A merchant bought 67 quintals of codfish, and in
a week had sold all but 35 quintals : how many did he
sein
26. A man began business with 42 thousand tlollai*s,
and in 5 years lost 22 tliousanl : how much had he leftl
27« Edgar had 10 peaches, he gave 7 to Mary and 6
to Minnie : Hov/ many had he left 1
28. IJouglit goods to the amount of 29 d liars : for
how much must I sell them to gain 13 .loUarsI
29- A bin has in it 55 bushels of oats, 23 bushels are
taken out of it at one time and 9 busliels at another : how
many bnshcls are leftl
30. Find result of 22 ~ 8-f 13 — 6+4 — l+7-|-9 —
20, and also of 86 + 14+20 — 15 + 10 — 30.
31- Joline?nnocl 80 cents one Jay, and spent 30 cents
of it, tlie next day he earned 50 cents : how much had ho
tlicn ]
32. 9 tenths — 3 tenths? 8 Iwcllthb — 4 iweUthsl
23 liueentlis — 15 lifteenths 1
26
MENTAL ARITHMKTIC.
Section III— Multiplication,
Examples. — 8,
I. Wliat will 2 apples cost at 4 cents each '»
Ans. — 1 Ap[)lG costs 4 cents, therefore 2 will codt
44-4 that is 2 times 4 cents or 8 cents.
2- What will 2 oranges cost at 5 cents each 1
3- A man earns 8 dollars a week, how much will he
earn in two weeks 1
4. How many is :
2 times 1 2 times 4 2 times 7 2 times 10 5 times 2
2 times 2 2 timen 5 2 times 8 2 times 11 8 times 2
2 times 3 2 times 6 2 times 9 2 times 12 10 times 2
5. Find the cost of 2 barrels of mackerel at 12 (ljllar»i
a barrel,
6. What is the cost of 4 yard's ■ f tape at 3 ceuts a
yard l at 4 cents % at 5 C(.'nt.s 1
7. How many is :
3 times 1 3 times 4 3 times 7 3 timos 10 8 times 3
3 times 2 3 times 5 3 times 8 3 times 11 11 times 3
3 times 3 3 tiuics 6 3 times 9 3 times 12 12 times 3
8. What will 3 barrels of Hour cost at 7 dollars a
barrel 1
9. A man earns 3 dollars a day, how much will he earn
in a week 1
10. Find the cost of 12 yards of calico at 3 pence ncr
yard %
II. What will 4 pounds of rice cost at 6 cts. a pound ?
at 7 cents'? at 8 cents 1
How many is :
4 times 1 4 times 4 4 times 7 4 times 10 2 times 4
4 times 2 4 times 5 4 times 8 4 times 1 1 5 times 4
4 timcB 3 4 times G 4 times 9 4 times 12 8 times 4
MULTIl»L:CAriuN.
27
12. What will 4 pounds of g i^av cost at 11 cents a
I
KHitid]
11 cost
^ill he
.imes 2
iimes 2
/imcs 2
(I jllai'fi
CO fits a
lines 3
iinea 3
Imos 3
lars a
10 cam
nco ncr
)ouud 1
times 4
times 4
times 4
13. Mary bought 4 yards of cotton at 9 cents a yard :
what did it cost herl
14. I piiid 4 dollars a day for a team and kept it 10
days : what did it cost me 1
15. How many iz 5 times: \ l 21 31 41 0l 61 71
81 y 1 101 11 1 12 ? How many is 8 times 5 1 6 times
5 1 7 times 5 ? 9 times 5 tenths 1 4 times 5 tens 1 7
times 5 Imndreuths 1
18. t'ind the cost of 5 cords of wood at 6 dollars a cord 1
17. boys received 11 apples each : how many did
tiiey all receive 1
18. At 5 cents a pound, what will 7 pounds of rice
.mi 1 8 lbs. 1 9 11)8. 1 10 lbs. 1 1 2 lbs. 1
19. How many is G times 11 21 31 41 51 Q1
71 81 91 11 111 121 2 tin«1 5 tensi 7
tjilnlsl 8 fourths 1
20. 1 piiid G dollars a ton for 9 tons of coal : what
was the whole cost 1
21- Jane bought 1 1 yards of cotton at C pence per
yard : what did it cost herl
22. How many is 7 times 11 21 31 41 51 61
71 8? 91 101 111 121 2 pence 1 3 shillings 1
4 tenths 1
23. A merchant averages a profit of 12 dollai-s a day :
how much is that a week 1
24" A merchant bought 7 quintals of codfish at 5 dol-
lars a (juintal : what did he pay in all 1
25. How much will 8 yards of silk cost at 9 shillings
a yard 1 9 inches of gold wire at 7 pence an inch 1
86. How man 7 is 8 times 11 21 31 41 51 61
m
28
MENTAL ARITUMFTIC.
7? 81 9? lOi 11? 12« How much is 12 times 8]
7 times 8 ^
27. i^^ind the cost of *^ 2)a of sugar at 10 cents per
[)Ound ? Of 8 barrels of flour at. "^ dollars a barrel ]
28. A steamer sails 12 miles an hour for 7 hours:
what distance does she make 1
29. What will be the cost of d lbs. of cheese at 8 pence
a pound t 9 yards of cotton at ^ pence a yard ?
30. How many is 9 times 1 ? 21 3 ? 4 ? 51 6 ?
7? 8? 91 10? 1). 1 12] How many is 8 times 91
7 times 9 1
31. How many incher^ are in 9 feet, there being 12
inches in one foot 1
32. A farmer make? an avei'age profit of 11 dollsirs an
acre : what profit has he ofi' 9 acres of land 1
33. How many is 1 times 11 21 31 41 51 61
71 81 91 101 HI 121 How many is 9 times
10 { 8 times 10]
34- What will 10 lbs. of butter cost at 9 cents a
pound? at 10 cents 1 at 11 cents 1
35- Whit will yards of muslin cost at 11 cents a
yard 1
36. How many is 1 1 times 1 1 21 31 4? 51 61
71 81 91 101 111 12 i ;12 times U1 9 times
111 7 times 111
37. Find the cost of 11 yn-ds of ribbon at 11 cents a
yard 1 10 quintals of codfish at 4 dolhirs a quintal?
38 1 bou<i;ht 11 lbs. ot halibut at 9 cents a pound :
what did it cost mel
39 . How many is 1 2 times 11 21 31 41 51 61
71 81 91 101 HI 121 2 farthings 1 4 ounces 1
5 tons 1 7 twelfths 1
i
I
MULTIPLICATION.
29
es8^
s per
ours:
pence
les 9 1
ing 12
ars an
11 61
times
ents a
ents a
1 ^i
times
cents a 1
pound :
51 6] ^,
)uuce3]
40- What will 12 dozen of eggs cost at 12 cents a
dozen 1
41. What will 9^ tops cost at 5 pence each ?
42- What will 8 knives cost at () dimes each 1
43- At 12 cents each, what will 9 primers costi
44- What will 8 yards of broadcloth cost, at 4 dollars
a yard 1
45. If a boat moves at the rate of 1 1 miles an hour :
how far will it go in 11 hours 1
46- Mr. Finkle's stage, moving at the rate of 6 miles
nn hour, takes 4 hours to go from Newburgh to Kingston :
how far from Newburgh to Kingston?
47- I^ * steamer sails 7 miles in an hour : how far
will she travel in 7 hours? In 9 hours? In 11 hours'?
In 12 hours?
48. At 7 cents a pound : what will 8 pounds of beef
cost? 10 pounds'? G pounds'? 12 pounds'?
49- How much is 8 times 2-fifths '? 9 times 3-tenths ■?
12 times 8-twelfths *? 6 times 3-elevenths '?
50. How much is 7 times 5 pence? 5 shillings? 5
hours? .^5? .£5? 5-tenths ? 5-twentieths? 5 hun-
dreds? i» thousandths?
tlXAMPLES 9.
1. What are the factors of 6 ? 10 ? 15 ? 21 ? 30 ?
2. When 10 is a factor, with what figure does the pro-
duct always end ?
3. When 5 is a factor, with one of what two figures
does the product always end ?
4. How much greater is 11X9 than 10x7?
6. A farmer sold 8 sheep at 5 dollars each, and 9 pigs
at G dollars each : how much did he receive in all?
30
MENTAL ARTTIIMETIO.
^4
6. How much if? !2x5? 5x11? 7x0'f 12X^^
7X7? 9X7? 7X9? 10x11? 9x14?
7. A man's wajjcs is 13 dollars n inonti). he Hnpnils
5 dollars a month : how much does he save in o. year?
8. 10 men can mow a field in 12 hours: how Iuti^
would it take one man to do it ?
8ol. — It will take one man ten times as long as 10
men — 10 times 12 is 120 hours?
9- If 5 men reap a field in 7 days, how long will it
take 1 man*?
10- A quantity of provisions will last 8 men 12 days :
how long would it last 1 man 1
11. 9 horses eat 80 bushels of oats in 20 davs : how
long will that quantity last 1 horse ?
12- It takes 8 men 8 days to do a piece of work : how
many men will do it in 1 day ?
*Sb?. — 8 men do it in 8 days .*. C4 m^n will dt) it in
one day.
13- How many men must be employed to d» a piece
of work in one day, which it takes 11 men 12 days to do ]
14- A. tailor has 43 yards of broadcloth ; if he sells 23
yards of it, what will the rcniain-ler be worth at G dollars
a yard ?
15- If 6 pipes of equal size can fill a cistern in 12
hours, in how many hours could one of them fill it?
16. 12 men dig a ditch in 11 days: how many men
would dig it in one day ?
17. Three times 26 are how many ?
BqI. — In 26 there are 2 tens and 6 units. 3 times 6
units is 18 units, or 1 ton and 6 units, and 3 times 2 tens
is 6 tons, which with 1 ten and 8 units make 7 tens and
8 units, or 78,
M1TLTIPT,ICATI0N.
31
18. How many is 4 times 18 ? 23 1 25 ^ 13 ^ 32 ?
5 times 75 ] ^. times S4 1 { times 92 ] "^ times 15
tens'?
19. What are the factors of 8 ] 151 221 35? 2\\
141 161 321 061 841 100 1 12^1
20. Find as many sots of factors as you can for 24.
For 30. For 48. For 16.
21- How much is 14 times 131
Analysis. — The Sectors of 14 are 7 times 2,*. 14
times 13 is equal to 7 times 13, multiplied by
2. 7 times 13 is 91 ; twice 91 is 182.
22. How much is 18 times 231 15 times 38 1 16
times 26 1 14 times 72 1 21 times 1^1 35 times 131
25 times 191 32 times 261
23- Five times twelve, less ten, plus 15, is how manyl
24- How much more is 8 times 8 than 7 times 9 1
25. Jf two men start from the same place and travel
in opposite directions, the one travelling at the rate of 3
miles an hour, and the other at the rate of 4 miles an
hour, how far apart will they be at the end of 5 hours 1
26- Two men start 50 miles apart and travel towards
each other, the one at the rate of 4 miles an hour, the
other at the rate of 3 miles : how far apart will they be
at the end of 5 hours 1
27. Find the result of 6X20X15 ; and of 21x7—3
xii.
28- For how much must I sell 25 barrels of mackerel
which cost me 8 dollars a barrel, so as to gain 50 dollars 1
29. Bought 5 cords of wood at 6 dollars a cord, and
handed in payment 4 ten-dollar bills : how much change
should I receive 1
80. A farmer sold 7 sheep at 5 dollars each, and 3
32
MENTAL AHITHMETIC.
lambs at 2 dollars each : how mu(jh did he get for them
ain
31. A tailor has a piece of cloth containing 23 yards ;
if he should cut from it 13 yards., what v/ilj the remain-
der be worth at 4 dollars a yard ] ,
32- A and B travelling toward each other met in 12
hours : how far apart were th( ir starting points, if A
went 10 miles an hour, and B 12 ?
33- Find first the sum, then tiie difference, and then
the pioduct of 10 and 35. Of 1 1 and 36.
34. How many yards m 14 pieces of cloth, each con-
taining 37 yards ?
35. Bought 23 cows for $i8 each ; sold them at ??60
apiece : what was the profit on each and on the whole 1
36. Two men start at the same place and travel in the
same direction ; one at the rate of 7 miles an hour, and
the other at the rate of 3 miles an hour : how far apart
will they be in 9 hours 1
37. A man bought a horse for $90, paid $3 a week fo*"
his expenses, and received $5 a week for his work ; at
the expiration of 8 weeks he sold him for $80 : did he
gain or lose by the operation, and how much '\
38. If a traveller, starting from any point, travels 10
hours, at 4 miles an hour, and then returns at the rate
of 5 miles per hour for 3 hours, how far is he then from
the place of departure ?
Section IV.— Division.
Examples. — 10.
1. At 2 cents each, how many apples can be bought
for 6 cents 1
^o/. — Every 2 cents will buy an apple ; 2 is con-
DIVISION. /
33
bhem
ircls ;
[uaiu-
iii 12'
if A
I then
j1i con-
at?^60
[ in the
ir, anil
r apart
eck fo^
■k ; at
did he
vels 10
le rate
n from
oained in 6 3 times : therefore 3 apples can be
bought for G cents.
2S. At 4 cents each, how many oranges can be bought
for 12 cents 1
3. For 24 cents how many |)ounds of sugar can be
bought at 8 cents a pound 1
4. Paid 32 dollars for 8 cords of wood : how much is
tliat a cord ?
6- 3 times 2 are 6 : how many times is 2 contained in
6 ? 3 in 6 1
6. 15 is how many times 3 ? how many times 5 ? 12
is how many times 2 1 how many times 6 ? how many
times 4 ? 3 ]
7. How many times 4 are 8 ? 16? 12 ? 201 241
281 ■ '
8- John spent 30 cents in pencils, at 6 cents each :
how many did he buy 1
DIVISION TABLE.
1 in
2 in
3 in
4 in
6 in
6 in
1, once
2,
once
3,
once
4,
once
6,
once
6.
once
2, twice
4,
twice
6,
twice
8,
twice
10,
twice
12,
twice
3, 3 times
6.
3 times
9.
3 times
12.
3 times
15,
3 times
18,
Stimes
4, 4 "
8,
4 "
12,
4 '•
1(5,
4 "
20,
4 "
24,
4 "
5, 5 '•
10.
5 "
15,
5 "
20,
6 "
25,
5 "
30,
6 "
a, 6 "
12,
6 "
18,
6 "
24.
6 "
30,
6 "
36,
6 ••
7, 7 "
14,
7 "
21.
7 "
28
7 "
35.
7 "
42,
7 "
8. 8 "
16,
8 "
24,
8 "
32,
8 "
40,
8 "
48,
8 "
9, 9 "
18,
9 "
27,
9 "
30,
9 "
46,
"
54,
9 "
10, 10 "
•20,
10 '•
30,
10 "
40,
10 "
50,
10 ••
60,
10 "
11, 11 "
22,
11 "
;«,
11 "
44,
11 "
55,
11 ••
m.
11 "
12, 12 '•
24,
12 "
30,
12 "
48,
12 "
GO,
12 ••
72,
12 "
bought
is oon-
9. A boy paid 12 cents for pens at 2 cents each : how
many did he buy 1
10. At 3 dollars a yard, how many yards of siJk can
be bought for 27 dollaisl
11. A horse trotted 48 miles in 6 hours : how many
miles an hour did he average 1
mi
34
\
MENTAL ARITHMETIC.
12. A farmer gave 60 dollars for sheep, paying 6
dollars a head : how many did he buy 1
13. A carpenter earns 12 dollars a week : how long
will it take him to earn 72 dollars ]
14- A bag contains 3 bushels : how many such bags
will be required to hold 36 bushels?
15- One man can do a piece of work in 66 hours : in
how many hours can 6 men do the work ?
16. It takes 50 men one week to do a certain work :
how many weeks would it take 10 men 1
Division Table — Continued.
, m
7, once
14, twice
21, 3 times
28, 4 "
35, 5 "
42, 6 "
49, 7 "
56, 8 *'
«3, 9 •'
70, 10 "
77. 11 "
84, 12 "
8 in
8,
once
16,
twice
24,
3 times
32,
4
40,
5
48;
6
56,
7
64,
8
72,
9
80,
10
88,
11
96,
12
9 in
9, once
10 in
10 once
18, twice 20, twice
•27, 3times| 30, 3 times
36, 4 " I 40, 4
■ 60, 5
00, 6
70, 7
45, 5
54,
03, 7
72, 8
81, 9
90, 10
99, 11
108, 12
<<
<<
t<
80, 8
90, 9
100, 10
110, 11
120, 12
<<
((
<<
«
11 in
11, once
'22, twice
33, 3 times
44, 4
55, 5
60, 6 "
77, 7 "
88, 8 "
09, 9 "
110, 10 "
121, 11 "
132, 12 "
12 in
12, once
24, twice
36, 3 times
48, 4 "
60, 6 "
72, 6 "
84, 7 "
96, 8 "
108, 9 "
120, 10 •*
132, U «
144, 12 "
17. When flour is 7 dollars a barrel, how much can
be bought for 63 dollars'?
18. How much will 70 yards of cotton cost at the rate
of 10 yards for 1 dollar ?
19. How much halibut at 12 cents a pound can be|
bought for 96 cents 1
20- A freight train is moving 1 2 miles an hour : hov^
long will it be moving 84 miles 1
21. How much is 6 times 10 divided by 5 1 by 12
by 4?'
22- 9 times Mary's age is 108 : find her age ?
23- If one horse can eat a quantity f oats in 144 days,
how long will it take 12 horses to eat an equal quantity 1
DIVISION.
35
ing 6
vlong
b bags
ars: in
work ;
12 in
12, once
24, twice
36, 3 times
48 4 "
60', 5 ::
72, 6
84, 7
9«, 8
108, 9
120, 10
132, 11
144, 12
<(
<<
«
(I
lucli can
It the rate
id can be]
lOur: bov'l
bl by 12
24- How long will it take 1 1 men to do a certain
work, if 55 men can do it in 1 day 1
Note. — The sign of division is -r-, thus 15-r-5 means
that 15 is to be divided by 5.
25. At 3 cents each how many apples could you buy
for 8 cents, and how many cents would you have left 1
26 What is the quotient of 40-^5? 40-^-8] 40-^101
27. 45 are how many times 5 ? 9? 101 111 15?
28- If you had 63 dollars, how many sheep could you
buy at 6 dollars each, and how many dollars would you
have left?
29. How many times is 4 contained in 28 ? 5 in 15 ?
$6 in $241 3 cents in 27 cents? £2 in €161 1 hour
in 9 hours f 5 dimes in 35 dimes 1 6 tens in 36 tens ?
2 fifths in 12 fifths 1 3 ounces in 36 ounces? 5 tenths
in 55 tenths?
30- How many times is 7 contained in 1 4 ? 9 in 36 ?
10 in 40 ? 8 in 56 ? 11 in 33 ? 9 in 54 ? 12 in 72 ? 7 in
70? 10 in 70? Jgll in £99? 8 guineas in 40 guineas?
31- How many times is 2 contained in 24 ? 12 in 24 ?
3 in 18 ? 6 in 18 ? 12 in 108 ? 8 in 96 ? 9 in 99 ? 1 1 tens
in 121 tens ? 12 hundred in 144 hundred ? 10 tenths in
120 tens ? 9 thousand in 45 thousand ?
32' What is the quotient, and what the remainder in
the following? 14-f-5 ? 68-^7? 9-^-2? 39-f-4? 112-i-
11? 62-5-10? 61-=-7? 5l-f-8? 19H-2? 63-^5? 140
days-5-12 days? 150 pence-5-12 pence? $133-j-$ll?
27 ounces-i-10 ounces ?
Examples. — 11.
1. 3 times a number-f-4 times the number — twice the
umber-j-7 times the number — 5 times the number
le?
144 days, ,
... ilequals 35 : what is the number?
M
li .'I
'< t '■'"
) II;
• T
36
MENTAL AniTHMETIC.
i
It,
J1:
ill-
2- John being asked his age replied : if you add 20 to
8 times my age the sum will be 100 : find his age.
3. What number must be taken from 95 so that the
remainder may be exactly divisible by 10 ?
4. What number must be added to 129 to get a sum
exactly divisible by 12 1
5. Divide 38 tens by 2 tens ; 64 tenths by 3 tenths j
65 by four ; 87 weeks by 5 weeks ; 136 by 4 ; 121 shil-
lings by 4 ; 238 days by 3 ; 308 months by 6 ; 150
guineas by 12.
6- Bought 12 yards of broadcloth at 6 dollars a yard,
and paid for it with wood at 4 dollars a cord : how many
cords did it take ]
7. The remainder is 4, the dividend I48, and the
quotient 12 : find the divisor.
8. A house was bought for $1200, and sold for $1500.
The profit was divided between 6 persons ; what was the
share of each ?
9. What number multiplied by 7 will give the same
product as 14 multiplied by 9?
10- What number must be added to 29, so that it may
be exactly divisible by 9 1
11. If the sum of 9 and 7 be multiplied by their dif-
ference, and the product divided by 8, what will the
quotient be ^
12- What number must 4 be multiplied by, so as to
produce twice 32 ]
13- The sum of the product of two numbers and 6 is
84, one of the numbers is 7, find the other 1
14. What number subtracted 1 1 times from 456, leaves
remainder 5 ?
15. A man gave $12 each to a cei*tain number of men,
and had $5 left of $125 : how many men were there ?
i
m
DIVISIOW.
87
16. Charles said : — if you multiply the number of
dollars I have by 12, and subtract $15 from the product
the remainder will bo $G9 : how much money Lad he 1
17. 5 times 12 is how many times 48h-C 1
18. 9 times 1 is h w many times 54-^-9 1
19. I received 30 yards of tweed for 5 tons of hay at
$12 a ton : what was the cloth a yard 1
20- Willie having been asked how many dollara ho
ha.l, -replied : if you add 9 to the number and multiply
the sum by 8, tho product will be $160 : how much had
he?
21< Minnie having been asked her ago, said : 9 times
my age 6 years ago is 81 : find her age.
22. 6 times my present age is- 9 times my age 5 years
ago : how old am 1 1
23. At 15 cents a yard how much wincey can be
bought for 300 cents ? for 400 1
24. If a quantity of provisions last 1 man 48 days,
how long will it last 4 meni G men? 8 men? 12
men?
25. A woman sold 12 dozen of eggs at 15 cents a
cl:zen, and with the proceeus bought raisins at 18 cents
a pound : how many pounds did she got?
26. At 15 dollars an acre how much land can be
bought for $180? $300? $450? $600?
27. If 6 times Mary's age is divided by 12, the
quotient, multiplied by 15, will be 75 : find her age.
28. A man paid $220 dollars for 10 months board :
how much did he pay per month ?
29. A merchant's expenses are $12 a day : in how
many days will they amount to $900 ?
S8
MENTAL ARITHMETIC.
Section V.— Miscellaneous Questions.
H'
M'
m
V
i, i
!'■ 1-'"
Examples. — 12.
I. Multiply 30 by 4, subtract 50, arid 10, divide by 5,
multiply by 7, and what is the result]
2 Subtract 10 from 6 multiplied by 8, to the rernainder
add 4, divide the sum by 6, multiply the quotient by 11,
subtract 7 from the product, divide the remainder by 10,
add 30 to the quotient, and what will be the sum 1
3. 70 barrdla of pork cost $5. 60 : what was the price per
barrel ]
4- One man can do a work in 55 days : how long will
it take 10 men?
5. A number multiplied by 8, divided by C, multiplied
by 10, and the product increased by 5, equals 45 : what
is the number 1
6, Multiply 15 by f), add r>, tUvide by 8, multiply by
6, subtract 10, divide by 5, add 2, multiply by 11, and
what will the product be 1
7- The divisor is 5, the dividend 39, the quotient 7,
Find the remainder.
8. The remainder is 5, quotient 6, divisor 7. Find
the dividend.
0. How many sets of factors in 24 ? in 48 1 in GO ^
in 125?
10. By what number must the product of the sum and
difference of 9 and 7 be increased so that the result may
be exactlv divisible bv 7 1
II. A man bought an equal number of pigs and sheep
for $63. Each pig cost |3, and each sheep $4 : how many
of each did he buy 1
MISCELLANEOUS QUESTIONS.
39
12- A woman bought 26 yards of dress g'lods at 30
cents a yard, and 22 yards of cotton at 10 cents a yard :
how much change did she receive out of a $10 )»ill ?
13. There is a number whirh, when divided by 4, and
the quotient increased by 9, tlie sum multiplied by 3, and
tlie product decreased by the difference between the arith-
metical complements of 4 and 7, gives 33. Find the
number ?
14- If 3 corls of wood are worth 18 dollars, and 10
cords are given for 12 thousand shingles, how much .irc
tlio Khingles a thousand 1
15. if 3 ])o\mds of Hour are worth 1 pound of sugar,
and 6 pounds of sugr.r are worth 1 pound of tea, hi/W
many pounds of flour are worth 2 pounds of te 1 1
16. A boat sailed up river for 10 hours at the rate of
3 uiih's an hour, r)ut returned over the samo <listance in
G hours : Ir^w fast did it sail down stream 1
17. When whv^at is sold at the rate of 6 buahcla for 12
dollars, how many bushels must be given for 4 cords of
wood, at 5 dollars a cord i
18. A ;;t( amboat can run 8 miles an hour down river,
jiud ..nly G miles an hour up river ; after running down
liver for 3 hours, how long will it be in returning?
19. Twenty acres of land are bought for §0: how
many dollars per acre mus'^ they be sold I'or, that the pur.
cl.aser mav doubh^ his UHnev]
20. 1 divide 25 oranujes between two bovs, trivinir ono
7 more than th(^ thcr : h.;w many will cacli have?
21- II' lour l.tarrels of Hour are worlh !?3G, liow nmnv
yards of clotii worth $3 a yaid will 2 bairel.s of the (lour
buy ?
22. A boy on hi;; way to market with 17 lobsters, lost
"i
YM
40
MENTAL ARITHMETIC.
3 of them; the rest he sold for $1.12 : how much was
that apiece ?
23- Dought C harrolfi of pork for 120 dollars : at how
much a bariol must, it bo sold to gaui $2 a barrel ?
24. Divide 15 t.onts between Jolin and James so that
John may have 3 r( nts 'cs«3 than Jaracs'.
25- At 2 dollars a biich(;l. iiow many bushels of wheat
must be given lor 4 barrels of flour at $8 a barrel?
26- A man can do a piece of work in 4 days when
the days are 12 hoiu's long : how long will he take when
the days are 8 hours long?
27. Exchangeil 11 tons of hay for 15 yartls of i loth at
C dollars a yard, and 4 yards at 5 dollars a yard : how
much was the hay worth a toni
28. A man can do i\ piece of work in 5 days by work-
ing 8 hours a day : how many hours a day must he work
t < do it in 4 days?
29- Two men are 96 miles apart, and are travelling
toward each other, one at the rati) of 5 miles an liour,
and the otiier at the rate of throe miles un hour : in how
many hours will they mcctl
Section VI.— Analysis.
EXAMPLKS. — 13,
1. When a number is divided by 2, the quotirnt is
one of the two equal parts which compose the number,
and is called one half of ihc number, thus : — 6 divided
by 2 gives quotient 3, which is one of the two equal
parts (3-|-3) that comi)o.so C, and is therefore one-half
ofC.
ANALYSTS.
41
2. So, when a number is divided by 3, the quotient is
one-third of the number ; when divided by 4 the quotient
is (ma-fourth ; when divided by 5, one-fifth ; and when
divided by 6, one-sixth.
3. What is one-half of 6? of 8 1 of 24? of 8 tens?
of IG hundred ? What is tlie one-third of 3 ? of 6 ? of 9
tifths? of 27 tenths? What is the one-fourth o{ 8 1 of
1 2 ? of 36 ? of GO twelfths ? What is the one-ffth of 6 ?
of 15 ? of 20 ? of 40 ? What is the one-sixth of 12 ? 18 ?
30 ? 42 ? 54 ? What is one-sixth of 36 pence ? 36 ounces ?
36 minutes? 36 tons? 36 tenths? 36 twentieths?
4- how many halves are there of any number ? How
many thirds? fourths? fifths? sixths?
6. How much is one-third of 9 ? 2 thirds of 9 ?
How much is one-fourth of 12? 3 fourths? .How much
is one-fifth of 15 ? 2 fifths? 4 fifths ? How much is
one-sixth of 24 ? 3 sixths ? 5 sixths ?
6. When a number is divided by 7 tho quotient is
called one-seventh of tho number ; when divided by 8, one-
eighth ; wlien divided by 9, one-ninth ; when divided by
10, one-tenth ; when divided by 11, one-eleventh ; and
when divided by 12, one-twelfth.
7. How many sevenths are there of any number?
How many eighths? ninths? tenths? elevenths?
twelfths ?
8. How much is one-seventh of 14? 21 ? 42? How
mnc]» is 2 sevenths of Sr-? 3 sevenths? 4 sevenths ?
9. How much is one-eighth of 40? 3 eighths? 7
eighths.
10. How much is one-ninth of 0? of 18? of 81?
How iiHich is 4 ninths of 27? 5 ninlhs? 7 ninths ?
ij
42
MENTAL ARITHMETIC.
h.
How mnch iw one-ninth of 27 ponnfls? 36 fnrtln'njrs?
45 days 1 54 frrains 1 63 tens ? 72 tontl^s ? 72 fiftlis 1
11. How mu..^h i3 one-ton th of 10 ] of 30 ] of 70?
How much is 'i tonchjs of 50? 3 tenths? 6 tenths?
10 tenths?
12. How much h onoclrvanth of 22? 2 olevonths?
4 elevenths? 7 elevenths ? 9 elevenths? 10 elevenths?
18. How much is one twelfth of 1 2 ? of 36 ? of 72 ?
of 84? of 06? How much is one-twelfth of 108? 3
twelfths ? 7 twelfths ? 9 t>veirths ? 12 twelfths ?
14. One half a numher is 10, what is the nunihor?
Sot. — J^ince one half is 10, tiro hulves, or the whole
number, is 2 times 10 or 20.
15 One fifth of my a^v is 6 years : how ohl am I?
16. What is tiie nu rubor whose sixth part is 10? The
number whose seventh part is 8 ? The number whose
ninth part iy 9 ? The number whoso tenth part is 10?
17. The rent of a ho\ise for a certain time is $60,
what is the rent for one-sixth of the time ? for 2 sixths ?
for 5 sixths ?
18. A man has 630 a month, and saves 2 ninths of
it: how much doe.; he save in 12 months?
19. OncvHPvcnth of the money I have is $12 : how
much have I ?
. 20. H 22 is ^;^ie-sixth of the value of a horse, find his
value ?
21. What is 5 eighths of 16 yards? of 16 dollars?
of 16 cents? of 16 years? of 16 days? of 16 pence?
of 16 farthings? of 16 hundredths?
22- There aic 12 months in a year, how many in one-
sixth of a year? in 2 sixths? in f) sixths?
23. One pound ol checbc costs 18 cents, what will ono-
ANALYSIS.
43
half pound ooet 1 one-third of a pound 1 5 sixths of a
pound.
24. Five-sixths of 72 are how many times 6 ] how
many times 12] how many times 101
25- James is 16 years old, and 3 fourths of his age is
6 sevenths of Harry's : how old is Harry ]
Examples. — 14.
1. If 3 oranges oost 15 cents, what will 7 oranges cost 1
Sol. — 3 Oranges cost 15 cents, one will cost one-
third of 15 cents, that is 5 cents, therefore 7
■will oost 7 times 5 cents, or 35 cents.
2. If 7 apples cost 14 cents, what will 11 cost?
3. If mackerel cost 81 cents, what will 12 cost"?
4. If 15 yai*ds of tape cost 45 cents, what will 8 yards
oost?
6. $84 are paid for 12 barrels of herring : what would
bo the price of 10 barrels ?
6. If six men can mow 1 2 acres of grass in a day,
how much can 13 men mow in the same time?
7. If 3 apples arc worth 6 oranges, how many oranges
are 20 apples worth %
8. If 8 dollars will buy 80 yards of cotton, how much
will 11 dollars buyl
9. When 60 cents are paid for 4 dozen of eggs, how
much must bo paid for 7 dozen?
10. If 50 cents will pay for 5 lbs, of sugar, how much
wilj 120 cents buy?
Sol. — 5 pounds cost 50 cents, 1 pound 10 cents,
and if 10 cents buy 1 pound, 120 cents will buy
120-f-lO, that is 12 pounds.
t ri
44
MENTAL ARITHMETIC.
' I ' ■ ' ■
i •' ■ I
11. If 8 men buikl a wall in 6 days, hov. many would
build it in 12 days ?
12- When $80 is paid for 8 barrels of mackerel, how
many barrels will $110 pay for ?
13. If 8 yards of calico can bo bought for 9G ponro,
how much can be bought for 132 pence 1
14. If 4r men do mow a field in 12 days, how long
would it take G meni
iiiol. — 4 men do it in 12 days, therefore 1 man will
do it in 48 days, and 6 men will do it in one-
sixth of 48 days, or 8 days.
15. How long would it tako 11 men to do wliat 10
-1 ' i • ould do in 11 days?
'If^:. :'10 cents will buy 5 herrings, liosr much will
40 iienvUiTS cost]
/7 Wir. '•--yards of broatMoth can be bought for
20 doliari:, h:.. >di will $56 buy?
18. If 8 copy-books cost 80 cents, wliat will 40 copy-
books cost.
Sol. — Since 40 is 5 times 8, 40 books will cost 5
times what 8 cost, or 5 times 80, thtij is 400
cents.
19. What will 15 oranges cost, when 3 cost 11 cents?
20- How many dozen of oggs can bo bought for 90
cents, at the rate of 2 dozen for 30 cents ?
21. What will 21 pounds of rice cost, if 13 pounds
cost G5 cents ?
22- How much will 40 barrels of Hour cos-., v/hcn 5
barrels cost 2C dollars ?
28. How much honey at 12 cents a pound must be
given for 4 pounds of coffee at In) cents a pound 1
24. What is the cost of 30 yards of cloth at the rato
of 5 yards for 9 dollars 1
ANALYSIS.
45
25- If 12 men do a piece of work in 10 hours, how
long would it take 8 men to do the same work 1
26. If a steamer make 48 miles in 4 hours, how long
will it take her to make 72 miles]
27. If 3 fourths of a number is 1 2, what is 6 times
the number ?
28. If 4 fifths of a pound of tea cost 60 cents, what
will 2 pounds cost?
29. If 10 horses eat 30 bushels of oats in 6 days : how
long will the same quantity last 15 hvrses 1
30. What will 3 fifths of a pound of tea cost, at 60
cents a pound ?
31. Charlie gave 7 apples for 21 marbles : at this rate
how many marbles ought he to get for 9 apples 1
32. How much will 5 bushels of apples cost, if 5
eighths of a bushel cost 40 cents ?
33. 3 tenths of the distance from Yarmouth to Digbj
is 21 miles: find the whole distance?
34. A man gave 16 bushels of wheat for 3 barrels of
flour : what was the wheat worth a bushel when $60
would buy 12 barrels of flour?
35. Frank has 60 cents, and 7 tenths of this sum is
equal to 6 sevenths of what Willie has : how much has
Willie?
36. A man paid $40 for a chain, which was 2 ninths
of what his watch cost : find the cost of the watch ?
37- A farmer has 36 geese, and 7 ninths of the num- .
ber of geese is 4 fifths of the number of turkeys : find the
number of turkeys ?
38. John has three times as much money as Edward,
and both have $16 : how much has each ?
Sol. — John has a certain sum and Edward has 3
It ■ I •
46
MENTAL ARITHMETIC.
m
'If-!;'
1 >
M
1;
I 1
i
times this sum, therefore both together have 4
times John's money, or $16, and therefore
John's is $4, Edward's $12.
89. A lot and house cost $900, the house cost 8 timea
as much as the lot : find the cost of each 1
40- Edwin is twice as old as Edgar, and their united
ages is 30 years : find the age of each 1
. 41- A horse and cart c- st $108 ; the horse cost 5 times
as much as the cart : find the cost of each 1
42- 72 cents are divided between Harry and Charlie,
for every 4 cents Harry receives, Charlie gets 6 : how
many does each receive 1
Sol. — Oi every 9 cents Harry gets 4 and Charlie
5, but 9 is contained 8 times in 72. therefore
Harry gets 8 times 4 cents and Charlie 8 times
5 cents.
43- Divide 60 marbles between Willie and Eddie, so
that forevery 2 Willie gets, Eddie shall get 3.
44. Divide $132 between Minnie and Susie in such a
way, that as often as Minnie gets $4, Susie shall get $7 % '
45- A newsboy saves 104 cents in 8 days : how much
will he save in 30 days at the same rate ?
46. Tf it take 20 yards of calico to* make 2 dresses,
how many similar dresses will 110 yards make?
47- A boy laid out 80 cents in oranges at 4 cents each,
and sold them so as to gain 40 cents : find how much he
got apiece for the oranges 1
48- On a certain holiday William caught 11 trout as
often as Cluirles caught 7 ; William cauijht 55 : how
many did Charles catch 1
49. Frank laid out 60 cents in apples, giving 5 cents
^or every apples; he kept a number for liimself and gave
\
ANALYSIS.
47
an equal number to each of 8 class mates : how many did
each receive 'i
60* If 9 barrels of flour are worth $63, how many
barrels of apples at $3 a barrel can be had for 6 barrels
of flour '?
51. A newsboy b»yught 9 papers at 3 cents each, and
8'others at 4 cents each; he soM all the papers at a uniform
price, and gained altogether 26 cents : find what he re-
ceived for each pa[>er 1
52- If $100 will support a family of 7 persons for 8
weeks, how many persons would it support for 14 weeks ?
53- Two-thirds of 36 are 3 times what number 1 4
times what number 1 6 times what number*? 8 times
what number]
64^ Eight-ninths of 81 are 6 times what number? 8
times what number 1 9 times what number ] 12 times
whiit number?
55- Four fifths of 60 are how many times 6 1 how
many times 8 1 Ten-elevenths of 55 are how many times
5] 10] 25]
Section VII.—Highest Common Factor, &c.
Examples. — 15.
1. What numbers multiplied together will produce 8 1
10] 16] 35] 48] 40] 4)] 51] 42]
2. Resolve into factors, 15, 20, 25, 33, 36, 40, 50.
3- WliMt factors have the following numbers : 2, 3,5,
7, 11, 13, 17, 19, 22, 23, 27, 32]
4. Name the prime and the composite numbers in the
following, 24, 25, 27, 28, 29, 30, 31, 34, 35, 37, 36, 39,
41,47,541
'/»'
48
MENTAL ARITHMETIO.
§;■
n
i ;
i;
6. Wliat are the factors of 6 *? 91 12? 151 101
181 211 321 331 351 391 491 511
6. V^h&t are the prime factors of U1 541 561 601
671 681 701 751 761
7. Name the divisors which are common to 8 and 10 '
12 and 16 1 10 and 30 ] 9 and 36 1 24 and 36 1
8. Find the liighest common factor of 8 and 24, 36 and
27, 32 and 48, 37 and Q8, 18 and 80 1
9. Find a common multiple of 2 and 3, 5 and 6, 4 and
8, 9anJ 12, 32 and 481
10- Find the least common, multiple of 8 and 12, 9
and 12, 12 and 20, 16 and 48, 10 and 35. 48 and 96 1
11. What is the square of 11 21 31 41 51 6?
71 81 91 101 111 121 131 161 141 201
12. Find the cube of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12.
18. What is the square roo< of 11 41 91 161 251
361 491 811 641 1001 1441 1211
14- 5 times the square of a number is 320 : find the
number 1
16- If the square ro'^t of a certain number be divided
by 6, the quotient is 2 : 6nd the number.
16- If 1 1 be added to Harry's age, and 1 is added to
5 times the square root, J of the sum will be nine : find
his age.
M
I f
Highest Common Factor and L. C. M.
Examples — 16.
1. What is meant by Common Factor, Highest Com-
mon Fact<^r1
2. Find the H.C.F. of 4 and 6, 7 and 14, 8 and 12,
27 and 36, 56 and 14.
..-^
' il
HIGHEST COMMON FACTOR AND L. C. M.
49
a Find the H.C.F. of 2, 4, 6, 8, and 12 ; of 5, 15, 25,
and 39.
4. What is meant by the multiple of a number t
whnt by the L.C.M. of two or more numbers 1
5. Find the L.C.M. of 4 and 6 ; 9 and 12 ; 8, 16, and
32; 4, 6, 9, 18, and 36.
6. Find the L.C.M. of 2, 4, 6, 8 and 12; 5, 15, 10,
20 and 30 ; 3, 6, 9, 24 and 36.
7. A farmer wishes to put 24 bushels of wheat and 36
l)ushel8 of silver chaff into the least number of bins that
shall contain the same number of bushels without mixing
the two kinds of wheat : what number of bushels must
each bin hold, and how many bins will be required?
8. A gentleman has a triangular plot, the sides of
which are 63, 84, and 105 feet, wishes to enclose it with
boards of uniform length and greatest possible : what
will be the length of each board 1 How many boards
will be required if it be 4 boards high all roundl
9. A, 6, and C agree to purchase pigeons at the high-
est price each that will allow each to invest all his
money ; A has 45 cents, B, 60, and C, 76 : how many can
each purchase 1
10. A can dig 4 rods of a ditch in a day ; B, 6 ; and
C, 8 : what is the least number of rods that will furnish
a number of whole days' work to any of j, the three men 1
11. The fore wheel of a perambulator is 3 feet in cir-
cumference and the hind wheel 5 : what distance will be
passed over before they are in the same relative pos-
ition as at first 1
12. The IT.C.F. of two nura>>ors is 2, and the L.C.M.
is 12 ; one of the numbers is 4 : what is the otherl
13. The H.C.F. of three numbers is 2, and their
i ■ '.
! ■!
f I
.'r!
If I
50
) i,"
'l{
<|!^
'i''
MENTAL ARITHMETIC.
L.C.M is 60; the first number is 4, the second 2 more
than the first : what is the third 1
14. Find the least number which, divided by 3, 5 and
7f leaves 2 for remainder in each case.
15. What is the smallest sum of money with which I
can buy rabbits at 25 cents each, pigeons at 15 cents
each, and hens at 30 cents each 1
16. A boy can dig 12 post holes in a day ; hir ^"^ther
can dig 18 : what is the smallest number which .^i fur-
nish exact number of days' labor for either alone or both
together ^
17. What is the least number which, divided by 3, 5,
7, 9 and 15, will leave 1 for remainder 1
18. What is the greatest and what the least number
that can be subtracted an exact number of times from 551
19. What is the greatest and what the least number
that can be subtracted from 153 an exact number of
times 1
CHAPTER n.
Section i.— Fractions
■* '•
INTRODUCTCRY.
Examples. — 1.
1. If anything, as a foot, a dollar, a pound, a number,
(fee, is divided into two equal parts, each part is one-half
of the thing divided; if it is divided into three equal parts,
each is one-third, and two of the parts are two-thirds ; if
it is divided into four equal parts each is one-fourth^ two
of them are <wo-fourths, and three of them </iree-fourths ;
if it is divided into five equal parts, each is one-fjfthy two
FRACTIONS.
M
of them are ft&o-fifths, three of them three-Mths, four of
them fov/rfifthi \ and so on for other divisions. Now,
instead of wordsy we may use figures to express one or
more of the equal parts into which the thing has been
divided, thus : —
One-half is represented by ^, two halves by J ; one-
third is represented by ^, <i(?o-thirds by |, ^^re^thirds by
I ; one-fourth is represented by |, <w;o-fourths by J, three
fourths by |, yimr-fourths by | ; one-fifth is represented
by J, twoMths by §, three-Mthn by J, ybwr-fifths by J»
/ive-fifths by | ; one-twelfth is represented by Jj, two-
twelfths by j^3j,^t;e-twelfths by /tj, ^reveTZ-twelfths by j"'^,
ei^A^-twelfths by j®^, &c. In these expressions the lower
figure shows the number of parts into which the thing is
divided, and indicates the fractional unity (one-half, one-
third, one-fourth, «kc.) ; the upper figure expresses a cer-
tain number of these equal parts, or fractional units.
The thing which is divided into equal parts may be calle^
die Unit op the Fraction.
2. How many halv ^ in 1 thing 1 in 2 things 1
in 3 things 1 in 2 dollars and one-half ? in 3 pounds
ind one-half? in 5 feet and one-half 1 in 6 acres and
\ of an acre 1
8- How many fourths in 4 1
Ans. — In 1 there are 4 fourths, therefore in 4
there are 4 times as many, that is, 16 fourths.
4. How many fifths in 5 ? in 8 ? in 1 2 1 How
many sevenths in 3j? iu 5 ? in 10? in 111 in 12 ?
in 131
6- Of wliat number is 2 the one-third ? 4 tlie one-
tourth? 5thei? 10 the Vq 1
6. Of what number is 12 the ^1
7»
i 1 Of what
number is | the \ %
the^l
the^l
52
MENTAL ARITHMETIC.
• i-'l
i 'I'M
i ':
f ii
7.
age:
8.
Charlie is 5 years old, and his age is | his father's
How old is his father 1
How many ninths in 8 ] in 9 1 in 10 *? Show
that three-tenths of one=o»e-tenth of three.
l=iof3.
Q, What is the fractional unit in 1 1
in U ^
That I of
7
5
m i1
in j% ]
in -i
il
1
in
?TJ
?
in if]
in
17
in
2 1
250
i^UV
10- How many fractional units in ^g 1 in
8 2
in
2 3 <>
7J5 '
in^Vu^ inlgfl in
|5f 1 What is the Unit
OF THE Fractions in $| *? £ J 1 4 ^i-^^^® "^ I ^"^® '^ | ton 1
11. What are all the fractional units, as far as 20 1
What is the fractional unit corresponding to the number
IQI to 30? to 451 tr 49? to 50 1 to 5001
12- Willie gave away ^ of an apple : how many
thirds had he left 1 How many eighths of a yard in a
yard ] How many tenths of a dollar in a dollar 1 How
many sixteenths of a pound in a pound ?
13. How much does | lack of 1 1 How much does ^
lack of 1 ? How many twentieths must be added to ^^
to make it equal to 1 ]
14. Take § from 1 and what i.. left] Take j\ from
1 and what is left]
15. Which is the greater, one-half or one-third 1
One-sixth or ono-fifth 1 One ninth or one-twelfth 1 One
twentieth or one-thirtieth 11
16. A horse cost $100, and a sleigh | as much :
Find the cost of the sleigh.
17. A man sold ^ of a piece of cloth which contained
46 yards : How many yards were left 1
18. If A can dig a ditch in twelve days, what part of
ii can he dig in 1 day 1 in 5 days ? in 7 days 1
FRACTIONS.
6a
19- If B can dig a ditch in 10 days, what part of it
can he dig in one day 1 in 5 days 1 in 9 days 1
20. If a person leaves his property, woi-th $1800, to
his wife and 8 children, in equal parts, what fraction of
the whole will each have, and how many dollars?
21. What is the ^ of 18? of 18 shillings 1 of 18
pence"? of 18 days 1 of 45 farthings ? of 45 homs. What
is the ,2 of 3G seconds'? of 3G ounces 1 of 3G t(,'ns 1 of 3(i
tenths Tof 36 twelfths'? of 30 fiftieths'?
22. I owned ^^' of a sliij), and sold ^ of my share : how
many sixty-fourths had I left 1
23. If you put up ten pounds of tea in packages of one
|)Ound, what part of the whole do you put in one pack-
age ? in 3 packages 1 in 7 packages "?
24. 1 is what part of iO"? of 5? of 15 1 of 91
One-seventh is what j)art of 2-sevenths '? 4-sevenths? 5-
sevenths? 6-sevenths ? of 5 '? of 16'? One-nineteenth
is what part of -^ 1 {'g 1 [§ 1 pg ? | ^ "? 3 is wiiat
part of 1 "?
25. A person having $85, earned $115 more, and then
gave away one-fourth of what he had : how much did he
give away : how much did he retain 1
26. Jane has 1 of a dollar, and Hany and James have
each I of a dollar : how much more hfive these than
Jane 1
27. If 4 pounds of almonds cost 80 cents, what jmrt
of 80 cents will one pound cost "? 2 pounds ■? 3 pounds ?
5 pounds ? 7 pounds '? What part ol" 1 2 is 7 ? 91 1 5 ]
28. What is 1 -seventh of 2^0 1 i^? ^i? 1^1 1,-; 1
29. What is 2-sevonths of J J 1 3-sevenths ? 5-8ev-
enths 1 6-sevenths ? 1 3-sevonths '?
30. If 12 oranges cost 36 cents, what part of 36 uent^
54
MENTAL ARITHMETIC.
^1'
^?
1:
will 1 orange cost 1 2 oranges 'i 3 oranges 1 5 oranges 1
8 oranges?
31. In a certain High Scliool there are 12 boys an<l
J as many girls; reciuired the number of girls, and the
number in the school.
32- What do you understand by 3-fourtlis ? S-sixthsl
7-ei,<?ht.hs ? /o? ^3? J^?
33- A cow was bouglit for $00, and was sold for ^ of
tlie c st : what was the gain ?
34. ,'\ of the number of hours in a day is tlie number
of hours I work , how many hours do 1 work 'i
35. 3-ninths of 18-f-5-sixths of 18 is how many? 6-
ninths of 54 are how many times >J of 201
36. 3 sevenths of 21 are how many times 3 1
Sol. — 1 -seventh of 21 is 3 ; 3-sevenths of 21 is 0,
which is 3 times 3 ; therefore 3 sevenths of 21
is 3 times 3.
37. 3-eighths of 24 are how many times 6 1 4-fiftha
of .f 15 are liow many times $3 ? | of 15 tenths are liow
many times 3-tenths1 | of 15-tweutietlis are how many
times ^\^ 1 7-ninths of 27 are how times 9 1
38 Fi'G 1 had $G0 ; J of it he spent for a watch, and
I of it for a suit of clothes, how much had he remaining?
39- A ]>ole whose length is 15 feet is in the air and
water, and 'j of the whole length., less 3 feet, is the length
in the water, recjuirc*! the length in the air 1
40- 'I'he interest on $G00 for G years is equal to J of
the principal : how much was the yearly interest?
41. What will 3-fourths of 8 pounris of coffee cost at
20 cents a pound 1
42. A is worth $2,400, and 5 sixths of A's fortune is
10 times the interest on B's fortune for a year : what is
the interest on B's fortune 1
FRACTIONS.
55
43 A road 160 miles long is composed of 10 equal
soctions. What fraction of the whole road are 6 of these
sections, and how many miles do they contain 1
44. If the rent of a house for 30 days is $90, how
mu';h will it be for 17 days?
45- The site of a sch ol cost $700 ; and 4-sevenths of
this $100 is 1 -eighth of the cost of the building : required
the cost of the building 1
< :i
Section II.— Reduction and Analysis.
of
Examples. — 18.
1. How many fourths in 4| '?
aSW. — 4j=4-|-j ; in 4 there are 16 fourths, there-
fore in 4-|-| there are 16 fourths-}-^ fourths, or 19 fourths,
that is -\K
2. How many thirds in 3J ? 4^'? 5J ? 6§? 13J1
8. How many fifths in 4^ ? 3| i 7^ 'i 8| ]
4. How many sevenths in 7^ 1 inS'^l in 10? 1 in 1 If 1
5- How many ninths in 1 J i in 2*5 I in 4^ i in 5|'?
6. By how much is 4^ greater tlian 3 J ? than 2| 1
7. What is the result ir. f) />. _ 1 J<- -f 6 ,4. — 4/^1
8. How many tenths in 3 ^\^ 1 in 2 ,-q 1 in 4 ,•*) i in
r,,i,? in 7,^,/;
9. How many twelfths in 2X1 in 1 ,H, ? 33? in
10- How, then, are mixed numbers reduced to improper
frdcflona ?
11. Reduce to improper fractions 3^ 42, 6§, 5|, 9 J,
10 •»
m
PI
66
MENTAL ARITHMETIC.
•' *.
;t !
*!
'
rf
i
'■,*
4 '
r
i ,
i
i:..
"■t
j
V,
.«
-r.j
* I.
1 ri
4-
i j'l<
•si
m\
12. Reduce to improper fractions ly^^^, 2/j, 3 ^%, 1 j^^,
18. How many fourths of a dollar will 7 yards of
cloth cost at $2 1 a yard 1
;^ol.—2l=-\^ and 7 times V ^V-
14. How many thirds of a dollar will 9 barrels of
flour cost at $G'l a barrel 1
16. What will ten yards of cloth cost at $2j a yard !
16- What will 10 lbs. sugar cost at Gj; cents per
pound 1 at 7i cents ? A^ cents 1
17. What will 7 yards of cloth cost if 2 yards can bo
bought for $C| ?
18. If 9 felt hats can be bought for $11 1, how much
will 8 hats cost 1
19. [f 3 J tons of coal cost $00, what will 4 tons cost
at the same rate l
20- How much will 14 lbs. of raisins cost when 3.| lbs.
cost 50 cents'^
21. 2i^ yards of muslin cost 48 cents: what will 10
yards cost at the same rate ]
Fractions. — Reduction.
UNITS.
Examples. — 19.
1. How many units are there in ^ 1
Sol. — 2 halves make one unit, and 7 halves contain 2
halves 3 tiuies with o?ic-half remainder .*. in ^ tliere are
3J units.
2. How manj; units in ^ ? in ?] 1 in y^^- 1 in J 1 in
£•'
in
to
r,3
in
FRACTIONS. — RfiDUCTTON.
57
3. How many units in ^^^ 1 in ^>i* 1 in $'^5. ] in
4. How many units in Y? in 5^--? in y 1 in ?J 1
infgJ
5. How, then, may any improper fraction be reduced
to a mixed number ]
6. Keduce to mixed numbers V , V* V» '^^Z' -^^V? '/
sliillings, -M-. Reduce to mixed numbers '^^ pence, **,"
hours, ^/- seconds, ?3 fartliings, ?}}, V^, ?f, VY-
7. At $6-^ a barrel, what will 12 ))an"els of Hour cost]
8. If 2 dozen of ^.gga cost 28 j cents, what will 3 dozen
cost]
9. I paid $9 for 2j ]«arrela of apples, what will 5^
barrels cost at the same rate?
10- If ^ of a pound of tea cost 48 cents, wliat will 1
lb. cost] 2 lbs. ] 3 lbs. ] 4 lbs. ] 3J lbs. ] 4^ lbs. ]
5 J lb8. ]
11. If I of a ton of hay is worth $4 J, what will 7"^
tons cost ]
12. A man walks 7 miles in 2 J hours : h w far will he
walk in 4'j hours ]
13. Find the number of bows, each containing ^ of a
yard of ribbon, that can be made out of 7;] yards.
14. At a church collection 43 dollars, 24 half dollais,
and 32 q\iarters were received : what was the whole
amount ]
16- » pint is one eighth of a gallon : how many pints
in 13^ gallons] How many gallons in 141 pints]
16- If a boy can split J of a cord of w od in a day,
how long will he take to split ^ of a cord] J ] 1 cord ]
2 cords ] 8 cords ]
17. How many quarter-pound weights will it take to
58
MENTAL ARITKNfETIC.
■A '.
U' ,
Kalance 56 pounds weight] How many half-pound
weights 1
18- How many lots ,\j of an acre in size can be laid
out of 5 acres'? from 7 acres 1 fiom 2,'^g 1
19. If a mail can do I of a piece of work in 2 hours,
Ih'w long will it take him to Jo the whole 1
20- If a boat is 3 hours in performing I of its trip,
how long at that rate will its whole trip take 1
21. If a locomotive can go six miles in I of an hour,
how many miles can it go in one hoiir ajid a half]
22- With $24 collected from one customer, $10 from
another, and $11 from a third, a pei*son paid jj of his
taxes : what did his taxes amounfto ]
23. 74-84-5 + 4, is.' of what number] -^j 4- -S^ 4- J^^
4" pT is .' of what number]
24. 5 is a third of how many times 6 ] Of what num-
ber is 3^ one-seventh ] One-ninth] One-twelfth ]
25- If a fifth of a yard of carpet cost two-fifth of a
dollar, what is that a yard] How much would $27 J
buy]
26. If a ninth of a pound of raisins cost 2 cents, what
will 4 ninths of a pound cost ] What will 3§ pounils
cost]
27. A man being asked the value of his horse said,
$^\['- is one-tenth of its value : what is its value ]
28. 9? is a seventh of what number] 5| is 1 -fourth
of what number] 77j is 1-ninth of wliat number]
29. 18 is 1-half of G times what number]
30- 15 is 1-sixth of 5 times what number]
31. A wagon cost $C)0^, which is 1-fourth the cost of
the buggy : what was ^lic cost of the bujrgy ]
32. 7| is \ of what number ] J of what number 1
th(
vai
f!
1 l
PRAOTIONS. — REDUCTION.
59
83- A man being asked his age, said his youngest son's
age, which was 15 years, was just one-eleventh of 3 times
his age : what was his age 1
34- A lady's shawl cost $9, which was 1 -eighth of 4
times the cost of her dress : what was the cost of the
dress 1
35. A honse cost $800 which was 1 -tenth of 4 times
the value of the farm on which it stands. Required the
value of the firm 1
36- 2 thirds of 21-j-3-fourths of 16, are how many
times 7 1
37' 3 sevenths of 21-f-3 eighths of 40, are how many
times -^ 1
38. If 3g lbs. of butter cost 60 cents, hov^ much can
be bought for 360 cents ?
39' i of 21 is ^ of what number 1 | of what number ?
40. 2-f-8 — 3 is I of what number]
41. 7 of 56 are how many times 8 1
42. How many fifths in 4 1 In 4| 1 How many
sevenths in 3*? In 341 How many ninths in 3? In
3^] How many tenths in 4 ? In 4| ? In 2J? In 31?
1
Fractions.— Reduction, &c.
Examples. — 20.
1. In J how many twelfths ?
Sol. — In 1 there are 12 twelfths .*. in ^ there arc
2 thirds of 12 twelfths, or 8 twelfths, that is j%.
2. How many sixths in Jl J 1 J ? ^1
3. Howmany eighths in J? {1 Jl )l IJ^
4. How many fifteenths in J ? J? 2| I
H'i
V
H^
3J?
!l:
ii
60
MENTAL AKITHMBTIC.
^'^l■}
,i
6. How many twenty-firsts inji §1 3|1
29
5 ^
l?t
6. Reduce J, §, |, |, l^^'.j, 2J to twenty-fourths.
7. Reduce J, f , }, 1^, 2J, /g, ly'g, 2^^ to thirty-sixths.
8- Since 4=J|, how may the latter fraction bn d(;rived
from the former 1
9. Since 1 1= J how may the latter fraction be obtained
from the former 1
10. How many fifths in -j?^ 1
4 1
TO »
1 1. How many ninths in 2 4 ] 14^ 1 g ^ ^5 ^ ^^i
6 1 6 ri
1 r, 9
3g »
J 8 <)
SO '
3 6 -?
4 5 •
12
13.
14
15
20 1
18 24 «l
4-1 * TTi '
How many fourteenths in ^f?
Reduce to eighths V»g, H k, fl, ?g.
Reduce to their lowest terms fi^, /g, J|, ^J, 4f , |f.
Reduce to lowest terms jf, J^, f |, '||, f J, ||, yV^.
i5
I4»
7 5 4 6 5 « 8 1
lOO» go» 4 8' i?"
16. Reduce to lowest terms §|, |
17. If 2J barrels of flour cost $20, find the cost of 3J
biirrels.
18. John has $40 a month, which is J of half of what
James has : how much has Jamesi
19. 16 is y^5 of three times some number : fin I | of
the number.
20- $4:5 is I of A's money, and B has § as much as A :
how much has each 1
21. A h-rse cost $100, which is | of 10 times what
the saddle cost : fin I the cost of the saddle.
22. Reduce J, J, |, j'^ to sixteenths.
23- Reduce J, J, y^, ^J to twentieths.
24- Reduce |, |, |, j\, ^:f to twenty-fourths.
25. How, then, may fractions be changed to equal
ones having a common denominator ?
26. Reduce J, J, J, y^^, to a common denominator.
27. Reduce I i, *„ §, J
((
it
it
FRACTIONS. — llKUUC'TIOIf, ETC.
61
61
7 *
36 1
4 5 *
A:
rhat
Inal
28. Reduce 4, -j^q, J, n*g to a ccinmon deno ni inalor
29. Reduce I I, I, 5
((
«(
«
i(
((
4<
((
((
i<
(i
<(
M
30. Reduce!, ^, U, |
31. Reduce j2> t?> tu» c
32. Reduce li, 2J, 3f, f
33. Reduce the following mixed numbers to improper
fractions : 5/^, 7J^, 12', 10|, 20J, 8|, 7/^.
34 Change the following to mixed numbers
17 _2 5_ _4 8 37 8 3 J 00 4 8 7 5 9 6 13
"4 » 5 ' 3 » ^ » 1 1» 12 » I 5> 30' ? ' an •
35. Reduce to their lowest terms :
23 8
T0> 5'
9 10 2 5 7
2i» T5» 55» T00»
3 2 16 7 8 11
«4' 2?» B0» ??»
1 _4 5 6 7 3 4
3» l80» 5l» TSff*
36. Harry gave his sister $40, which was | of all he
had : how much had he 1
37' John being asked his age said : 3 fourths of my
present age equals my age five years ago : how old is he 1
38. Find the sum of J-f J-f 2^J_|_J.
39. I gave 8120| for a horse, and $19| for a saddle:
find the cost of both.
40. Mary says that J her present age is § of her age
three years ago : find her present age.
41. James being asked how much money he had, said :
If I had $20 more, | of the sum would be j^^ of what I
now have : how much had he 1
42. What is the result of ^ J- ^^ ? j^ j_^7^ t ^-J—^^ 1
43. I owned J| of a ship, and sold g\ of the ship :
what part had I left 1
44. John gave f of his money to Charles, ^j of it to
Ida, and had 20 cents left : how many cents did John
and Ida each receive 1
62
MENTAL ARITHMETIC.
Ii'^ ' t
Fractions.— Section III.
ADDITION AND SUBTRACTION.
4*'
Hi
Sifl-
i.i.
Examples. — 21.
1. John had f of a dollar, and his father gave him |
more : how much had he then 'i
2. One man had | of an acre of land, a second had
|, and a third had J : how much had they all ?
8. Bought a barrel of flour for $7|, and a cord of
wood for $42 : how much did he lay out 1
4.
5.
Bought
7
E
Find the result of /^ + j\-
Find the sum of § and J.
.616
TO J^T
3
Sol-^=j%, |=,Hj, and j%-\-T%=\hoT\i\,
6. Find the sum of § and | : of J and |.
7. Find the sum of § and | : of | and |.
8. I had f of an acre of land, and bought J of an
acre : how much had I then ?
9. Find the sum of 8f +2i-f-3|.
10. Add i, I, f, i. Add ^ and 3§.
11. Find J+ j-f 2j+3iH-74.
12 Add /g, J, j% and J.
18. Find the sum of 2^+3^+81 +12J.
14. J of a number increased by § of the number is
equal to 70 : find the number.
15. Willie being asked how much money he had, said :
if the amount were increased by | of itself, I should
have $84 : how much had hel
16. i of A's money increased by J of his money,
equals $81 : how much had hel
17. A man gave $80 for a watch, and $40-|-| of the
ti'U -
mA,
FRACTIONS. — ADDITION AND SUBTRACTION.
63
cost of the watch is 4 times what his chain cost : find
its cost.
18. I had 5 of a dollar, and paid § of a dollar for a
[)OiiHd of coffee, how much had 1 left t
19. A man owned f of a ship, and sold ^\ of the
sliip: what part had he left 1 ,
20. Find the difference between J and J, J and g,
•J and j\.
21. What is the result of 52+8J~3| 1
22. Subtract ^ from \, J from J, J from {, J
from \.
23- Subtract § from J, § from |, J from §, I
from ^.
24. Subtract ^ from |, ^ from §, 2J from 3J.
25. Subtract 31 from 4^, 2J from 3J, 3i from 5^.
26. What is the result of J+J ~i ] of A + J- J <
27- What is the result of ^Ve" 1 ^ o*" 5— i^o+i '^
28- What is the result of 2.^+41—4^1 of IJ-f-li
— 2i1
29. What is the result of 3|+2J— 5J? of 2J— IJ
30. What is the result of 4g---4i-f-CJ 1 of 2^+2;
31. What is the result of 1 J+2I| 3J ? of 7§— 5i ?
32. From the sum of w\ and ^^ take I J — :^^^.
33. Findthe valueof"3j+4J--2j--U.
34. A can do a piece of work in 5 days, and li in 4
days : what portion of the work can both together do in
oiK^ day ? in 2 days ? in 3 days ?
35- 5 of a [»ost is in tlic ground, and there are 7 feet
of it al)Ove ground : find its entire length.
36. The difference between § of my money, and } of
it, is ^IGJ : how much have 1 1
if
* !
64
MENTAL AUITUMETIC.
87- Bought a coat for $11 yg, and a vest for $5^, and
handed in payment 2 ten dollar bills : bow much change
did I receive?
38. From 18 J subtract 7|.
^oZ.-18J-7|=18|-7|=17-hl|-7i
=17— 7+i— |=10§=10J.
89. Find the results of 4|— J, of 12—6^9^, of 36j
-24|.
40. I bought two articles, one costing $15 J, the othei
$20^, and gave in payment a $50 bill : how much change
did I receive ?
41. t\ ^^ ^^® candidates at an examination failed ii
arithmetic, | in other branches, and 20 passed : ho\i
many candidates were there ? /
42- How do you add two or more simple fractions 1
two or more mixed numbers ?
48. How do you find the difference between twc
simple fractions ? between two mixed numbers 1
Fractions — Addition, &c.
f
Ii '
<^-
EXAMPLES. — 22.
1. A can do a work in 4 days and B the same work
in 5 days : what part of the work can both together do in
one day 1
2. John can do a piece of work in 1| dr .uw
in 2J days : what part of the work cn^ »">♦ ay 1
8. A grocer sold J dozen of orang. i> oii> an, j of a
dozen to another, and | of a dozen to .i third, aad had 3 J
dozen left : how many dosen had he at first \
PRAf'TIONS. — ADDITION, ETC.
65
36j
>hei
ng(
I ir
twc
ork
oin
not
fa
4- Sold I of an acre of land to one man, § to another,
and j'j to a third : how mu«:h did I receive at 60 cents
an acre 1
6. A can do J of a piece of work in a day, B J and C
I : how much can all three do in a day 1
6. If a boy who had $4 J, earned $2| more, and had
$lj'g given him, how many dollars had he then ?
7- If a person buy a razor for J of a dollar and a strap
for g of a dollar, for how much must he sell them both in
order to make half a dollar ]
8. If 6 is I of some number, what is J of 3 times the
some number 1
9.8 is J of some number : what is | of the same
number?
10. Henry's horse cost 90 dollars, which is -^\^ of 5
times the cost of the cart : required the cost of the cart.
11. A watch cost $90, which is j of 10 times what the
chain cost : required the cost of both.
12- What number added to | will make J 1
13- A gave 48 cents, and | of this is 4 times as many
as he had remaining : how much had he at first 1
14. Jane having 50 pins, lost i of them and then
found as many as remained : how many had she then 1
15. What fraction is that which exceeds ^g by f^ 1
16. What number is that from which if 4i be taken,
the remainder will be 3|| ?
17. A beggar met four persons ; from the first he ob-
tained J of a dollar, from the second J, from the third
I, and from the fourth j*jr : how much did he get from
ain
18. Thomas spends 6J- cents for sweets, 12J cents for
a top, and 5 J cents for a slate : what did they all cost 1
'♦if-;
"• 'I
.'I
fi6
MENTAL ARITHMETIC.
.1'
K'
1, t
1 I
i, ■ - i.
19- Jamos spent | of a dollar for a book, J of a doUai
for half of a ream of paper, and had J of a dollar left ;
how much had he at first?
20- A man paid 2J dollars for a hat, 3J for a vest
and 9 J for a coat : what did the whole cost ]
21. A man travels 2^ miles the first hour, 3J miles
the second, and 4^ the third : how far did he travel in
the three hours 1
22. The sum of two numbers is 16 1, and the less is
4 ,3jj : what is the greater 1
23- What number must be added to the sum of 3 J,
2^3^, to make lO/g ?
24. What number is that which added to the sum of
i, j'j, and j\ will make §|?
25. A grocer, having a bushel of potatoes, sold J of it
to one customer, J to another, and j^g to a third • what
part remained unsold 1
26. What number added to ohe sum of 2 J and 3 J will
make the result a whole numlier'^
27. A stage, after making \ and | of its trip, had 7
miles yet to go : how long was itj trip 1
28. From two remnants of cilic), containing resjioc-
tively 4f and 8 J yards, were cut 12 1 J yards for a drciss :
how much did what was left lack of a yard 1
29. Bought some paper for $12j^j^q, bold it for $13rj'jj :
by how much did the cost exceed the profit 1
80. A can do a piece of work in 12 days, and B in 8
days : what part can each do in one day ] How much
can both together do in 3 days. Afte ' they have worked
2 days, how much will then remain to be done 1
81. £ can do a certain job in 9 hours, and F in 6
hours. After they have worked together at it one hour
and a half, what part of the job remains to be done 1
FRACTIOKS. — ADDITION, ETC.
67
32- A. can do a piece of work in G days, B in 8, an 1
in 12 : how much more work does A do in a day tlian
B, and B than 1
33> f of a certain number increased by J of the same
number, equals 34 : required tlie number 1
34. A. certain sum of money diminished by its J and
^, equals $15 : required the siim.
35. What number is that which diminished by its |,
equals 36 1
36. Find the difference between 9+12f and 8|-f-4i.
37. If j of James's age increased by ^ and J of his age
equals 57 years, what is his agel
38- f of B's money increased by the difference between
1 and J of his money equals 190 dollars: required his
money.
39- $40 is 4 tines what A paid for a chain, and the
cost of the chain, increased by its 11 tenths, is \ of the
cost of his watch : required the cost of the watch.
Section IV.— Multiplication.
Examples. — 23.
1. What is J of J ?
^ol.-{=l and i of l-i;. J of \=l (or ^^J).
What is I of i 1
Sol. — f=J5 1 fifth of this is r^^, and 2 fifths i^
2. Find the result of J of J, J of }, i of i, | of J, J
of t%y h of T3-
8. Find the result of J of 2J, If of \l, J of j% J )f 4J
4. I owned f of a ship and sold J of my share : what
part of the ship did I sell 1
«!T
68
MEVTAI- ARTTHMKTIC.
>i. '.
WJ
1- I
''ffl
h 1
'■^
6 7 of 4 1 of $50 is -^^ of the cost of a watch : find its
cost*?
6. Find tlie result of § of f of 2;^, of | of 2|.
7. j\ of the candidates at an examination failed in
English grammar, | of the remainder failed in geo-
gj-aphy, and 10 passed: how many candidates were there 1
8. An orchard has 60 fruit ti-ees, f^ of these are apple
trees, and | of the remainder are ])ear trees, and the rest
are cherry trees : find the number of each kind.
9. John's age is | of Henry's, and the diffeience of
their a^es is 4 years : find the age of each.
10. Find the results of I of y\ of |, of | of V, of | of
11. I paid .f 500 for a building lot, and ,",^ of its price
is I of the cost of the house built on it : find the cost of
the house.
12. How many is 3 times JJ rj ? J ? 5 ? « ? « ?
13. How many is 7 times ':5 ? -^I J 1 ^'i j'^^-, ? ^^^
14. Jlow many is 8 times A4 ? times ,-«^ 1 10
times {•;?
15. How many is 1 1 times A 1 _5^ ? 7,, -? J.«^_ ? 1 ^3^]
16. Multiply n,y J.
W.— JX3=-0 ; J is the J of 3. '4 X 3 in { of « =
30
4 x6'
Ex A Ml' IKS. — 24.
1. If H family cunsuu!'.; ? ot a barrel of flour in 1 week,
how much will it consunu; in 6 weeks'?
2. What will cost 6 yarus of cloth, at J of a dollar a
yard 1
8. At J of a cent a piece, whjit will 12 oggs cosf?
4. Ha man earns -j of u dollar in a day, how much
Vfi\[ he earn in 12 days?
MULTIPLICATION.
69
3k,
ii* a
6. 6 times 4 and | of 4 are how many 1
6. What will 5 J barrels of flour cost, if a barrel cost
7- 7 times 6 and g of 6 are how many 1
8. If a barrel of flour cost $0, what will 7| barrels
cost 1
9. At 6 J cents, what co^t 9 pounds r.f ricel 12
pounds? 151 181
10- If a peck of corn cost j\ of a dollar, how much
will 2 bushels costi
11. Find the cost of 20 bushels of wheat, at $2i a
ImshcH At $2\1
12- How many are 4 times 2A 1 6 times Sj] 1
13 How many are 8 times oj 1 9 times 5!^ 1
14. If a horse can trot 9^^ miles in 1 hour, how far at
ih.it rate can he trot in 8 houisl
15. How much can be earned in a year at $I1;| a
m nthi At $U)'l a month?
16 If 8 men can do a piece of work in 3 j days, how
loni,' will it take 1 man to do the work 1
17. If g of a bushel of oats is worth S^, what is a
bushel worth 1
Aiidh/nis. — If J ,f a bushel of oats is worth $^, g or 1
bushel is worth G tiuies $^, which is $'^ or $J.
18. When J of a barrel of lioui' is worth $1^, what in
a l)ai')el worth I
19. If a nu\n can reap -^(^ of an acre in J of a Jay,
how much can he rea[) in a day ]
20' It i ot t* melon is worth as niu(;h as Gi aj)ples, how
mauy ai)ple8 are worth as uuu-h as 1 m(;lon 1
21. 5,^ is I of wiuit number] Jq of what uuudtri-1
Vn of what number 1
70
MENTAL ARITHMETIC.
22. 5 times 2y'^ is J of what number I
23- 2 times 3| is J of what number 1
24' If 20 pipes of a certain size can fill a cistern in
y^^ of an hour, in how long will a single pipe J as large as
each of them, fill the same cistern 1
25- Two and 3-fifths, is one-fifth of what number ?
26. One and 3-seventhai^ is one-eighth of what numberl
27* If the current of a river be j^^ of a mile an hour,
how far would it carry a boat in 8 hours 1
28. How many are 5 times 3"4,X7 "^
29. How many are 8 times 12^ — ^1
30. How many are 9 times 10| — 1 1
31. 7 times 20 and | of twenty are how many 1 '
32. Multiply 4} times 10 by § of 15 ]
33. Multiply 2 times 9 J by 2^ times 4 1
34- Emma is 3J years old, Laura is 5 times as old as
Emma. In how many years will Laura be 2H
35. What two ways are there of multiplying a fraction
by a whole numberl
Division.
Examples.— 25.
Divide 4 by 2.
JSul. — If we divide 4 units of any kind by 2, we
get 2 units of the same kind, therefore 4-
seven'^hs divided by 2 give 2-sevenths, that
IB
li V 0.
27ul Sol. — To divide anything by 2 is to take J of
it, and J of ;}=-,'*^=^.
Divide i by 3, j\ by 4, jj by 5, ^J by C, |f by 7,
DIVISION.
71
3. Find the quotients in the following cases : |-7-3, J
-^5, l~Q, 2i--4, 3J-T-7, 8i-f-34.
4. Since :}-i-2= |, or j'*^, what are the two ways of
tlividing a fraction by an integer]
5. If 100 lbs. of flour cost $4, how much can be bought
for $i ? how much for 7 dimes ? for 60 cents?
6. I gave $3| for silk at ^4 a yard : how much did I
buy ?
7. Divide 4 by J.
Sol. — In 4 there are 20 fifths, and 20 units of any
kind divided by 3 of the same kind=2/=6 'j.
8. How many times is ^ contained in 3J? in 4J? in
5| ? in 6 f .
9. Find the quotients in 3-^}, 4-^-|, 5-^J, 4|-j-^.
10- If a yard of cotton costs 'J of a shilling, how much
can be bought for 6 shillings ? for 8 ? for 10?
11. If a man can earn | of a dollar in j of a day, iu
how many days can he earn $10?
12. Find the quotients in 2j-v-yi3, l?-v-^i„ IV*^-^-^.
13. How much will 10 boxes of herring cost, if 3 j
boxes cost $5 J ?
14. 3 men can do a work in 6^ days : how long will
it take 12 men to do it ?
16. If 3 J barrels of apples cost $14, how many barrels
can be bought for $20 ?
16. If John can v/alk 2 J miles in J of an hour, how
far can he walk in 3 hours ? in 5 J hours?
17. A man paid $30 for a piece of linen, at $J per
yard : how many yards were there ?
18. How often is j gallon contained in 7 gallons ? ^
week in 8 weeks ? } penny in ddl | of a mile ia 4
miles 1 I of an inch in IJ feet?
72
MENTAL AllITIIMETlC.
u:- 1
W
III}
m
m
m
11
PI
!1
19. If J bushel of potatoes will last a family 6 daya
how long will 3 bushels last them 1
20. Divide f by ^.
1«< Sol. — The divisor is fifths ; and the dividend
reluced to fifths=Jx5=y fiftjis and y units
of any kind, divided by 2 units of the same kind
=J of Y' = '^"', which may be got by multi-
plying I by |.
2nd aSW.-— | = V^ and |=/(j ; but 15 units of any
kind divided by 8 units of the same kind— ^'g^
.-. j (or Ag) divided by ? (or .«o)-= '/ (o»" |X J).
21- How many times is '| contained in | ? | in | ?
8
m J? 1
in
1 I
^ Un^^l
,-\t in 4 i ?
g Xli g r g XX. yj. X ,-^ XXX ^ 3
22- How many bags of oats can be bought for | dol-
lars, at \ of a dollar a bag %
Anahjsis. — As nnmy bags can be bought for -^ dol-
lars, as ^ of a dollar is contained times in |
dollars ; § is contained in |, Jg^ times=l^ :
therefore 1^ bags of oats can be I ought for |
dollars.
23 If '<^ mwn can mow J of an acre in an hour, how
long will it take liiin to mow g of an acre ?
24. At i of a dollar each, how many knives can be
bought for \\ dollars?
25. If a horse can run g of a mile in I minute, how
manv minutes would he require to run | of a mile ?
26- If John saves | of a dollar, and James | of a dol-
lar in a week, how long, at that rate, would it take them
to save 1^ dollars ?
27- How many yards of cloth at $1J a yard can be
bought for $2J ?
28. It »^ horse eat | of a peck of oats in a day, how
long will 3J pecks last him ?
DIVISION.
73
JOW
be
be
lOW
29. A yacht was hired for 10^ dolhirs a day; if each
person paid § of a dollar, how many persons were there
in the company ? If each were charged | of a dollar,
how many then in the company ?
30- In order to raise 6| dollars, how many contribu-
tors must there be at /^j of a dollar? at | of a dollar
each 1
31. If ft miller takes for toll, /'^ of a bushel of every
bushel oi wheat that he grinds, how many bushels must
he grind, that he may receive 9| bushels ]
32- If tine cars run | of a mile a minute, how long
will it take them to run 25 miles 1
33- If a nian walks | of a mile in | of an hour, how
long will it take him to walk 12 miles'?
34. A boy having 12 quarts of berries, sold § of them
for$.^ : what was that a quaitl
35. Amongst how many boys can you divide | of I'l
oianges, if you give | of ^ of an orange to each ]
36. If a turkey cost ^1|, how many can be bought
foi- $1) ?
37. IIow many times will 4 J gallons of oil fdl a lamp
tliat hohls J of 5 of 1 gallon ]
38- If a stage run 24| miles in 3 J hours, how far does
it run in one hour]
39. F'ought I of 4 J cords of wood for J of 54 dollars,
what did it cost a cord }
40. Divide J of i' of 14 by ? of 3 J.
41- A farmer divided 213] acres of land among his
tluee sons ; to the first he gave i of it, and the remainder
he divided equally between the other two : how many acres
did each receive ]
42. A farmer bought g of a farm which was J of what
6
74
MBNTAL ARITHMETIC.
his neighbor bought : what part of a farm did his neigh-
bor buy 1
48. Divide $42 in dollars, half dollars, and quarter
dollars, and of each an equal number 1
44. H(^w many gallons, quarts and pints, and iif each
an equal number, are tiiere in 44 gallons t
45" A man met some beggars, giving to the women
20 cents each, the bo}'S 10 cents each, the girls 5 cents
each. He gave to all $3.50 : how many beggars were
there ?
Examples. — 26.
1. What part of 3 is 11 of 3 is 2 1
Sol—1 is J of 3. -.2 is f of 3.
2. What part of 7 is n of 6 is 2 1 of 9 is 7 ?
3. What part of 8 units of any kind is 9 units of tho
saniokind'? of 11 is51 of 12 is 4?
4. What part of 5 is 1 1
iSol. — 3=73 and |=,Rt, because 1 twelfth is \ cf
8 twelfths.*. 9 twelfths iu the | o< 8 twelths.
5. What part of | is ^ ? of | is J '{ of J is f ? What
of i is A ?
I) 19
of J
is 1 1
part of ? is I ?
6. What part of 5 i-j J ? of 3J is 3 i of 4| is 6 ?
7. What part of ;<„ is 6 1 of | is 4 1 of | is 3| '♦
8. What part of a foot is 4 inches 1 3J inches 1 and
9 1 inches 1
9. What part of a mile is 140 rodnl is 160 rods '»
10- What part of an hour is 15 minutes 1 is 40 niin. •
11. What part of 10 miles is | of 8 miles 1 is 2s. Qd. of
£2.58. 1
12. A man having $12, gave $2 J for a hat and $3 J
i'or a pair of boots : what part of his money did he iim'i
g
M
til
h
o
t;
Y
n
h
n
ii
DIVISION.
75
13. If the interest on $100 is $4, what part of the
principal is the interest 1
14. If a man buys a horso for $60, and sells him for
$75, what part of his outlay is he gaining 1
15. If a vessel sail 60 miles in 5 hours, what part of
240 miles will she sail in 9 hours 1
16. One man walks 4| miles while another walks d| :
what part of the distance that the first walks does the
second walk?
17. What part of 3 J acres is J of 4 J acres 1 of 1^
gallons is 1 qt. 1 pt. 1
18. A merchant gained on a hogshead of sugar ^ of
46 1 dollars, which was J of two times what it cost him :
whiEkt did it cost him 1 what part of the cost was the
gaini
19. John earns 9 cents as often as James earns 12 ;
when John has earned 63 cents, how much has James
earned ]
20. Two men start from different points and travel
towards each other, the first travels 5 miles while the
other travels 3 miles, and when they meet the first has
travelled 20 miles more than the other : how far apart
were they when they started 1
21. ii^ 4 men can do a piece of work in 8 days, how
many men can do a piece of work 6 times as great in
half of the time 1
22. If 5 horses eat 1^ tons of hay in 1 month, how
many tons will six horses eat in 2| months 1
28. How many days will it take 5 men to earn $11|,
if 3 men earn $^ in ^ of a day t
24. Keduce 1 year and 4 months to the fraction of a
year.
76
MENTAL ARITHMETIC.
.^J
!l^'
T*i;i
25' Reduce 1 year and 8 months to the fraction of a
year.
26' Reduce 2 years and 5 months to the fraction of a
year. 3 years and 10 months to the fraction of a year.
27. 5 years 9 months to the fraction of a year. 4
yens and 8 months to the fraction of a year
28. Reduce 5 years 7 months to the fraction of a
year,
29. Reduce 9 years 11 months to the fraction of a
year.
30. Reduce 2 years 4 months 15 days to the frac
tion of a year of 360 days.
81. Reduce 4 years 6 months G days to the fraction
of a year ?
32. Reduce 5 years 9 months and 18 days to the
fraction of a year.
33. What part of a barrel of potatoes at $6| for 2
bai rels, can be bought for $3| 1
34. A carter drew 13| tons of freight, taking 1| ton
at a load : how many loads did he draw 1
35. If $100 gain $6 in one year, what part of the
principal is the interest ? If the time is a year and 4
months, what part of the principal would be the in-
terest 1
36. If $100 stock be bought for $98 in money, what
fraction of your outlay are you gaining, if the dividends
are 8 per cent 1
37. When mackerel are at $9J a barrel, how much
can be bought for $2 J ?
38. If § of 9 were 5, what would J of 18 be I
39. If tho principal is Sl4 and the interest $4, what
fraction of the principal represents the interest.
m
DTVTSTOK.
77
40. If a merchant buys clover seed at $6 a bushel
and sells it at $8, what traction is bis gain of his outlay,
and what would be his gain on $100 outlay ]
41- If 3 be made 4, what should 100 be made to be
in the same ratio ]
42. If a merchant buys tea at 60cts. a pound and sells
it at 80cts. a pound, what fraction of his outlay is his
gain, and what is his gain on $100 outlay 1
43- If a broker buys $100 stock for $75 cash, the
stock yielding 5 per cent., what fraction of his outlay is
his gain, and what is his gain on $2000 outlay ]
44 What fraction is | of •?, ? of | is .^j 1 of f is j\ I
45. If I of a certain numler is J of | of | of 8, what
is the number 1
Section V.— Analysis.
Examples — 27.
1. If 4 bbls. of apples cost $14|, what will -^\ of a bbl.
cost]
Sol— 4: bbls. cost $^J2-, 1 costs \ of -\2^j.r -^ _8^
costs Y^j of ^^=$1J.
2. What will three bushels of peas cost, if Ig bushels
cost $5 1 1
3- When 2 1 bushels of wheat cost $6 J, what will |
bushels cost 'i
4. If 5J yds. of silk cost $7§, what will 2 J yds. cost]
5* If I of an orange cost S of a cent, what will '2
oranges cost 1
6. If 2 yds. of satin cost $4|, what will 5 J ytls. cost ?
7. If a man can cut 8 cords of wood in J of a week,
how much can he cut in 2^ weeks ?
78
MENTAL AHITHMETIC.
\f
1; •
m^.
jtiS
8. Tf a man can walk 7 miles in 2 hours, how far can
he walk in 3 days, by walking 10 hours a day t
0. If 3J- barrels of apples cost $5 J, wkat will J barrel
C08t. 1
10. A carpenter worked 11§ days, and after paying
his board and other expenses with | of his earnings, had
|20 left ; hor much did he receive a day.
11. If 3 mer. incur an expense of $27 1, how much
more than ^7 J must each pay.
12. If 3 pair of socka cost $j'q, how many pairs can
be bought for $2 y''^'?
13. If 8 men can build a wall in 5f days, in how many
days could 5 men do it 1
14. If 9 men can perform a piece of work in 9 J days,
how long will 7 men take to do it"?
15. -V is three score years and ton ; if ^ of B's age i^
4 of O's
and I of C's is j^g of A's, how 'Aid is B 1
16. If to J of the number of sheep in a flock you add
70, you will double their number, how many sheep are
there in the flock 1
17. Jamea is 18 years old, and J of his age is § of
half his brother's age : how old is his brother 1
18. If from a certain number increased by 7 you sub-
tract 3, and multiply the remainder by J. of 20, the pro-
duct is 80 : what is the number 1
19. If a pole 6 feet long casts a shadow of 6f feet,
what will be the length of the shadow a pole of 9 feet
will cast?
20- If 6 gold pens cost $7}, what will 7 gold pens
ooitl
21* What is the length of a polo, the shadow of which
is 10 feet long, at the same time a pole 5 J feet long casts
» shallow of 11 feet 1
Willi
can
ANAT.ySIS.
7d
22- If a ro«n earns $10J in 4 days, how many dollars
will he earn in 14 days t
23. If J of 9 be 6, what will a fifth of twenty be ]
24. If J of 10 be 3, what will i of 20 be ?
26. If 8 yards of ribbon coat $1 J, how in^ny yards
can be bought for ^3 J 1
26. If 2 apples are worth 1 orange, 2 pears are wortli
3 apples, how many poars are worth 6 oranges 1 '
27. If i be 9, what will 7 be ]
28. How many yards of cloth f of a yard wide are
equal to 12 yards | of a yard wide ]
29. If 840 exceed by $10 J of f of what I gained
by the sale of a house and lot, how much did I gain ]
30- If J of a yard of cloth coat $§, what will 3 of a
yard cost ^
31 A man being asked his age, said that were he 3
times as old. j*j of his age would be 8 years . how old
was he 1
32. If } of A's age is § of B's, and f of B's age is J of
O's, how old are A and B, if C is 81 years old ?
Examples. — 2b. ■.
1. 7 is § of what number 1
Sol. — § of some number is 7, 1 third is J, and 3
thirds, or the whole is 3 times J, or ^^^=104.
2- 6 is J of what number 1
3. 25 is I of what number 1
4. 14 is 3 of what number 'i
5. 9 is I of what number 1
6. f of 20 is I of what number 9
7. 13 is I of what number 1
8. 15| is j( of what number 1
ji
80
MENTAL ARITHMETIC.
9- I is I of what number ]
10
f is
jAj of what number]
11. I of I is § of what number 1
12: Jamt 3 gave 9 cents for a slate which was | of his
money : how UAUch liad he 1
13. A man bought a horse for $90 which was Ij of his
money : hovv much had he]
14. A gentleman was married at 'M) years of age
which was h of ^^> of his wife's age : how old was the
wife 1
15- TvYO men agreed to build a wall, one man built. 15
rods, which was ^ of what the other built : how manv
did the secon 1 build, nnd what was the Iciigth of the wall 1
16. A man sold 3i cords of wood at $'My a cord, which
was I of what he received for a ton of hay : how much
did he receive for the hay]
17. Taid $1 for a neck tie, wViich was ^ of what nij
vest cost : what was the cost of the vest ]
18. A son's age is 20 years, and it is f.^ of the father's
ase : what is the age of the father ]
19. 1'^ is I of how many times 7 ?
Sol. — g of some number is 1.5, 1 -eighth is 3, and
8-eighths is 8 times 3 or 24, 24 is 3^ times 7.
20- 49 is J of how many times 8 ]
21. 3G is :j of how many times C ]
22- ^^^ If* ii t>* l^O'^^ many times 5 ]
23. 28 is 5 of how many times 5 ]
24. s is 7 of how many times 31
26
TO
is 5 of how nijtny times ^ ]
31 .'
26. 1^ is V% ^^' '^^^^ many times 2.^ 1
27. *5 of 21 is 3 of wliiit number ]
-SW.— ? of 21 is 15, 15 is I of 25
of 25.
^ of 21 is IJ
IS
ANALYSIS.
81
28. I of 27 is i of what numlipr ]
29- I of 04 is 1 of wliat imnibcr 1
30- 3>| is 4 of liovv many times U- 1
31- I of 36 is I of how many times 5 't
32- I of •'^6 is I of how many times 7 ?
33- I of 48 is I of how many times U?
34- /o ^^ '^■^ ^^ i ^^^ ^^*^^^' "^''"y times ?
35- I of .'iG is I of 3 tim(s wluit numher?
Sol--'^ »f 50 is L>4, 24 is f^ of 27, which is 3 times
9 : therefore!) is the reiiuired numher.
36. e of 54 is ^ of i) times wliat niimlter?
37- <7 of 81 is ,"", of 4- times wliat nnmherl
38. i of 36 is ;^ of 10 times what number'?
39. I of 108 is ,^n of 8 times wluit niimhor]
4:0- ^ of I is I of G times wliat number?
fS
Examples. — 29.
1. A horse cost f^SO, and i of the cost of the horse is
^ of four times the cost of the cari'iage : what was the
cost of tlu! cairiaiie ?
2- A watch cost $00 ; and f of the cost of the watch
is '^ of G tinies the cost of the chain : tlie ))rice of t!;o
chain is re<|nir(Ml.
3. A cow cost .f40, and ^ of this is '^ of 8 times the cost
of a sh(!ej) : what is the cost of a sln;ep'?
4. A house is worth ^12,00*), and ;^ of its value is J of
100 times the value of the lot : what is the value of tiia
lot?
5. What number added t(> 4 times ' of 21 'vill make
62 (
(J. The insurance of a house amounN'd to !?S0, and ]
of that is jj'0 of 3 times its value : wiiat is the value of the
house 1
»2
MENTAL ARITHMETIC.
\*&
. ^
I ' ^
7. A horse cost $180, and | of the cost of the h>rse is
§ of 6 times the coat of a cow : what was the cost of a
cow 1
8. The distmce from Montreal to Prescott is 112
miles, ^ of this distance is ^\ of 1 6 times the distance to
Kingston : what is the distance from Montreal to King-
ston, and from Kingston to Prescott 1
9. Kingston is 48 miles east of Belleville, and J of 11
times this distance is § of '^ times the distance between
Montreal and Cobonrg : what is the distance from Men.
treal to Cobourg 1
10. Port Hope is 33 miles from Whitby, which is A
die distance between Napanee and Cobourg, and -fj ol
this diistance is J of ;J of the distance from Montreal to
Ottawa, and of 60 miles more : what is the distance from
Montreal to Ottawa ?
11. A yard of a certain kind of cloth, 4 qnartei-^ « de,
is worth $4: what will a yard and a-half of the same
kind of cloth, 5 quarters wide, be worth ]
12. I of J of 60, is ^ of how many times f of § of 24 ^
13- A man had J of his money stolen from him ; the
thief was not caught until he had spent | of it, the re-
mainder, 50 dollars, was given back : how much monev
had he at first 1
14. A farmer dividing his farm between Iws two sohs
gave the elder 10 acres more than '4 of the whole, and the
younger the remainder, which was 22 acres more than ^
of the whole : how many acres in the farm 1
16. Bought a piano for $240, and 'j of tho cost wa?
I of what I received of 8 young ladies for the use of it
one year : how much did each young lady pay?
16. A shoemaker's tools are worth $80 ; ^ of this is
ANALYSIS.
83
vvde,
same
of 24^
; the
;lie re-
[() sohs
liul the
:>iiaii J
^t wa?
of it
bhis is
§ of J of 2 times the value of the stock : what is the
value of the stock 1
17. A farmer, after selling $200 worth of Ids stock,
finds that f of the remainder is equal to | of three times
the amount sold ! what was the value of his stock at
first?
18. Two boys comparing their money — one said he
had 60 cents, the other said, j'^ of your money is just
-j^Tj of 6 times my money : how many cents liad the latter ?
19. A boy being asked his age, said that 18 years was
2 years less than | times | of his age : how old was he'?
20. A man pays $600, and | of this is just § of J o^
twice his annual income : what is his annual income]
21. A gentleman is 64 years old, which is 2§ times
the age of his eldest son, and the eldest son is 2"^ times
as old as his youngest brothei- : whit is the ditleronce in
the ages of the two brothers ?
22- A and B engaged in play ; A lunl § as much
money as B, B gaining $16, which was | of 1^ times as
much as he commenced with : how much did he com-
mence with, and how much had he loft ?
23. A farmer gave § of 1 1 times his ready money for
a buggy, I of what was left for a harness, and had re*
maining $12 : what did he pay for the buggy ?
24- A does a piece of work in 4 days, and B in 5
days : in what time could both together do the work ?
Ans. — A in 1 day docs J, and B ^/.both do ^'o in
1 day, :v'j} in ^ day .'.the wholp in ''j/^r:::r2| days.
25 One tap (ills a cistern in 3 hours, another in 5
hours: in what time would both running together liSl it?
26. A does i( of a v^^ork in 4 days> when B comes to
help him, and they finish it in J days: how long would
each bv hintself take to do the work ?
84
MENTAL ARTTHMETTC.
I )
27. If A can do a pioce of work in 6 days, and B
^ as miicli again as A in a day, how long would B take
to comj)lot() tlie work after A liad worked 1^ days ?
28- ^ t;«H <lt> a piece of work in 6 hoiirn, and li in 8
hours : how long would B take to finish the woik after
A hfid worked 3 hours ?
29- A do(?s ^ of a piece of work in 16 days, h(! then
calls in B, and they do the work in 4 days more : how
long would B take to do the work 1
30- A does a jaeceof work in 3 hours, which is twice
the time B and C together take to do it, and A and (J
could do the work in 1^ hours : how long would B alone
take to do if?
31. A, B and C can dig a ditch in 20 days, A and B
in 40 days, and A and C in 30 days : how long would
each take to do it 'i
32- One »hoeui8,ker makes a pair of boots in § of a
day, another in | of a day : how many paii- can both
make in a 3.>\y 1
33- A, B and C can do a piece of work in T) days, B
and C can do it in 8 days ; in what time can A do it
alone t
34. A and B can do a jHece of work in 30 days, B
in 70 days : how much more of the wo» k does A do
than B 1
35- If ^^ "it^n can do u work in 10 days, how many
m«n could do 4 times as much in one-fifth of the time?
36. If a banel of flour suj)ply 4 persons T) weeks, how
much v'ill su|)ply 3 persors 'ij weeks ?
37' ^f 3 furnaces consume 1 2^ tons of coal in 2o days,
how long will 8^ tons last 5 furnaces?
38- A and I? can do a piece of work in 1 !j days, A and
ANALYSIS.
85
of a
both
s, B
ulo it
lA ao
Lany
lime '?
how
C in IJ clays, and B and C in 2| day« : in what time
could B alone do it 1
39- A can do a piece of work in 3 dayx, B in 4, and
C in 6. A leaves off h a day befoio the work is finished,
and B | of a day, C finishes the work : how many days
did A, Band C work?
40- A crew can row down a stream a certain distance
in 30 minutes and back again in 32, what fraction of the
distance is the rate of tlio stream an h ur ^ H the rate
of the stream be half a mile an hour, wnat will the dis-
tance be 1
41. A crew rowed down stream 7 miles iii 30 minutes
and up stream the same disffv^oein 35 minutes : find the
rate of the stream per hour.
42- A crew can row down a stream in 20 minutes and
back again in 30 : find the distance, the rate of the
stream being IJ miles an hour.
CHAPTER Til.
REDUCTION AND COMPOUND RULES.
Section i.—Currency.
EXAMPLKS.— 30. , '
1. How many farthings in 1 half penny ? in 2 pence ?
in 3 pence 'J in i)(;nct>'? in 5^ pence I in 7^ pence I
2. How nuiny \)ence in 5 cents 1 in 101 in 20 1
in 25 1
3. How manv f) Cf nt pieces make a dollar ] how
many K) "J how many 201
4. How many cents in 3 pence? in 6d? in 9 j)enee1
in 12 pence I iu 30 pence? in GO? in 15 pence?
86
MENTAL AHITHMETIC.
5. How many farthings in 8 pence ] in 12<U in 60d1
in 7J(1 1 in 9 Jd 1
6. TTow mriny shillings in $1 1 in $2 1 in $4 ? in
$10 ? in ene-fifth of a dollar ? in S-fifths 1 in 4-fifth8 1
7. How many sixpences in 1 shilling? in 2 shillings 1
in 3 shillings 1 in 4s. 6d1 in 7s. 9d 1 in 3s. lldl
8. How many 5 cent pieces are «qual in ralue to 60
pence? 12 pence? 10 shillings? 7s. 6d ?
9. How many dollars in 1 pound? in £2? in £5 ?
inX112.s? in £2 138?
I
i'i^
^ii
English . Money.
EXAMFLBS. 31.
1. How many farthings in 1 penny? in 2 pence?
in 6 pence? in 20 pence? in 12 pence? in 5jd ! in
6^d? in 7Jd? in lOJd?
2. How many pence in 4 farthings? in 12 farthings?
in 30 farthings? in 48 farthings? in 63? in 50 ? in
47?
3. How many y)ence in 1 shilling? in 4 shillings I
in 7 shillings? in 10 shillings? in 20 shillings? in
4s. 6d? in7s. 9d? in 8s. lid?
4. How many shillings in 12 pence? in 48 pence ?
in 3G pence ? in 60 pence ? in 240 ? in 50d ? in 69d I
. How man
•y
1'
in £10? iu£l 10a? inXlGa? ini'3 15s? in £'2
19s ?
6. How u»any pounds in 20 shillings? in 40s? In
80h ? in 1 20s ? in 30s ? in 49s ? in G7s ? in 75s ?
7. How uian^ pence in 4s. Gd ? iu 5s Cn\ \ in ICs.
3d{ in I2s. Gd? iu XI VU. Gd'l
ENGLISH MONEY.
87
8- How many shillings in £1 Gs 1 in £3 9s 1 in £6
lOsI
9. At 3 Jcl a pound, how many shillings will 24 pounds
if 1 ice cost 1
10- At 5 shillings and 6 pence a yard, how many
i)Ouiuls will 16 yards of carpeting cost?
11. How many crowns in £1 ] in £5? in £10 5s]
in£ll lOsI
12- In reducing £3 10 shillings to shillings, which is
Lhe multiplier, the 3 or the 20 ? Give reasons for your
inswer.
UNITED STATES MONEY.
Examples. — 32.
1. How many mills are there in 8 cents 1 in 1 2 cts?
in 15 cts. 1
2. How many cents are there in 60 mills 1 in 80
mills 1 in 40 mills ? in 45 mills 1 in 57 mills 1
3' How many cents in one dime 1 in 3 dimes K in 7
dimes? inHdiujes?
4. How many dimes in 10 cents] in 20 cents? in
13 cents 1 in 90 cents % in 85 cents 1
6. How many dimes in $1 ? in $3 1 in |7 ? in $8 ?
in 2-lifths of a dollar ? in 3-tifths ] in 4-fifth8 1
6. How many dolhirs in 1 eagle 1 in 2 eagles? in <
eagles? in 11 eagles?
7. How many eagles in 10 doUai-s? in 20 dollars? in
70 dollars? in 120 dollars?
8. How many dollars in 1©0 cents? in 200 cents? in
700 cents? in 125 cents? in 235? in 510?
9> Bought 20 yards of cloth at one-half dollar a yard :
liow many dollars di<l I pay ?
\ir
88
MENTAL ARITHMETIC.
10- How many yards • f cloth at 6 dimes a yard cap
you buy for 2 eagles 1
11. How many cents in one-half dollar ? in one-
fifth of a dollar 1 in 3-tifths 1 in 7-tenths ? in 9-tenths 1
' . 'i
1^ l\
'■■».■ r
fir'
m
Section II.
MEASURES OF WEIGHT— TROY WEIGHT.
Examples. — 33.
1. How many grains in one penny-weight 1 in 2
penny-weights 1 in 4 penny-weights 1 in 3 dwt. 9 gr. ?
in 2 dwt. 8 gr. ?
2. How many penny-weights in 24 grains 1 in 48
grains'? in 96 grains? in 60 grains? in 75 grains'?
3- How many penny-weights in 1 ounce 1 in 2 ouncesi
in f) ounces? in 2 oz. 10 dwt. ? in 3 oz. 15 dwt. ? in 7
oz. 13 dwt. ?
4- How many ounces in 20 penny-weights? in 40
pen ny~ weigh ts ? in 100 penny-weights?
5- How many ounces in 1 pound ? in 2 lb. ? in 5 lb. ^
in 9 lb. ? in 1 2 lb. ? in 3 lb. 8 oz. ? in 4 lb. 9 oz ?
6 How many pounds in 12 ounces? in 36 ounces?
in 60 ounces ? in 144 ounces ? in 65 oz. ? in 90 oz. ?
7. How many penny-weights in 2 oz. 10 dwt ?
3. In 5 lb. 7 "Z., how many ounces ?
9- Find the value of 4 oz. of gold, if 3 dwt. ar^^ worth 18
shillings ?
10- In 1 pound how many grains ?
11. How many spoons, weighing 35 dwt. each, can be
made out of 1 lb. 2 oz. of silver ?
12- A jeweller boaght 7 dwt. of pure gold, 9 dwt. of
MEASURES OF WEIGHT. — APOTHECARIES' WBfOHT. S9
can
ices 1
this
gold coin, and 16 dwt. of silver : how many ounces did ho
buy altogether ]
13- If 10 dwt. of silver are worth 70 cents, find the
value of 3 pounds of silver.
Reduction.—Apothecaries' Weight.
Examples. — 34.
1. How many scruples in 5 oz? in 1 lb.1
2- In 95 gr. how many drams'? in 4 lb. 5 oz., how
manv drams]
3. How many grains in 3 dr. 5 scl
4- Mow many grains in 1 oz. ] in 2 ounces 1 in 5
ounrt'f
5- How many drama will it take for 20 powders, each
c<^)ntaining 20 grains'?
6. How many powdeis of 1^ sc. each can be put up
from an ounce of soda '?
7- If a druggist chaiges 50 cents for ten powders con-
taining 15 gr. each, at what rate is that [)er ounce %
8- A druggist charges 8 cents for 4 drams of opium :
what rate is that per pound '?
9. How many scruples, drams and ounces, and of each
an equal number, are there in 7 pounds 1
10- Two-thirds of 18 scruples of a certain drug cost
30 cents : what will 4-sevenths of 1 4 pounds cost 1
In be
t. of
Examples. — 35.
1. How many drams in 4 oz.*} in 8 oz.1 in 10 oz.1
in 5oz, 10 \i.% in 7 oz. 12 dr.?
2. How many ounces in 2 pounds 1 in 5 pounds ? in
7
\^^
90
MENTAL AltlTUMETlC.
IM<
Ki
»|
■ i' 5
Hi -^
32 drams 1 in 3 lb. 5 oz.] in 4 lb. 9 oz.l in 2 lb. 11
0Z.1
3. How many pounds in 2 quarters 1 in 3 quarters ?
In 4 quarters] in 48 ounces'? in 96 ounces) in 2 qr.
12 lb.1 in 3 qr. 15 lb.?
4. How many hundred-weight in 4 quarters] in 8
quarters] in 16 quarters] in 20 quarters]
6. How many hundred-weight in 2 tons ] in 3 tons 1
In 2,000 lb. ] in 4,000 lb. ] in 2 tons 3 cwt.
6. How many lbs. in 1 cwt. 2 qr. 13 lb. 1
7* How much will 2 cwt. 1 qr. of beef cost at 10 cents
a pound ]
8. How many four-ounce weights can be made out of
2J pounds f brass ]
9. How many 7 1-. packages of sugar can a grocer put
up from 2 cwt] from 2 qr. 13 lb.]
10. Bought 1 cwt. of meat for $17.50 ; sold it at 22
cents a pound : what was the whole selling price] What
was the i)rofit ]
11. I gave 3 cwt. 2 qr. t f hay worth $20 a ton, for
butter worth 25 cents a pound : how much butter did I
get]
m
Section III —Measures of Length, Surface,
and Volume.
I, '
ft'
ii
Examples. — 36.
LONG MEASURE.
1. Mow many inches in 1 foot ] in 2 ft. ] in 5 ft. ]
in 2 ft. 6 in. ] in 5 ft. 1 1 in. ] in 8 ft. 4 in ]
2. If 4 inches make a hand, what is the height in feet
of a horse 15 hands high ]
m
CLO'fH MEASUiiE.
n
8- How many feet in a yard ? How many in a fathom 1
in 2 yds. 2 ft. t in 12 yds. 1 ft.1
4- How many times will a stick 5 yards long be con-
tained in a mile ?
5. How many yards in 4 furlongs ? in 7 fur. 1 in
5280 feet? in 272 feet 1
6. How many chains in a mile? in 160 rods] in 6
furlongs'? in 136 in., how many yards 1
7. How many inches in 3 yds. 2 ft. 10 inches ?
8- What will it cost to dig a ditch a quarter of a mile
long, at 50 cents a rod 1
9. The roads in Ontario are 1 chain wide, what is the
width in rods 1
10- If it takes 5 minutes to travel a furlong, how long
will it take to travel a mile 1
11. A man travels 50 rods in 5 minutes, how long will
it take him to travel one mile 1
12. How many steps, each 2 feet long, will a boy take
in walking 110 yards 1
Cloth Measure.
Examples. — 37.
1. How many nails in 2 quarters'! in 6 qrs. 1 in 18
inches 1 in 24 inches 1
2. How many quarters in 4 yards 1 in 3 yards 1 in
12 yards 1 in 5 yds. 2 qrs. ] in 6 yds. 3 qrs. 1
3. What cost 10 yards of velvet, at $10 an ell, Eiig-
Ush ]
4. What will 18 yards of cloth cost, at $12 a French
ein
5. How many dresses each containing 12 Flemish
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Hiotographic
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92
MENTAL ARITHMETIC.
ells can be made from a piece of cloth containing 18
French ells 1 ■
6. How many nails in three yds. 3 qrs. 3 nails ] in 75
nails, how many yd«. &c. 1
7. How many dresses each containing 10 yds. can be
made from a piece of cloth containing 40 ells, English 1
8. A coat requires 3 yds. of cloth : how many coats
can be cut from 40 Flemish ells 1
9. tn 7 yds. 2 qrs., hovr many E. B. 1 how many
E. Fr. % how many E. Fl. i
10. Tf 5 yards of cloth cost 7 dollars, how many yards
can be bought for 56 dollars 1
u
m
Square Measure
Examples. — 38.
1. A black-board is 4 feet wide and 12 feet long : how
many square feet of fu-'face has the board 1
2. A slate has a surface of 80 sq. in., it is 8 in. wide :
find its length.
8. How many sq in. m one sixth of a sq. ft. 1 in
3-sixths1 in 5- sixths)
4* How many square inches in a board 4 inches long
and one inch wide 1 in 4 inches long and 2 in. wide 1 in
4 inches long and 3 inches widel
• 5. A board is 3 yds. long and ono yard wide : how
many square yards in it 1
6. How many square feet in 3 square yards 1 in 8
square yards i
7. A yard of carpet is 3 ft. long and 3 ft. wide : how
many square feet in it 1
CUBIC MEASURE.
93
coats
8. How many square feet in a yard of cloth 2 feet
wide ? in 5 ft. wide 1
9- How many square feet in a room 12 ft. by 15 ft. 1
how many sq. rods in 1 ac. 20 rd. or land 1
10. How many yards of caipefc 2 ft. wide will bo re-
quited to cover the floor ot tho above room 1
Cubic Measure*
m
long
in
how
in 8
how
Examples. - 39.
1. How maiiV cubic feet in one ninth of a cubic vard ?
in 4-ninths ? in 7-ninths 'i
2. How many cubic feet in 3 cubic yardi? 9 cubic
feet?
3. A brick is 2 by 4 by 8 inches • find its solidity ?
4. How many cubic feet in i cubic yard i in 3 oubic
yards ? in 4 cubic yards 'I
6- How many cubic yards in 27 cubic feet? in 81
cubic feet? in 100 cubic feet'f
6. How many cubic feet in 2 tons of timber 'i in 5
tons?
7. How many cords in 32 cord feet? in 24 cord feet?
in 80 cord feet ?
8* How many cords in a pile of wood 24 het long. 4
feet wide, and 4 feet high ?
9. How many loads of earth, each 1 cubic yard, must
be removed in digging a cellar 21 feet long, 18 feet wide,
and 6 feet deep ?
10. How many cubic feet are in a stick of timber 16
inches wide, 9 inches thick, and 21 feet long 1
94
MENTAL ARITHMETIO.
Liquid Measure
Examples. — 40.
1. How many gills in 4 pints? in 8 pints? in 12
pints? in 11 pints, 2 gills? in 13 pints 3 gills?
2. How many pints in 16 gills? in 32 gills? in 36
gills? in 47 gills?
8- How many quaHs in 3 gallons ? in 8 gallons ? in
15 gallons? in 10 gallons .^ quarts] in 13 gallons 2
quarts 1
4. How many gallons in a pipe ? in 1 hogshead ? in
1 tun ? in 4 barrels ? in 6 barrels ?
6. If a tumbler hold half a pint, how many times will
1 gallon of water fill it ?
6 Thought 5 gallons of oil for $10, what is the price
per quart ?
7. Bought a pint of milk for 4 cents, at what rate is
that per gallon ?
8. 3 pints of molasses having been sold out of 2 gal-
lons, what is the remainder worth at 80 cents a gallon ?
9. A merchaQt bought a hogshead of molasses for $40
and sold it at the rate of 30 cents for 6 pints, how much
did he gain by the bargain ?
10. How many pint bottles will be required to hold 4
gal. 2 qts. of tomato catsup ?
Drr Measure
Examples. — 41,
1. How many pints in 2 quarts? in 5 quarts? in 7
quarts ? In 8 qts. 1 pt. ? in 9 qts. 1 pt. ?
2- How many quarts in 1 peck ? in 2 pecks ? in 5
pecks 1 in 4 pks. 3 qts. ? in 5 pks. 2 qts. ?
TIME TABLE.
95
in 7
in 5
8- How many pints in 1 peck 1 in 3 pecks'? in 7
pocks 1 in 2 pks. 1 gal. 2 qts. ?
4. How many pints in 3 bushels, 3 pkSo 3 qts. 1
6. If a chaldron of coal costs ^12, what is the price per
bushel '?
6. How many baskets, holding 2J pecks each; will 5
bushels of apples fill ?
7. If a horse is fed 6 quarts of oats a day., how long
will it take him to consume 6 bushels 1
8. If 8 pints of strawberries cost 32 oents, what will 1
bushel cost at the same rate ?
9. A sold to B 1 bushel and 1 peck of currantSj at 2
cents a pint, and received in payment 1 bushel of rasp-
berries at 4 cents a pint : who pays the difference, and
how much ?
10. A farmer sold 2 bushels 3 pecks of clover soed at
$6 a bushel, receiving in payment 5 bushels 2 pecks of
wheat at $1.50 : what is yet due him 1
11. A boy gathered 3 bushels 4 quarts of chestnur« :
how many times would they till a pint measure 1
TIME TABLE-
EXAMPLES. —42.
1. How many seconds in 2minute8l in 4 minutes?
2. How many minutes in 2 hours 1 in 4 hours 'i
in 1 20 seconds 1
8. How many hours in 2 days? in 4 days? in 360
minutes 1 in 3,600 seconds ?
4. How many days from 1st January to the 17th of
March 1 from 3rd February to Ist July?
5' How many months from August 9th to November
J I
\m
I til i Hi
ihm
mi
lis I
ii
■ »r !, ,.
^ii ■
y.t:;
96
MENTAL ARITHMETIC.
9th t from June 2iivl to November 2nd 1 from April 6th
to October 6th 1
6. Which years are lea]) ywirs? Wliicli of the months
have 31 Jays? How many clays has 5th month] the
11th month 1
7. What are the natural divisions of time 1 how are
the year and day divided 1
8- If a man can do a piece f w )rk in 30 minutes, how
many hours would it take him to do 15 times as much 1
9. A can d>> a piece of work in 20 minutes: how many
hours would it take him to <lo 24 times as much 1
10- How many months an ' days from the 2nd of
January to the 10th September 1
11. If a man earns 125 cents in 6 hoius, how much
■will he earn in 12 days of 10 hours each 1
12. If a man earns $12 a week, and pays for expenses
$12 per month of four weeks, how much will he save in
40 weeks 1
13. A man walks one-fourth of a mile in 5 min tes,
how long will it take him to walk 10 miles?
14. If 12 men c»in do a work in 1 hour 45 minutes,
how long would it take 1 man] 2 in^n ? b men 1
m
i'S"
MISCELLANEOUS TABLE.
EXAMPI.KS.— 4.'i.
1. How many units in a dozen 1 in 4 dozen 1
2. What is the cost of 4 dozen of peaches at 2 cents a
piece 1
8. What cost 1 gross of writing bor>ks at 10 cts. each ]
4. How many score in 60 1 in 80 1 in 100 ]
6. What cost a ream of paper at 10 cents a quire 1 1
gross of pens at 5 cents a dozc^n 1
COMBOUND RULES.
97
111 6th
lonths
] the
)w are
s, how
nnich ]
many
Slid of
much
(penses
ijive in
in tes,
inutes,
lents a
each ]
] I
6- At $11 a hundred-weight, what costs 1 barrel .f
beef 1 3 barrels of beef 1
7. Bouglit a barrel of pork at 12 cents a pound, an*
sold it at $15 a cwt.: how much was made by the salel
8. Bought wheat at 3 cents a pound, and sol I it at $2
a bushel : how much was made on a bushel 1
9. Paid 6 cents a pound for flour : how much was that
a barrel 1
10> Bought 170 lbs. of oats : what was the cost at 62
cents a bushel 1
11. Bought 300 lbs. of wheat at 2 cents a pound, and
sold it at $1.50 a bushel : how much lid I gaini
Compound Rules.
Examples. — 44.
1. Add 7 bushels 2 pks. and 8 bushels 3 pks t
2- A grocer sold on Monday 5 gals. 2 qts. of m lasses ;
on Tuesday, 2 gals. 2 qts., and on Wednesday 4 gals. 3
qts. : how much did he sell in the three lays 1
8. How many acres are there in two fields, one con-
t lining 9 acs. 70 rds., the other 8 acs. 9i rds. 1
4. A fore quarter of lamb weighed 7 lbs. 9 oz., and a
hind quarter 8 ios. 12 oz. : how much did both quarters
weigh 1
6. Find the sum of 3 yds. 2 ft. 9 in., and 4 yds. 2 ft.
6 inches.
6. A farmer sowed 1 bushel 4 qts. of clover-seed, and
1 bushel 2 pks. 3 qts. of timothy-seed : how much did he
sow of both kinds ?
7. Ad! together 50 cubic yds. 13 cubic ft. an.'' 10
cubic yds. 17 cubic ft. 1
98
MENTAL ARITHMETIC.
8. A coal dealer delivered 12 tons 10 cwt. of coal to
one man, and 8 tons 15 cwt. to another : find the whole
quantity sold to these two men.
9- A man had 9 bushels 3 pks. of potatoes, he sold 5
bushels 2 pks.: what quantity had he left?
10« A grocer had 1 3 lbs. 8 oz. of castile soap, he sokl
8 lbs. 10 oz. : how much Lad he left?
11. From 16 ft. 5 in. take 11 feet 7 inches?
12. From a cask containing 16 gals. 2 qts. of vinegar,
10 gals. 3 qts. were drawn : how much was left ?
13. I have 9 weeks vacation and 6 weeks 4 davs have
already passed : how much of it is left ?
14- A crock with the butter in it weighs 34 lbs. 8 oz.,
the crock alone weighs 7 lbs. 12 oz. : how much butter
does it hold ?
16. From a piece of land containing 7 acres, 3 acres
70 sq. rods were sol I : how much is left?
16- It takes one hour 45 minutes to go by rail from
Toronto to Hamilton, and 3 hours and 20 minutes to go
by b at : how much time do I save by rail ?
't'.,
EXAMPL/S. — 45.
1. How much tea will it take to fill 6 canisters, each
containing 1 lb. 8 oz.
2. If a horse eats 2 pks. 6 qts. of oats in 2 days, how
much will lafit him 14 days?
3. Multii)ly 3 qts. 1 pk. by 10.
4. It takes 7 yds. 3 qrs. of cloth to make one suit of
clothes : how much will be i-equired for 5 suits ?
5. If S cows eat 3 tons 18 cwt. of hay during the
winter, how much would keep 6 cows ?
oal to
whole
sold 5
le soUl
ncgjir,
-^s have
1. 8 07..,
butter
I acres
lil from
to go
I, each
J, how
I VI I
I or
t of
the
COMPOUlfD RULES.
^
6- If it requires 2 bushels 1 pk. 2 qt«. of wheat to sow
an acre of land, how much will be required for 5 acres t
7. Jenni. is 9 years 7 months ohl, and her mother is
4 times as old : find her mother's age "?
8. If a family use 8 dozen 9 eggs in 2 weeks, how
many dozen would they use in 8 weeks 1
9. Find the weight of 6 cubic feet of granite, when 1
foot Aveights 1 cwt. 1 qr. 15 lbs. 1
10- Multii)ly 2 gals. 1 qt. 1 pt. by 7.
11. If 1 1 bushels 3 pks. of grain sow 5 acres, how
much is required for 1 acre 1
12- Divide 21 miles 40 rds. by 4.
13- I^ a cooper can make 4 barrels in 5 hours, how
1 ng will it take him to make 3 barrels 1
14. Four bags weigh together 8 cwls. 2 qrs. 10 lbs :
what is the average weight of each bag 1
15. Divide 35 years 6 m nths byfi.
16. If one barrel h Ids ^ bushels 3 pks. of apples,
how many barrels will be required to h Jd 5 bushels
2 pecks 1
17- I divided 12**. 6d. among a number of boys, giving
each 2s. Qd. how many boys were there 1
18. A stationer sold 21 gross 7 dozen of copy books
in ^' days : find the average daily sales.
19. A farmer cut 15 tons 5 cwt of hay from 5 acres :
what, was the average per acre]
Examples. — 46.
1. What is the sum of 10s. 9d. and 3s. 6d.
2. What is the sum of £1 3s. 9d. and £5 9s. 4d.1
8. A boy throws 3 pks. 6 qts. of potatoes into a barrel
iMm
100
MEN TAL ARITHMETIC.
already containing 2 pks. 3 qts., how many bushels, &c.,
are then in the barrel 1
4- A grocer mixes three kinds of tea ; 5 lbs. 11 oz. of
the first kind, 6 lbs. 7 oz. of the second, and 3 lbs. 10 oz.
of the third : how many pounds in the mixture]
5. From a bin containing 10 bush. 3 pks. 1 qt. of oats,
a person took 3 bush. 9 pks. 6 qts., how much was left]
6. How much of my fence remains to be built, if there
is 15 rods 5 yds. to be built in all, and 11 rods 2 yds. 1
ft. is completed ]
7. What are the contents of 8 pitchers, if each hold 1
qt. 1 pt. 1 gim
8- If 1 nian can do a piece of work in 4 hours 45 min.,
how long will it take 6 such men to do itl
9. How many quart boxes will 2 pke. 6 qts. of bellies
fiin
10. How much must I pay for a I'iece of rand 10 rols
by 12, at the rate of $160 an acre ?
11. A school walk containing 240 sq. ft. is 12 ft.
wide, what is the length 1
12. How long must a box be that is 4 ft. wide and 3
ft. deep to contain 1 8 cubic feet 1
13- What will 3 gross and 6 buttons cost at 10 cents
a dozen]
14- At 40 cents a square foot, what will be the cost
of a piece of land 30 ft. by 50 ft.]
16- A boy observes that the fore wheel ot his little
wagon makes 55 revolutions more than the hind wheel
ill goinij 20 rods : what is the circumference of the ^e
wheel, that of the hind one being 3 feet ]
16. The difference between the product of two num-
bers and 9 is 171. One of the numbera is 12, what is
the other ]
COMPOUND l{L LKS.
101
17. A room 16 ft. long by 12 ft. wide costs $30 to
carpet it : what would it cost to carpet a rorm witli the
same carpet if it were one yard less in length, and 2 feet
less in Mridth 1
18. How many days of 6 hours each will it take 15
men to do a piece of work, if 5 men can do it in 9 days
of 10 hours eachi
19- How far will a locomotive, moving at the rate of
6 miles in 15 minutes, go in an hour and a half?
20. At 3 cents an inch, how much will 2 yards, 2
feet, 2 inches of silver wire cost ?
•51. How many bricks 9 inches by 4 will bo required
for the bottom of an oven 8 ft. by 6 ft. *?
22- The divisor and quotient are the same, the re-
mainder is 7 inches, which is tw • less than the divisor :
what is the dividend ?
28. A room 12 feet wide costs $30 to carpet it, but
if it had been 3 feet less in length it would only have
cost $24. Find the length of the room.
24. A owes B $25.20, and gives him on account
$17.75. If he pays the balance with a ten-dollar bill,
how much change should ^i j receive 1
26- Divide 20 bush. 7 pks. 3 qts. of potatoes into 10
equal heaps : how much have we in each heap 1
26. At $2 a square rod, a man paid $960 for a build-
ing lot : how much land did the lot contain 1
27' From a pile of wood containing 7 cords, a man
sold 4 loads, each 12 feet long, 4 feet wide, and 4 feet
high : find how much remained.
28- When peas are worth $1.60 a bushel, what will 6
quarts cbst ?
29. Find the cost of 12 lbs. 16 oz. of ham, at 16 cents
a pound.
102
MENTAL ARITHMETIC.
ing
80. It costs $20 to carpet a bedrocm with carpet cost
a square yanl ; the room is 12 feet wide: how
long is it 1
31- Find the cost 'f fencing, at .f 3 a r^d, a field which
is 60 rods long and 40 rods wide.
82- How much clover seed will be required to sow a
field of 8 acres, one acre requiring 1 peck, 5 qts 1
88' A stationor paid $3 a ream for paper, and sold it
at 27 cents a quire : find his gain on 5 reams.
84. A market woman took 6 dozen of eggs to mar-
ket, broke 9 of them, and sold the remainder at 28 cents
a dozen : how much did she receive?
85. What is the value of a load of oats weighing
1037 lbs. at 40 cents a bushel 1
86. Find the thickness of a block of stone containing
360 cubic feet, its length being 30 feet, and its width 4
feet.
87- A floor is 21 feet long and 6 yards wide : what
will be the cost of painting it, at 30 cents a square yard 1
88. What will be the cost of 17 cwt. 3 qi-s. 10 lbs. of
iron, at $60 per ton 1
89* How many bushels of wheat are there in a load
of 32 bags, each bag containing 92 pounds 1
40. How many pint ai^d quart bottles, of each an equal
number, can be filled from 19 gals. 3 qts. 1 pt. of cur rant
wine]
iJUESTIONS FOR EXAMINATIONS,
lOS
CHAPTEK IV.
)S. of
load
iqual
rant
Questions for Examinations.
(1)
1. John had 26 marbles, he <von 32, and then sold
40 : how many had he left?
2. A drover bought 25 sheep at $5 a head, and 5 cow?
at
a
ad : find the cost of the whole.
3. A farmer sold 35 barrels of apples at $4 a barrel,
and bought with the proceeds pork at $5 per cwt.: how
much pork did he get ?
4. If I bought 80 turkeys at the rate of 10 for $6, and
sold them at the rate of 16 for $14, how much did I
gain ?
5. A boy b( ught a book for half a crown, a slate for
6d. : how much hange did he get out of half a guinea 1
6. How many lbs. of sugar at 4d. a pound, can be
bought for a crown and a shilling piece 1
7- The L. C. M. of two numbers is 24 and their G. C.
M. 4 ; one of the numbers is 8 : find the other 1
8. I own f of -^% of a ship worth $30,000, and I sell |
of my share : what is the value of my remaining interest
in the ship ]
9. If the four-pound loaf is worth 10 cents when wheat
is $1 a bushel, what should be charged for it when
wheat is worth $1,10 per bushel 1
10. Susie being asked her age, said : If the difference
between -f^^ of my age and | of it is multiplied by 12, the
product will be 20 : find her age ?
11. Multiply 16 by 12, add 8, divide by 400, multiply
104
MENTAL ARITHMETIC.
Ell
ml
m
•vt
■,ii">
>^ »
by 128, take the square root, and multiply by 50 : what
is the result?
12- A can do a piece of work in 4 days, and B in 4 J
days : in what time will both working together do § of
the work?
13. I of 56 is f of how many times 16 ]
(2.)
1. I bought a horse for $175, kept him 7 weeks at a
cost of $35, and sold him for $275 : how much profit had
I?
2. The dividend is 285, the quotient 17, and the re-
mainder 1 3 : find the divisor.
8. Bought 10 reams of paper at 20 cents a quire, and
sold it for $4.50 : what was my gain on each quire ?
4- I divided .£1 7s. 6d. among a number of children,
giving Is. 3d. to each : how many were there 1
6. Div'ide $75 between A and B, giving B $15 more
than A.
6. -,-\ of the candidates at an entrance examination
failed in English grammar, j^^ of the remainder failed in
arithmetic, and 15 passed : how many candidates were
there 1
7. The distance from Yarmouth to Boston is 240 miles,
and twice the distance from Yarmouth to St. John is 30
miles less than J of the distance from Yarmouth to
Boston : find the distance from Yarmouth to St. John.
8. A man working 9J houi-s a day can do a piece of
work in 8 days : how many days will it take him if he
works only 6 J hours a day 1
9> A and B can do a work together in 2J days, A can
do 3 times as much in a given time as B: find the time
each would take to do it.
QUESTIONS FOR EXAMINATIONS.
105
niles,
is 30
~i to
n.
of
: he
can
lime
10- A boy spent | of his money, and then found that
was j^2 of what he had remaining : how much had
he at first 1
11. It costs $72 to carpet a room 24 feet long and 18
feet wide : what would it cost if the room were a yard
wider 1
12- If to my age you add | of it and 15 years, thd
sum will be 39 years : find my age.
(3.)
1. A farmer sold a horse for $132, and a cow for ^G8 :
how much had he left after i)aying $85 for a waggon 1
2- $450 is divided between Harry and James ; as often
as the former gets $8 the latter gets $7 : how much does
each receive ?
3. When $400 is paid for 25 acres of land, what will .
1 acre and 1 rood cost 1
4. A market woman sold 4 lbs. 4 oz. of butter, at 32
cents a pound, and took her pay in cotton at 8J cents a
yard : how many yards did she have 1
6. Find the least number from which 17, 34, and 51
can be subtracted an exact number of times.
6. A man after paying an income tax of 2J cents in
the dollar, had $1,5G0 left : find his income for a yearl
7. A can do j\ of a piece of work in 9 hours, and B
in 15 hours ; after A has worked 3 hours B comes to
work : in what time will the work be finished ?
8. A boy being asked how much money he had, re-
plied : if you add 1 to 6 times what I have, 13 times the
square root of the sum will be 117: how much had h<: 1
9. How many yards of carpet 27 inches wide will it
take to carpet a floor 18ft. 9in. long and 12ft. wide 1
106
MENTAL ARITHMETIC.
1^'
if ■
11
u,
I
t 9
ftKS»
- jk
10. A man failing in business was able to pay only t
of his debts ; a certain creditor received $940 : what was
the amount of his creditor's full claim 'i
11. In a High School | of the scholars study Latin,
I of the remainder study Goi'man, and the rest trigonome-
try, and there are 5 more in trigonometry than in German :
find the number of scholars in the school ?
12- A father and his son earned $75 in one month ;
the father earned l^ times what the son earned : iind
what each earned v)er month.
A.
1. A man bought a house-lot 10 rods square for $400,
and sold it for $41 a square rod : how much did he gain
or lose 'i
2. A boy bought a number of oranges for $2.75, and
sold them for 7 cents each : how many did he tuy"?
8. The area of a room is 20 J square yards ; its length
being 15ft. Gin. : find its breadth.
4. A man invests ^ of his fortune in land, ^ in bank
stock, ^ in business, and has $3,375 left : find the amount
of his fortune.
5- What number must be added to 355 to get a sum
exactly divisible by 171
6. I of my present age is | of my age 10 years ago :
find my present age.
7. Bought 12 yards of tweed at $2.75 a yard, 16 yds.
of silk at $2.12 a yard, and 50 yards of cotton at I Ah
cents a vard : find the amount of the bill.
8. Of all the numbers (besides unity) which may be
subirycted an exact number of times from 255, which be
taken the greatest and which the least number of times 1
QUESTIONS FOR EXAMINATIONS.
107
9- Square 15, subtract 25, divide by 50, multiply by
225, take the square root, add 34, take the square root,
and multiply by 250 : what is the result ?
10- J of 7 is I of how many times 31
11. A garrison in a state of sies'e is put on short
allowance : each man receives 12 oz. of bread, which is ^
of a full ration, and 10 oz. of meat, which is | of a full
ration : find th^ daily rations.
12. A horse cost $1,200 and | of its value is i of 2 J
times the value of the farm on which it stands: find the
value of the farm.
(5.)
1. A man bought a pig for ^1 15s., a sheep for 158.
more than he gave for the [n^j;, and a cow for twice as much
as he paid for the sheep and pig : how much change did
he receive out of a £20 note 1
2- If a man take 3 steps in going 10 feet, how many
would he take in going a mile 1
3 Find the L. C M. of 3, 17, 51, 102?
4. Charlie and Willie had each the same number of
cents; Charlie spent 10 cents, and then they together had
70 cents : how many had each at first 1
5. If A can do a work in 3 days, B in 4 days and C in
5 days, in what time could all working together do the
work 1
6. A has a certain amount of money, and B lias 1 J
times as much, both have $180 : how much has each 1
7. A man owns J of a ship and sells J of his share for
$1,275 : find the value of the ship.
8. The length of a room is 18 feet 6 inches, and its
breadth is 12 feet : how many yards of carpet 27 inches
wide will cover the floor 1
0U
108
MENTAL ARITHMETIC.
W.
1 iff- r >«
f ■
iM"., *'
■ -"If -,
m
9- J of 40 is j®2 of how many times 10 J ?
10. A boy being asked how many cents he had, said
4 times the number is 18 less than 7 times the number
how many had he 1
11. If 3 pints contain 114 cubic inches, how much
will bo contained by a rectangular boiler 2 feet 6 inches
long, 1 foot 7 inches wide, and 18 inches deep *?
12. If § of a yard of cloth cost 80 cents, what will j
of a yard cost 1
13- 7 men can build a wall in 8 days of 10 hours each :
in how many days of 12 hours each could they do it 1
(6.)
1. Find the result of 75+85— 27-f- 12.
2. A man undertook to split 400 ratls at the rate of 1
rail in 3 minutes, agreeing to pay 5 cents for every rail
he was short of the 400, he worked 10 hours and gave up :
how much had he to pay 1
8- A buy being asked his age replied : if you add 5 to
my age, take the square root, multiply by 5, add 5, and
take the square root, the result will be 5 : how old wap
hel
4. A man bought some apples for 88 cents, at the rate
of 5 for 11 cents, and divided them among his 5 children :
how many did each receive 1
6. A and B can together do a piece of work in 25 days,
B can do 2J times as much as A in a given time : find
the time required by each alone to do the work 1
6. If G persons spend $36 in 3 days, how much will 10
persons spend in 6 days 1
7. A farmer sold 12 sheep which was f of } of his
flock : how many were in the flock after the sale 1
I
th
m
m
be
th
cli
1^
th
QUESTIONS FOR EXAMINATIONS.
lOd
|e rate
Iren :
lays,
find
II 10
his
8- $500 is to be divided between A and B so that as
often as A gets a dollar, B gets § of a dollar : what will
each receive 1
9. A quantity of sugar was sold for 12 cents per
pound, the gain being ^ of the cost price, the total gain
was $3 60 : find the quantity of sugar.
10. I^ one-third of a shilling were Qd., what would |
of £1 hiil
11. J of 64 is I of how many times | of 32 ?
12. A flag-staff 80 feet high was broken into two parts
by the wind, it was found that ^| of the longer part was
i\ ^^ ^h times the shorter part : find the length of each
part.
18. I of 72 is I of how many times j\ of 601
(7.)
1. A man bought two building lots, one for $246 and
the other for $328, and sold the two for $1100: how
much did he gain 1
2. If a machine can cut 100 rails in a minute, how
many can it cut in 10 days of 10 hours each 1
8- A teacher having a school of 100 boys and 120
girls, divided the scholars into the largest possible num-
ber of classes so that each class of girls should number
the same as each class of boys : find the number of
classes.
4. Bought a gold chain 18 carats fine, weighing 2oz.
14dwt. 10 grains, at $24 an ounce : find the cost.
5. I of 27 is I of how many times y'^ of 90 1
*6. A.t what hour between 3 o'clock and 4 o'clock will
the hour and the minute hands of a clock be together 1
* Se<d *' Examination Pa])er8 in Arithmetic,'' page 26.
no
MENTAL ARITHMHTIC.
m
I,
ft ^
if
mi
I'htf-
7. A horse cost $80, and | of his cost is | of four times
the cost of the carriage : find the cost of the cariage
8. If the ten-cent loaf weighs 4 lbs. when Hour is $6
per barrel, what should it weigh when flour is $7.80 per
barrel 1
9. A drover bought a number of sheep at $3| a head,
and lackt^d $7 of the amount required to pay for them ;
bad he bought them at $3^ a head he could have paid for
them and had $3 left : how many sheep did he buy 1
10. A woman gave $1.20 to some children ; each boy
received 9 cents, and each girl 7 cents ; there were 3
times as many girls as boys : how many were there of
each class 1
11. I sold a farm for $4800 by which I incurred a loss
of ^ of what it cost me : how much did I lose 1
12. If 8 men in 6 days of 10 hours each can do a cer-
tain piece of work, how many men will be required to do
the work in 8 days of 7J hours each 1
(8.)
1. A boy can pick 3500 stones off a summer fallow in
a day : at 20 cents a thousand, how much will he earn
in a week 1
2. A farmer exchanged 10 bushels of wheat at $1.20
a bushel for 20 bushels of oats and $3 cash : what were
the oats a bushel 1
8. A goldsmith manufactured 2 oz. 5 dwt. of gold into
rings each weighing 9 dwts., and sold the rings at £1 4s.
each : What did he receive for them 1
4. A and B can together do a work in 6 days, and B
can do ^\ of the work in a day and a half : how long
would it take each working alone]
i
QUESTIONS FOR EXAMINAMOK.
Ill
• times
age
L- is $6
80 per
I head,
them ;
)aid for
ich boy
were 3
here of
3d a loss
o a cer-
d to do
lllow in
16 earn
$1.20
It were
lid into
Ul 4s.
land B
long
5. If I of an inch on a county map correspond to 6
miles, what distance will represent 3| miles ?
6. I of 32 is i of how many sixths of 18 1
7. In a drove of 1 20 animals there are 50 cows and
the rest are horses : how many horses must be sold that
there may be left 4 horses for every 5 cows 1
8. How far may a person ride in a stage which makes
6 miles an hour, so that he may drive back at the rate
of 8 miles an hour, and be gone only 9 hours 1
9- I sold a house for $2800, by which I gained | of
what it cost me : find the cost.
10- Harry is 10 years old and Mary 15 yeai*s : in
how many years will Mary be 3 times as old as Harry 1
11. After losses in two engagements a cavalry troop
was found to consist of 950 men ; in the first engage-
ment they lost 1 in 12, in the second ^^ of the remainder :
find the number of men in the troop at first.
12- In a municipality the assessment is 18 mills on
the dollar : for how much is a man assessed whose taxes
are $63 ?
(9.)
1. What number must be subtracted from 3050 to get
a remainder exactly divisible by 55 ?
2. Hannibal won the battle of Cannae, B.C. 216, being
then 32 years of age ; he was defeated at Zama, B.C.
202 ; he died at the age of 65 : how many years before
his death was the battle of Zama fought 1
8. Emma bought a book and slate and a pencil for 3s.
8'1. ; tl^e book and slate cost 3s. 4d. ; and the slate and
pencil cost Is. 4d. ; fin I the cost of each.
4. A man agreed to work for 30 days on the conditions
that for every day he worked he should receive $1.50, but
12
MKNTAL ARITHMETIC.
7' .'
1' '
■i
•41
should pay 50 cents a day for his board every day he
should be idle ; at the end of the time he received $40 •
How many days did he work 1
5- The dry goods in a certain store cost $1,200, an 1 |
of their cost is j\ of three times the cost of the groceries :
find the c^st of the grocaries.
6. By selling cigars at 70 cents a lozen j^j of their cost
■was gained : find the p -ice at which each cigar should
have been sold to gain f of their cost.
7. A farmer sold ^q of his farm at the rate of $40 an
acre, and received $2,800 for it : what was the remainder
of the farm worth at the same rate 1
8- A boy said : if from the square of my age you sub-
tract 48, Y*j of 5 times the square root of the remainder
will be 15 : find his age.
9. Divide $192 among Harry, John and James, so
what John may have twice as much as Harry, and James
1^ times as much as John.
10' How much cl )th at 5s. 3d. per yard can be bought
for 21 guineas 1
11. If T receive $12 for the use of $150 for 1 year,
how much should I receive for the use of $375 for 18
months 1
(10.)
1. Bought 26 barrels of mackerel at $8.25 a barrel,
paying $100 cash, and giving my note on three months
for balance : find the face of the note.
2. Find the greatest number that will exactly divide
both 38 and 59, leaving 6 and 11, respectively, as re-
mainders.
8. Two towns A and B are 45 miles apart ; a person
sets out from A to B at the rate of 3 miles an hour, and
QUESTIONS FOR EXAMINATIONS.
113
two hours later, another sets out from B to walk to A at
the rate of 3J miles an hour : how far from A will they
meet 1
4. Simplify \ (72+82)-2 [ X ^ 93+45x3 y,
6. Find the cosfc of 7,200 yards of cloth at 9s. 6.1. per
yard.
6. What is the length of the longest stick that will ex-
actly measure 3 yards, 2 yards, and 9 inches ?
7. How many yarls of carpet 27 inches wide will be
required for a room measuring 18 feet by 25 feet 6
inches 1
8. Find the L. C. M. of 126, 225, 630, and 900.
9. If from a certain number 5 less than its half be
taken, and from the result 4 more than J (of this result)
be taken, the remainder will be 22 : Find the number.
10. A cistern has 3 pi{)es ; the first alone can fill it in
12 minutes, the seconl in 16 minutes, and the third can
empty it in 8 minutes : if the cistern is empty, and all
three pipes be opened, in what time will it be filled 1
11. Reduce 2' lbs. 2 ozs. to the fraction of 1 quarter,
and 9Jd. to the fraction of 7s. 6d.
12. Reduce to lowest terms ^^q, and y?f g.
irrel,
mths
tvide
Ls re-
Irs an
and
(11.)
1. The River St. John is 450 miles long, and the
Miramichi 225 miles ; the sum of these lengths will give
the length of the St. Lawrence, lacking 87 miles : find
the length of the St. Lawrence.
2- A boy bought a lot of lead pencils for 80 cents, an \
sold some of them for 36 cents at 3 cents a piece, losing
thereby one cent on each : for how much each must he sell
the remainder t ". gain 4 cents on the lot 1
114
MENIAL ARITHMETTO.
m
8> A stationer sold a dozen articles for a certain price ;
J his gain on 5 articles was his selling price for 3, and he
sold 4 for 40 cents : fin.l the whole cost.
4. Two men bought a quantity of flour for $40, the
first paying $3 for every $2 paid by the second ; the flour
was $6 a barrel : how much will each have ]
5. "Hj *f the population of Dartmouth is | that of
Yarmouth, and the population of Yarmouth is 2,400
greater t?ian that of Dartmouth : find the population of
each.
6. Divide $144 among A, B, C, giving A $2 as often
as B gets $3, and C $4.
7. Kggs ai"^ sold at the rate of 35 for 54 cents, and
the gain at this rate is one fifth of the cost : find at what
rate ; er dozen they were purchase^l.
8. If an army marches 130 miles in 6 J days of 9 hours
each, how far can it march in 4 J ^lays of 10 h )urs each 1
9. If a horse eats | of a bushel .;f oats per day, how
loner will 5| bushels last him ?
10. In a certain business a partner whose share is j*jj
of the capital, receives $900 of the profits : what share is
owned by a partner who receives $800 of the profits 1
11. Lead weighs 11| times anl platinum 21 times an
equal bulk of wal;er : find the weight of a piece of platinum
equal to a piece of lead weighing 190 lbs,
(12.)
1. The population of Newcastle, N.B., is 2,125, and of
Moncton, 2,275 ; find the population of St. John, which
would make nine Newcastles and as many Moncfcons.
2. Find at $4 a cord, the value of a pile of wood 76
feet long, and 6 feet high.
QUESTIONS FOR EXAMINATIONS
115
IS A
ire is
1
?s an
inum
id of
ihich
76
3' The expense of carpeting a room was $G0 ; if the
breadth had been 2 feet greater, the expense would have
been $70: fin 1 the breadth of the room.
4- Charles having been asked his age replied ; 5 times
my age is greater, by 24 years, than three times my age :
fi'id his age.
6. The population of Woodstock (N. B.), is 2,500 and
I, of this is I of 2 J times the population of Fredericton :
find the popuJati(A of this city
6. The population of Toronto is 6| times that of
Charlottetown, anl | of the population of Charlottetown
is greater by 1,000 than ^ of that of Toronto : find the
population of each of these cities.
7. If A and B can do a work in 3 days, B and C in
4 days, and C and A in 6 days, in wliat time could each
by himself do it
8. A grocer mixed a quantity of sugar worth 8 cents
a Qpund with an equal quantity worth 10 cents a pound,
and sold the whole at 11 cents a pound, gaining on the
whole $10 : find the quantity of each kind.
9. If a room is 12 feet wide and 15 feet long, what
must be its height that the area of the walls may amount
to 72 square yards?
10- Find in dollars and cents the cost of a piece of
English cotton containing 72 yards, at 5^d. a yard — the
shilling sterling being worth 24 J cents
11. B can work twice as fast as A, they both can in
5 days do a work for which $20 is to be paid ; they
work together 3 days and then B leaves, and A finishes
the work : how should the money be divided )
116
MENTAL ARITHMETIC.
(13)
1. What portion of 3 cwt. 14fi)s. is J of 1 cwt. 2 qrs.
7!b.s?
2. The longitude of Halifax is 65° 4', and that of
Montreal 73° 37' : find the difference in time between
these two cities, 15° making a difference of one hour.
3- What number increased by 3, multiplied by 4, 3
subtracted, and the remainder divided by 11, gives
quotient three 1
4. If John had as many more marbles as James, and
half as many more, and 8 besides, he would have 63 :
how many has James H
5. A boy agreed to carry 100 glasses on the conditions
that for every glass he carried without breaking, he
should receive 10 cents, and pay 30 cents for every one he
broke ; he received $6 : how many did he break ]
6. A boy found a sum of money, and on giving it to
the owner he received as a reward ^ of the sum ; had he
received J of J of the sum his reward would have been
25 cents more than it was : how much did he receive 1»
7. A merchant sold some cloth at 87 J cents a yard,
gaining $6 ; had he sold it at $1 a yard he would have
gained $9 : how many yards did he sell 1
8. What sum of money increased by | of itself, and
then by § of | of this sum, gives $45 ?
9- The distance from Halifax to Shubenacadie is 40
miles. A starts to walk from the former place to the
latter, and B from the latter to the foinier ; when they
meet, j\ of the distance walked by A is found to be equal
to J of that travelled by B : how far had each walked ?
lO. Sold two horees at $200 each, on one of them
gaining J of what he c st, on the other losing J of what
be cost : find the net gain or loss.
QUESTIONS FOR EXAMINATIONS.
117
qrs.
have
f, and
is 40
|o the
they
lequal
bdl
them
Iwhat
11. C apples and 4 oranges cost 18 cents ; 3 apples
and G oranges cost 21 cents : tind the ci)8t of one of each.
(14.
1. The longitude of St, John is 60° and of Toronto
79° 25' : find the difference between St. John time and
Toronto time.
2. A farmer wishes to bnild a board fence 270 ft. long ;
he has boards 13 J, 18 and 22 J feet long resp, : what k
the least number of post holes he can dig so as to leave
no waste in the lumber 1
3- It" the population of St. Andrews is multiplied by
20, and the square rcot of the product is di\ ideil by 4, 7
times the quotient will be ^^ of the population of St.
Stephen, which is 2500 : tind the iMjpulation of St. An-
drews.
4- If water expand tj\ of its bulk by freering and a
cubic foot of water weigh G2J^ lbs, Hnd the weight of a
cubical block of ice having a surface of 54 square feet.
6. Find the value of 27 articles at £2 3s. 4d. each.
6. V/hat is the smallest amount of money with wliich
I could purchase either sheep at $2|^ each, hogs at $4 J
each, or calves at .f6|.
7. Find the value of 44d lbs. of wheat at $1.50 per
bushel.
8. A man has 5 days' statute labour to perform.
Working hours from 8 a.m. to 5 p.m., 1 hour for noon.
A team and plow are reckoned equal to two men and a
team and scraper equal to 3 men. He commences work
with his team on Monday morning, ploughs the first half
day and scrapes the rest of the time. AVhat day and
at what hour witi he be done 1
lid
MENTAL ARITHMETIC.
9. Divide $120 into 3 parts which shall be to one an-
other as 3, 4, 5.
10. A train running at the rate of 40 miles an hour
takes 46" to cross a bridge J of a mile long : find the
length of the train ?
11. 4 times a number is 15 less than 6 J times the
number : find it.
12- A can do a piece of work in a day, B in a day and
a half, C can do twice as much work in the same time as
B : how long would it take C to do a piece of work that
took the other two 5 days 1
m
m
'ii
(15.)
1. The population of iJalhousie is 1000, of Bathurst
the same, of Newcastle, 2000, and of Chatham 2500 : find
the population of Montreal, which is 24y^3 times the u.iit-
ed population of these towns ?
2. A boy sold a number of oranges at 2 cents each ; had
ho charged 2^ cents each and sold 4 more, his receipts
would have been 16 cents more : how many did he sell 1
8. Divide $65 among 3 men, so that as often as the
first gets $J, ihe second shall get$J, and the third $J.
4. Four men started on a hunting expedition with
provisions to last 10 days ; before they had eaten any they
were joined by 5 others who had provisions to last (the
five) 6 days : if one of the second party could eat twice
as much as one of the first, how long would all thi pro-
visions last the whole company 1
5. Divide $88 among 3 men, 4 women, and 5 boyg,
giving a man $3 when a woman gets $2, and a boy $1.
6. If millers take out j'^ for toll, and a bushel of wheat
produces § of its weight in flour, how many bushels of
QUESTIONS FOR EXAMINATIONS.
119
wheat must be taken to the mill to receive back 220 lbs.
of flour ?
7. A and B can do a work in 2 days, A and C in 3
days, B and C in 2 J days : they begin together and finish
the work : how should the $6 paid for the work be
divided 1
8. What must a boy ask for a pair of skates that cost
$1.20, that he may take J off his asking price and still
make a profit of J of their cost 1
9. When gold is at 105, what is the value of a $10
gi'eenback 1
10. A and B are 30 miles apart, and they travel to
meet each other ; A goes 4 miles an hour, and after he
has been travelling 2 h urs, B starts off and after travel-
ling J of the whole distance meets A : find B'a rate per
hour.
(16.)
1. A lealer bought 113 quintals of codfish at $3.65 per
quintal : what lil he pay for the whole"?
2- My horse is worth J as much again as my buggy :
what fraction of the price of the horse is the buggy worth
less than the horse?
8' Having laid out J of my money, and lent | of the re-
mainder, I have $24 left : how much ha I 1 at first ?
4. A man has to be at a railway station at a certain
time; if he walk 2J miles an hour he will be 12 minutes too
late, but if he walk 3 miles an hour he will be 12 minutes
toe soon : at what rate must he walk to be just in
time 1
6- A number which is divided into 3 parts, which are
as 1, 3, 5 ; the socond part is 24 : find the number.
6. A merchant bought wheat at $1.20 a bushel by
120
MENTAL ARITHMETIC.
measure, and just gets his money back by selling it at
$1.10 a bushel by weight: how many pounds to the
bushel did the wheat over-run 1
7. If to J the cost of my horse you add $80, the sum
will be IJ of the cost : find it.
8. 10 square yards of cloth are required, the cloth
selected is one yard wide, but when sponged will shrink
j*^ in length and y'g in width : how many yards must be
purchased 1
9. If 40 lbs. of sea-water contain 2 lbs. of salt, how
much fresh water must be added so that 3 lbs. of the
mixture may contain 1-^g^- ounces of salt t
10- A boy sold 2 dozen orani»es, 5 of his gain on 1 2
was his selling price for 4 : what fraction of selling price
is cost 1
11. Three men or four boys can do a work in 12 days :
in what time can 3 men and 4 boys do iti
12. A school is allowed 1 J houTs for dinner ; a boy
walks home at the rate of 4 miles an hour, takes 20
minutes to eat his dinner and is back iu time, walking at
the rate of 3 miles an hour: how far does he live from the
school ?
(17.)
1. The latitude of St. John is 45° 18', that of Toronto,
43° 40* : allowing 70 miles for a degree, how many miles
is St. John north of Toronto 1
2. 5 men or 8 boys can do a work in G J days : in what
time will 3 men and 4 boys do 2| times as much 1
8. A man sold a horse and gained j^g of the selling
price ; if he had bought him for $12 less, he would have
gained J of the cost : find the cost.
4. A and B do a piece of work, A receiving $2 a day
QUKSTIONS FOR EXAMINATIONS.
121
mto,
liiles
^hat
ive
and B $3 a day ; A works twice as many days as B, and
$70 is j>aid for the work : how many days did each
woi'k 1
*5 The sides of a right angled triangle are G ft., 8 ft.
and 10 ft. res[»ectively : finti the length of the j>erj)endi-
cular on the hypothenuse.
6. Find the cost of J of ^, of 40 bushels of wheat at
$1.1 2J per bushel.
7. What is the first time after 12 o'clock at which the
hands of a clock form an angle of GO*^ 1
8. A boy being asked how much he was worth said:
add $17 to the number of dollars, tak(5 the square root,
multiply by 5, add 5 to the product, extract the sfpiare
root and multi-ply by 80^ ; the result will be 402 : how
much was he worth 1
9- An agc^nt sold $2700 worth of goods, receiving for his
trouble $3| on every $100: how much did h(; n^ceive
in all ?
10. A brakesman is noticed running in the same
direction as tht^ train, on the top of a freight train going
at the rate of 10 miles an hour, and is observed to take
^ a minute to pass 2 telegrM[)h polos which ar<i 20 rods
apart : at what rate is the man running, independently of
the train 1
(18.)
1. Bought 10 chickenr; at GO cents each, G ducks at
50 cents each, and 4 turkeys at $1 each, paid on account
$G.80 : how much is still due? how many ten cent pieces
will pay the balance'?
2. A teacher being asked how many scholars he had,
lay
*Note tlmt the |>ri>(luct nf tho perpemllrulnr on tin* h.v|M)tliutiiiHo i>quala the
product of tho othor two titles.
122
MENTAL ARITHMETIC.
m
answered that 30 of them were boys, and | of them, less
20, were girls : how many scholais were there in all ]
8. If 4 <^f **^y **o® ^**^ passed since I was 36 years old,
how old am 1 1
4. An equal number of geese, chickens and turkeys
were sold for $11.40 ; each goose brought 60 cents, each
chicken 30 cents, and each turkey ^^- of the cost of a
goose and a chicken : how many fowls were sold ]
5. How much water must be added to 30 gallons of
braiwily, at $4 a gallon, to make it worth $2.50 a gallon?
6. A man went to market and bought a turkey and a
goose weighing in all 24 lbs., the goose at 8 cents a pound
and the turkey at 12 cents a pound ; the whole cosi was
12 cents more than if he had bought both at an average
price of 10 cents a pound : what was the weight of the
tuike> 1
7. What o'clock is it if the time past 10 is J of the
time ])ast 9 1
8. One number is 7 J times another: if the difference
between them is 65, what are .the numbers'?
9. liow many boxes 9 inches long, 6 inches wide and
3 inches deej), can be packed in a space 3 ft. each way?
10. A owns 5 of a lot of land, and B the remainder
Thr' lot is sold, A receiving ^ of his shaie of the money
and B j^ of his. B afterwards received $40 from the nur-
chaser, and the balance then due was divided equally be-
tween A and B : what was the lot sold fori
(19.)
1. A waggon is going at the rate of 8 miles in 1 hour
and 20 minutes, and a buggy is coming up behind at the
m, less
alU
irs okl,
:urkeys
s, each
jst of a
Ions of
gallon ]
J and a
I pountl
)si( was
iverage
of the
of the
ference
lie and
ray
?
inder
uoney
pui-
ly bt>-
I
QUESTIONS FOR EXAMINATIONS.
123
[hour
Ltthe
rate of 6 miles in half an hour. If the biiof»y overtakes
the waggon in IJ hours, how far was it behind at first?
2. The product of two nnnibera is 48 : if one of the
factors is \ of 27, the otlier is ;} of what number %
3- A and B hire a livery at Brampton, to drive 12
miles, each to pay in proportion to the distance ho rides.
A calls at B's residence which is 4 miles from Brampton,
and leaves him there on tlieir return : what should each
pay, if the hire of the rig cost 3 dollaisl
4. A'm and B's ages together are 48 years, 4 years ago
B's age was \ of A's : required tlioir present ages %
6. A pole is 51 feet long, is broken by the wind, ^ of
the length of the longer is equal to \ of the length of the
shorter: find the length of each.
6- If If of a piece of work can be done by three men
in 2 days : how many men will it take to finish the re-
mainder in three days'?
7. What o'clock is it, if the time past 3 is J of the
time from now to 4 ?
8. Which is the cheaper, a hat that costs $1.40 and
lasts 7 months, or one that costs $2.70 and lasts 9
months'? What is saved in three years by wearing the
chea[>er hat "?
9. Two blocks of wood, each 6 ft. loniif, contain the same
number of cubic feet, the first is 2 ft. by 1 J, and the
second is 9 inches one way : what are its dimensions the
other ]
10. The expense of carpeting a room with carpet is
$20, but if it was 3 ft. wider it would cc:it $25 : find
the width of the room %
124
MENTAL AllITIIMETIC.
(20.)
1. A parco) of 12 lbs. weight is canicd 25 miles for
30 cents, and the rate for the distance ovei- 10 miles is §
of the rate for the fii*st 10 miles : how far can a parcel of
9 lbs. be carried for 20 cen^s 1
2. Two hens and 3 ducks cost $1.15 and 3 hens, and 5
lucks cost $1.85 : how nmch more does a duck cost than
a hen 1
3. A does ^ of a piece c>f work in 4 hours, T> does ^
in an liour, and C finis!ies it in ^ of an hour : how long
would it have taken all working together to do the work 'i
4- B travelled 102 miles in throe days ; the first day
he travelled J as far as on the last two days, and on the
last day J as far as on the first two days : how far did ho
travel on the first day ^
6. A dishonest milkman adds a quart of water to every
gallon of mile and then sells the mixture at ^'^ more than
it cost him : what is his profit on an expenditure of $101
6. A farmer having bought a certain number of sheep
for $100. when a dog killed 8 of them, he sold J of the
remainder for cost and received $20 : how many did he
buy ]
7. Two men, A and B, enter into partnership and
gain $300 ; A owns '^ of the stock, lacking $40, and gains
$180 ; required the whole stock and share of each 1
8- A thief has 220 yards the start of an oflScer, in the
next half mile ho gains 10 rods more, after which the
office-- nins 3 ro !s while the thief runs 2 rods : how fur
V wvl i. ^ i^i^ when the thief was overtaken?
vi* CiiVhfeL' of the pupils in a class are girls, the other
IS
•QUESTIONS FOlt EXAMINATIONS. 125
half are boys; the giils own 65 books, the boys 91 ,.aeh
having tbe same nunibe.-. What is the la.gest .ui. be.
of pnpils that could be in each class ?
10. How many flowe.s can be planted alon™ the
boidei-s of a flowe.. bed ,2 ft. long by ft. wide: Z
flowers being inches apart ?
11. What is the vahio in cents of the hirgest coin with
which I can pay the following three bills! 2 cro "
sovereign, and I guinea? '
End of Part I.
MILLER'S NEW
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10
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S
SWINTON'S LANGUAGE LESSONS.
Adapted to Canadian Schools.
By J. A. MACMILLAN, B.A., Ottawa,
COLLEGIATE INSTITUTE.
S
M
*■
ft
8
I
e
Specially arranaedaa an introdiictory Text Book to MASON'S
GBAMMAB, the authorized text book for Public Schools. The
Definitions, Classification of Pronouns, Verbs and Genkrai.
Treatment are uow brought into complete harmony with
MaBon'8 Larger Grammar.
PRICE 25 CENTS.
e
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FROM SOUTH HASTINGS' BOARD OP EXAMINERS.
Miller's New "Swinton's Language Lessons." by Macmillau, is
enpecially adapted to the wants of elementary classes. The as-
similation of the rules and definitions to those of the advanced
text book, Mason's Grammar, is a decided improvement and
makes it much preferab'e to any of the other editions. With this
Edition of Language Lessons in hand, the most inexperiencid
teachor may safely be entrusted with a tzrauiniur and composi-
tion class. B. DAWSON, B.A ,Ph.D.,H.M.H.S., Helloville.
H. M. HICKH, M. A., H.M. H School. Trenton.
JOHN JOHNSTON, P.S.I., South Hastings.
WM.-WILKINSON, M. A.. Head Master Model and Central School
firantford.
Your "5th Edition of Swinton's Language Les8ons"by Macmillan
is the most complete Primary Grammar I have seen. Theeditor
deserves every prfiso for making his dofluitions ngrco with those
of Masons' Grammar, thus j)re venting the loss of time and con
fusion, that always result from learning two sets of definition".
He has accomplishel this without rendering the work a whit
more difficult, or in any way destroying its pt'cnliiir character.
I observe that the matter is so arranged that tliis edition can be
used in the same class as your other editions without any incon-
venience, i wish for it as nmuh succesN as its predi el<.ssur^ iiavo
had. which since 1 speak from some months actual use of the
bouk i^, perhaps, the highest pruise I can giva it.
C. CLAKKSUN, B.A., Head Master.
I huvH examined carefully your
Model School, lirnckville.
" New Swinton's Language
Lessons." b / MacmiHau. The book is excellent. It was a decided
improvement to bring it into entire harmony with Mason's. Tlie
only difficulty I experience is to kekp it out of the Third class,
for which no, text book is authorised. Pupils use the book pri<
vatel^ A% au Kid to follow the oral teaching.
millsr's vew swinton's lamouaoe lessons.
N. GORDON, rioarl Master, Model School, Picton.
After a careful perusal and comparison of the Fifth Edition
of "Swinton's Lani^uriqe Lo880us,"by Macmillan, with previous
editions, I find chnnf^oa of an important and highly bene-
ficial character, viz :— the deliuitious are the 8ame as those in
Mason's Gramma: , also the treatment of the Verb, etc., this is a
step in the ri«ht direction, as the text-books iu all our PnbUo
Schools should be bo arranged as to make those used in the
junior classes an introduction to those (on the same subject)
used in the senior divisions. I consider the plan hiRhly com-
mendable as the changes do not prohibit its use with your other
edition of the same excellent little work.
JAMES DUNCAN, Principal Essex Model School.
Have carefully examined the Fifth Edition of" Miller's New
Swinton's Language Lessons by Macmillon," — The mat-
ter is put in clear, concise and interesting language, and the
subject is kept abreast of the age. I consider it an invaluable
auxiliary to the Public School Teacher. It is as it professes to
be " an introductory work on Grammar," as well as a forerunner
of Mason's more advanced text->ook.
W. J. SUMMERBY, Principal Kingston Model School.
To prevent the loss of much valuable time, the agreement of
the oJoiaentary and advanced text-books, in all essential points,
is aii absolute necessity, and I am glad to find that, in definitions
and general treatn^ent, the Fifth Edition of " Swinton's Lan-
guage Lebsons," by Maomillan, is iu harmony with Masou s Text-
book.
SAMUEL B. WESTERFELT, H M.M.S. Mount Forest.
As the aim is to make it uniform iu defi'iitions and clasifi-
cfitiou with Mason's Grammar, and as it is such an excellent
Elementarv text book, especially for the use of young teachers,
1 would heartily reoommeud its introduction.
Ulan
Iditor
fhose
con
lion".
Iwliit
iter,
n be
(con-
liavu
the
le.
W. F. RITTENHOUSE, Teacher, Central School, St. Catharines.
I consider •' Swinton's Lan 'uage Lessons," by Macmillan, as
the l)est text book for teacliing grammar extant, and the revision,
making thf dofinitituis corr spoiul with those iu the advauced
text book, leaves nothing to be desired.
GEO. MILDEN, Head Master, M, 8., Cornwall.
Miller's new " Swinton's Language Lessons," by MacmilUm,
I lo k upon as an adniirable little work, well and caieftdly
got up, anil will render valu able assistance to those teachers who
are engaged iu prei)aring pupils for the coming exauunatious.
REV. J. MAY, L P. S., Co. Carfton.
I have examined " Swindon's Language Lessons, by Macu^il-
lan," and am of opinion that it will prove a very useful text-book
in our schools.
JAMES McBRIBN, Ins. P. S., Co Ont.
Miller's new " Swinton's Language Lessons" possess too in-
valua: le obaraoteristics, gradation and adaptation to youth. I
would like to aee it in all our beet Bohoola.
miller's new swinton'8 language lessons.
W. E. SritAGUE, Head Master, Model and Public Schools,
Cobourg.
Millor'Bnew ' Swinton'sLanguaqe IiOS8onH,"by Macmillan.iRa
decidud iinprovem )iit on pitbor of the other editious. Tlio defl-
nltiouB are verbacim with tho^eiu Mason's Grammar, wliicb is
certainly a very praiao worthy feat';re. The treatment of tlie
Pronouns, Verbs, etc., ctd., is in strict harmony with M.isou'8
text-book, and at tlio sanio tinjo does not interfere with the sub-
ject matter lu-oper— LanRnajjo Lessons. It can be introduced
into classes already using any of Macmillau's former editions.
It Is very d< Birable that elementary and advanced text-books
slionld a^rree in the more essential points as Fifth Edition
" Language LrsKons" and *' Mrpour Grammar" do.
JNO. H. McFAUL, Head Master, Model School, Lindsay.
The objection urged against the formtJi* editions of " Swin-
ton's Language Lessons," by Macniillau.was the want of conform-
ity in thedefinitiond of the parts of sftoech, to those given in the
Standard Grammir. In the present Fifth Bdition, the publishers
have not oi lyr placed the faulcy detlnitioua by those of Mason's,
but have also given hisclasiflcation of the Pronouns and Verbs,
thus rendering it no longer obligatory on the part of pupils to
memorize cme set of definitions in an elementary work, to be
abandoned for another set in a inore advanced treatise, a fact
which must enhance th« value of and increase the demand for
the Fifth Edition.
JNO. IIIWIN, Head Master Model School. Belleville.
Miller's new " Swinton's Language Lessons," by Macmillan, is
the best elementiry grammar yet offered to our Canadian schools.
The great fault in thj other editions, the want of harmony be-
tween the elementary and advanccvl text-book, has been over-
come by making the definitions and classification cf verbs and
pronouns agree with Mason's Grammar. It cannot fail to be
adopted in all our public schools.
THOMAS HISLOP, Principal Model School, Haldimand Co.
I have carefidly examined " Miller's Language Lefsons," by J.
Macmillan, and compared it with other works of the same kmd,
and I consider it superior to any. I think this work contains
many exorcises which ai'e admirably sniied to pupils commenc-
ing the study of English, as it is not only an excellent work for
teaching composition to the junior clasKcs, but ut the same time
it gives uU t at is necessary in grammar to enable a pupil to be-
gin the authorized text-book on that subject. A very important
uoint is this, that when the definitions in it have been pre|)ared
a part of Mason's Grammar is also prepared, for the dufluitions
are the aame in both.
A. WARK, Principal Model School, Savnia.
1 have no nesitatlon in saying that SliUer's new " Swinton's
Language Lessons," by Macmillan, is the only text-book I
have yet seen that treats the subject as it ought to be presented
to a class of beginners. It is certainly of the utmost importance
that an introductory textbook on any subject shall be in har-
mony with the more adviinced, thnretore tue changes which have
been made in this edition, in the definitions and the treatment
of the Verb and Pronoun in order to bring it into harmony with
Maoon's, render it more valuable than the previous ones. I think
its introduction into all the schools in the Province is greatly to
be desired.
SSONS.
blic Schools,
[acmillan.isa
iS. Tho defl-
lar, wliich is
noiit of tlie
mth Mason's
vitli tlie sub-
e introduced
nor OfUtions.
d text-books
ilth Edition
Lindsay.
1 of "Swin-
b of con form-
given in tho
e publishers
J of Mason's,
5 and Verbs,
of pupils to
work, to be
itise, a fact
demand for
jville.
acmillan, is
ian schools,
irmouy be-
been over-
' verbs and
' fail to be
land Go.
JOiis," by J.
same kmd,
k contains
coMimenc-
t work for
mme time
upil to be-
important
1 prepared
lofiuitions
Swinton's
Kt-book I
prosonted
iportance
i in har-
liich have
reatmeut
ony with
. I think
I'oatly to