^^VJ
-,%^
v
IMAGE EVALUATION
TEST TARGET (MT-3)
^ ''■4L' '..
^
1.0
!.l
1.25
IS Ma
i" —
IM
2.2
I 1^ l^
'- ._ — — —
1.4 111.6
*^
^^'
7
'^1
cr-:
c?-
%
Photographic
Sciences
Corx)rdtion
23 WEST MAIN STREET
WEBSTER, N./. 14580
(716) 872-4503
:-►'"*- \
,<if
A^
C<?
U.
CIHM/ICMH
Microfiche
Series.
CIHM/ICMH
Collection de
microfiches.
Canadian Institute for Historical Microreproductions / institut canadien de microreproductions historiques
Technical and Bibliographic Notes/Notes techniques et bibliographiques
The Institute has attempted to obtain the best
original copy available for filming. Features of this
copy which may be bibliographically unique,
which may alter any of the images in the
reproduction, or which may significantly change
the usual method of filming, are checked below.
D
D
D
n
n
Coloured covers/
Couverture de couleur
I I Covers damaged/
Ccuverture endommagde
Covers restored and/or laminated/
Couverture restaurde et/ou pelliculie
I I Cover title missing/
Le titre de couverture manq*je
I I Coloured maps/
Cartes g^ographiques en couleur
Coloured ink (i.e. other than blue or black)/
Encre de couleur (i.e. autre que bleue ou noire)
I I Coloured plates and/or illustrations/
Planches et/ou illustrations en couleur
Bound with other material/
Relid avec d'autres documents
Tight binding may cause shadows or distortion
along interior margin/
Lareliure serree peut causer de I'ombre ou de la
distorsion le long de la marge intei ieure
Blank leaves added during restoration may
appear within the text. Whenever possible, these
have been omitted from filming/
II se peut que certaines pages blanches ajoutdes
lors d'une restauration appartiissent dans le texte,
mais, lorsque cela 6tait possible, ces pages n'ont
pas 6td filmdes.
L'Institut a microfilm^ le meilleur exemplaire
qu'il lui a 6t6 possible de se procurer. Les details
de cet exemplaire qui sont peut-§tre uniques du
point de vue bibHographique, qui peuvent modifier
une image reproduite, ou qui peuvent exiger une
modification dans la mdthode normale de filmage
sont indiqu6s ci-dessous.
T
t(
I I Coloured pages/
P
s/
D
D
D
D
Pages de couleur
Pages damaged/
Pages endommagies
Psges restored and/or laminated/
Pages restaurdes et/ou peiliculdes
Pages discoloured, stained or foxed/
Pages ddcolor^es, tachetdes ou piqudes
Pages detached/
Pages d6tachees
Showthrough/
Transparence
Quality of print varies/
Qualit^ inigale de I'impression
Includes supplementary material/
Cornprend du materiel supplementaire
I I Only edition available/
Seule Edition disponible
Pages wholly or partially obscured by errata
slips, tissues, etc., have been refilmed to
ensure the best possible image/
Les pages totalement ou partiellement
obscurcies par un feuillet d'errata, une pelure,
etc., ont 6te filmdes d nouveau de facon ct
obtenir la meilleure image possible.
T
P
o
fi
b
x\
si
o
fl
si
o
T
si
T
w
U
dl
ei
b<
rii
re
rr
n
Additional comments:/
Commentaires suppl6mentaires;
This item is filmed at the teduction ratio checked below/
Ce document est filmd au taux de reduction indiqui ci-dessous.
10X 14X 18X 22X
26X
SOX
/
12X
16X
20X
24X
28X
32X
7 J
I
tails
t du
odifier
une
mage
The copy filmed hers has been reproduced thanks
to the generosity of:
D. B. Weldon Library
University of Western Ontario
(Regional History Room)
The images appearing here are ths bast quality
possible considering the condition and legibility
of the original copy and in Iceeping with the
filming contract specifications.
L'exemplaire film6 fut reproduit grice h \a
gin^ro .it* de:
D. B. Weldon Library
University of Western Ontario
(Regional History Room)
Lee images suivantes ont it6 rsproduites avec le
plus grand soin, compte tenu de la condition at
de la netteti de l'exemplaire filmi. et an
conformity avec las conditions du contrat de
filmage.
Original copies in printed paper covers are filmed
beginning with the front cover and ending on
the last page with a printed or illustrated impres-
sion, or the back cover when appropriate. All
other original copies are filmed beginning on the
first page with a printed or illustrated impres-
sion, and ending on the last page ws*h a printed
or illustrated impression.
The last recorded frame un each microfiche
shall contain the symbol —»•( meaning "CON-
TINUED"), or the symbol V (meaning "END"),
whichever applies.
Las exemplaires originaux dont la couverture an
papier est imprim^e sont filmis en commen^ant
par le premier plat et en terminant soit par la
dernidre page qui comporte une emprainte
(Compression ou d'illustration, soit par le second
plat, salon le cas. Tous las autres axempiaires
originaux sont filmis en comment ant par la
premiere page qui comporte une emprainte
d'impression ou d'illustration et en terminant par
la dernidre page qui comporte une telle
empreinte.
Un das symboles suivants apparattra sur la
derniAre image de cheque microfiche, selon le
cas: le symboie — »>signifie "A SUIVRE ", le
symbols V signifie "FIN".
Maps, plates, charts, etc., may be filmed at
different reduction ratios. Those too largo to be
entirely included in one exposure are filmed
beginning in the upper left hand corner, left to
right and top to bottom, as many frames as
required. The following diagrams illustrate the
method:
Les cartes, planches, tableaux, etc., peuvent dtre
filmte A des taux de reduction diff^rents.
Lorsque le document est trop grand pour dtre
reproduit en un seul cliche, il est film^ d partir
de I'angle supdrieur gauche, de gauche d droite.
et de haut ar bas. en prenant le nombre
d'images n^cessaire. Las diagrammes suivants
illustrent la mdthode.
rrata
:o
oelure,
1 d
D
32X
1
2
3
1
2
3
4
5
6
■■i
* ii\
AN
REVISED EDITION,
THE
AMERICAN
INTIIIIJCTIIAL
DESIUNED FOR
SCHOOLS AND ACADEMIES i
CONTAINING
AN EXTENSIVE COLLECTION OF PRACTICAL QUESTIONS,
WITH CONCISE AND ORIGINAL METHODS OF SOLU-
TION, WHICH SIMPLIFY MANY OF THE
MOST IMPORTANT RULES IN
WRITTEN ARITHMETIC.
BY JOHN F. STODDARD, A.M.,
AUTHOE OF TKE " NOEMAL aiATHElIATICAL SEEIES," ETC.
TORONTO :
ADAM MILLER, 62 KING ST. EAST.
1865.
nu
PREFACE,
Neither a desire of pecuniary gain nor a wish
to appear as an author,prompted the presentation
of this work to the public. Having felt the ne-
cessity of a more extended and systematic Intel-
lectual Arithmetic for the younger, as well as
more advanced pupils, I prepared and used in
manuscript, in my own school, for a number of
years, such a series of questions as I deemed
best adapted to the purpose. After observing
the superior mental training derived from their
use, and the ease with which pupils thus trained
comprehended the more advanced branches of
mathematics, I venture to submit them to the
public in the following pages, hoping that they
may prove as useful to other schools as they
have to my own.
The rule which I have observed in its prepa-
ration is to tell but one thing at a time, and that
in its proper place.
^ It would be laborious to point out all the par-
ticulars in which this work differs from others
of a similar character ; I shall, therefore, give
only a brief exposition of its general plan, leaving
the other differences (which, doubtless, will be
considered of importance) to be found by those
who study the book.
Chapters First, Second, Third, and Fourth,
treat respectively of Addition, Subtraction, Mul-
IV
PREFACE.
liplication, and Division of simple numbers ;
each of which is rendered familiar by an exten-
sive collection of practical questions. The last
Lesson in Chapter Second^ consists of questions
which combine Addition and Subtraction, the
last Lesson in Chaptti^ Third^ of (juestions com-
bining Addition, Subtraction, and Multiplication.
Thus, an intimate connection between Lessons
and even Chapters is kept up through the entire
work, with the exception of Chapter Fifths
which contains a few of the most important
tables of Weights and Measures ; each of which
is illustrated with appropriate questions.
Chapter Sixth is devoted to the subject of
Fractions, and contains twenty lessons, in which
many original combinations and concise solu-
tions occur.
Chapter Seventh consists of practical and in-
tricate questions of various kinds, which require
for their solution a thorough knowledge of the
preceding Chapters. This Chapter (which, it
is believed, is not contained in any similar work,)
v/hen thoroughly understood, will be of incal-
culable benefit to those who are studying, or
intend to study Algebra.
Chapter Eighth includes Interest, Discount,
and per cent, of every description, in their vari-
ous modifications. The method of treating these
subjects is original ; and renders the rules in
Written Arithmetics, under these heads (which
are often incomprehensible to pupils) perfectly
intelligible by reducing the whole to one con-
tinued train of reasoning.
PREFACE.
imbers ;
n exten-
The last
Liestions
tion, the
ns com-
lication.
Lossons
le entire
r Fifth,
iportant
)f which
bject of
n which
se solu-
and in-
L require
3 of the
7-hich, it
r work,)
if incal-
^ing, or
r* is believed that this Chapter, if thoroughly-
taught, can not fail to quicken, strengthen, and
develope the reasoning powers ; bringing into
exercise, as it does, nearly every principle
taught in the twenty lessons of Chapter Sixth,
and also, the greater part of Chapter Seventhy it
must of necessity cause the pupil to acquire the
habit of systematically classifying his know-
ledge, that he may, at any time, be able to call
to his aid, such portions of it as will assist him
in illustrating or demonstrating the subject
under consideration.
The mind is composed of a variety of faculties
which require for their development appropriate
and constant exercise. That Intellectual Arith-
metic, when properly taught, is better calculat-
ed, than any other study, to invigorate and
develope these faculties, ta produce accurate
and close discrimination, and, to enable the
pupil to acquire a knowledge of the Higher
Mathematics with greater ease, can not for a
moment admit of a doubt.
J. F. STODDARD.
New York, August 1, 1860.
iscount,
eir vari-
ng these
rules in
(which
)erfectlv
ne con-
Suggestions to Teachers.
«.atVht%olif' "' *"'' -'^o^o experience i, limited, I
the I upj required to repeat and analvze it without nter
rnption, unless it be to .nake a „eoe.a.y critieil'l: cot
noHn'i7i''*r".^''^'^"'^^ upon promiscuously and
not in rotation, to take part in the recitation
Care should be taken that the language they use b.
strictly correct a. to construction and IrtifuIatZ.
If not carefully guarded, pupik, i„ their hurried solu
luteJlectual Arithmetic is a practical lesson in elocution
givl^foTCS ^"r*"".*'-* ^l^^ P-«cular forms '
imited, I
the most
)ranch of
Nation, to
ion ; the
exercise,
tly, and
Lit inter-
1 or cor •
sly and
use be
d solu-
. For
ivhich,
V pro-
!, v^en,
son in
ution,
in the
forms
inless
S.
ARITHMETIC.
I
CHAPTER I.
•
Lesson
I.
1.
2
and
1
are
how
Solution, -
—Two and one are 3.
2.
2
and
^
are
how
3.
2
and
3
are
how
4.
2
and
4
are
how
5.
2
and
5
are
how
6.
o
and
6
are
how
7.
2
and
7
are
how
8.
2
and
8
ar3
how
9.
2
and
9
are
how
10.
3
and
2
are
how
11.
3
and
3
are
how
12.
3
and
4
are
how
13.
3
and
5
are
how
14.
3
and
6
are
how
15.
3
and
7
are
how
16.
3
and
8
are
how
17.
3
and
9
are
how
18.
4
and
3
are
how
19.
4
and
4
are
how
20.
4
and
5
are
how
21.
4
and
6
are
how
22.
4
and
7
are
how
23.
4
and
8
are
how
24.
4
and
9
are
how
many ?
many ?
many?
many ?
many?
many ?
many ?
many?
many ?
many?
many ?
many ?
many ?
many?
many ?
many?
many ?
many ?
many?
many ?
many ?
many?
many ?
8
ADDITION.
did'LhTm p'"'^' - "'■«" '""' J"'- 1 = how many
^^^T^Sr^^^^^ ^l l^^Jo,n , ...y eogotbcr
how many cents did both receive ?" ° ^"'"^ '
3 |L^"rwirCd'UL^'; "-"'^^ ^- ''^'"
w n.a^;:ow':ti a;"/ "^ '"-^^''-^ ^ -- >
motL™H!!f!:''\S"'' ''''" 2 oranges, and his
31 PMo di o*"" "'ry ^'^ te receive in all ?
how'malfCd h Jrht', '"''''' -^ "-«•'* « -- .
-Jt Sran^haVhrtfe:'?"^ ^^^ «- ■'^ ^
Jny h'adtfe' ' "PP^-- -" I S-e hin. 3 ; how
^.Srhoir^t^rdtdT^^^^^^^^^^^
39. EalnhitT '^°'^, Many barrels did he buv C
hot"n.^c&brcostT'^' """^ " P'"-PP'e cost 8 ;
a
n
5
u
a]
P'
di
i
i
ADDITION.
9
ow
many
jy together
Harvey j
jave him
gave me
5 more ;
and his
B in all 1
ler gave
;ave me
) more ;
bim2
3 J how
4 cents
' both ?
nts for
and 6
> buy ?
vhat is
lost 8 ;
-, and
I
42. If it take 4 yards of cloth for a coat, and 3 for
a vest, how many yards will it take for both ?
43. Samuel bought 4 marbles, and found 4 ; liow
many had he then ?
44. Isaac bought 4 sheets of paper, and I gave him
5 ; how many had he then ?
45. A man bought a peck of apples for 4 cents, and
a peck of pears for 6 cents ; how much did the apples
and pears together cost ?
46. If Mary has 4 books, and her father should
give her 7, how many books would she then have ?
47. William has 4 marbles in his hand, and 8 in his
pocket ; how many has he in all ?
^ 48. Charles walked 4 miles, and rode 9 ; bow "far
did he go?
49. In a certain class there are 5 boys, and 4 girls ;
how many pupils are there in the class ?
Lesson II.
I.
5
and
4
are
how
2.
5
and
5
are
how
3.
5
and
6
are
how
4.
5
and
7
are
how
6.
5
and
8
are
how
6.
5
and
9
are
how
7.
6
and
5
are
how
8.
G
and
G
are
how
9.
6
and
7
are
how
10.
6
and
8
are
how
11.
6
and
9
are
how
12.
7
and
6
are
how
13.
7
and
7
are
how
14.
7
and
8
are
how
15.
7
and
9
are
how
many ?
many ?
many ?
many ?
many ?
mauv ?
ft/
many .'*
mauv ?
many ?
many ?
many ?
many ?
mauv ?
many ?
many ?
10
ADDITION.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
^ and 7 ire how
8 and 8 are how
S and 9 are L„..
8 and 5 are how
ow
9
9
9
9
9
9
and
and
and
and
and
and
6
8
9
many
many
many:
many
are how many ?
are how many ?
are how many ?
10 are how many?
7 are how many ?
11 are how many?
^b. Mary has answered 5 questions correctlv and
4 incorrectly ; .ow many questions was /he asked ^
nn q ^k .f'^^'^^ ™^^ *'''^ ^°.^^^' 5 one gave him 5 cents'
and the o her gave him 6 cents ; hovv many cent' did
they togetder give him ? ^ ^
h.!f ■ / '^^'' ?,''''^^^ ^^ ^^^ ^*^^' ^ doiiars, and a pair of
boots for 6 dollars ; how much was the cost of bothi
29. There are 9 boys on one bench and 8 on an-
frf \^^'T ^^^^^ ''^^'^ t^^^i-e on both ?
rfO. Maria gave her teacher 5 pinks and 7 rosea •
how many flowers did she give him P '
>^ . i^w ^''^' 'i"?u^ ^ ^q^^'rrols, and Henry cauoht
« ; how many did both catch ? ^ ^au^at
o^ sball we learn m two weeks ?
fnr ?'.. rV""^^ ^ """^^^ ^^^ ^ ^^^ts., and an or.nae
M f ' u'^'VI^^^' ^^^'^ *^^^ ^^« ^ec^i^e for both '^
how'ma^^ha'rhflL^^^^' ^^' '^^^^^^ ^^^ ^-^^ ^ ^
hofA.P'''^ bought G candies, and Sarah bought 8 •
how many were bought hj both ? ^ '
hot -^^^^^^^ ^^^ ,^ orangfis, and Catharine has 9 •
liow many oranges have both ? '
h,'pf 6 ^^;°Jrt'?^^i* 7 applet and his father ^ave
"-i-i ^ , now rnniiy had he then ?
■■*
I
ADDITION.
11
;^9. Minerva bought 7 yards of ribbon,and her mother
gave her 6 ; how many yards did she then have ?
40. There were 7 boys sitting on one bench, and 8
on another ; how many were on joth r
41. There were 7 hoys at pLay, and 9 other boys
joined them ; how many were there in all ?
42. If I have 8 cents in one hand, and 7 in the
other, how many have I in both ?
43. If Mary has 8 peaches, and Margaret has 9,
how many have both ?
44. Sally gave 9 cents for some thread, and 7 cents
for some needles ; how much did the needles and
thread cost her ?
45. Charles has 9 marbles, and Albert has 5 , how
many marbles have Charles and Albert ?
46. 9 birds were in a tree, and 6 were on the ground;
how many were there in all ?
47. Sarah gave 9 cents for some cinnamon, and 7
cents for some raisius ; how many cents did these
cost her ?
48. (reorge shot 9 pigeons, and James shot 8 ; how
many did both shoot ?
49. Eussel caught 7 fish, and Robert caught 5 ;
how many did both catch ?
50. In ore field there are 8 horses, and in another
there are 9 ; how many are there in both ?
Lesson III.
1. How many are 10 and 2 ? 10 and 3 ? 10 and
4? 10 and 5 ? 10 and 6 ? 10 and 7 ? 10 and 9 f 10
and 8 ? 10 and 10 ?
2. How many are 2 and 2 ? 2 and 12 ? 2 and 22 ?
2 and 32 ? 2 and 42 ? 2 and 52 ? 2 anH 62 ? 2 nnd
72 ? 2 and 82 ? 2 and 92 ?
12
ADDITION.
3. How many are 3 and 3 ? 3 and 13 ? 3 and 23 ?
3and33] 3and43? 3 and 53 ? 3and63? 3and73?
3 and 83 ? 3 and 93 ? 90 and 4 ?
4. How many are 4 and 4 ? 4 and 14 ? 4 and 24 ?
4 and 34 ? 4 and 44 ? 4 and 54 ? 4 and 64 ? 4 and
74 ? 4 and 84 ? 4 and 94 ? 98 and 2 ?
5. How man}^ are 5 and 5 ? 5 and 15 ? 5 and 25 ?
5 and 35 ? 5 and 45 ? 5 and 55 ? 5 and 65 ? 5 and
75 ? 5 and 85 ? 5 and 95 ?
6. How many are 6 and 6 ? 6 and IG ? and 26 ?
6 and 36 ? 6 and 46 ? 6 and 56 ? 6 and 66 ? 6 and
76 1 6 and 96 ?
7. How many are 7 and 7 ? 7 and 17 ? 7 and 27 ?
7 and 37 ? 7 and 47 ? 7 and 57 ? 7 and 67 ? 7 and
77 ? 7 and 87 ? 7 and 97 ?
8. How many are 8 and 81 8 and 18 ? S and 28 ?'
8 and 38 ? 8 and 48 ? 8 and 58 ? 8 and 68 ? 8 and
78 ? 8 and 88 1 8 and 98 ?
9. How many are 9 and 9 ? 9 and 19 ? 9 and 29 T
9 and 39 ? 9 and 49 ? 9 and 59 ? 9 and 69 1 9 and
79 ? 9 and 89 ? 9 and 99 1
10. How many are 10 and 11 ? 10 and 21 1 10 and
31 ? 10 and 41 ? 10 and 51 ? 10 and 61 1 10 and 71 ?
10 and 81 ? 10 and 91 ?
11. How many are 10 and 12 ? 10 and 22 ? 10 and
32 ? 10 and 42 ? 10 and 52 ? 10 and 62 ? 10 and 72 ?
10 and 82 ? 10 and 92 ?
12. How many are 10 and 4? 10 and 14 ? 10 and
24 ? 10 and 34 ? " 10 and 44 ? 10 and 54 ? 10 and 64 ?
10 and 74 ? 10 and 84 ? 10 and 94 ?
13. How many are 11 and 3 ? 11 and 13 ? 11 and
23 ? 11 and 33 ? 11 and 43 ? 11 and 53 ? 11 and
63 ? 11 and 73? 11 and 83 ? 11 and 93 ?
14. How many are 11 and 4 ? 11 and 14 ? 11 and
24? 11 and 34? 11 and 44 ? 11 and 54? 11 and 64?
11 and 74? 1184? 1194?
15. How many are 10 and 5 ? 10 and 15 ? 10 and
35
10
25
11
3i
3i
8i
8
7
7
8
8
ADDITION.
13
35? 10 and 45? 10 and 55? 10 and 65 ? 10 and 75?
10 and 85 ? 10 and 95 ? 10 and 25 ?
16. How many are 11 and 5 ? 11 and 15 ? 11 and
25? 11 and 35? 11 and 451 11 and 55? 11 and 65 r
11 and 75 ? 11 and 85 ? 11 and 95 ?
17. How many are 3 and 8 ? 3 and 18 ? 3 and 28 (
3 and 38? 3 and48? 3and 58? 3 and 68? 3and78 .
3 and 88? 3 and 98? ^ ,., o ^ o^ ?
18. How many are 8 and 4 ? 8 and 14 ? 8 and 24 ?
8and34?8and44? 8and54? 8and64? Sand 74?
8 and 84? 8 and 94? -..^.^ ao>7 7
19. How many are 7 and 7 ? 7 and 17 ? 7 and27 ?
7 and 37? 7 ond 47? 7 and 57 ? 7 and 67 ? 7 and 77?
7 and 87? 7 and 97 ? ..... ^op7
20 How many are 8 and 6 ? 8 and 16 ? 8 and 26 r
8and36? 8 and 46? 8 and 56? Sand 66? 8 and 76?
S and 86 ? 8 and 96 ?
Lesson VI.
i
1.
2.
3.
4.
5.
6.
7.
8.
9.
10,
11.
12.
13.
14.
15.
8 and
11 and
10 and
7 and
6 and
and
11 and
15 and
14 and
16 and
21 and
24 and
25 and
27 and
23 and
9 are
7 are
9 are
14 are
12 are
1.5 are
18 are
12 are
13 are
14 are
12 are
lo are
15 are
13 are
17 are
how
now
now
how
how
how
how
how
how
how
how
how
how-
how
how
many ?
many?
manv?
many
many ?
many ?
many :
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
14
ADDITION.
16.
17.
18.
19.
29 and 11 are how- many ?
30 and 20 are how many ?
34 and 15 are how many ?
32 and 18 are. how many?
1 dime ^^ ~ ^ '^'™''' '" '■^''^^^' 1« cents (J^ma^
tJh!S''^"^"^'/*'.''^""^^^"•^'• ^nd clenotes that the qiiauti-
-r «!?.!? T^"'^ ^^' '^ f'^^^«^^^' ^'^ to be added. Thus^4 + 2
20.
21.
22.
23.
2i.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
^9.
40.
41.
42.
43.
33 + 44 are how many ?
35+^5 are how many ?
36 + 12 are how many ?
40 + 36 are how many ?
40+29 are how 7nany ?
44 + 20 are how many ?
48 + 32 are how many ?
45 + 35 are how many ?
4 + 8 + 6 are how many?
8 + 2 + 7 are how many ?
10 + 7 + 3 are how many ?
12 + 10 + 9 are how maiay ?
15 + 12 + 6 are how many ?
1 8 + 4 + 10 are how many ?
24 + 16 + 12 are how many ?
22 + 33 + 11 are how many?
15 + 16 + 2 are how many*?
28 + 12 + 15 are how many ?
46 + 24 + 19 are how many ?
12 + 8 + 6 + 4 are how many^
24 + 10 + 6 + 12 are how many ?
22 + 32 + 6 — 10 are how many?
37 + 23 + 15 are how many ?
64 + 26+12-8 are how many?
J*
ADDITION.
15
?
f
nd wheo
i equal to
Qts equal
! qnauti-
IS, 4 + 2-
our plus
t
I
Lesson V.
1. Three boys, James, Joseph, and Jacob gave
some money to a beggar ; James gave him 6, Joseph
8, and Jacob 10 cents ; how many cents did they give
him ?
2. Give 8 cents to John, 4 cents to Morgan, and
2 cents to Samuel ; how many cents did all receive ?
3. Henry has 3 marbles, Harvey has 10, and Harry
has 7 ; how many marbles have all ?
4. Give 7 nuts to one boy, 6 to another, and 7 to
another ; how many nuts did the three boys receive ?
5. Eought a basket of strawberries for 7 cents, a
basket of cherries for 4 cents, and a basket of plums
for 8 cents ; how many cents did all cost ?
6. Lydia has 9 piiiks, Mary 10, and Ann 7 ; how
many pinks have they all ?
7. Bought a knife for 14 cents, and a ball for 12
cents ; how much did both cost ?
8. Gave 18 cents for an arithmetic, 2 for a pencil,,
and 10 for a slate ; how much did all cost ?
9. James had 12 cents, and his mother gave him
13 more ; how many had he then ?
10. Eobert shot 9 birds, Eichard shot 11, and
James shot 12 ; how many did they shoot ?
11. A boy bought a pound of butter for 14 cents,
a pound of meat for 8 cents, and a bunch of lettuce
for 7 cents ; how many cents did these articles cost ?
12. Bought a pound of raisins for 10 cents, a pound
of candies for 12 cents, and a pound of cinnamon for
15 cents ; how much was the whole cost ?
13. John had 20 marbles, Matthew 9, and Morgan
12 ; how many had they in all ?
14. James bought a pigeon ^br 9 cents, a robin for
10 cents, and a squirrel for 11: cents ; how much did
all cost him ?
15. A lady bought some pins for 15 cents, some
16
ADDITION.
thread for 10 cent?, and some lace for 18 cents ; bow
many cents did all these articles cost her ?
16. A gentleman bought a hat for 6 dollars, a vest
for 5 dollars, und a coat for 20 dollars ; how many-
dollars did he pay for them all ?
17. A man bought a watch for 40 dollars, a gold
chain for 15 dollars, and a gold pen for 5 dollars ;
how much did he pay for these three articles ?
^ 18. Jackson gave 25 cents to his sister, and 23 to
his mother ; how many cents did he give away ?
19. Bought a barrel of flour for 7 dollars, a barrel
of pork for 12 dollars, and a barrel of fish for 11 dol-
lars ; how much was the whole cost ?
20. Bought a horse for GO dollars, a cow for 20
dollars, and a colt for 25 dollars ; how much did all
cost ?
21. If your father should give you 12 cents, your
mother 14 cents, and your sister 4 cents ; how manv
cents would you then have ?
22. A boy spent 12 cents for confectionery, 9 cents
for a ball, and 5 cents for a top ; how many cents did
he spend for all ?
23. A man bought some butter for 57 dollars, and
some molasses for 23 dollars ; how many dollars did
both cost ?
24. A boy travelled 17 miles one day, and 23 the
next ; how far did he travel in the two 'days ?
25. A lady bought a hat for 7 dollars, a dress for
9 dollars, and a gold watch for 60 dollars ; how manv
dollars did all cost ?
26. A mechanic sold a wagon for 57 dollars, and a
sleigh for 43 dollars ; how much did he receive for
both ?
27. A boy saw 24 pisreons on one tree, and 36 on
another ; how many did he see in all ?
28. In a certain recitation 21 questions were an-
swered corrpnflv- nn^ Q iiinnT'T'ooflv . h'\\^ 'v in-
tions were asked during the recitation ?
ADDITION.
17
S ; bow
J, a vest
V many
a gold
dollars ;
s?
d23 to
a barrel
11 dol-
for 20
1 did all
ts, your
w manv
9 cents
mts did
irs, and
lars did
: 23 tbe
'ess for
tv many
i, and a
;ive for
136 on
3re an-
Y ques-
'M
29. Gave 87 dollp"s for a cbaise, 2 dollars for a
wbip, and 11 dollars far a buffalo robe ; bow mucb
was given for all ?
30. If a borse is wortb 60 dollars, and a sleigh 75
dollars, wbat is tbe value of both ?
31. Mattbew is 15 years old, Morgan is 7, and
Martin is 10 ; wbat is the sum of their ages ?
62. A man bought a load of hay for 7 dollars, a
load of rye for 36 dollars, and a load of wheat for 57
dollars ; how much was the whole cost ?
33. A man is 48 years old, and bis wife is 32 years
old : what is the sum of their ages ?
34. A farmer bought a horse for 60 dollars, and a
yoke of oxen for 75 dollars ; bow much did the horse
and oxeu together cost him ?
35. John gave 11 candies to his brother, 9 to bis
sister, and kept 12 himself ; bow many candies had
he at first ?
36. Simeon hoed 12 rows of corn, Simon 15, James
13, and John 11 ; how many rows did they together
hoe ?
37. A merchant sold 30 barrels of flour one week,
3«7 the next week, and 33 the following week ; bow
many barrels did he sell during the three weeks ?
38. A merchant sold a barrel of sugar for 25 dol-
lars, a barrel of rum for 15 dollars, and a hogshead of
molasses for 23 dollars ; how much did he receive for
all these articles ?
39. A man bought a firkin of butter for 9 doll'-'S,
a keg of molasses for 7 dollars, a box of cheese for 4
dollars, and a box of raisins for 5 dollars ; how much
wasthe entire cost ?
40. A lady bought a silk dress for 18 dollars, a mr-f
for 11 dollars, a shawl for 17 dollars, and a pair of
gloves for 1 dollar ; the entire cost is required.
18
SUBTRACTION,
CHAPTER 1 1.
Lesson I.
1.
If I have 3 apples, and give 1 of them to Rich-
ard, how many shall I have left ?
Solution.— If I have 3 apples and give 1 to Richard, I shall
have remaining the difference between 3 and 1 which is 2
apples.
2. William had 4 chesnuts, and gave 1 to his
brother ; how many had he left ?
3. Martha had 5 books, and on her way to school,
lost one of them ; how many had she left ?
4. Cornelia had 6 apples and gave 1 to her brother ;
how many had she left ?
5. Rachel had 10 pins and lost 1 of them : how
many had she left ?
6. Martha had 12 pears and gave 2 to Elizabeth ;
how many had she left ?
7. If you had 5 candies and should give 2 of them
away, how many would you have left ?
8. James had 6 apples and gave 2 away ; how many
had he remaining ?
9. Cornelia says she learned 12 letters yesterday
and has forgotten 3 of them ; how many does she re-
member ?
10. James had 10 marbles and lost 3 ; how many
had he left ? ^
11. Mary found 9 roses on her bush, and picked
oif 4 of them ; how many remained on the bush ?
12. How many are 4 less 2 ?
13. How many are 5 less 3?
14. How many are 6 less 3?
15. How many are 9 less 4?
f
th(
on
fr<
IG. How
many are 9 less 3?
SUBTRACTION.
19
to Bic bi-
rd, I shall
hich is 2
L to his
) school,
brother ;
m; how
zabeth j
of them
w many
jsterday
I she re-
w many
picked
:sh?
4
I
17.
18.
19.
20.
21.
22.
28.
24.
25.
26.
27.
28.
29.
80.
How
How
How
How
How
How
How
How
How
How
How
How
How
How
many
many
many
many
many
many
many
many
many
many
many
many
many
many
are 9
are 6
are 11
are 10
are 11
are 14
are 8
are 13
are 14
are 17
are 15
are 13
are 23
are 27
less
less
less
less
less
less
less
less
less
less
less
7?
5?
4?
4?
5?
4?
6?
3?
5?
7?
5?
less 10?
less 3?
less 7?
Remark. — The symbol— , is called mijitfs; and denotes that
the quantity on the right of it is to be taken from the quantity
on the left. Thus, 6—4 = shows that 4 is to be subtracted
from 6 ;— and ia read, 6 tninus 4 equal 2.
.•?f<
31. 8 — 5 are how
32. 9 — 7 are how
33. 10—8 are how
34. 11 — 8 are how
35. 12—6 are how
36. 13—8 are how
37. 14 — 8 are how
38. 18—8 are how
39. 22—12 are how
40. 24 — 14 are how
41. 12 — 4 are how
42. 28 — 8 are how
43. 20—5 are how
44. 20 — 8 are how
45. 20—9 are how
46. 20—7 are how
47. 20—10 are how
48. 20 — lo are how
49. 24—10 are how
many :
many?
many ?
many ?
many?
many?
many?
many?
many ?
many?
many?
many?
many?
many?
many?
many?
many ?
many ?
many ?
^
i
20
SUBTRACTION
50.
51.
52.
53.
54.
55.
66.
57.
58.
59.
60.
61.
62.
03.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
25—10 + 5 are
26—10 + 4 are
28—10 + 5 are
27—10 + 5 are
29—10 + 6 are
32—10 + 8 are
34—10 + 7 are
36—10 + 8 are
35-10+4 are
37—^0 + 7 are
38—10 + 8 are
39—10 + 9 are
47—10 + 6 are
40—12 + 9 are
42—20 + 7 are
45—20 + 5 are
45—20 + 6 are
47— 20 + S are
47 + 37 + 4 are
49—19 + 9 are
52—22 + 10 are
54 — 34 + 11 are
26—46 + 22 are
57—27 + 14 are
58—48 + 9 are
how
how
liow
how
how
many :
many ?
many '!
many ?
many ?
liow many ?
how many ?
many
many
many
many
many
many
many
how many
how many ?
how many ?
how many ?
how many ?
how many ?
how
]iow
liow
how
how
liow
how
many
62-
55-
68-
how
how many ?
how many ?
how many ?
how many
-30+10 are how many
-40 + 15 are how many
-48 + 16 are how many
are
74 — 34 + 15 are how many f
79. Gave 7 cents for a spool of thread, and 4 cents
for a lemon ; how much more did the thread coat
than the lemon ?
80. Paid 18 cents for a pound of butter, and 8 cents
for a pound of meat , how much more was paid for
the butter than for the meat ?
81. James bought 18 candies, and gave John 7 of
them ; how many had he left ?
i
..ii
SUBTRACTION.
21
82. Sold a quantity of wool for 27 dollars, aud re-
ceived ill payment a barrel of flour worth 5 dollars ;
how many dollars remain duo ?
83. James has 27 mar])les, and John has 17 ; how
many more has James than John ?
84. Harry is 15 years old, and Henry is 9 years
old ; how many years older is Harry than Henry ?
85. A teacher being asked how many pupils he
had, answered that he usually had 37, but at present
he had only 27 ; how many were absent ?
8G. A man purchased a watch for 37 dollars, but
found he had only 24 dollars with him ; how much
must he borrow to pay the balance ?
87. A has 9-1 sheep, and B has 44 ; how many
more sheep has A than B ?
88. Morgan gave 23 cents for some cake, and 14
cents for some cinnamon ; how much more did the
cake cost than the cinnamon ?
89. Michael had 29 cents and lost 14 : how many
had he left ?
90. In a certain recitation 47 questions were asked,
and 9 of them were answered incorrectly ; how many
were answered correctly ?
91. A man sold 23 sheep from a flock consisting of
93 ; how many sheep remained ?
92. Mr. B bought a horse for 35 dollars, and sold
it for 4G dollars ; how much did he gain ?
93. A cow was bought for 25 dollars and sold for
19 dollars ; how much Avas the loss?
94. A merchant bought a quantity of goods for 95
dollars, but being damaged was obliged to sell them
^ for 80 dollars ; how much did he loose ?
95. Frcm a vessel containing 57 gallons, 27 gallons
leaked out ; how much remained in it ?
i 96. A merchant bought a quantity of silk for 47
1 dollars, and sold it for 67 dollars ; how much did he
^ gain by the bargain ?
22
ADDITION AND SUBTRACTION.
97. A butcher has 57 sheep, and 4 4 lambs ; how
many more sheep has he than lambs ?
98. Paid 97 dollars for a quantity of sugar, and 43
dollffrs for some molasses ; how much more did the
sugar cost than the molasses .
iK
Lesson II.
CHAPTER FIRST COMDINED WITH THE PRECEDINO LESSON.
1. A boy has 7 chesnuts in one hand, and 4 in the
other ; how many more has he in one hand than in
the other ; and how many in both ?
2. Bought a barrel of fish for 8 dollars, and some
quinces for 3 dollars ; how much more did the fish
cost than the quinces ? "What was the cost of both ?
3. Gave 15 dollars for a cow and 6 dollars for a
sheep ; how much more was given for the cow than
for the sheep ? How much was given for both ?
4. Phineas gave 50 cents for a grammar, and 25
cents for an arithmetic ; how much was the cost of
both ? How much did one cost more than the other ?
5. Paid 15 dollars for s mrrel of rum, and 6 dollars
for a barrel of flour ; how much was the cost of both ;
and how much more did the rum cost than the flour ?
6. Sold a firkin of butter for 10 dollars, a kf - of
cheese for 5 dollars, and received in payment a bnixel
of flc \r worth 6 dollars ; how much remains duo /
7. James gave 12 cents for oranges, 15 cents for
cake, and had 13 cents remaining ; how much had he
at first ?
8. Mary b<H ght a comb for 10 cents, a spool of
thread for 12 - ?ntB, und a paper of needles for 8
cents ; she i■iimd^d the c^erk 37 cents ; how r.iuch
change ought she to receive ?
^
vfi
ADDITION AND SUBTRACTION.
23
bs ; how
r, and 43
I (lid the
ESSON.
4 in the
I than in
nd some
the fish
of both ?
rs for a
ow than
)th?
', and 25
i cost of
e other ?
6 dollars
of both ;
le flour ?
a kf , cS
a b;:in.. ;
due/
ents for
[i had he
spool of
es for 8
9. A man sold a cow for 20 dollars, a calf for 4
dollars, and a sheep for 3 dollars, and in payment re-
ceived a waggon worth 17 dollars ; how muca remains
due?
10. A lady bought a ribbon for 24 cents, some tape
for 8 cents, and some thread for 12 cents, — she had
only 60 cents ; how much remained after she paid for
these articles ?
11. Stephen, at a game of marbles, won 4 and lost
G, and then had only 8 remaining ; how many had he
atOrst?
12. Sampson having 9 apples, gave 4 to his mother,
and 3 to his sister j — for his generosity his father gave
him 13 more ; how many had he then ?
13. A man bought some cloth for 12 dollars and
sold it for 18 dollars ; how much was his gain ?
14. A farmer bought a horse for G3 dollars, and
exchanged it for a yoke of oxen,— these he sold for 87
dollars ; how much did he gain by the operation ?
15. A man bought a yoke of oxen for 97 dollars,
their services amounted to 40 dollars, and their keep-
ing to 13 dollars, — he then sold them for 80 dollars ;
did he gain or loose, and how much ?
16. A box of raisins was bought -for 3 dollars, a
firkin of butter for 15 dollars, and were both sold for
20 dollars ; how much was gained ?
17. A farmer sold a cow for 29 dollars, which was
5 dollars more than she cost, how much did she cost ?
y S. A drover bought some sheep for 40 dollars,
some cattle for 180 dollars, and sold them all for
200 dollars ; how much was his gain ?
19. A jeweler bought a watch for 20 dollars, a chain
for 40 dollars, a key for 2 dollars, and sold them all
for 42 dollars ; how much did he gain by the bar-
gain
20. 24 + 12 + 9 are how many ?
21. 10 + 30 + 15 are how many?
24
aj:)ditiox and subtraction.
22. 14 + 16 + 11 are how mnny ?
23. 36 + 9 — 12 are how inauy?
24. 38 + 22—15 are how many ?
25. 43 + 37 — 20 are how many ?
26. 13 + 26 — 25 are how many ?
27. 44—22 + 10—12 are how manv?
28. 27 + 1^3— 20 + 2 are how many"?
29. 15 + 25 — 30 + 15 are how many ?
30. 20 + 40—30 + 10 are how many ?
31. A boy bought a ball for 6 cents ; for how much
must he sell it to ^ain 4 ?
32. A merchant bought a hogshead of molasses for
47 dollars, and paid 3 dollars fov cartage; for how
much must lie sell it to gain 12 dollars ?
83. A grocer bought a hogshead of sugar for
30 dollars ; for what must he sell it to gain 18 dol-
lars ?
34. A drover bought sheep as follows : of one man
he '-ought 24, of another 8, and of another 22, : he
then sold 20 of them ; haw many remained unsold ?
35. A watch cost 40 dollars ; how must it be sold
to gain 13 dollars ?
36. Pour boys bought a melon ; one gave 3 cents,
another 4, another 8, and the other 6 ; how much did
they pay for the melon ?
37. Mary bought 16 candies at one shop, and 13 at
another, — on her way home she ate 11 of them ; how
many had she left ?
38. Mattheu- had 9 nuts, Mary gave him 10 more,
and John gave him enough to make his number 39 ;
how many did John give him ?
39. A fanner had 25 sheep in one field and 15 in
another, — he then bought enough more tomake h is
number 6G ; how many did he buy ?
40. John has 34 marbles, and Albert 25 ; how
many have they both ; and how many more has Jonu
than Albert ?
"^(Si
MULTIPLICATION.
25
CHAPTEE III.
Lesson I.
ow much
iasses for
for how
ugar for
18 dol-
one man
22,: he
msold ?
b be sold
3 cents,
Quch did
nd 13 at
im ; how
LO more,
ber 39 ;
d 15 in
lake h is
5 ; how
as Jonn
1.
2.
3.
4.
5.
6. Two
7. Two
8. Two
9. Two
10. Two
Two times
Two times
Two times
Two times
Two times
times
times
times
times
times
1
2
3
4
5
6
7
8
9
10
11. Two times 11
12. Two times 12
are
are
are
are
are
are
are
are
are
are
are
are
how many?
many-
how
how many ?
how many ?
how many I
how many ?
how
many
how many ?
how many ?
how many ?
how many ?
how many ?
mk 13. What will 2 oranges cost at 3 cents a piece ?
Solution. — If one orange cost 3 cents, 2 oranges will cost two
times 3 cents ; which are 6 cents.
14. What will 2 peaches cost, at 2 cents a piece ?
15. What will 2 apples cost, at 3 cents a piece ?
16. What will 2 pine-apples cv>st, at 8 cents a piece ?
17. What will 2 pounds of meat cost, at 5 uenta a
pound ?
18. What will 2 pounds of cinnamon cost, at 11
cents a pound ?
19. What will 2 pounds of raisins cost, at 12 cents
a pound ?
20. What will 2 citrons coat, at 10 cents a piece ?
21. What will 2 quarts of cherries cost, at 9 cents a
quart ?
22. What will 2 lemons cost, at 4 cents a piece ?
23. Three times 2 are how many ?
25. Three times 4 are how many ?
fesr.lfL'^:*''-^;^**^-
m,
2(6
MULTIPLICATION.
26. Three times 5
27. Three times 6
28. Three times 7
29. Three times 8
30. Three times 9
31. Three times 10
32. Three times 11
33. Three times 12
34!. Four
35. Tour
36. Four
37. Four
38. Tour
39. Four
40. Four
41. Four
42. Four
43. Four
times
times
times
times
times
times
times
times
times 11
times 12
3
4
5
6
7
8
10
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
how
how
how
how
many ?
many ?
many ?
many "
how many ?
how many ?
how
how
how
how
how
how
how
how-
how
how
how
how
many r
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
44. "What will 3 quarts of cherries cost, at 6 cents
a quart ?
45. What will 3 lead pencils cost, at 5 cents a piece ?
46. What will 3 quarts of milk cost, at 4 cents a
quart.
47. Whatwill 3 yards of ribbon cost, at 7 centsayd.?
48. What will 4 quarts of chestnuts cost, at 6
cents a quart ?
49. W hat will 4 yards of edging coat, at 5 cents a
yard?
50. What will 3 ounces of snuff" cost, at 8 cents
an ounce?
51. What will 4 ounces of cinnamon, cost at 7 cents
an ounce ?
52. What will 3 pounds of cheese cost, at 10 cents
a pound ?
53. What will 4 sheets of wadding cost, at 8 cents
a, ouccb '
M
54. What will 3 yards of calico cost, at H cents a
yaxd?
MULTIPLICATION.
27
r 9
•?
•?
'?
^?
■?
?
•P
P
9
?
*
?
?
■
?
■
■
it 6 cents
s a piece ?
4 cents a
sntsayd.?
ost, at 6
5 cents a
t 8 cents
at 7 cents
i 10 cents
it 8 cents
.1 cents a
55. What will 4 skeins of silk cost, at 9 cts. a skein ?
56. What will 3 yards of ribbon cost, at 12 cents
a yard ?
57. What will 4 pounds of starch cost, at 12 centa
a pound ?
58. What will 4 candlesticks cost at, llcts. a piece ?
59. What will 4 tops cost, at 10 cents a piece ?
60. What will 5 apples cost, at 4 cents a piece ?
61. Pive times 6 are how many?
are
62. Five times
63. Five times
64. Five times
Pive times
Five times
Five times
Five times
Six
65.
6Q.
67.
68.
69.
70.
71.
72.
73.
74.
75.
Six
Six
Six
Six
Six
Six
times
times
times
times
times
times
times
7
8
5
10
9
12
11
6
8
7
10
9
12
11
76. Seven times
77. Seven times
78. Seven times
79. Seven times
80. Seven times
81.
82.
Seven times
Seven times
6
8
7
10
9
12
11
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
are
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
how many ?
83. What will 5 barrels of flour cost, at 6 dollars
a barrel ?
84. What will 5 bushels of potatoes cost, at 5
dimes a bushel ?
85. What will 6 primers cost, at 6 cents a piece ?
uO.
..,^11 ft Vio««/^la /^f flqVi nnqf of. 7 finWaTS a
barrel ?
*%■
28
MULTIPLICATION.
a po J^ ""^^ ^ P'"^^^ ^^ "^^^*<^^ ^ost, at 7 cents
a hLT?^"^ "^'^^ ^ ^''^'^^ ^^ ^^g^^ ^°^*> ^* 12 dollars
centaTo" ' ^°"^'^ °^ ^^^^'^^^ -«^' «^ 10
oenTsaTo'undf ' ^^^"'^ ^^ ^^-^^« -«^' ^^ 12
92* mft li/l r^''''!f °^/°^'^ ^°«^' ^^ ^10 a bbl.?
93 What w . P°^^^' "^/^"^^^^^ ^^^^' ^^ ^^- ^ lb.?
qt wf . • 5 f°^*' ^ost, at 9 dollars a piece '^
piece> '''^^ ^ handkerchiefs cost, at 11 Lnts'a
96* wtl 7'U ^ i^^'*"^^^ '''^' ^* S ^^^*« a piece ?
97 Wh^ • I ^T^' '''^^ ^^ ^ ^i^^« a piece ?
98 wtl • ^P^^'^' "°'<^» ^* 8 dollars a piece ?
99* Wha :; 7 ^''-'^ '^ ?P^ ^°^^> ^ 1^ ^- - box ?
a qui;e? ^ ^^'''' ^^P^P^^ ^°«*' ^^ H cents
^. m What will 7 letter-folders cost, at 11 cents a
101. Eight times 8
ino' J^S'bt times 10
103. jNme times 8
104. Eight times 7
105. Nine times 9
106. Eight times 9
107. Nine times 11
108. Eiglit times 12
109. Nine times 10
110. Eight times 11
111. Nine times 12
are
are
are
are
are
are
are
are
are
are
are
liow many ?
bow many ?
bow many ?
bow many ?
bow many ?
bow many ?
how many ?
bow many ?
bow many ?
bow many ?
bow many ?
a bunoh^''''* "'^^ ^ ^'""'^'' "^"^''^ ^S'9 cents
lu Vbattl^r^'^T' T'' "' ^2 cts.a piece?
c»nft: wi*. ^ ''""«''^* of grapes cost, at 12
a
a
MULTIPLICATION.
29
at 7 cents
12 dollars
)st, at 10
)st, at 12
Oabbl.?
:9c. alb.?
a piece ?
I cents a
i a piece ?
piece ?
L piece ?
5. a box ?
II cents
L cents a
?
?
?
?
?
?
?
?
>
9 cents
I piece?
at 12
115. What will 11 yards of calico cost, at 11 cents
a yard ?
116. What will 19 balls of cotton cost, at 12 cents
a ball ?
117. What will 11 pounds of ginger cost, at 12
cents a pound ?
118. What will 10 blocks of tape cost, at 8 cents
a block ?
119. What will 12 yards of cloth cost, at 12 dimes
a yard ?
120. What will 13 pair of boots cost, at $4 a pair ?
Lesson II.
CHAPTEE3 FIEST AND SECOND COMBINED WITH THE PEECEDING
LESSON.
1. At 7 cents a piece, what will 9 pine-apples cost ?
2. If the postage on 1 letter is 3 cents, what will
be the postage on 8 letters ?
3. If it require 8 yards of calico to make 1 dress,
bow many yards will it require to make 7 dresses ?
4. If John obtain 2 credit-marks in 1 day, how
many will he have in 15 days ?
5. A man hired a horse to ride 12 miles, at the rate
of 5 cents a mile ; how much must he pay ?
6. Margaret's cloak contains 7 yards of merino,
worth 9 dimes a yard ; what is the value of her cloak ?
7. If a stage-coach go 9 miles in an hour, how far
will it go in 7 hours ?*'~"*^
8. At 2 dollars a^week,|how much will 20 weeks*
board come to ?
9. The fair by railroad from Albany to Boston is
5 dollars for 1 person ; how much will it be for a
family of 9 persons ?
so
MULTIPLICATION.
10. Helen had 8 rose bushes, and there were 7
roses on each ; how many roses had she in all ?
11. At 3 dl-^es a gallon, what will 15 gallons of
molasses cost ?
12. There are 10 rows of trees in an orchard, and
12 trees in each row ; how many trees are there in the
orchard ?
13. A traveller meeting 13 beggars, gave to each
of them 3 dimes ; how many dimes did he give to all
of them ?
14. A woman bought 11 yards of cloth and paid for
it with butter, — giving 9 pounds for a yard i how
many pounds of butter did it take to pay for the cloth?
How much did the cloth cost, provided the butter
was worth 10 cents a pound ?
15. In a certain corn jBeld there are 24 rows, and
30 hills in each row ; how many hills in the field ?
16. What will 40 steel pens cost, at 2 cents a
piece ?
17. What will 8 pair of snuffers cost, at 3 dimes a
pair ?
18. When 2 dimes are paid for 1 duck, what will
be the cost of 8 ducks ? of 10 ducks ? of 12 ducks ?
19. When hay is worth 8 dollars a ton, what is the
value of 2 tons ? of 4 tons ? of 3 tons f of 7 tons ? of
5 tons ? of 10 tons .? of 12 tons ? of 14 tons ?
20. At 2 dimes a piece, how many cents will 4 books
cost .^ 6 books ^ 10 books .? 12 books ? 11 books ? 7
books .? 16 books ? 13 books .^ 14 books .?
21. If 5 cents will buy 1 primer, what will be the
cost of 4 primers? of 6? of 9? of 8? of 10?
22. 6 plates, at 5 dimes a piece, will cost how
much ?
23. At a dime a piece, how much will 4 handker-
chiefs cost? 6 ? 8 ? 10 ? 12 ? 11 .? 14 .? 16 ^
24. At 6 dimes a 'niece how
cost? 4? 5? 8? 10? 12? 9? 7?
3 were 7
ill?
allons of
ard, and
3re iu the
> to each
ive to all
I paid for
rd i how
10 cloth?
3 butter
iws, and
field?
cents a
dimes a
hat will
lucks ?
at is the
ons .? of
4 books
Doks ? 7
be the
►st how
mdker-
2 geese
MULTIPLICATION. 31
25. At 12 cents a piece, how much will 3 candle-
sticks cost ? How much will 6?5?8?9?10?7?
26. If I pay 5 cents for riding 1 mile, how much
must I pay for riding 7 miles ? 8 miles ? 6 ? 9 ? 10 ? 12 ?
27. At 7 cents a yard, how murh will 5 yards of
ribbon cost ? 6 yards ? 8 yards ? 9 yards ? 10 yards ?
12 yards ?
2*8. If a tooth-brush cost 18 cents, how much will
4 cost ?
29. 9 turkeys will cost how much, at 8 dimes a
piece ?
30. At 14 cents a quire, how much will 2 quires
of paper cost ? 3 quires ? 4 quires ? 5 quires ?
31. How much will 7 pictures cost, at 5 cents a
piece ? at 6 cents a piece ? at 8 cents a piece? at 10
csnts a piece ?
32. How much will 8 knives cost at 6 dimes a
piece ? at 10 dimes a piece ?
33. At 10 dimes a piece, how much will 4 caps
cost? 5? 6? 8? 9? 12? 14? 17? 19? 21 ? 25 ?
34. At 40 cents a day, how much will 2 day's work
amount to? 5 days work.
35. If one paper of candy cost 6 cents, how much
will 3 papers cost ? 5 papers ? 8 papers ? 12 papers ?
36. At 7 dollars a hundred, how much will 4 hun-
dred feet of cedar boards cost ? 9 hundred feet ? 10
hundred feet ?
37. If 1 bushel of wheat cost 60 cents, how much
will 6 bushels cost ? 4 bushels ? 5 bushels ?
38. How much will 8 muffs cost at 5 dollars each ?
39. How much will 19 lead pencils cost, at 5 cents
each?
40. How much will 11 boxes of cheese cost, at 4
dollars a box ? at 5 dollars ? at 8 dollars a box ?
41. How much will 12 1 ^rrels of pork cost at 5
dollars a barrel ? at 8 dollars ? at 9 dollars ? at 10
dollars ?
42. How much will 9 tons of hay cost, at 13 dol-
lars a ton ?
4
32
ADDITION, SUBTRACTIOX.
43. James ia 9 years old, and his father is 4 times
as old as he ,s ; how old is his father ?
44. Jane's froct contains 7 yards of silk, worth 8
dimes a yard i what was the value of the silk ? Pro-
c" st' f tdt:'. ""'' ' •^""'"^^ ' "- ■"-" -« the
hot'ioStl'il -rLfve'r^al'? ^^-^^ '' -"^^ « '^»^''
46. If I earn 12 dollars in a month and spend 8
how much shall I have at the end of 12 montC ? '
47. If I earn 12 dollars a month and pay 25 cents
a week for washing, and 2 dollars a week for board
moIthT)"? "'" ^ '^"'■^ ''^ '^' '"^ °f ^"^ ^««M10
»plf fi /' ^ '"^^i^ *?"?? °^ '"'^' "' 1- ^o"'"'s a ton, and
tons at 10 f ,/^ "^"^ "= ", *°"' '""1 '"^^ 3 remaining
tr;ptatlit ""'''"' tow much shall I gain b^
yard ■ h7t^ ^ V'"''' f broadcloth, at 4 dollars a
yard, but, bemg damaged, I was obliged to lose 18
ddlars by the sale of it ? how much Si I receive for
Sn bf sfiofng ? '"-^ ''' """"^ '>°- »-'^ ^"^^U I
51. A man bought a horse for 80 dollars, mid 2
dollars a week for his keeping, and received 4 dXs
a week for his work ;-at the expiration of 10 weeks
thVotttlfon'T '° '"'''''' ■' '°- --^ ''' ^^ ^^t
52. For how much must I sell 4 barrels of wheat
which cost me 8 dollars a barrel, to gain 8 dol W
each ? " ^" '"'* °^ ^ '°'''' ** 25 dollars
54. Provided a hunter should kill 5 pigeons and
wound 4 at every shot ; how manv wonlL!, V°» ."?
wound respectively, by shooting 8 times ? ' """
AND MULTIPLICATION.
33
i 4 times
worth 8
c? Pro-
was the
8 days,
spend 8,
ths?
25 cents
c board,
leks (10
OD, and
maining
s^aiu by
lollars a
lose 18
eive for
i a bar-
shall I
paid 2
dollars
' weeks
jain by
wheat
irs?
dollars
IS and
ill artrl
55. If a man travel 29 miles in a day, how many
miles will he travel in 6 days ?
56. How much will 8 months' wages amount to, at
18 dollars a month ?
57. If 10 men eat 18 pounds of butter in 1 week,
how long would it last 1 man ?
58. If 80 dollars will pay for 4 dinners for 20 men
how many dinners would it buy for 1 man ?
59. Bought 3 yards of cloth for a coat, at 7 dollars
a yard, the buttons and cord cost 2 dollars, buckram
and wadding 1 dollar, — paid for making it 6 dollars ;
for how much must I sell it to gain 5 dollars ?
60. If 17 men can do a piece of work in 9 days,
how many days would it take 1 man to perform the
same work ?
61. Two men start from the same place, and travel
in opposite directions ; — one at the rate of 7 miles an
hour, the other. 9 miles an hour ; how far apart will
they be in 2 hours ?
62. Two men start from the same place, and travel
the same way ; — one at the rate of 3 miles an hour^
the other, 8 miles an hour ; how far ap art will they
be at the end of 8 hours ?
63. Two men are 50 miles apart, and approach each
other " ^t the rate of 2 miles an hour, the other,
3 miles. . iv ; how far apart will they be at the
end of 5 ^
64. If 1 Oiange is worth 4 apples, how many apples
must be given for 13 oranges ?
65. A man earned 80 cents a day, and paid 50
cents a day for his board and washing ; how much
had he left at the expiration of 6 days 1
* 66. Jane bought 4 yards of silk, at 2 dollars a yard,
3 shawls, at 10 dollars each, and some delaine for 10
dollars ; she paid 5 ten-dollar bills ; how much ought
she to receive back ?
67. Mary bought 5 yards of silk, at 8 dimes a yard,
•i
34
ADDITION MULTIPLICATION.
and 8 yards of linen, at 9 dimes a yard ; how many
yards did she buy, and how much did all cost ?
bS. In a certain school there are 12 girls, and 3
times as many boys, less 8 ; how many boys in the
school, and how many boys and girls together ?
69. John has 7 books, and Mary has 4 times as
havTboth ? '' '"'"''^ ^'' ^^""'^'^ ""^ ^°^ '^^"^
70 Albert has 9 marbles, Aaron 3 times as many,
less 7, and Amos has twice as many as both, less 8 :
etleiT^ ^''''^' ^""^ ^""^ "^^""^ ^^""^ ^^^y *°-
71. Perry worked for Elisha 4 days, at 6 dimes a
day ;---±^li8ha gave him 7 bushels of corn, at 3 dimes
a Dusnel ; how much was then due Perry ?
72. A merchant bought 25 pounds of sugar for 125
cents and sold 15 pounds of it, at 6 centos a pound,
and the remaining 10 pounds, at 4 cents a pound
how much did he gain by so doing ?
73. tf the interest on i dollar for a year is 6 cents,
pound 7^^^ ''''" ^^ ^°''''^' °^ ^®^^ ''°'*' ^* ^ ^®^*' ^
75. When beef is 5 cents a pound, and pork 9
cents ; how much more will 9 pounds of pork cost
than 9 pounds of beef ? ^
76. Mary bought 35 quarts of milk, and on her way
home she spilled 4 times 2 quarts, less 3 quarts : how
many quarts had she remaining ?
77. Henry is 4 feet in height and John is 5 : and 5
times the sum of their heights, considered as a num-
oIIIa TVI ^^''' ^^*^""'^ ^g^ + 1^ years. Ee'^
quired, the father's age.
m.lt ^^J"" °''^°^^ ''^'^^ ^^^^^'^ lemon twice as
much, and a melon 4 tunes as much as the orange and
'^^^^F
DIVISION.
35
low many
>st?
Is, and 3
)y8 in the
ler?
times as
low many
as many,
3, less 8 J
they to-
dimes a
; 3 dimes
r for 125
a pound,
pound ;
6 cents,
he same
I cents a
pork 9
irk cost
her way
;s ; how
; and 5
a num-
3. Ee-
vice as
ige and
lemon together, less 14 cents, how much more will 3
melons cost than 3 oranges and 3 lemons ?
79. James has 9 walnuts, John twice as many
less 8, and Joseph twice as many as James and
John + 7 ; how many has each, and how many have
all?
80. If an apple cost 2 cents, an orange three times
as much less 4 cents, and a pine-apple three times as
much as the apple and orange + 5 cents, what will
be the cost of all three ?
CHAPTER IV.
Lesson I.
1. 8 are how many times 2 ?
times 2 ?
times 2 ?
times 2 ?
times 2 ?
times 2 ?
times 3 ?
times 3 ?
times 3 ?
times 3 ?
times 3 ?
times 3 ?
times 3 ?
times 2 ?
times 2 ?
times 2 ?
times 2 ?
times 2 ?
times ^ I
times 4 ?
SOLUTION.-
-8 are as many times 2 as 2
8, which are
4 times.
2.
6
are
how
many
3.
4
are
how
many
4.
,10
are
how
many
5.
12
are
how
many
6.
14
are
how
many
7.
6
are
how
many
8.
9
are
how
many
9.
12
are
how
many
10.
15
aia
how
many
11.
18
are
how
many
12.
21
are
how
many
13.
24
are
how
many
14.
16
are
how
many
15.
18
are
how
many
16.
20
are
bow
many
17.
22
are
how
many
18.
24
are
how
many
19.
26
are
how
many
20.
28
are
how
many
36
DIVISION.
^^i::z;^X LTi: lr„.^^ istt tSiT
SoLUTioN.-If for 2 cents I cnn buy 1 apple, for 1 cent T „„„
b.y_|^of an app.e , «„„ f„, 4 eeots, /timc's'^^Wci ^ '/or S
buy fcA- c/nt? " ''''''• '■"^ """^ "■■""e^^ «"■> I
boughtlw's ::„!;?"""' '"" """^ P^""^^' "- ''«
can te toughir iVd"!^^ "■''"^- ^"'^^ "^ -''-
bollnVoTelT""'' ''°" ""'"^ '«"°- -^ b^
be tugt fo/io c^en'tf?' '°" """^ ''''' °' '"?« "^
27. At 2 dimes a bushel, how many bushels of
apples may be had for 12 dimes ? ^
28. How many pounds of ginger, at 2 dimes a
pound may be had for 14 dimes ? •
a b?si.e?°e:nTLS\VLr P ''^''"^^' ^* ^ "=^"'^
be'L.^aTs'dSraVarT?"''"^ ^"'^ °' "'"''' "-
ol. For 18 apples; how many oranges can ha
bought at the rate of 2 apples for 1 oranle ?
rafeantl"7t S d°fllts"' ^* ' '"'"' '' "^
34. For 22 dollars; how many sheen mav h^
bought, at 2 dollars a piece ? ^ ^ ^ ^^
3 dtes^'a pie'ceT "'''"' "'^ ^' '^^ ^^^ '' ^™««' ^*
DIVISION.
37
I can jou
Bents I can
fiich are 2,
he above.
cent I can
are ^ or 2
!S can I
s can be
•f calico
can be
;ape can
ihels of
imes a
3 cents
>th can
jan be
can be
a bar-
iy be
teS; at
36. At 8 cents a piece, how many tops may be had
for cents ?
37. If 1 peck of beana coat 3 dimes, how many
pecks can be bought foi 21 dimea ?
38. At 3 cents a mile, how many miles can I rid©
for 24 cents ?
39. How many bushels of rye, at 4 dimes a bushel,
may be bought for 12 dimes ?
40. How many books, at 4 dimes each, can be
bought for 20 dimea ?
41. 8 are how many times 4 ?
42. 12 are how many times 4 ?
43. IG are how many times 4?
44. 10 are how many times 5 ?
45. 15 are how many times 5 ?
46. 20 are how mauy times 6 ?
47. 28 are how many times 7 ?
48. 32 are how many times 4 ?
49. 30 are how many times 5 ?
50. 35 are how many times 5 ?
51. 36 are how many times 4 ? '"_
52. 40 are how many times 5 ?
53. 44 are how many times 4 ?
54. 30 are how many times 6 ?
55. 48 contains 8 how many times ?
Solution.— 48 contains 8, 6 times [because 6 times 8 are 48.]
56. 24 contains 8 how many times ? 4 ? 12 ? 3 ?
57. 36 contains 9 how many times ? Q? Z? 2?
58. 54 contains 2 how many times .^ 3 .^ 9 .?
59. 75 contains 3 how many times ? 5 .? 15 ?
60. 63 contains 2 how many times ? 4 ?
61. At 5 dimes each, how many turkeys can be
had for 25 dimea ?
62. If the wages of 1 day is 4 dimes, what will be
the wages for 9 days ?
63. How many days will a man be required to work
for I'Z dimes, if he icceive 4 dimes a day ?
D
38
DIVISION.
64. If a boy spends 5 cents a day, how many days
will it take him to spend 15 cents ?
65. A boy had 20 marbles, and divided them
equally among his 5 brothers ; how many did each
receive ?
QQ. A boy divided 28 cents equally among 4 poor
women ; how many cents did each receive ?
67. A farmer gave 4 of his laborers 32 bushels of
corn ; how many bushels did each receive ?
68. If 5 quarts of molasses cost 30 cents, what will
1 quart cost ?
69. At 5 cents a yard, how many yards of ribbon
may be had for 35 cents P how many for 50 cents ^
70. How many pine-apples, at 8 cents each, can be
obtained for 40 cents ? for 56 cents ?
71. If a man travel 45 miles in 9 hours, how many
miles does he travel in I hour ?
72. If a man travel 5 miles in an hour, how many
hours will it take him to travel 40 miles ?
73. How many yards of cloth, at 4 dollars a yard,
can you buy for 32 dollars ?
74. In a certain orchard there are 48 trees standing
in rows, and 6 trees in each row ; how many rows are
there in the orchard ?
75. "Fov 56 dollars, how many barrels of pork can
be bought, at 8 dollars a barrel)
76. If a man can travel 6 miles in an hour, how
long will it take him to travel 42 miles /
77. How many yards of cloth, at 4 dollars a yard,
can you buy for 36 dollars /
78. A butcher gave 39 dollars for sheep, at the rate
of 3 dollars a head ; how many sheep did he buy ?
79. 45 dollars were given for 9 barrels of flour ;
how much was it a barrel ?
^ 80. How long would it take to travel 72 miles, at
the rate of 3 miles an hour P
many days
ided them
ly did each
ong 4 poor
bushels of
*
I, what will
i of ribbon
)0 cents ^
ich, can be
how many
how many
iirs a yard,
>s standing
ly rows are
' pork can
hour, how
irs a yard,
it the rate
le buy ?
3 of flour ;
\ miles, at
DIVISION.
Lesson II.
39
1. 20 are how many times 2? 4if 10 /
2. 22 are how many times 1 i ?
3. 24 are how many times 3 ? 4 ? 2 ?
4. 25 are how many times 5 ^
5. 28 are how many times 2 .? 7 ?
6. 30 are how many times 2 ? 3 ? 5 .?
7. 32 are how many times 2 ? 4 .^ 16 ? 8 ?
8. 34 are how many times 17 ?
9. 40 are how many times 2 ? 4 .? 5 .? 8 ?
10. 44 are how many times 2 ? 11 .?
11. 46 are how many times 23 ?
12. 48 are how many times 2 5* 3 ? 4 ? 6 ?
13. 50 are how many times 2? 10?
14. 56 are how many times 2 ? 7?
15. 57 are how many times 3 ?
16. 60 are how many times 2? 3? 4? 5? 6?
17. 64 are how many times 2 ? 4 ? 8 ?
18. 66 are how many times 2 ? 3 ? 6 ?
19. 68 are how many times 2 ? 4 ?
20. 70 are how many times 10? 2?
21. 72 are how many times 2 ? 4 ? 6 ? 8 ?
22. 5 are how many times 2, and how many re-
maining ?
Remark— Whenever there is a remainder, it may be men-
tioned simply as a remainder.
23. 7 are how many times 2 ?
24. 17 are how many times 4 ? 2 ? 5 ?
25. 18 are how many times 6 ? 4 ? 2 ?
26. 34 are how many times 4? 6? 5? 2?
27. 25 are how many times 5 ? 4 ? 2 ? 3 ?
28. 16 are how many times 9? 4? 8? 7?
29. 32 are how many times 7 ? 5 ? 6 ?
30. 63 are how many times 9 ? 4 ? 6 ? 6 ?
31. 74 are how many times 2 ? 4? 6? 7?
40
DIVISION.
32. 80arehowmanytimes2?3?4?5?6? 788?
33. 84 are how mauy times 2 ? 3 ? 4 ? 5 ? 6? 7 ? 8 ?
34. 15 are how many times 4?6?7?*8?
35. 29 are how many times 2?3?4?5?6972
36. 90 are how many times 2?4?6?8?9?11?
37. 144 are how many times 2 ? 4 ? 6 ? 8 ? 12 ?"
Lesson III.
for\4'^c*entsf *' '''^' ^""^ many lemons can you buy
SoLUTioN.~If 1 lemon cost 2 cents, for 14 cenU T n«« u
as many lemons as 2 is contained times in 14 which areT ^
Another SoLUTioN.-If for 2 cents I can buy 1 lemon for i
cent, lean buy 1 half of a lemon, and for 14 cYnts UrL 1
half, which are 14 halves, or 7 lemons. ' ""^^^ ^
2. How mauy boxes of cheese, at 4 dollars a hnr-
may be had for 12 dollars ? ^ ^""^^
3. If one hundred pounds of hay cost 3 dollars, how
many hundred may be had for 15 dollars ?
4. If one barrel of flour support 20 persons one
week how many persons will it support 4 weeks ;
5. If 1 man can ride 1 mile for 4 cents, how far
can 2 men ride for 80 cents ? ""w lar
6. If 10 men accomplish a certain piece of work in
2 days how long wil it take 1 man to do the samel
7. It 3 yards of cloth make one coat, how manv
coats will 18 yards make ? ^^^
8. If I receive 12 dollars interest in one year in
how many years will I receive 144 dollars interest
9. A man travelled 7 miles in one hour, at the same
rate how long would it take him to travel 63 mT,'
^e\'Jol eZZs'' '-''''' '^^^ ''^'^y -- -^
11. How manv noriH ^an ■''•'^p ^"■~ ^ — '^'^ • •« -
pen cost 3 cents ^ '
MULTIPLICATION AND DIVISION.
41
) ? 6 ? 7 ? 8 ?
5?6?7?8?
?8?
?5?6?7?
8?9?11?
3?8?12?
m you buy
ts I can buy
h are 7.
lemon, for 1
, 14 times 1
lars a box,
>nars, how
rsons one
^eeks ;
, how far
f work ju
he same ?
low many
> ytar, in
Qterest ?
the same
33 miles ?
!Ows may
mid, if i
12. If 8 apples are worth 40 chestnuts, how many
chestnuts is 1 apple worth ?
13. How many cents is 1 lemon worth, if 12 lemons
are worth 48 cents '(
14. How much will 1 cord of wood cost, if 20 cords
cost 40 dollars ?
15. If 1 pound of beef cost 7 cents, how much will
19 pounds cost ?
16. For 147 cents, how many pounds of sugar can
be bought, at 7 cents a pound ?
17. If 9 yards of cloth cost 53 dollars, for how
much must it be sold a yard to gain 10 dollars ?
18. If 7 barrels of flour cost 88 dollars, and were
sold, at 7 dollars a barrel, what was the gain ?
19. How many peaches, at 4 cents each, may be
bought for 96 cents ?
20. How many yards of cloth, at 4 dollars a yard,
can be bought for 110 dollars ?
21. How many oranges, at 3 cents each, must be
given for 18 lemons worth 4 cents each ?
22. If 15 sheep cost 75 dollars, what will 1 sheep
cost ?
23. "Which will cost the most, 4 barrels of wheat
flour, at 9 dollars a barrel, or 12 brrrels of corn, at 4
dollars a barrel, and how much ?
24. How many barrels of beef, at 3 dollars a barrel,
can be bought for 64 dollars ?
25. How many pounds of fish, at 5 cents a pound,
may be had for 95 cents ?
26. At 7 cents a pound, how many pounds of lead
may be had for 84 cents ?
27. How long will it require to travel 105 miles,
at the rate of 5 miles an hour ?
28. A person divided 72 peaches equally among 6
boys ; how many did each receive ?
29. 148 marbles were divided equally among some
42
MULTIPLICATION AND DIVISION.
boys ; how many boys were tbere, provided each bov
received 2 marbles ? *^
30. How many pounds of butter, at 14 cents a
P°o? \?^' ^^ ^-^^Sbt for 28 apples, at 3 cents each ?
31. At 7 cents a bottle, how many bottles of ink c-
you buy for 14 sheets of paper, at 2 cents a sheet ? '
62. In how many days can 1 man do as much as 7
men in 8 days ?
33. In how many days can 2 men do as much work
as b men m 3 days I
34. In how many days can 4 men earn as much as
8 men m 6 days ?
35. In how many days can 15 men earn as much
as 3 men in 25 days ?
36. In how many months will 6 horses eat as much
as 18 horses m 5 months ?
37. How many men can in 7 days earn as much as
28 men m 4 days ?
38. In 10 days 6 men will earn as much as how
many men m 5 days ?
39. How many yards of cloth, at 4 dollars a yard,
may be had for 4 sets of chairs, at 12 dollars a set ^
40. A farmer gave ]3 barrels of flour, worth 4 dol-
lars a barrel, for 26 yards of cloth; how much was
the cloth a yard ?
1^
«
Lesson IV.
CnAPTERS FIRST, SECOND, THIRD, AND FOURTH COMBINED.
1. 4 times 6 are how many times 2 ?
2. 4 times 9 are how many tim^es 8 ?
3. 4 times 8 are how many times 2 ?
IN,
M
FUNDAMENTAL RULES.
43
3d each boy
4.
5.
14 cents a
6.
cents each ?
7.
IS of ink c; .
8.
1 a sheet ?
9.
3 much as 7
10.
11.
much work
12.
13.
as much as
14.
15.
■n as much
16.
17.
at as much
18.
19.
as much as
20.
21.
ch as how
22.
^ 23.
irs a yard.
m ^^'
rs a set ?
m 25.
orth 4 dol-
W 26.
much was
27
28.
29.
30.
31.
32.
33.
)MBINED.
34.
35.
36.
Therefore)
37.
^B 38.
Jl 39.
WtM 40.
4 times 10 are how many times 5 ?
4 times 12 are how many times 6 ?
4 times 14 are how mauy times 7 ?
5 times 9 are how many times 15 ?
6 times 8 are how mauy times 4?
5 times 12 are how many times 15 ? 6 ?
6 times 7 are how many times 2 ?
6 times 8 are how many times 12 ? 3 ?
4 times 6 are how many tim'^s 8 ?
7 times 15 are how many times 5 ?
12 times 7 are how many times 21 ?
8 times 7 are how many times 4 ?
How many times 12 are 9 times 4 ?
How many times 20 are 5 times 4 ?
How many times 9 are 3 times 21, + 9 ?
How many times 5 are 7 times 15, + 10 — 5 ?
How many times 9 are 3 times 36, — 2 + 11 ?
How many times 12 are 9 times 4, + 24— 12 ?
How many times 21 are 9 times 14,-! 42 1
How many times 7 are 3 times 14, + 21 — 14 ?
How many times 5 are 8 times 10, + 5 — 15 ?
How many times 5 are 10 times 6,+ 15 + 5 ?
How many times 5 are G times 1 5, + 10 + 15 ?
10 times 4, + 2 are how many times 7 ? 2 ?
8 times 9, — 2 are how many times 5 ?
12 times 8, — 8 are how mnny times 2 ?
26 times 11, — 6 are how many times 28 ?
7 times 8, + 4 are how many times 12 ^
6 times 7, + 4 are how many times 2 ?
5 times 8, + 8 are how many times 6 ?
4 times 9, — 4 are how mauy times 8 ?
9 times 5, — 3 are how many times 7 ?
7 times 12, — 14 + 5 are how many times 5 ?
4 times 15, + 7—3 are how many times 8 ?
6 times 7, + 14 — 2 are how many times 9 ?
11 times 13, + 11 — 14 are how many times 7 1
11 times 1 5,-10 + 15 are how many times 17 ?
44
♦I
SIMPLE PROPORTION.
Lesson V.
PBAOIIOAI, Q0IST.ONS OOMBZKr.VG OHAPTra, THIRD AND FOURTH.
cos^t ?^''^ "^^'"^ "™* * "'''*'' '"''" """=•' ^'U 3 apples
cost 8 times 2oe;,s;;th "e'e^'L^^^r' ' ""•" ' "PP'^'"'"
2. If 2 pears cost 16c., how much w , pears cost ?
quL"ets?r" *="' '^ •=^"*^' '^^ ■"-'^ ^^
oratge's cosu"^'' "°'* '' "'''''' ''"^ '""<'•' ^"1 9
pefches" cLrr'^'' '"^^ '' '=^''*^' '^"^ ■"«<=>> will 9
lemlYcostr""' "°^* '* •'^"*=' ''°^ ""»<='' will 7
6 /ard^f 2u ' "^ ^''P^ '=°^* 18 cents, how much will
wilteUSuSir 2« <^--' '"- "--y cents
-ill V'y'aKstt """^"'' '=°^* ^'^^ <=«"'«' •>»- »uch
7 bo^oWsu"''' '""*^* '^''"''' '"'"' "^y oe^te will
12* If 10 t»:f' ""'''■,"'"* ^^ •=""*'■ what will 2 cost ?
be|eSjr7fetor2ro?a^^^^^^
cost 45^dimeTr'' "" '' ^'"^^ of silk cost/if 5 yards
thillfY " ""^J *?^'' 15 "''«» i" 3 tours, how far at
this rate can he travel in 9 hours ? 5 hours 2 7 hours
4 dollars how A '^' f/.i?*^ "^ P'^^^r 20 miles cos
nouars, how far could it be carried for 12 dollarq ?
21 yard^oT clTh^ T.' "' ?""'*'?"»' <=- >- -fou of
ZfJ,^!.. °* ??^^' 't 3 pair can be cut out nf a -
-I ""o isarae Kind of cloth ?
.#
'-•A
"^ J ITS, -^.U^
r
SIMPLE PROPORTION.
45
IND FOURTH.
U 3 apples
^ostihalfof
apples will
3ars cost ?
Lch will 3
ch will 9
ch will 9
5li will 7
mch wi]l
ny cents
►w much
mts will
! 2 cost ?
uch will
5 yards
^ far, at
hours ?
es cost
liars ?
out of
7 l.Ti Vl^J
17. How much will 30 pounds of sugar cost, if 6
pounds cost 42 cents ?
18. How much will 18 pounds of veal cost, if 6
pounds cost 42 cents ?
19. How much will 75 pounds of pork cost, if 9
pounds cost 75 cents ?
20. How much will 20 weeks' board amount to, if
7 weeks' board cost 14 dollars ?
21. How much will be the wages for 1 year, if 4
months' wages amount to 48 dollars ?
22. How much will be the cost of 25 bushels of
apples, if 13 bushels cost 260 cents ?
23. How much will 14 pounds of cheese cost, if 6
pounds cost 54 cents ?
24. If 7 quarts of milk cost 35 cents, how much
will 36 quarts cost ?
25. If 4 men can do a certain piece of work in 12
days, in how many days will 3 men do the same
work?
26. I gave 72 dollars for a quantity of cotton, and
sold it for 12 yards of cloth ; how much did the cloth
cost me a yard ?
27. Gave 15 pounds of sugar for 5 pounds of but-
ter ; how much did the butter cost a pound, provided
8 pounds of sugar were worth 56 cents ?
28. If 4 chestnuts are worth 8 walnuts, how many
walnuts are 27 chestnuts worth ?
29. If 7 yards of broadcloth are worth 35 dollars,
how many boxes of butter, at 3 dollars a box, would
9 yards of this clota buy ?
30. A man bought 4 barrels of flour for 20 dollars,
and gave 3 of them for cider, at 3 dollars a barrel ;
how many barrels of ciJer did he get ?
31. A man bought 14 barrels of cider for 56 dol-
lars, and gave 5 barrels of it for cloth, at 2 dollars a
vard ; how manv vards did he receive ?
32. A merchant having 15 yards of cloth worth 75
46
SIMPLE PROPORTION.
+1
dollars, gave 10 of them for pork, worth 10 dollars a
barrel ; how many barrels did he receive ?
33. When 9 bushels of rye were worth 45 dimes
"f shels were given for 15 yards of cloth • how
much did the cloth cost .a yard ? '
34 If 35 yards of cloth iost 140 dollars, how much
will 95 yards of the same cloth cost ?
36. How many boxes will be required to contain
56 bushels, provided each box contains 8 bushelsT
d7. How many barrels of onions, at 3 dollars a bar-
r^,^must be given for 21 boxes of raisins, at 2 dolts
38 A farmer bought 9 yards of cloth, at 4 dollars
a yard, and paid for it with dder, at 3 del ars a barM
how many barrels did he take ? '
rdu "^^Y ^"""^ "^^^^^ '^ *^^« a man to lay up 24
dollars, if he save two dollars a week ? ^ ^P -^^
him p f if^'^'f ^'''^ ^ ^^^'"'^'^ ^"d agreed to give
Inm 6 dollars lor every 3 days' .-ork ; how much did
he receive a week, allowing 6 working days in a
Tofth ?'" ""'' ' "°"*'' '"^--^^ ^ weZto the
41. If 4 oranges are worth 12 cents, how manv
42. How many yards of cloth, at 2 dollars a vard
can^be bought for 4 reams of paper, at 5 ddilrTa
43 6 men bought a horse for 80 dollars, and paid
Ittll "" ''■'f} l<^'^'^i»"S l.im ;-at the end of 10
eTefmanw' "" '°" '' "''""^^^ l«>w much did
..^..eo nre woilli j. orange, and 2 oranges
TABLES AND REDUCTION.
47
10 dollars a
1 45 dimes,
3loth ; how
, how much
th running
ains on the
inutes will
to contain
bushels ?
liars a bar-
fc 2 dollars
b 4 dollars
s a barrel j
lay up 24
3d to give
much did
lays in a
>ks to the
3w many
kvorth 12
s a yard,
dollars a
and paid
ud of 10
luch did
are worth 1 lemon ; how many lemons can be bought
for 48 apples ?
45. If 5 oranges are worth 1 pine-apple, and 2 pine-
apples are worth 1 melon ; how many oranges may be
bought for 4 melons ?
46. A fox is 80. rods before abound, and the hound
gains 5 rods on the fox every 10 minutes ; in how
many minutes will the fox be caught ?
47. If 7 men can do a certain job of work in 12
days, in how many days could 21 men do the same
work ?
48. In how many days can 9 men do as much work
as 7 men can in 18 days ?
49. How many men in 10 days can perform the
same amount of work, that 8 men can in 5 days ?
50. Bought 5 iirkins of butter for 35 dollars ; for
what must I sell it to gain 10 dollars ? what is the gain
on each firkin i
CHAPTER V.
Lesson I.
Table oi? United States Cuerency.
10 Mills (w.)
10 Cents
10 Dimes
10 Dolfavs
make 1 Cent,
" 1 Dime,
" 1 Dollar,
« 1 Eagle,
marked c.
d.
1. How many mills in 4 ceuts?
Solution. — In 1 cent there are 10 mills, and in 4 cents there
are 4 times 10 mills, or 40 mills.
2. How many mills in 3 cents ? In 5 cents ? In 8
cents ?
3. How many cents in 2 dimes ? In 4 dimes ? In
5 dimes ? In 6 dimes ? In 9 dimes ? In 10 dimes ?
48
TABLES AND RKDUCTIOW.
J.^IIo^ many dimes in 1 eagle and HI In 2 eagle:
7. How many dollara in 80 dimes '
Solution. — Thoro .,.. m j- .
the number of dbe,eoual^t'' 'J *'' "'"^fore, 1 tenth of
InVceTtsr^'''''"^^'"^" «-*«? ' In 70 cents?
yards can be bought for 1 donfrf ''' ^°" ""y
^ -I V ' "^^^^^^^^^^^^ ^^" ^°" ^"^ '•-
1^ eaglS^^ToTouCs If Z^olStsf ^''^ ""^ ^^
Lesson II.
Table of English I^^onet
aOShilliDgg ., ,i|'""'"g, '^ ,.
LS,-rr''^''^"^=^^^«Miings.
the «umC-ofXds;o„lHt""°«V'' ' ^- "-'f-e 20 time,
In'e^t" many shillings in'l£ ? ''in'st^g 3^ ,
TABLES AND REDUCTION.
49
In $3? In
In 2 eaglcc
ru$3? In
re, 1 tenth of
• 1 tenth of
70 cents ?
>00 centa ?
Qts?
ho^ - many
•u buy ibr
u buy for
20 times
20 times
4. How many pence in 2£ 10 shilliDgs 5 pence ?
5. How many pounds iu 60 shillirgs ? In 8O5. ?
In I2O5. ?
6. How many pounds in 480 pence ? In 720f/. ?
7. At 4 shillings a bushel, how many pounds will
40 bushels of potatoes cost ?
8. At 10 pence a piece, how many pounds will 48
pine-apples cost ?
9. At 5 shillings a yard, how many yards of cloth
can be bought for 2/* 15 shillJngs ?
Lesson III.
Table op teoy Weight.
24 Grains (gr) make 1 Pennyweight, marked dwi.
20 Pennyweight ** 1 Ounce, " oz.
12 Ounces " 1 Pound, ** lb.
1. How many pennyweights in 240 grains ?
2. How many pennyweights in 4 ounces ? In 5
ounces ? In 6 ounces ?
3. How many ounces in 1 pound ? In 3 pounds ?
In 5 pounds ? In 8 pounds ?
4. In 24 ounces how many pounds ? In 48 ounces ?
In 36 ounces ? In 60 ounces ? In 84 ounces ?
5. How many ounces in 20 pennyweights ? In 40 ?
In 60 f In 70 ?
6. If 7 grains of gold cost 168 dimes, how much
will 10 pennyweights cost ?
7. What will 1 pennyweight of gold cost, if 2
gi'ains cost 18 dimes ?
8. How many pennyweights in 4 ounces and 6
pennyweights ?
?. How many pounds in 480 pennyweights ?
10. How many grains in 2 oz., 2 dwt., and 2 gr.
TABLES AND REDUCTION.
Xiesson IV.
Taule OP AvoiHDurois Weioht.
io Drams, (dr ) r«„i , />
lOOcnoor •' ^koIOuno^, marked o..
25 Pounds ., 'P™-'!. » 4:
pounds ? In coo pound, ? Tr. ??nr"'"^" • !'» 400
4. How many prunds in /^ '^OOpounda?
qrs. ? -^ P""""^ « 3 qra. ? In 2 qrs. ? In 7
^ 7. ifsoirofh^jTosTn,-!;""''*'^ ^^■■s'>'?
ters cost? will 1 cwf ? w II 2 .^^f' '':^'^' ^'" ^ guar-
8. What will 2 (•!;„<. i • "'^'- """^ ^V-^
dime? ' ^ *°»« °f "-"I cost, if 1 ]b cost 1
io.lttt!it 'r ftr ' 1 ^ '^'-^ =* ^r. ?
pound ? at 5 cents a^und? « "'"'' "* * *'''»« «
,*t;
•I
12 Inches (m)
3 Feet
5^ards.orl6|feet
8 Furlongs, or 320 rods, '
3 Miles „
69i Miles
860 Degrees
Lesson V.
Table of Long Mbasuee.
make 1 Foot,
" 1 Yard,
" 1 Rod,
1 FurloDff,
1 Mile,
1 League,
1 Degree,
1 Circle of the Earth.
marked ft.
" k
u -fr-
mt.
lea.
deg. or «>
1 TT . * ^^^c^e of the Earth "
In'5f?rirxST^^-l«-^In2ft.Tl.fe.P
TABLES AND REDUCTION.
51
arked oz.
" lb.
gr.
t* cwt.
" T.
In 10 oz ?
?In81bs?
? In 400
da?
[rs. ? In 7
ight ?
ght?
ill 3 quar-
Ib cost 1
Desaqr. ?
* dime a
■d /If.
yd.
rd.
fur.
mi.
lea.
deg. or o.
1 4 ft. ?
,4^
2. Haw niftny feet in 2 yds. ? In G yds. ? In 5 yds. ?
In 12 yds. ?
3. How many yards in 2 rods ? In 4 rds. ? In 8
rds.? Ill 10 rds.'?
4. How many furlongs in 4 miles ? In 6 mi. ? In
mi. ?
5. How many inches in 4 yds. 2 ft. 10 in. ?
6. In 216 inches, how many yards ? In 288 in. ?
7. How many rods in 1 mile ?
8. How many miles in 1760 yards?
9. How many feet in 2 rods, 3 yds., 2 ft., 11 in. ?
10. How many feet in 1 mile ?
Lesson VI.
Table o¥ Cloth Measuee-
2^
4
4
3
5
6
Inches
Nails
Quarters
Quarters
Quarters
Quarters
4i
<(
make 1 Nail, tnarkod na.
1 Quarter of a yard, " qr.
1 Yard, " yd.
« 1 Ell Flemish, " E. Ft.
" 1 Ell English, " E. E.
" lEU French, " E. Fr.
1. In 4 yds. 3 qrs., how many quarters ?
2. In 7 yds. 2 qrs., how many Ells French ?
3. In 3 yds. 3 qrs., how many Ells Flemish ?
4. In 8 Ells English, how many yards ?
5. In 7 Ells Flemish, how many yds. and quarters ?
6. In 3 Ella French, how many yds. and quarters '^
7. In 4 Ells Fr., and 8 Ells FL, how many ya rds ?
8. In 1 qr., how many inches ?
9. "What will 6 E. E. of cloth cost, if 6 nails cost
48 cents?
10. What will 3 E. E. + 2 E. Fr. of cloth cost, if
3 nails cost 12 cents ?
52
TABLES AMD REDUCTION.
Lesson VII.
Table of Land or Sqfaeb Measuee.
'1 I^Te Je^er ' ^''' *'«•> ^^^^ J i'l-e foot. .,.^,
30i Square yards « i 1^^'® ^^/''' '9.id'
40 Square rods u ] 1^"^ '°^' ^' P^^«' ^'
640 Acres . /^^°''^' ., A.
- „ 1 Square mile, sq.m.
sq. ;d?7 "^'"^ '^"'^^ ^^^^- ^^ ^ «5- y<i^. ? In 8
2. How many poles in 4 roods ? In 6 roods ?
3. How many acres in 40 roods ? In 160 roods ?
^^4.^ How many square yards in 81 sq. ft. ? Z'loS
5. How many square yards in 1 rood 10 rods ?
Lesson VIII.
Table op Cubic Measure.
24J Cubio feet „ ] S"*"? y*'"''' ««■ V.
16 Cubic feet „ ^ P«''f of stoue, jo,;^:
8 Cord feet, or ) 1 Cord foot, c.//-
128 Cubic feet J- " 1 Cord of wood, O.
1. How many cubio feet in 4 cubic yards 1-
3. How many cubic feet in 4 perch olatoL ,
3. How ™any cords in 96 cord feet "fo*?,/ ft P
In'e 0^:?""""^ '"'^ '■*«" '" ^ «ords ? In 6 cords ?
TABLES AND REDUCTION.
63
or pole, P.
R.
A.
sq.m.
ds.? In 8
oods 1
>0 roods ?
? lulOS
' rods ?
cu.ft.
cu. yd.
> pch.
eft'
C.
le?
J c. ft. ?
'4 cubic
cords ?
Lesson
IX.
Table op
Wine Measube.
4 Gills (^0
make 1 Pint,
marked
Pt.
2 Pints
i(
1 Quart,
ii
qU
4 Quarts
i(
1 Gallon,
K
gal.
42 Gcallons
{(
1 Tierce,
t(
Her.
8H GalloDs
u
1 Barrel,
<(
bar.
2 Bar. or 63 Gallons
((
1 Hogshead.
(i
hhd.
2 Hogsheads
li
1 Pipe,
U
pi.
2 Pipes
l<
1 Tun,
4(
tun.
1. How many gills in *i pints 1 In 4 pints ?
2. In 3 qts., how many gills ? ^
3. In 12 gallons, how many pints ?
4. "What will 5 gal. of rum cost, if 4 gi. cost 5 cents ?
5. How many pints in 2 pipes f
6. A merchant bought a hogshead of molasses for
20 dollars, and sold it, at the rate of 15 cents for 3
pints ; how much did he gain by the bargain ?
7. How much will a gallon of wine cost, if 7 gills
cost 21 cents 1
8. In 1 tierce, how many pints ?
9. In 4 quarts and 2 pints, how many gills ?
10. In 1 tun, how many gills ?
11. In 1 barrel, how many pints ?
Lesson X.
Table op Dbt Measuee.
2 Pints
8 Quarts
4 Pecks
make 1 Quart,
" 1 Peck,
« 1 Bushel,
marked qt.
pk.
bu.
1. In 1 peck how many pints ?
2. 2 pecks will fill how" naany pint measures ?
3. In 3 pecks and 3 quarts how many pints?
E
"»»*-,.
h4
TABLES AND REDUCTION.
S.' lu ? bir ? ''"''''' ''°" "^y quarts .
pints ? '""'"'' '^°»' "'"=7 quarts? low many
cost at'thi'i^t?';^;'^, ""' '' -"*'' -i-^' will 3 necfa
how much did she gal P ""' '*' ^ "^"'^ » Pw* i
at lo^riTnS Ltt:„t ' p^ V --^^.
.ooseberHes.^., . eenfs 7^^?^' Inll tit
9- What will 5 nnartq nf „i, j.
cost 128 cents ? ^ "* "^^'"^ cost, if 1 bushel
10. A farmer sold 1 l^n q i
seed, at 040 cents a bushel and in"'"' ^ P'" °^«^°^e^-
1 bu., 2 pk. and 3 quartrnf t " Payment received
bushel ; Lw much Suf dlz^r''''' "* "'^ "^^'^ "
♦I"
,1'
60 Soconda (wc.)
60 Minutes ^
24 Hours
VDays
4 Weeks
12 ^lendar months
62 Weeks
866 Days
366 Days
100 Years
Lesson XL
Tablk of Time.
make 1 Minute,
1 Hour,
1 Day,
1 Week,
1 Month,
1 Year,
1 Year,
1 Common Year,
1 Leap Year,
(i
marked m.
<(
((
((
«
«
hr.
d.
tc.
mo.
yr.
yr,
yr.
yr.
C.
Ti.^^71 . 1 Century, « w
7^^':^t^^Vt\l^\^^^ the divisions of th„
ixi each
ana the number
of day
s
""M r,
TABLES AND REDUCTION.
55
quarts ?
iiow many
will 3 pecks
f strawber-
nts a pint ;
►f currants,
1 bushel of
h remains
f 1 bushel
of clover-
fc received
20 ceats a
d m.
hr.
d.
to.
mo.
yr.
yr,
yr.
yr,
c.
of the
fdays
Ist month, January,
2d " February,
3d *' March,
4th " April,
5th " May,
June
July,
August,
September,
October,
November,
Jth " December,
«
has
((
<<
((
((
81 days.
28, in leap year 29.
31 days.
30 "
31 "
30 "
31 "
81 "
SO
81
30
31
«(
((
The following lines will help to remember the num-
ber of days in each month :
" Thirty days hath September,
April, June and N^overaber ;
All the rest have thirty-one,
Except February alone.
Which hath but twenty-eight in fine,
Till leap year gives it twenty-nine."
JJ^" In our calculations on interest we shall reckon 80 days
to the months and 12 months to the year, although not strictly
accurate*
1. In 2 hours how many seconds ?
2. In 2 weeks and 5 days, how many days?
3. In 48 hours, how many days ?
4. 7200 seconds, how many hours ?
5. How many hours in a week ?
6. In 1 day, 12 hours and 10 minutes ; how many
minutes 1
7. How many hours in a month ?
8. If a boy can do a piece of work in 40 minutes,
how many hours would it take him to perform 12
times as much work ?
56
TRACTIONS.
9. If I can do a piece of work in 10 minutes, how
many hours would it take to perform a piece of work
12 times as large ?
10. How many days in 3 weeks and 5 dajs ?
Lesson XII.
Miscellaneous Table.
12 Units
12 Dozen
12 Gross
20 Units
24 Sheets of Paper
20 Quires
56 Pounds
60 Pounds
196 Pounds
200 Pounds
make
u
«f
«{
«
r
1 Dozen.
1 Gross.
Great Gross.
Score.
Quire.
Ream.
Bushel of Corn.
Bushel of Wheat.
Barrel of Flour.
Barrel of Beef,
Pork, or Fish.
ai> T^^^ ^^^^ ^ ^^^^^ of paper cost, at 15 cents a
2. How many sheets of paper in 1 ream ?
3. How many years in « 3 score years and 10*' ?
4. How many units in a gross ?
5. How many units in 6 dozen dozen.
6. How many units in a half of a dozen dozen I
CHAPTER VI.
Lesson I.
1. John has 6 nuts, and Joel 1 half as many : how
many has he ? j > ^^
mSrh^riir^n.^ 3 nut'"""' ' >"'«--»y. j«.i
FRACTIONS.
57
2. Mary had 4 dresses, and Kachel 1 half as many ;
how many had she ? . ^ ■, . -, ^ ^e ^A
3. Jacob is 8 years old, and John is 1 half as old ;
how old is John ? ^^ ^e cj.\, 4.
4. Moses having 2 marbles, gave 1 half ot them to
his brother ; how many had he left ?
5. If you divide 6 apples equally between 2 boys,
what part of them will each have 1
6. What is 1 half of 6 ?
7. How many halves in 1 ? i -, v li*
8. If an orange cost 8 cents, and a peach 1 halt as
much, what is the cost of the peach \
9. James had 12 cakes, and John 1 half as many ;
how many had John 1 4. ^ a «nT.f a
10. If 3 apples cost 6 cents, what part of 6 cents
will one apple cost ?
11. What is 1 third of 6 ?
12. What is 1 half of 8 ? 10 ? 12 ^U ? 16 U8?
20 f
13. If 3 quarts of strawberries cost 18 cents, what
part of 18 cents will 1 quart cost ? What part of 18
cents will 2 quarts cost ?^ , ^ „,.,..- ^ ,
14. What is 1 third of 18 ? 1 half of 18 ?
15 If 4 pounds of raisins cost 8 dimes, what part
of 8 dimes will 1 pound cost ? 2 pounds ! 3 pounds f
4 pounds 1 5 pounds ? 6 pounds ?
16 What is 1 fourth of 8 ? of 12 ? of 16 ? of 20?
i?: What is 1 fifth of 15 I of 10 ^ of 20 , of 30?
18 If 1 fifth of 15 is 3, what is 2 fifths of 15 ? d
fifths ? 4 fifths I 6 fifths ? 8 fifths ?
19. AVhat is 1 sixth of 12 ? ^
20. If 1 sixth of 12 is 2, what is 2 sixths of 1^ ? ^
sixths 1 4 sixths 1 5 sixths ? 7 sixths ? 8 sixths ?
21. What is 1 seventh of 21 ?
22. If 1 seventh of 21 is 3, what is 2 sevenths of
21 1 8 sevenths ? 4 seventnsY o sevuutuB i ^ «8tx...vIi^ .
23. If 1 pound of candies cost 12 cents, what part
58
FRACTIONS.
.¥
f<^^;L7IZYlJ%iT. ^ ^- ^ -ts . for
cents ' ,/l [ZZoZu^l r*'' ^"""'r' "f 36
twelfths? iVtwemt? '^""^'^ 9 twelfths? 10
30. y\ aat uo you understand by 1 third ? 2 thirds'
are called 2 tUrds '"^' ^""^ '"» "^ "'ese plrts
q?" wl!''J "^j" "°" understand by 1 half ?
fourftsTslouHh jr ""'^'^"'='"'' "y 1 f-'tb 1 2
3 lfttsT4lfth7?''" ""^'''''"'^ ^' "■ fi^* • 2 fifths?
34. How many thirds make a whole one ?
ds. Jlow many fourths in 1 «
sevenths MseveLhsr5:rv'enthsY ' "''''*''^ ' ^
rfS. ±low many sixths in 1 ?
89. How many ninths in 1 ?
40. How many eighths in 1 ?
41. How many sevenths in 1 ?
4J. How many tenths in 1 ?
XT
ow many twentieths in 1 ?
FRACTIONS.
59
44 What do you understand by 7 twelfths ? 6
twelfths ? 9 twelfths ? 8 twelfths ]
45. James had 9 marbles, and Jacob had 2 thirds
as many ; how many had he 1
SoLunox -Tf James Ims 9 marbles, and Jacob 2 thirds as
46. Mary bought 12 candies and Sarah bought 2
thirds as many ; how many did S^f ^^uy ?
47. Eachel has 12 primers, Mary ^ fourths as
many, and Anthony 2 thirds as many as Mary ; how
many have Mary and Anthony respectively ?
48. Albert is 15 years old, and Ebenezer is 4 fifths
aa old : how old is be .^ . r. k
49 Augustus has 40 cents, and Augusta has 5
eighths as^many ; how many has she ?
50. Morgan had 36 marbles, and gave 4 s^«»8 »'
them to Martin ; how many did he give to Martin,
■'I^Zrha^li fo-ferackers, and Nathan has 7
^ Sn L'rceXand Mrtlhew had 5 ninths
" sTLLbr i^sTyett o'ld! and his father is 9 fifths
as old ■ what is his father's age 1
54 A farmer had 84 sheep and a wolf killed I
third of them ; how many had he remaining 1
55 In a certain school there are 12 girls, and 7
four'ths'as many boys ;--required the number of boys,
and the number of boys and girls together.
56 In a certain recitation 36 questions were asked
and 1 ninth of them answered wrong ; how many
were correctly answered ] , anellin^
^7 4 fifths of all the words given out in a spe^im^
57. 4 Wtas 01 ^^ .Q,„^^tlv, and 8 were misspelled ;
lesson w«ru ispciivv. ^^^----- -J' '„i. i
of how many worde did the lesson consist ?
60
inf.;
J.I'
part
FRACTIONS.
flfth^fthSr -tol'' \ ^''' -'-'«' for 7
60. A received «Mnr T.""^ "»« *•>« gam ?
1 fifth of It for boirS? L^ '"''l!^' '''''°^' """Ipaid
week ? '"'^'^'' * ^°'' "'"ch did he save each
61. How many are 4, fifths of 75 ?
l^er age e,u,,s i^T^t ^ht^ ^S at' f"' ' ^'^'"'"^ "^
4 sixths ^5 -ths'r^lS /oTe -LV°"^'''«^
eiSs?7^eighZ re UZif^ f ^3?tLths . 5
. 66. 3 nintlfs of 27 4e^tw ^ "^,*.^ ' ^ tWrds ?
ninths; 8 ninths ? 2 thirds r ^°^ ^ "'"*''«' ^
»r 18. Is'areVrtits'sf* '' '' ""^ ' ""'^'"^ -« 3 time, 6,
70. 9 thid of 1 st 1''°^ """"y «"^« 6 ?
71. 4 fifths of 25 Cl.*'"'" ""^V times 3 ?
72. 6 n nths of IS »! 7 """"y *'»«« 2 ?
73. 7 S» of qo r ^^ """"y *'•»«« 6 ?
75. 15 seventeenth nf .7 """^^ ''««» 2 ?
76. Hc/manrtime?17 a «^^^^ «mes6?
77. Jlaw many times 8 aril 9 H •^?'''"*« "^ 36?
78. How many t mea 5 ar« in *'';'''^^°"'« "f 26 ?
7q tt« ^ «^iuit;s o are JO thirds nf Qft ?
79. How many times 4 are 2 thirds of 97 o ,
«0. How many times 6 nra q t i „ '' ~ 2 ?
how manv Ld h« .4.-^- ^ -^ ^ °^*^^"^ *« ano^iier •
»^. A had $120 • 1 fhi^A r.ff vi
1 third of It he spent for a watcb,
FRACTIONS.
61
1 fourth of it for a suit of clothes, and 3 tenths of it
for a sleigh ; how much had he remaining ?
83. Mr. B. being asked the cost of his hat, replied,
2 thirds of 30 dollars is 4 times its cost , required
the cost of the hat ?
S4. 14 ninths of $27 is equal to 7 times the cost
of a pair of boots ; required the cost of the boots.
85. An individual, having $90 on interest, received
2 forty -fifths of the principal for the interest , how
much interest did he receive ?
86. The interest received on $360, was 1 eighteenth
of the principal ; how much was the interest ?
87. B is worth $2000, and 3 fourths of his fortune
is 3 times A's ; required A*s fortune.
88. 3 eighths of the number of hours in a day, is 3
times the number of hours I work ; how many hours
do I work ?
89. A pole, whose length is 16 feet, is in the air
and water ; and 3 fourths of the whole length, — 4
feet, equals the length in the air ; required the length
in the water.
90. 3 fifths of $2000, + $120, equals B's fortune ;
how much is B worth ?
91. The building of a certain house cost $560, and
4 sevenths of this, + $80, is 1 tenth of the cost of the
farm on which it stands. Bequired the cost of the
farm.
92. 5 eighths of 72, -] l3, are how many times 2?
93. The interest on $960 for 5 years, was equal to
1 third of the principal ; how much was the yearly
interest 1
94. What will 2 thirds of 12 pounds of coffee cost,
at 13 cents a pound ?
95. What will 3 fourths of a gallon of alcohol cost,
at 9 cents a pint ?
96. What will 1 sixteenth of a bushel of flax-seed
cost, at 6 cents a pint ?
, M t
FRACTIONS.
97. How much will 7 fifteenths of 30 pine-apples
cost, at 2 dimes each ?
98. How much will 7 ninths of a hogshead of mo-
lasses cost, at 4 dimes a gallon ?
99. How many cents will 3 fifths of 100 oranges
cost, at 1 half dime each ?
100. If 1 pennyweight of gold cost $2, how much
will 2 fifths of an ounce cost ?
101. What will be the cost of 2 thirds of 36 pounds
of butter, at 2 dimes a pound ?
102. 2 thirds of 24, + 3 fourths of 16, are how
23 any times 7 ?
lOi?. 2 thirds of 30, +3 fifths of 40, are how many
times 8 ?
104. 3 sevenths of 21, + 3 eighths of 40, are how
many times 6 ?
105. How far can I walk in 3 eighths of a day, at
the rate of 3 miles an hour ?
106. If Marcus earn 1 dime in an hour, how many
cents can he earn in 3 eighths of a day ?
10'^ If a horse travel 10 miles in an hour, how
many times 10 miles can he travel in 5 twelfths of a
day?
108. How many cents will 1 quart of gin cost, if 1
gill cost 15 mills ?
109. How many dollars will 4 sixths of a pound of
gold cost If 1 pennyweight cost 12 dimes ?
110. How many eagles will 25 fourths of a gallon
of brandy cost, at 1 half dime a gill ?
Lesson 11.
1. If 1 third of an orange cost 2 cents, what will
1 orange cost ?
Solution.— If 1 third of an orange cost 2 cents; 3 thirds, or
1 orange, will cost 3 times 2 cents, which are 6 cent?.
FRACTIONS.
63
2. If 1 half of a pound of raisins cost 8 cfjnls, what
will 1 pound cost ?
3. Bought 1 third of a barrel of sugar for $3 ; how
much will 2 thirds of a barrel cost, at the same rate I
4. If one third of a pound of pork cost 5 cents, how
much will 2 pounds cost ?
5. 2 is 1 third of what number ?
Solution.— If 1 third of some Dumber is 2, 8 thirds, which is
that number, are 3 times 2, or 6.
6. 5 is 1 half of what number ?
7. If 1 fourth of a lemon cost 2 cents, what will 1
8. If 1 fourth of a lemon coat 5 cents, what will 1
cost ?
9. 3 is 1 fourth of what number ?
10. 7 is 1 third of what number ?
11. 12 is 1 fifth of what number?
12. 7 is a fourth of what number ?
13. What will 4 fifths of a pound of cinnamon cost,
if 1 fifth of a pound cost 5 cents ?
14. If 1 fifth of a yard of cloth cost $2, what will
a yard cost ? . n *.
15. If 1 sixth of a gallon of vinegar cost 2 cents,
what will 1 gallon cost ? , ^ , . , . j
16 A man, being asked the value of his horse, said,
that 1 eighth of its value is $12 ; what is the value
of the horse? , . , , • v i,
17. A man gave 15 cents for his lodging, which
was 1 seventh as much as his breakfast cost him ; how
much did he give for his breakfast ?
18. Bought 1 eighth of a yard of cloth for 4 dimes J
what will a yard cost at that rate ?
19. If 1 tenth of a yard of cloth cost 47 cents, how
much is that a yard ? .«^ *• i.i. v
20. AVhat wi'll 1 yard of cloth cost, if 1 ninth ot a
yard cost 5 cents ?
■«
ii
^1
64
FRACTIONS.
»!•
eAy:i:i:,tft''°^ -w. cos, if x
euLI^ri "'",'"' *''^, '°'' °^2 cords of wood, if 1
wfit I "• *"'^'^"' "^ ""^ distance from Albmv to
^5™9Ts rten"? '"f "^' '^ ""^ entire dine" P*°
o« T r ! *'""'^ "^^ ^''•"'t number ?
07 IP 1' r«<.T''*o°"; "^ ^^l^at number .^
28. 12 IS 1 fifth of G times what number ?
qn 1 Q !' J V^^ "^ ^ *™«^ "-hat number '
31. 10 ,s 1 eighth of 20 times what number 1
34 lo 1 1 tl^Tfr ^? "■"«« ^bat number
is required. ^^^^ °^ ^^® '^o^'se
wafi t^StCf I s (rntuK f r- T'?-'"^
cost bi „Hat was thrst^^hl^ajL f'"*
l^^elfth of 3 times^his^'-':!' X^S^l^^l
3 tlmeelhe To'st oVi' "''.'* *"' ^1"'='' ^"^ ^ *«"«" of
her dress? "" ''^^^^ ^ ^^at was the cost of
your a/eiYSuh'^r/:'- "'° '^ """■ '^ -^--^ "Id,
FRACTIONS.
65
Lesson III.
1. If 2 thirds of a melon cost 4 cents, what will 1
melon coat ?
Solution. — If 2 thirds of a melon cost 4 cents, 1 third will
cost 1 half of 4 cents, which is 2 cents, and 3 thirds, which is I
melon, will cost 3 times 2 cents, which are 6 cents.
2. If 2 thirds of an orange cost 5 cents, what will
1 orange cost V
3. If 3 fourths of a pound of candies cost 9 cents,
what will 1 pound cost ?
4. If 4 thirds of a pound of spice cost 16 cents,
what will 1 pound cost ?
5. If 3 fourths of a pound of cinnamon cost 12
cents, what wiU 1 pound cost ?
6. If $4i will buy 2 fifths of a barrel of fish, what
will 1 fifth of a barrel cost ?
7. What will 1 yard of cloth cost, if 4 sixths of a
yard cost 1 20 cents ?
8. What will 1 hogshead of molasses cost, if 5
sevenths of a hogshead cost $15.
9. 8 is 2 thirds of what number ?
Solution. — If 2 thirds of some number is 8, 1 third of that
number is 1 half of 8, which is 4; and, 8 thirds, which ia that
number, are 3 times 4, which are 12. Therefore, 8 is 2 thirds
of 12.
Remark. — Representing the conditions and solutions of ques-
tions by symbols will aid young pupils in comprehendiug the
more difficult parts of arithmetical analysis. The condition and
analysis of the preceding question may be represented, thus :—
If
= f of some number = 8,
H< '
and
i of that number = 4,
=^, which is that number, = 12.
66
FRACTIONS.
^.i
17.
18.
19.
20.
23.
24.
25.
26.
15. 12 is 2 thirds of what number ?
16. 4 is 2 thirds of what number?
10 is 2 sevenths of what number ?
9 is 3 fourths of what number ?
12 is 3 fourths of what number ?
12 is 6 elevenths of what number ?
5j1. 14 is 7 eighths of what number ?
22. 14 is 2 sevenths of what number ?
6 is 3 tenths of what number ?
9 is 3 sevenths of what number 1
15 is 5 sixths of what number ?
15 is 3 haifs of what number ?
27. 18 is 9 eighths of what number ?
28. 20 is 5 thirteenths of what number ?
29. 24 is 8 fifths of what number ?
30. 26 is 13 ninths of what number ?
31. 2 thirds of 12 is 2 fifths of what number ?
32. 3 fourths of 12 is 3 eighths of what number ?
33. 3 fourths of 8 is 2 sevenths of what number ?
34. 3 fifths of 25 is 5 fourths of what number ?
35. 2 sevenths of 14 is 4 ninths of what number ?
36. 4 sevenths of 21 is 3 tenths of what number ?
37. 2 thirds of 15 is 5 fourths of what number ?
38. 7 eighths of 48 is 3 halves of what number ?
39. 8 ninths of 36 is 4 fifths of what number ?
40. 7 thirds of 18 is 3 fifths of what number ?
41. A watch cost $16, and 3 halves of the cost of
the watch is 8 thirds of the cost of the chain. "What
was the cost of the chain ?
42. A horse was sold for ^96, which was 8 sevenths
of what it cost j what was the cost of the horse ?
43. In a certain school there are 36 ladies, and 5
fourths of the number of ladies equals 3 fifths of the
number of gentlemen. How many gentlemen were
there in the school ?
44.
TIT-
,• I I
rears old, and 4 sevenths of her
age is 2 thirds of Hezekiah's age ; what is his age ?
ivxarjr IB ±^
FRACTIONS.
67
45. A piece of clotli containing 12 yards was sold
'for $60, which was 5 fourths of what it cost ; how
much did it cost, and what was the gain on each yard?
46. A has 48 geese, and 3 fourths of his numberis
equal to 9 sevenths of B's number ; how many geese
has B ? . , , JO
47. The head of a fish is 12 inches long, and 6
fourths of the length of the head is 3 fifteenths of the
length of the body. Required the length of the fish.
48. A farm was sold for $1200, which was c^ly 6
sevenths of what it was worth. How much was lost
by the bargain ? , ,. i . i.
49. $48 is 3 fifths of the cost of 12 yards of cloth ;
for what must it be sold a yard to gain $16 on the
whole? ■ .^ r 1 4.1,
50. A man gave 60 dollars for a suit ot clothes,
which was 1 fifth of his yearly income ; 1 sixth of the
remainder he spent for a watch, and what then re-
mained was 4 fifths of his brother's yearly income.
What was the yearly income of each ?
in were
Lesson IV.
2 thirds
1 half
1 third
1 fourth
1 sixth
1 seventh
3 fourths
7 eighths
9 tenths
5 sevenths
2 fifths
5 thirds
&c.
is written thus f.
((
it
«
((
t(
(t
((
((
((
((
((
((
((
it
((
((
((
(t
((
((
((
<(
((
(<
<«
((
«
((
1
¥•
1
7*
1
1
1
T'
3
^*
7
"8*
9
TIT*
5
f
2
&(
68
REDUCTION OF FRACTIONS.
it
m
],.
Remark.— The above expressions are called fractions. The
figure above the short horizontal line is called the numerator,
and the figure below the line is called the denominator. For
example, m the fraction f, the 3 is the numerator, and the 4 is
the denominator.
ThQ denominator of a fraetTon shows into how many equal
parts the thing is divided ; and the numerator shows how many
ot these parts are taken.
. }' ? 7°^ ^^* ^^ orange into 3 equal parts, what
IS 1 of these parts called ?
2. If a lemon be cut into 4 equal pieces, what will
1 ot these pieces be called ? 2 ? 3 ? 4 ?
3. If a bushel of apples be divided into 6 equal
parts, what will 1 of these parts be called? 3? 4? 6?
4. If a basket of peaches be divided into 8 equal
parts, what will 3 of these parts be called ? 5 ? 6 ? 7 ?
5. How can you find 2 thirds of an apple ?
6. How can you find 3 fourths of an orange ?
7. In ^ how many times 1 ?
Solution.— In 1 there are 2 halves, therefore 1 half thenum-
oer ot halves equals the number of ones. I half of 4 is 2 •
therefore, f equals 2.
how many times 1 ?
how many times 1 ?
how many times 1 1
how many times 1 ?
how many times 1 ?
how many times 1 ?
how many times 1 ?
how many times 1 ?
how many times 1 ?
how many times 1?
how many times 1?
how many times 1 ?
how many times 1 ?
how many times 1?
how many times 1 ?
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
In
In
In
In
In
In
In
In
In
In
In
In
In
In
In
T6,
In
6
8
To
2
1 2
"J
Xj^
2
6
3
X 2
TT
9
7?
1 5
1 8
"2
18
TT
21
¥
8
1 2
¥
IG
T
20
how
many times 1 ?
REDUCTION OF FRACTIONS.
69
?
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
In
In
In
lu
In
In
In
In
In
In
In
In
In
In
In
In
In
2 4.
'i.
4)
5
5
10
5
2_5
5
1 5
5_5
5
GO
5
1-3
3_6
y
48
«
_50
10
±A
1 5
1.2.
1 8
10
2
■li'
7
6JJ
y
1?
1?
1?
1 ?
1?
1?
1?
1?
1?
1?
1?
1?
1?
1?
1?
how many times
how many times
how many times
how many times
how many times
how many times
how many times
how many times
how many times
how many times 1 ?
how many times 1 ?
how many times
how many times
how many times
how many times
bow many times
^^. ^.. y how many times
41. What kind of a fraction is it called, when the
mmerator is less than the denominator ?
42. "What kind of a fraction is it called, when the
denominator is greater than the numerator ?
43. When is the value of a fraction greater than a
unit ?
44. When the denominator is less than the numera-
tor, what kind of a fraction is it called ?
45. What kind of a fraction is it called, when the
numerator is larger than the denominator?
Remark.— This is called reducing fractions to xchole or mixed,
numbers. A mixed number is a whole number with a fraction
added to it. Thus 3^1- is a mixed number.
Whenever the numerator is less than the denommator, the
value is less than a unit, and the expression is called a proper
fraction;— hni when the numerator is equal to or greater thao
the denominator, the value is equal to or greater than a unit,
and the expression is called an improper fraction.
46. Reduce {- to a mixed number.
47. Keduce | to a mixed number.
70
ADDITION OF FRACTIONS.
48.
Eeduce
15
4
to
a
mixed
number.
49.
Eeduce
1
3
to
a
mixed
number.
50.
Keduce
2 3
4
to
a
mixed
number.
51.
Eeduce
2 1
5
to
a
mixed
number.
52.
Eeduce
5 7
4
to
a
mixed
number.
53.
Eeduce
89
1 2
to
a
mixed
number.
54.
Eeduce
94
s
to
a
mixed
number.
55,
Eeduce
2 5
3
to
a
mixed
number.
56.
Eeduce
3 7
9
to
a
mixed
number.
57.
Eeduce
4
to
a
mixed
number.
58.
Eeduce
7 8
7
to
a
mixed
number.
59.
Eeduce
3 7
6
to
a
mixed
number.
60.
Eeduce
3 4
to
a
mixed
number.
Lesson V.
I
1. James had f of an apple, and John gave him i
more ; how many had he then ?
2. Mary had f of an orange, and her father gave
her -f- of an orange more ; how many had she then ?
3. Eobert had | of a melon, and bought f of an-
other ; how many had he then ?
4. Susan had f of a pint of walnuts, and gave f of
a pint to her sister ; how much had she left ?
5. James bought V of a pound of candies, and on
his way home ate f of a pound ; how much had he
left?
6. John gave ^ of a pound of raisins to James, 4
of a pound to Mary, and kept | of a pound himself;
how many had he at first ?
7. Mortimer gave f of a dollar for a hat, $1| for a
vest, and had $3f remaining; how much had he at
first ?
O. Jane nfl,n .^ T^minf^Q nfoinnamrk-n on/l TTn«.«* y%f %..«/}
^ ---ti-si-iiiiiiviij itiivi j_taii. lew iiau.
2^ pounds ; how many more had Jane than Harriet ?
71
ADDITION, &C., OF FRACTIONS-
9. Henry gave f of a dollar for his breakfast, f of
a dollar for his dinner, and 3^ of a dollar for his sup-
per ; how much did his day's board cost him ?
10. I + "I are how many ?
11. -J + f are how many ?
12. f + f are how many ?
13. iiy+To ^^® ^ow many ?
14. f + f ^^® ^^"^ many ?
15. y + t are how many ?
• iQ^ 1^ 4. I are how man V ?
17. 1^4 ^ 1^6 are how
18. "
17. 1^ -I- 1^6 are how many ?
18. |. + 1^3 are how many ?
19. f -H f + I are liow many ?
20. f + f + t are how many ?
21. •rff+ A+ 1^ »r® how many ?
22. f + I -H f ^re how many ?
23. f legs ^ are how many ninths ?
24. y lessV are how many ?
25. 1^3 — f are how many ?
26. V — f ^^® ^^^ many ?
27. V — f are how many ?
28. V" — § are how many ?
29. ¥- ^ '
30. T9
are how many ?
are how many ?
are how many ?
are how many ?
-g. are how many ?
f I are how many ?
. i "" f are how many ?
35. 1. ^ .| _ I are how many ?
36. * + y — f are how many ?
37. yl+Tf ""tI ^re how many ?
38. 2. of 60— J of 24 are how many ?
39. 7. of 40— f of 10 are how many ?
31.
32.
33.
34.
35.
36.
2
y — y
*J^ — \9
47 6
IS s
57 37
1 +
7.
8
4
^ 01 uU — f 01 zi-a are now many r
7. of 40— f of 10 are how many ?
4 of 15 + I of 9-f of 12 are how many ?
72
MULTIPLICATION OF FRACTIONS.
Lesson VI.
1. At I of a cent apiece what 2 apples cost?
Solution.— If an apple cost f of a cent, 2 apples will cost
twice f of a cent, which are f or H cents.
2. At |- of a cent a piece, what will 5 apples cost ?
3. At at -^ of a dime a pound, what will 10 pounds
of candies cost ?
4. At If dimes a pound, how many cents will 8
pounds of starch cost ?
6. At •§- of a cent a pieeo, what will 25 filberts cost ?
6. At f of a dime a piece, how many cents will 8
chickens cost ?
7. At f of a dollar a yard, what will 15 yards of
linen cost ?
8. If a man spend f of a dollar a day, how much,
at this rate; will he spend in 23 days ?
9. If a man receive f of an eagle in a week, how
many dollars will he receive in in 52 weeks ?
10. If a pound of sugar cost 1| dime, what will
12 pounds cost ?
11. At 5f cents a pound, what will 6 lbs. of beef
cost ?
12. At 9 f cents a pound, what will 8 pounds of
pork cost 1
13. At 6|- cents each, what will 12 lemons cost ?
14. At 7 f cents each what will 20 rabbits cost »
15. At 12^ cents a dozen, what will 4 doz. eggs
cost ?
16. At llf cents a pound, what will 6 pounds of
honey cost ?
17. At $7-1 a bal. what will 10 bals. tobacco cost ?
1 8. At $9f a barrel, what will 10 bals. of pork coat ?
19. "What will 6 boxes of raisins cost, at $3|- n
box?
MULTIPLICATION OF FRACTIONS.
78
20. What will 14i busbela of wheat cost, at $lf a
^21! What will 7 barrels of cider coat, at $3-^- a
^^2. If a barrel of flour cost $4, what will 5J barrels
cost ? „ 1 o
23. 5 times 4 and f of 4 are how many ^
24. 7 times 6 and ^^ of 6 are how many i
25. 9 times 7 and ^ of 7 are how many r
26. 12 times 9 and ^ of 9 are how many?
27. 5 times 10 and f of 10 are how many ?
28. 13 times 4 and a of 4 are how many :»
29. 8 times 7 and a of 7 are how many ?
30. 10 times 13 and H of 13 are how many ?
31. 7 times 20 and a of 20 are how many ^
32. How many are 4 times | ?
33. How many are 4 times 2% f
34. How many are 3 times 4^ f
35. How many are 5 times ^f, + 7 ^
36. How many are 7 times .ip^ + 3 r
37. How many are 8 times 12|, f f
38. How many are 9 times lO^, —^^s^
39. How many are 6 times 12|, + ^y
40. How many are 12 times Jy, -+- >; r
Lesson VII,
1 If yo" give to 6 persons, each f of a dollar, how
"TXrwml'thfcTst of 4 yard, of clotb, at |
°'3.'l"l7arS'cloth cost Uh what will 10 yards
*^°l' '-Er„„ in„i,v nran^es will it require to give to
■ab. J.J.WVT riitvi-j C3 -
each of 9 boys H oranges «
74
MCLTIPICATION OF PKACTIOJfS.
„wf ■ r """y^'^wrels of flour dpea that man eive
away who g.ves to each of 12 beggars | of a barre"
6. Anthony gave to each of hit 7 companions «nf
a pound of candies, and had i of a nnnn\??ff ?
many pounds had he at first j " ^ ^ '"" ' ''"'^
ji.'']'°i? *°° S"^^ *o each of 9 beggars -»- of n dniu.
and had $7 remaining; how much !fd heat flrs? '
ri: ? J ^'"'^ A "^ "-^ "--ange to Jackson !' ' to
hrreti^'gt '" ''"'" ' ^"^' P-' "^ - -4e\ad
gave t^raTwran"! f frdX^rnrt' ' 'T '"«"'
of a dollar, and then had onll «! ?"•'='' "f" *
wuch had he at firsli ^ " remammg ; how
had she at first ? "' "^"^ "^"^es. ilow many flowers
COSH oTtle^t" ' '""''' "' ''"'^'^ -^t' 'f 1 pint
2 guartYcosf ! °^"°'''''' ""'^' * "^ " ^'^"t. -hat will
peck cisM ^'"'' '"' '"""' '"'^' ^ "'"''' -''«* will 1
wilfi p" t'c?:*'" "' ""'=''"'"'''' <=-' »« <^^-ts. .vhat
cosMSr'entrf '' ^'^'"^ °' «'>-- -'• if 1 yard
ly/rdtle'dSesT*'"'"'*-^''"^' °^^"^-'- "•
cosUoTentsf" * °''' "^^^^ °^'"-'- <=™'' '^ l^a^d
COeSfTeitr"' ''P°°'-'"=-'^ -^-fl spool
* MULTIPLICATION OF FRACTIONS. T5
20. What will 8| yards of silk cord cost, at 6 cents
^ ^21, If one yard of wadding cost 5 cents, what will
9^ yards cost? ^ -c -, j
22,. What will 6|- yards of muslm cost, if 1 yard
cost 8 cents ? „ , .. i. t- *.
23. What will Sf pounds of veal cost, at 5 cents a
^°24. How much will 9f barrels of cider cost, at $4.
a barrel •
25. What will 12 hats cost, at $3f each 1
26. What will 6f yards of gingham cost, at 4 dimes
^ '"27. What will be the cost of 13 yards of bishop
lawn, at Ux% » Y^^^ • „ , 1 • i *.
28. What will be the cost of 8 looking glasses, at
$15i a piece "? • a 4-^
29 What amount of money will be required to
purchase 30 pounds of rice, at 6f cents a pound J
30. What will be the cost of 23 pounds of crackers,
^^ ll wVatViuTbarrelsof fish cost, at ei2f a barrel ?
32*. If 1 grain of gold cost 9^ dimes, what will 1
penny weig ^o^ .^ ^^^^ ^^^ ^^^ ^^^^ ^.^^ ^ ^^^^
34.; How many pounds of meat, at 5 cents a pound,
can you buy for $3f ? ^ r. 4. «4.aa
35. What will be the cost of 3 quarts of nuts, at 64
cents a peck ? .mi,
36 If a coachman charge 5-|- cents a mile, how
much must that man pay who rides 12 miles 1
37 How many dollars, dimes, and cents will 1^
yards of cloth cost, at 62 cents a yard?
38. How manv dollars, and cents will 4 pecks ot
grass seed cost, if 1 pint cost 5 cents ? .,..,,
39. How much will 13 yards of shalloon cost, at Id^
cents a yard i
76 Mui.x,Pr..cAT,oN or phact.o^s.
oes
liesson VIII.
1 TT ^
1. How
inany are 5 times -x. ?
_« *; - 10*
2. How
Tjy are |, or Si.
I'k we have
o* ^^^ «iany are 3 times ^J ?
4 S°^ ^anj are 9 times i P
^. How many are 5 times 'i?
fi :^ow many are 6 times A%'
^ 5°^ ^a^J are 9 times i! ?
c • S°^ '"any are 9 times 11 9
g f °.^ ^^°J are 7 times il ?
9. 8 times if are how many?'
il' ^^ *!^es if are how many ?
it P *imes iA are how mo„i /
19 9+' 2 6«ioiiowman^
1/t n J.- 2 -iiC UOW
14. 6 times ^| are how
t^' ZJimes 4z are how
many
17 TT^^™®^ i-f are how many
times
40
18. How many times 12 are 9 times V, "j
20 w ""^"^ *™«« 8 are 11 t^es " ?
f- How many times 100 are 2^T ^ '
21. How imnt f,- nl^ '^ Mmes *pj ?
22. 5 time7"^i!^!- ^° "'^ ^^ times sJp /
ag, , t'-^^^ / >« 4 t,mes Mary's age ; v^gat
is her
potatoes
Iciptjiing
dividing
bare
ber
MOLTIPLICATION, ETC., OF FRACTIONS. 77
. 23. 13 times ¥." «q"«l^ ^ "^'^'^r^f °/ ^ftTe
a certain wagon cost. Bequired the cost ot the
""Tm times W equals, b of ««"°™l''''°f|«"'
Gen. Santa Anna had at the battle ot Buena V.sta.
° ^ITS^st^t ^if the number of men he had
-fflJ^i!^ Tthirr^- -a he had
"ir9tmes^ri^Tith^m-Wofn.enhehad
killed. How many were killed ?
?9. 8 times if is \ of how many times 3 /
30. 4 times -tf is- 4 of l>ow many times 5 /
31 A laborer worked 12 months at the rate of $104
a month : how much did his years's wages amount to (
^2 If 2 quarts of wine cost 48 cents, what will 1
^'"3° How much ought I to pay for 3 oranges, at f
"''aV'IfVc'tain piece of work can be performed
in % hours, how ma'ny days will be required to per-
'^Z ^^t'cL^d^ra ditct^ 15 days, how long
of 4 persons 16 days, how long would it last a lamiiy
"'aVTs men can perform a certain piece of work
in 56 days, in how many days can 112 men do the
'"38.' If 3 men can plow 18 acres in 6 days, in how
many days' could 9 men do the same C
39. 4 men can mow a certain field m 6^ days, m
,„v -i-vs "xn five men perform the same worK .
XXJ.J "-»"j " """ — — *
IS
MULTIPLICATION, ETC., OF FRACTIONS.
40. A man bought (i barrels of cider at «qi a
it for'«oo'"'v''r* ''""R'^' « yards of cloth and sold
It a5;?d ? '•' "" '' "^ "•"" '* "-'' -hot did"
82^ w)?°r*''"' ^^ ^'"''^' °*"«'°"'' and sold J of it for
no, whici, wasi of what it cost; how much wo .Id T
would it takp ' / "^"^ ?° *"™ »10' how long
woum It take 1 man to earn the same ? ^
of Henry '.'i;',"!/""'' ?^"«'' '^^^'^ " i "^ ^e age
IVhTi- ; Tu" ii?"""-'' ■* " t""«s as old as Georee
45 . ft%f^ 1 ^^"'•y ""'i <"■ G^o'ge respectivefy 7
4fi I f 00 !' ? *'.""'« ^ °^ ^■'^at number ? ^ '
4fi 3 °i^S !^ f °j *«"=e what number f
cost IhL "i "' "' """"y doHars as Mr. B's horse
cost „ hat was the cost of his horse ?
80 was i l?i°\>''""^ ^'^'^ ^'' "Se. said, that J of
50 Mn! ten times h,s age. What was his age ?
of fL ^?> '.' ^^ Jfa'-a.old, and f of his aee is ♦
oMhe age of h,s brother. What w"as his brltber-;
S'<
Lesson IX.
1. How many thirds are there in 3 ?
3 thirdZh^h "are t '' "* ' "''"''' ""'' '" ' ""'" ""' '^ '»"
Tie following solutiou is preferred to the abore:
aumbe?i7;i;oreo„e'/7al7H ''""^t """efore, 8 time, the
are 9. TheX^S thTreaJ'eT "''''• '"""*''
2. How many fourths are there in 3 ?
". xiow many halves are there in 6 ? '
OIVI8ION or FRACTIONS.
iro
4. How many fifths are there in 4 ? m 5 ?
6. How many fifths are there in 7 ? m 8 ^
6. How many sixths are there m 4 ? m 3 ? m 5 ?
7 How many sevenths are there in 2 ? in 4? in 6?
8. How many eighths are there ^n J ^ n 4? n 6?
9. How many fifteenths are there in 2? in 3? m 6?
10. How many tenths are there in 4 r in6? inT/
11. How many fourths are there m 3 and ^ r'
12. How many tliirds are there in 4 and ^ ^
13. How many thirds are there in 3 and i i*
14 How many halves are there in 8 and i t
15*. deduce 6f to an improper fraction f
16. Keduce 9^ to an improper iraction f
17. Eeduce 7?- to an improper fraction ^
18. Beduce 5| to an improper fraction ^
19. Beduce 41 to an improper fraction ?
90 Among how many men, can 5^ Dusneis oi
whea't be d' s&ibuted, provided each receives | of a
^ll'^Amon- how m^ny boys, can 7f oranges be
divided; provided each receives -^ of an orange ?
22 8 and f are how many times -„- f
Soi!..io..-8 and i equal V; t - contained in V 37 time.-
23. 9f are how many times f ?
24. 9f are how many times f f
26. 7f are how many times ^t
26*. 12f are how many times It*
27. 7t are how many times f r
28. 7-| are how many times i r
29. 41 are how many times %r
30*. 10| are how many times^f ?
31. 8f are how many times -^ r
82. 12? are how many times f r
33. 4 times 3i are how many times ^ /
34. 9 times H are how many times ^ r
oe r. 4-;vv^oc, «2 are how many times ^ r
80
DIVISION OF FRACTIONS.
I
^'
36. 8 times 8| are how many times | ?
37. 6 times 2-f- are how many times -^ ?
38. A boy distributed 9f apples equally among his
companions, giving to each | of an apple j how many
companions had he ?
39. Homer distributed $12f equally among some
poor women, giving to each $1| ; how many women
were there ?
40. Mary gave f of a pie to each of her 9 visitors ;
how many pies did it take ?
41. Bought 8 yards of cloth, at $5| a yard ; how
many yards of silk, worth %\\ a yard, will it take to
pay for it ?
42. Bought 9 yards of cloth, worth $1|- a yard,
and paid for it with raisins, at %\% a box ; how many
boxes did it take ?
43. How many bushels of turnips, at $| a bushel,
can be bought for 8 bushels of apples, at $f a bushel ?
44. How many apples, at f of a cent each, can be
bought for 6 oranges, at 2\ cents a piece ?
45. How many yards of cloth, at $f a yard, can be
bought for 10 boxes of butter, at %^ a box P
46. How many geese, at $| each, can be bought
for 14 ducks, at $| a piece ?
47. How many boxes of cheese, worth $2f a box,
may be had for 17 boxes of butter, at %\\ a box ?
48. How many barrels of flour, worth $5| a barrel,
may be had for 17 bunches of cotton, at %\\ a bunch 1
49. How many sheep, at %\\ a head, may be had
for 8 calves, at $3| each ?
^ 50. How many quarts of alcohol, at f of a cent a
pint, may be had for 12 quarts of molasses, at 41
cents a quart ?
51. Mary and Jane together picked 5 times 2^
quarts of strawberries and shared them equally with
their companions ; how many companions had each,
provided each received \\ quarts ?
DIVISION OS FEACTIONS
81
Lesson X-
„ .«n TENTH COMBINED.
j«. KMAEKS.-A f''^«7 ""S numerator.
9 If 3 apples cost ^ o^ *"
■wortli ? , . „ 7 are fk '
9. How many times
10. Howmanytmes.
11. Howmanytime^? ^^,16*;
12. Sow many t me« ^ 33 ^ ,
13. Howmany me«» 1 ,
14. How many times '4^^^
15. HowmanytmeBlL ,
16. How many toeB i 4 ^,
17. Howmanytime^^ 7^,
18. How many t^e« « 9^ ,
19. How ma^y t-^*;, 15 are 33^ t
20. How many times xo
'U?j
82
DIVISION OF FRACTIONS.
■if
I
J'i pi'ro"!?''"'^^" ^"^^ «-- ''-- -"-y '=-*^
eaS'?^^'"''''" ^ i""'''"^'''' ''"^' '*■ 3 co^t 1% of an
centLm'tr5nfe:'r^' ''°^' ^2 ''--' i^- --y
29. If 6 pouuda of cheese cost 31a, cents wl,nf
will 1 pound cost ? ■" ' ^"*'
on eg" ^^ '^^' '°'' °* "™''' "'■'''* ^'" be the cost
eosu' ^" ^'*'"''' °'''''°*'' "='"' *-'^' ^'"''t ^i» 1 yard
apfe^cef^'" «"t shawls cost $274, how much is that
8 pat ^'"^ '"''' "'^ '""'*' '°'' *^^*' ''°''' '""'='' ^^ *">'
Jrtf dteret'friX'X''' '""'"^^' '"'' -''"^
dilhe tt I/r^enVr'^ '"- ''* "-'^-=> '-- ""V
n.anydae|:TfolV^r/°^''^ '='>-*-*^' >>-
38. If 3 yards of broadcloth are worth 18^ varda ,
DIVISION OF FRACTIONS
83
n iq miles v;hUo Josiah ia
John is walking i mue. ^. ^^ ^nd 20
chestnuts are w 01 til , on^
1 lemon worth 1 ^ ^^.^t ^Ul 1 orange
41. If 2 oranges cost -3 ot .1 tea ,
coat ? ___^ ^ , ^ ^^,., 1 one orange will
•at? .nfflcent 1 one orange will
Tf o oriUigeB cost f <^* ^ *^ '
SoLUTioN.-It - o'^;'"? , . 5 of a cent,
cost i of t of a cent, wbicb is ^ ^^^ ^^.^^ ^
_» ., ,1^ nf linen cost
Solution.— XI - : \„wh is I of a cent.
;t ^ of t of a cent, ^vbIcb s^ ^.^^ ^
42. If three yards of Imen cost $!-„ wU
-* cost? "^- -■«— TrrVini-, Will 1
4,2. It three yui^^
rard cost 1 . -^^^^ cents, what will 1
43. If 7 y^^''^^ °* ^ P
yard cost ^ . .-i. » 2 riimpa. how many
3 is con-
43. if ^ y^^^^'* ""' ^
nV If 2 pints of mow. cost H 0--,how ...y
cents will 1 ga"o" f ."'* ' a «re 6 -, '
45. How many times Bare b,^
46. How many times 6 are 5
47„ How many times 4 are 4i I
48. How many imes 2 are 1.5^
48. How many times J «e >
tailed i. V V. « <''^.'-;;- i„ ti^es 2A «
52. How many timoB 9 are lU ^^^^
53. How many time^J a^^ ^5 times 3^V?
54. How many t mes 5 a.e 1 ^ ,
55. How many times 7 are ^j !
56. How many t.mes 5 are 6
% f^r-ySoTXth are worth $2i, what is 1
^ta^'imhunches of .rapes are worth 40 cents.
ia 1 basket'of peaches worth •
\"
84
FRACTIONS.
Lesson XL
1. What is i of 2 ?
2. Whatisiof4? of 8?
?• ^hat!siof2? 3? 5? 7? 9?
4. WhatisiofS? 5? 7? 9? H ?
5. ;w^hat,3iof2? 3? 4? 71-8? '
f-^^^t|«iof2?3?5? 7? 9?
7. mat,s|of2? 3? 5? 4? 3' 9? 11 ,
8.mati3iof2?4?3?5»6?7?9V
10-Ww'*°^IJ^^7?6?3Vl2?l^
10. What 13 tV of 7 ? 2 ? 4 ? 6 ? 9 ? 14 ? 15 a
cents, which is 4, o, U cenie! ' "'''''* "'^'^'^ * °f 8
13 ■ Tf f '''''''^' ''°'1 ^ '=^'^*''' ''•>»* T^ill '■ apple cost '
14" If I PTl '"f ? '='°'^' '•'"»' ^i" 1 pen cost' '
yard cost ? ^ ^' °* ^'P-^ <=°^' ^4 ««°t^. what ^{ 1
rel'«,st'P '""^'^ '''■''""=• '=°^' «21, what will 1 bar-
-ill"- pLl L"u °' ''"'' "''P'^^ -^* 23 dimes, what
Jti ^^' ''"''''""' cost 9 dimes, what will 1 chicken
poundsTosl*27di Jesr"' °' ^'"""-^^ <=-*. ^f «
cosM2l^' "'■"' ba-el of flour coat, if 3 barrels
^|;Sjot;fcltKS;r"^^
^1. Joshua had 13 rrarbleq nnrl t«„- t. i
many + i of - ma.i.]. ^es, and Lewis had
y -t ^otu marble ; how manj had he ?
1
as
FRACTIONS.
85
V -rlprl s barrels of flour equally among
22. A man divided 6 ^ff' . ^^^ gacli receive ?
11 families ; -^^t T^H of a W did ^ ,.
did he give to each ^ ^^^ ^^ared them,
each receive 1 ^s of raspberries, shared
" r \^^l":UlT;uua of prUBeB cost, if 5 pounds
•=^7' wlTwUl 2 boxes of fig. cost, if 7 bo.es cost
'''itw -ill 4 1«' *^ °^ strawberries cost, af 9
quarts cost 7 dimes ?
^ oq "What IS i ot ^ i , 3 , „ ,
io inof2isl,wliatistof2.
31. What is % of 5 . ^^^ „^ •
> nt 5 is *, and i are 2 times ,,
32. What is f of 3 of 5 T 6 -^ , ^g j
33. Wb^^^f : fyfrl' 51 7? 9n2? 20?
34,. What IS t of V,°*/5> 8 ? 9 ? 15 ? „ ,
35. AVhat IS f of 3 ? ot & . » 3 ? 11 ? 17 ?
36. What siof4?of6^8^ ,^5P
37. What s J of 3 ? of ? >^gS 6 1 10 ? 12 ?
38. What is rr of |? 0.4- | , ,^5, 3^,
39. What s^^of2? ot4. s ^ ^2^ ^g, 251
-t2"wh^:t"l°b3 tie Ct of i of a bo. of ra.s.ns.
'' 1^° Wbft III be the cost of |- of a yard of cloth,
at 7 dimes a yard !
86
SIMPLE PfiOPORTlON.
COS?? ^^ ' *'° °^ ^'y ^^«t 'WO, what will 2f tons
45. Jeremiah is 91 years olrl «t,^ -» ^i •
damaged I til f ^oft It/!' ^^ 'f '' b"*. being
mainder for what it eo^^f tt * " ^^'''^' '"""1 'be re-
47. Bought l1 yardf ;.• 5.7 f"'']" '^''^ ^ ^°^^ ?
P.ece eoat. What did it it f JrdV'^" *^"''°'«
a. t^uetasTer tlft^dTth^t'' ^^ ^* «»-
'?: Whaf:?^ Sun;.::f otf --l -"> ^ yard,
coat $42 ? "^ " °' "I"""" cost, if 5 pounds
Vo^illojr^' "' ^"""g" ^o^t $32, what will .
it St.; ^^:^^ K?. which was , of wha.
travels Jlheret;^^^^^^^^^^^ -- P'-. and
10 hours ; the other a^t the rate of ■ ' 'f ^^ """'' '°
W; how far apart will th ' fcf i,%T'^^ '" ^ of an
55. By a Dine 4° anU^, T ^ "°"^8 ?
« X minL Xw LucMidl^^^^^
It was filled in 9 niZtes ' "'"''"' ^°^^ P™"ded
inl3,'l;™To:fll7i -t Ta^''': P'- "^ -.
same ? ^ ^^"^^^^ '^ *ake 4 men to do the
57 Tf ''
week« wiratPpTrt °of aXreTwL'f ??' °^ ^"^ - »
5 weeks? "'^''' ^oula they cousuroe in
«i^wlirt^sSi.^.r^s.:f»%*i.how
SIMPLE PROPORTION.
87
69. Anthony Bpent f of all bis ^-oney and the re.
mainder he gave tor B ya;ds of cloth, at $2, a yard.
how much had he at lir«t garments,
'' m "From a piece of cloth a tailor cui. o gaiua ,
>tl.S^°hrS Cnds*of Le cost, if 7 pound,
cost 43 centsj snenduiK i^- of all his
J!;^uTSto .t^Jngt hoi ™uo. .ad he
"^ef^ln old lady bought 30 eggs, at the rate of 2
nrillw'ret 'm\3 yra. of co^ee cost, if 26
P'ef What will 7 gallouB of molasBCS cost, if 6 pints
^tf If'umps cost |T|, what wUl 7 J^^-PB -^ . ^
""eS.' If 15 gold Pen^ <=°«* «20, what will 5 of them
'"tl If I of an acre of land be worth $U, what are
^^o"1'2ri'sTof the cost of W. watcU". what was
the cost of his watch ? ^^ ^ of his
' V2°1f a man in A o« a day walk 8 miles, how far
can he walk in 8 days J containing 20 E. Fr., a
-;.n?Vr crtl U^ wood .5 hour,
bow many cords can he cut m 4 days, Dy
if
4
88
SIMPLE PROPORTION.
75. A man bought 7 sheep, at the rate of 9 for
^5i ; what did they cost him ?
70. A boy bought 13 oranges,— giving 9 apples for
oranges ; how many apples did his oranges cost him ?
77. It 25 cents buy 7 Jemons, how many cents will
9 Jemons cost ?
78. -I of 45 equals ^1 as many dollars as Andrew
has ; how many dollars has he ?
79. $3G| is i of all the money A had ; how much
money had he ?
80. What will 3 pecks of flax-seed cost, if 3 pints
cost 3 dmies ? ^
^.^;o^^^?^JH^ ^ ^^^^'* of clover.seed cost, if 2 pecks
cost $3 and 2 dimes.
82. 4i times 7 is | of what number ?
83. f of 30 is -f; of what number ?
84. I of 36 is V^ times what number ?
85. f of A's age is 3 times B's age: and Bis 9
years old. What is A's age ?
86 An individual, being asked the number of hours
he labored each day, answered, Ix times the number
of hours in a day is 3 times as many hours as I labor
How many hours did he labor each day ?
87. I of 15 is ^ of what number i
88. I of 21 is 1| times what number ?
89. f of 24 is If times \/hat number ^
90. Wrighl; is 10 years old, and If times his age is
If times Charle's age. How old is Charles ?
4^
)
Lesson XII.
LESSONS IIGHTH, KIXTH, AND TENTH COMBINED.
^ JlEUAJiK.—Frcpils must exercise their oion judqment in
employing the shortest of the methods given in lessons eighth and
tenth for multiplying and dividing. ^
1. If 3 barrels of flour cost $13f, what will 6 cost I
Solution.— $1S| equals %'^'. Jf 3 baii-eis of flour coat | V,
of 9 for
pples for
ost him ?
ents will
Andrew
w much
' 3 i^ints
2 pecks
SIMPLE PROPORTION.
89
Bis 9
f hours
lumber
labor.
age IS
nent in
th and
cost!
3t IV,
e ,a.eU. wWcb are . time. 8 ba.reU, V.U cost 2 times $V,
wliich are $¥.<>•■ «"i- . „, what will 20
2. If 5 pounds of opium cost $27 „ what wui
Dounds cost ! . I. ^ /.pnta. what will
3. If 3 pouuds of sugar cost 17 , cenis, «
24 pounds cost ! „ „ orantres, if 8
4 How many apples will pay tor J orang
apples are wortli 12 J orauges ^
So»T,o«.-12'. orange, equal V orange, I % -^h is
worth 8 apples I o an orange »^^Hh\ ^_^ PF ^^^ ,.^^
^>:s\: ::ro"^^"pp" atidtUes - wor.U9 times I.
-trtlny chestnuts.. 11 pa^^
7 chestnuts are worth 10^ "!„,! 833^ what will 20
6. If 8 barrels of flour cost ifdd,. ^^"'"'
ijarrels cost ? , , .• loth to make 3 coats,
7. If it require 9 » .f "^^ ?'/i° ^^ke 8 coats ?
how many yards will it require to ma ^_^^j^
8. If 10 meu can perform ^ certain p ^^^^^^
in 9; days, how long will it t..ke S men p
the same? ,„„t„ffteheeD.if IScostSlOi?
9. What will be the cost of 6 f ej'" , f ^^^at in
^f\ Tfl nerson corsume lu^o uu&ucio _^ • i-i.^
a month, liow much will 13 persons consume lu the
'"Z ^ifg ' cents will buy 4 peaches, what wUl be the
""V'lt i:fwill pay for 5 weeks' board, howmany
dotos will p y 1- 8.n.^^;^;e£ in 3* hours, how
13. If 6 orifices will ^Vj reauired to fill it in^
many of, the same size will be requirea
of an hour t ,, -u „ i,„nt in 54 days, in how
14, Tfn men can build a Doatiu u» j
mmy days could 6 men build It (
H
1!^
00
SIMPLE PROPORTION,
A>
l'»f
week; r^"' ^"^ ^ y^'''-'^ bo^'d cost, at $;;| fo^ 4
rels tsYf '""■'■^'^ "^''^^ <'°»' «54i, what wiJI 27 bar-
if /7'l,"'^°T """"y '^''"'"•s will 1 barrel of fnl„„
30 '""''•e's cost 51 J eagles ? tobacco cost,
20. If J3 pounds of tea cosf ina j-
5 pounds cost ? ' ■'"* "injes, what will
.21. If7| tons of hay tppn « i,
winter, how many ton, will t «"?^' *''''°"8'> the
time ? ^ '""^ «'" keep 9 horses the same
tofhe h^ou^Ysfho^'^^'frrVd' °"°^".^-- 3 -ds
to overtake thefoxT ■^/fe^'Prfi '^/ '^°"°'' ^"n
., 2S. How many dolla Jil "* "'^ ^°^ ''"" »
If he earn $3f inVdaJs' » " """ ""^ '" ^^ days,
cost a piece, an'd ho^:; much a^S^,''"- '»-'' ^^ it
win be th: fet thSeTadl^ ''f '"'°", ** ''^'' -h-t
feet long, at th! samVtLtofTavl " '°'' "''''"' '» ^^
30. At a certain time of dav 1 1 . ,
01 day, a pole 5 feet long
i
RUDUCTION OF FRACTIONS.
91
<3a8t8 a shadow 74 feet ; what is the length ot that pole
which at t .e same time, casts a shadow 4. leet ?
31. If it require $211 worth of provisions to serve
8 men 2 days, how many dollar's worth will serve 5
"32' mat is the length of a pole the shadow of
which is 12 feet long, at the same time, a pole 2 steel
in length casts a shadow 4 feet long 1
Lesson JIIII*
T> „.„«. Bv inane* Wm Le^^ons 8th and 10th, we obserTe,
same number, does not ultor tbe v» ue ot tbe f. AcUon^ .^ .
to convert a traction *»»" f5»\t,h „' mSX°d d^
quired denominator.
1. I is how many eighths ? . , r • ^
SoJxio..>-There are f in one, and in i there .s i of |. or
3. and in I there are 3 tiraes f or -j.
^ BEMraL^MuUiply -h teru. of the giv^^^^^^^^^^^
number that will causo the deuommator to become vu 4
denominator. Solution 2d.-i» equal ^.
2. i is how many eighths ?
3. i is how many tenths r
4*. I is is how many sixths ?
5. i is how many sixths ?
6. \ and i are how many sixths i
7. f are how many sixths 1
8. ^ are how many twelfths 1
9*. I are how many twelfths %
10. I are how many eighteenths ■
11. f are how many tenths ?
12. f are how meny tenths ?
13. f are how many twentieths 1
14. I is how many tenths 1 ^ ^
15. Harris gave f of an orange to his sister , how
many fifteenths did he give her \
.BJ'-f
IMAGE EVALUATION
TEST TARGET (MT-3)
4rj
1.0
III >•>
1.25
If? IB
I! m
M
M
1.8
1-4 ill 1.6
%
o^
.%
%
.% >
7^/
-%
v
w
v/
%
Photographic
Sciences
Gcrporation
\
23 WEST MAIN STRfceT
WEBSTER, N.Y. i4580
(716) 872-4503
iN
^\.
C%
\
\
6^
r#
>-:^'
K?,
V C^
.V A
.^
^
m, ^
Ua
4S
92
ADDITION AND SUBTRACTION.
f^
)i5l
It'
16. How many sixteenths in
17. How many sixteenths in | ?
18. How many sixteenths in {- ?
19. How many fourteenths in -f ?
20. How many fourteenths in a ?
21. How many fourteenths in f ?
22. How many ninths in f ?
23. How many twentieths in |- ?
24. How many fortieths in | ?
25. Hew many forty-ninths in f ?
26. How many fifteenths in -f ?
27. A man gave i of a bushel of potatoes to one
poor woman, and VV of a bushel to another; what
part of a bushel did he give to both ?
28. How could you dinde an apple so as to give |-
of it to 1 boy, and i of it to another ?
29. f +1 are how many fifteenths?
Solution.— I equals j%, and § equals J-§, /^ and 4§ are if,
or 1 j\.
30. f + f are how many twelfths ?
31. f + ^ are how many eighteenths ?
32. 1+ 1 are how many twenty-fourths ?
33. -f- are how many times -^\ ?
34. What is the sum of f and f ?
35. What is the sum of -f- and -f ?
36. What is the sum of i and f ?
37. What is the sum of f and f ?
38. What is the sum of f and | ?
89. What is the sum of ^ and | ?
40. What is the sum off and f ?
41. What is the sum of -} and i ?
42. What is the sum of f and f ?
43. What is the sum of -f , -i and | ?
44. What is the sum of f , |- and | ?
45. Prom | subtract |-.
46. From |- subtract ff .
47. From f subtract f .
4
4
t
OF FRACTIONS.
48. Prom 2 ^ subtract f . .
4,9 T'rom 4 subtr^ict a-
50 :From 3 subtract i-
5l! Tj'rom 9 subtract t-
52 Prom 5 subtract |.^
53; rrom 3 subtract U-
54. :From 8 Bubtr.. 2-3.
^^5 ;From 6 subtract 64^.
56 U-3^.arehowTnauyT
^7 7-2f are bow many?
^^- 9^3| are how many?
59 10-3I- are bow many?
rft 12-3^ are bow many?
A? 13 Ja^ are bow many?
fi 9i-4 are bow many?
fio 7^— 5f arebowmany?
^1* Qi-li are bow many?
65-4-liarobowmany1
fifi 5^-2! are bow many?
fi7 9I-7I are bow many ^
fift 23+3|-|arebowmany?
^^- .1 T ? t ^ !^ are bow many ?
70-||^3|^3arebowmany?
.l^J-l are bow many?
itl+i-l are bow many?
... 1+ ^ ^lUw manv times -^ ?
TA 2i are now m^^v ^^ 4, ?
74). -6^ »*^ TYianv times -fo •
75. 3'r are bow mauv . • ._ ^ 7
7VS «!- are bow many tunes , e ;
T^* -i? ?. i,nw many times
93
71-
72.
73.
74).
are bow mau y y^-- - ,
are bow many tmes .
are bow many times j^
are bow many toes . ^
are bow many tunes , .
are bow many tme«.e.
J..2 81 eve bow many times ^ ^r
00 i6>- are bow many times TO •
^r ;-' ^--^ v^^w many times 1* •
b4. I'^a "^" "^
77.
78.
79.
80.
81.
82.
2
4
T
1^
9
5 _
\ 3
94
REDUCTION OF FRACTIONS.
J, V.I
»»:
l.i
fift' ftltl -^ , *"^ '""'''' '"^^ *■=«" a whole one ?
S7 1 1 °/* " ^T "'"''' '■'^^ *•""» a whole one ?
,nfa' ^-h^^ S^y^ * "*■ ''" ''«■' >"»"ey for a dress
wh'a^ pL^'omTj^Trptd r'' ^ *"'^^° P"~ ^
50oHn!r f™^ was killed, | taken prisoners, and
500 escaped = how many were there in the army ?
90. t af the length of a pole is in "the ground, x of
lengtl':fThrprr' ''-' '" "'^ "'-' -^^' « *e
91. A market woman sold -J of all her oranees to
one man and i of them to another, and then had on^
9 remaining ; how many had she at first, and how
many did she sell to each ?
t}lhi^ ^r'/*'J^''u'P.'?''',"^ ^ °f ^'^ fo'-t^ne. found
hifortunir * ' ^'^^'^ remaining; what was
.»f^iA''r'r.f'"'Sht * of Euphemia' chickens a
cat killed i of them, i of them died, and she had l^
remaining ; how many had she at first, and how many
'S trrL\ y: ''•"'^ "''' '"' ^espeeHvIlyT"^
y^ baid A to B it to my age you add its and i ifa 2
the sum will be 38 ; how old was he ? ' *' ^'
92. A IS 40 years old, and f of his age is a of twice
as much as his wife's age ; how old wa^s his Vife?
Lesson IV.
1 !Redllf»P ± i-.n if a l«or, — i J.
REDUCTION OF rRACTlONS.
95
a
-R prince ^ to its lowest terms.
I* deduce i to Its lowest terms.
i'Re^luee^ to its lowest terms.
t' leduee X to its lowest terms.
r deduce li to its lowest terms.
7* See P to its lowest terms.
R lleduce U to its lowest terms.
q deduce li to its lowest terms.
in deduce ii to its lowest terms.
1 1" See i| to its lowest terms.
1 V leduee 'A to its lowest terms.
1 q deduce 4 to its lowest terms.
I!' Eeduce i|- to its lowest terms.
15". Beduce if to its I^^^^.^^Xction remaiu the
1 A -Wbv does the value ot the tracwon .
saS wheJyou divide both numerator ..Xdenonn.a
for by tbe same number . „„niprator and de-
XaTorh/The"'^Ca^wh^oes it not
=?nh^tmfs^-Sowest terms.
20. Eeduce 8 times ^ ^^^ ^^^^^^ .
21. Beduce 6 times , to ^^^^ ^^^^^_
22. Beduce * tvmes i^^° ^^^ ^^^^^^
23. Beduce 12 times to ^^^^^_
24. Beduce ^2 .^'^f_^Cit, lowest terms.
*5- 5i"^! 7 t mes " to its lowest terms.
26. Ked»f/ *^^';, 11 to its lowest terms.
27- 5'f ! 4 t mes " to its lowest terms.
28. Eeduce 4 1 mes 3^ w .^^^ t^^ms.
fo:Sre 9^11 to its lowest terms.
^0
COMPOUJVD FRACTIONS.
DPI
Lesson XV.
wilV/Vfi!" ''''^.'''' ""PP^^^ ^"^° ^^^'o ^qual pieces, what
will 1 ot these pieces be called ?
2 If you cut } of an apple into two equal nieeps
ralfedT ''' "'^^^ ''^^^'^^ ^^'^" ^ of thesrpie^ces be
3. If Alice has i of a lemon, and »ives half of it- f«
Am, what part of a lemon will Ana receive ?
of a
ie»'oTs-ii irftiL:"^"-^^"- ^"^ -^-'-^ i "f
4. George, having half of a melon, gave i of it to
Marcns; what part of a melon did JlLusreceve?
5 Crary had -J- of a dollar, and gave ^ of it to
TnV\'t P/^' f'' '^'•"''' '"d J°'hra ;ece ve ,
6 Kobert had J of a dollar, and gave * of it for a
cake ; how many cents did the cake cost him ?
I,n,l . . '■^'"■t' ¥ * °f " P<""^d of candies, and Mary
had 1 as much ; how much had Mary ? ^
8. Jane had a of a poand of sugar, and Ann -'- a,
much; how much had Ann ? '
gave '\f tL!!??^^^- "^- f ^ 9»art of chestnuts, and
fhlreceive ? " ' '* P"'' °'' " '""^^ '^''^
> ond'"*"uT°^'^*5^'''^''«'" a bank, and sold
. of that ; what part of a share had he remaining ?
wW f"^?^^ *; "^^ "'''P' and sold i of his share •
what part of a whole ship did he sell? '
J-^. What is ' " - -
Solution.--* of ^ is ^\^,
13.
14.
15.
16.
17.
18.
What
What
What
What
What
What
IS
is
is
is
is
is
X
5
l_
3
1
i
1
8
I
T
1
of
of
of
of
of
of
-. p
OI
1?
5
1?
2 •
X7
7 •
i 9
6 •
i.?
9 ■
i?
8 •
•1?
COMPOUPm FRACTIONS.
97
of i?
19. What is . ^
20. What 18 T^ °: j' ^felUoftheway
to the ground It ^^/^^^^^^^^^ distance was it
the ground ; what part of tue wnoi«
above the ground ? ^ ^ Nelson is
^tr;?r.! owning ^^^^^j^^i:i^:^^az
modated his neighbor with | ot it , now
remaining ? , . „ i ^f „« eagle, gave i of it to
24. A man, having ^ ^t ^\^?^._'(f. ^hat part of
cents had each ? i? „ r>;p and save i of it to
25 Elizabeth had | of a pie, ana gav« 3
Or, Solution. — ^ of | is f ,
26.
27.
28.
29.
30.
81.
82.
83.
34.
35.
36.
37.
38.
39.
40.
What
What
What
What
"What
What
"What
What
What
What
What
What
What
What
What
is
is
is
is
is
is
is
is
is
is
is
is
is
is
is
2
1
4
1.
5
5
JL
7
1.
8
1.
9
1
9
X,
8
5
1
4
1.
9
1
7
1
7
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
3 ?
1^
3 •
2.?
3 •
3.?
4 •
3.?
4 •
a.?
3 •
4 ?
5 •
3 7
3.?
8 •
6 ?
98
COMPOUND FRACTIONS
• (I
fttitfl
I ■ ■■;
' ■ i
41.
42c
43.
44.
45.
46.
47.
48.
49.
50.
51.
52,
63.
54.
55.
5Q,
57.
68.
69.
60.
61.
62.
What
What
What
What
What
What
What
What
What
What
What
What
What
What
What
What
What
What
What
What
What
What
s
IS
.1
J.
4
3
5
a
3
T
3
X
8
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
of
part of 1 IS
..^^„ part of 2 is *
Solution.— f of + is 2 2 :g ^ ^f , „„ . .'^
h which is ^ of 2. ^- ^ '' ^ of 1' «nd 18,
Solution 2c1. — 1- of i I'q 2 i :„ i « „
of h or A of 2, auc?|*a;:|- time': ^t'o^-^ Jf^ ',■'» * "^ 2. i ie*
64. What part of 2 is '
part of 2 is
part of 3 is
part of 4 is
part of 5 is
part of 9 is
part of 2 is
part of 2 is
part of 4 is
part of 6 is
part of 3 is
:s
13
's
s
is
L3
's
y
4.
5"
3
f
5
'£
3.
4
^
8
Jt
5
*.
7
J5
7
8
IS"
i?
7 •
5 *
A?
y •
-i ?
4 *
i ?
8 •
I?
1?
f?
2.?
7 •
«.?
8 •
7 *
6.?
7 *
8 ?
9 •
3.9
7 *
2-?
3 •
1
he
ta
•w
a
r
of
of
therefore, | of
6 •
3 •
64.
Q5.
QQ,
67.
68.
69.
70.
71.
72.
73.
74.
What
What
What
What
What
What
What
What
What
What
J.
4
3.
4
X
«
JL
3
1
5"
3.
7
2_
6
1
3.
5
J.
7
i
of
of
of
of
of
of
of
of
of
of
of
1 * ?
-I?
i?
If?
f.p
H?
i?
JL ?
lO f
I?
4f?
iof
COMPOUND FRACTIONS.
99
I of
3
1 ') R ?
76. What part of 4 i= „ ^-^ ^,.,|^
76. -What l«r of 7 ^ . ^^ ^.^^^^^^ .
77. Anthony had » o' * °\" ^
what part of ^"'""yr.f a quart of Btrawberries ;
78. Albert had V 9^1^^' ,'^e provided 1 quart con-
bow many strawherriea had he, pr
tained 42 Btravvbernes . ^ ^^^^ ^^ y, ^^otUer ;
wJ^tptli^o^^C^Shere.^^^^^^^ ^^.
and on nis way borne spilled 3
a Dail-fuU had be remainiDg . ^ ^^^^d of molas-
Ifant ro"»K N''^' P^'^ °^ "^ '°^*"'
Ld be remaining ? ^ £ candies, and gave
.^f^£tASslaf:hT;artofapouudd.dshe
what part of a do"" ^ad he rema ^^ ^ le-augar,
f g^ 'XtWaSer • ?bat part of a pound d.d
to the one that could te 1 how mu ^^^ ^
what part of a P«e-appl« ^d J^c^ob ^^^ ^ ^^^ . ^^,
87, Jamea gave | ot s oi »
«an; cer^ts did the op cost hm ^^ ^ . ^„^ ^^ny
88. Eobert gave v °' .'^^"i""
cents did the cap cost hun^ ^.^^^^ for a comb; bow
100
SIMPLE PROPORTION.
I
4 I
».-.
h
jll:.
91. A man. having 4| barrels of flour, sold J of it ;
how much remained unsold ?
92. A man gave J of $3i for a silver pencil ; what
was the cost of the pencil ?
93. Jane worked 8.^ hours in a day, and Delilah
worked only * as many ; how many hours did Deli-
lah work in a day ?
94. B. gave $32J for a cow, which was .J as much
as A gave for his ; how much more did A's cow cost
than B's ?
^ 95. Darius is 18| years old, which was | of Dan-
iel s age ; how old is he ?
96. If 1 yard of cloth cost $5f , what will -?. of a
yard cost ?
97. If 4 yards of cloth cost $9^ what will 4 of a
yard cost ? - o
98. If 6 barrels of beef cost $18i what will i of a
barrel cost ?
99. If I of an apple cost | of a cent, what will 1
apple cost ?
100. If I of an orange cost 1} cents, what will -^
ot an orange cost ?
101. If 4 pounds of butter cost 6i dimes, how
many cents will If pounds cost ?
Lesson XVI.
1. If 4 bis. of flour cost $14f, what will 4 of a bl.
cost f "
coai?^^ ^ ^"^^' °^ ^^^^^ ^^^^ ^^^' ^^^* ^^^^ ■^^^ ^"®^*
3. If 2i bushels of apples cost 6i dimes, how
many cents will | of a bushel cost ?
4. If f of an apple cost | of a cent, what will 1
apple cost ?
6. If I of an orange cost f of a cent, what will -'
01 an orange cost ?
I
DIVISION OF FRACTIONS.
101
im^
6. If2f yds.of silk cost $3^ what will 51 yds-cost?
7. If 5 1 yds.of satin cost $5 ,^, what will 2 yds. costf
8. If in 3t hours A can do a piece of work, how
long will it take him to do a piece 1 1 times as large ?
9 f of A's age is f of B's age ; and 1 of B s age is
f of C's age. How old are A. and B respectively,
provided C is 8L years o\d1
10. Bought 31 boxes of goods, at $6y\ a box, and
paid for it with sheep at $2 a head ; how many sheep
did it take ?
11. How many times -| is -^ ?
Solution Isx.-f equals ^j,, and f equals i^. ^^ is contaia-
ed in ^^, V or 1| times.
Solution 2nd.-^ is contained in 1, ^ times, and in f, 1
times f times which are V. or 1| times.
Solution 3ed.-1 is contained in h f times. If 1 is contain-
ed in I, f times, i is contained in ^ 5 times f times, ^tidi are
Vtimf; and | is contained in it, i of V ti«nes, which is V. or
1-J times.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
2^.
24.
25.
26.
27.
How
How
How
How
How
How
How
How
How
How
How
How
How
How
How
How
many
many
many
many
many
many
many
many
manv
many
many
many
many
many
many
many
times i
times ^
times
times
times
times f
times f
times ^
times T
times -f-
times
times
times
times
times
times li
6
3.
8
2
3
I?
8. 7
7 -
■3
14 •
8 •
5.
9
2.
S
4
7
^
6
8
IS
is
is
is fV^
is li?
is
is
is 3^?
is 21?
is 2i?
is 5f ?
ia -^'^
la T¥ •
is 3i?
is 4i?
is 2i?
102
DIVISION OF FRACTIONS,
'ffi
*i
'I
Ml'
m
,11
28. How many times 2^ is 1|?
29. How many times S\ is 5|?
80. How many times 4^ is 6g?
31. A farmer sold a quantity of rye for $96, which
was only * of what it was worth ; how much did he
loose by the bargiu ?
32. A man sold a cow for 1} times what she cost
him, and by so doing gained $(5 ; how much did the
cow cost him ?
33. A merchant sold a quantity of goods for \-} of
what they cost, and by doing so he lost $lo ; how
much did the gooda cost him ?
34). A farmer, having lost 12 sheep, found, that only
l of his flock remained ; how many sheep had he re-
maining ?
35. An individual being asked how many geese he
had, answered, that if to -^ of the flock 24 geese were
added, the sum would equal 1|- times his original
flock ; how many geese had he ?
36. If I of a yard of cloth cost $|, what will % of a
yard cost ?
37. A boy, being asked his age, said, that 8| years
•was f of twice as much as his age : how old was
he?
38. If gof the candies I have cost;7 J cents, what
will i of them cost ?
39. What will | of a barrel of flour cost, if 5 of a
barrel cost $2| ?
40. What will f of an orange cost, if 4 of an orange
cost 2i cents? & t s
41. How many yards of cloth will be required to
make a coat, if 1| will make f of a coat ?
42. f of 2 are how many times f ?
tV of 8 are how many times -| ?
I of 7 are how many times 3 ?
of 8 are how many times |- ?
of 12 are how many times | of 6 ?
43.
44.
45.
46.
3
■4
3.
4
)\
FRACTIONS.
103
47. I of 7 are how many times j? of 2 ?
48. If f of 3 yarda of cloth cost Uh what will -J
of 7 yards cost ?
49. If I of G yards of cloth cost $2 J. how much
will J of 7 yards cost ?
60. If 1 of ] of a barrel of flour cost $11, what will
} of i of ^' of a barrel cost ?
1. 12
Lesson XVII.
of what number ?
Solution.— If f of some number is 12, ^ of that number is j^
of 12, or 4 ; and ^ which is that number, are 4 times 4 which
are 16. Therefore 12 is | of 16.
2.
3.
4.
5.
6.
7,
8.
9.
10.
11.
12.
18.
14.
16.
36.
17.
18,
19.
20.
16
18
20
26
25
30
32
39
36
36
24
9
12
38
16
16
16
40
40
8 f
8 ^
S ■5.
S -r'
5
7
5.
»
8
»
7
Jl
1 1
(!
7
3.
7
1l
"5
2.
4
"5
7
2
"5
S
ji
5)
of what
of what
of what
of what
of what
of what
of what
of w^hat
of what
of what
of w^hat
of what
of what
of what
of what
of what
of what
of what
of what
number ?
number ?
number ?
number ?
number ?
number?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number *?
number ?
number ?
-40 is I of 45.
Solution. ^
Remark.— When pupils are familiar with the analysis of these
questions, the intermediate steps may be omitted, as m the
above solution.
I. -- <.
104
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31,
32.
33.
3d..
35.
36.
37.
38.
39.
40.
72 is
72 is
12 is
16 is
18 is
32 is
46 is
48 is
48 is
36 IB
30 is
30 is
10 is
16 is
24 is
25 is
35 is
40 is
48 is
96 is
8
9
10^
2.
3
4
2
5
jL
7
"3"
*.
5
Jk.
G
"7
_5_
'J
8.
7
A
9
_*_
1 5
3.
3
Jl
9
_5_
1 2
8
. 6
10
2.
3
BRACTIOJSS.
of what number?
of what number ?
of how raauj times
of how many times
of how many times
of how many times
of how many times
of how many times
of how many times
of how many times
of how many times
of how many times
cf how many times
of how many time.i
of how many tfmes
of how many times
of how many times
of how many times
of how many times
of how many times
2?
3?
9?
4?
23?
5?
4?
2?
iofl2?
iof]0?
f of9?
i of 16?
f ofl2?
iof9?
f of9?
f oflO?
f of25?
f ofl6?
1 ^
2.
2
■"5
3.
3
4
4.
o
T
5.
*.
3
6.
3
10
7.
3
9
8.
6
^9.
5
10.
6
7
11.
f
12.
f
13.
*
S
Lesson XVIII.
of 6 is I- of what number ?
o( 10 is I of what number ?
of 8 is f of what number ?
of 21 is I of what number ?
of 15 is f'o of what number ?
of 40 is I of what number ?
of 27 is -I of what number ?
of 27 is 1^ of what number ?
of 81 is Y%^ of what number ?
of 49 is -^ of what number ?
of i 2 is 1^ of how many times 2 ?
of 16 is f c f how many times 2 ?
of 10 is f of how many times 4 ?
FRACTIONS.
105
14. i of 16 is T^ of bow many times 6 ?
15. ^ of 15 is f of how many times 6 ?
16. f cf 20 is f of how many times 3 ?
17. -I of 12 is f of hcv many times 5 ?
18. f of '20 is f of how many times 3 ?
19. ^ of 36 is 4^ of how many times 4 ?
20. I of 72 is -| of how many times 12 1
Solution.— f of 12 is 64. 64 is ^ of 96. 96 is 8 times 12.
21. I of 96 is I of how many tiroes 90 ?
22. 1^ of 117 is J of how many times 4 ?
23o -f of 56 is f of how many times 8 ?
24. -I of 60 is f of how many times 5 ?
25. f of 36 is f of how many times 12 ?
26. f of 72 is f of how many times 5 ?
27. I of 40 is yV of how many times 21 ?
28. f of 32 is I of how many times 9 ?
29. f of 15 is -f- of how many times 2 ?
30. •§- of 15 is i of how many times 9 ?
31. I of 24 is f of how many times 3 ? •
32. i of 45 is f of how many times 3 1
33. -f of 14 is f of how many times 5 ?
34. I- of 18 is f of how many times 7 ?
35. _5_ of 40 is f of how many times 6 ?
36. ^ of 45 is -5^ of how many times 3 ?
37. f of 35 is f of bow many times 2 ?
38. f of 81 is f of how many times 9 1
39. f of 5 is -f of how many times 7 ?
40. f of 7 is ^ of how many times 3 ?
41. B's horse cost $60, and | of the cost of the
horse, is i of two times the value of his wagon ; what
is the value of his wagon ?
42. A coat cost $20, and 4 of the cost of the coat
is I- of 8 times the price of a hat ; the price of the hat
is required 1
43. If a cow coat $30. and f of this, is f of 10
times the price of a sheep ; what is the price of a
sheep ?
106
FRACTIONS.
1*^
>
4i. A's farm is worth $1200, and |- of its value, is
I of 10 times the value of its yearly productions ;
what is the value of the yearly productioDS ?
45. The articles contained in a certain store cost
$500, and tV of their cost is g of 3 times the amount
paid for the silks ; how much was the cost of the
silks, and of the other articles respectively ?
46. A's wedding clothes cost |180, and | of the
cost of his clothes, is |^ of 6 times the cost of his
wife's wedding dress ; how much was the cost of her
dress ?
47. The insurance of a ship amounted to $800, and
I of that is ^V of 2 times the value of the cargo ;
what is the value of the cargo 1
48. A's house cost S1400, and J of its cost, is 3^
times i of the cost of the furniture contained in it ;
what was the cost of the furniture ?
49. Provided a house was Mwth $1200. andf of its
value was f of i times the value of the farm on which
it stood ; what was the value of the farm 1
50. If a sleigh cost $100, what would be the cost of
a wagon, if f of the cost of the sleigh was xt of twice
the cost of a wagon !
51. Lambert is worth $2500, and |- of his fortune is
31 times | of Latham's fortune ; how much is Latham
worth ?
Distances on the Railroad between Albany and Buffalo.
52. The distance from Albany to Schenectady, is
16 miles, and J of this distance, is f of i times the
distance from Albany to Eome ; what is the distance
to Kome ?
53. Fort-Plain is 56 miles from Albany, and ^ of
this distance is 15- times ^V of the distance from Al-
bany to Eochester ; what is the distance to Eochester 1
54. Waterloo is 192 miles from Albany, and J^ of
this distance is
1 o
FRACTIONS.
107
to Utica, and 3 miles more ; v/hat is the distance to
XJtica ?
55. Buffalo is 825 miles from Albany, and f of this
distance is 7^ times Jj of the distance to Batavia,
and 5 miles more ; what is the di&tance from Albany
to Bavatia ?
Distance on the Railroad between Albany and Boston.
56. Boston is 200 miles from Albany, and f of this
distance is 1?- times ^ of the distance to West Spring-
field; what is the distance to West Springfield?
57. From Albany to the State line is 38 miles, and
Ij times this distance, is 4| times }j of the distance
to Wilbraham ; what is the distance to Wilbraham ?
58. Kinderhook is 16 miles from Albany, and f of
this distance, is f times -| of the distance to Dalton ;
what is the distance to Dalton ?
59. Brighton is 195 miles from Albany, and f of
this distance is i of 2 times the distance to Worces-
ter ; what is the distance to Worcester 1
60. Grafton is 162 miles from Albany, and f of this
distance is \ of 3 times the didtance to Westfield, less
2 miles ; how far is it to Westfield ?
Lesson XIX.
1. J of 9 is f of how many times -|- of 25 ?
2. f of 16 is ^ of how many times -f of 21 ?
3. f of 40 is ^ of how many times ^ of 16 ?
4. I of 80 is f of how many times |^ of 21 ?
5. f of 36 is \ of how many times f of 1 2 1
6. f of 45 is f of how many times f of 14 ?
7. |- of 30 is f of ^ow many times ^ of 10 ?
8. \^ of 48 is \ of how many times f of 7 ?
9. 4 of 45 is I- of how many times f of 8 ?
Solution.— 4 of 45 is 36.
is 27 times 6.
86 is # of 162. i of 8i3 6, 162
108'
10.
5
T
11.
7
12.
3
5
13.
4
T
14.
4
9
15.
5
6
16.
4
9
17.
i
18.
8
9
19.
4
20.
4
5
FRACTIONS.
of 35 is -I of how many times -f-
of 54 is ^ of how many times f
of 25 is f of how many times f
of 28 is I of how many times |-
of 18 is f of how many times |-
of 36 is f ot how many times |-
of 54 is f of how many times ^
of 32 is I of how many times -|
of 108 is f of how many times
of 40 is -j^ of how many times
of 20 is f of how many times I
of 111 ?
of lOi?
of 10?
of 25?
of 12?
of 12?
of 16?
ofO?
f of 1 of 15?
i of i of 20?
of f of 12 ?
Lesson XX.
1. If 1 horse eat i of a bushel of oats in 1 day,
how many horses will eat a bushel in the same
2. If the wages of 8 weeks amount to $48, what
will' the wages of 2f weeks amount to ? _
3. A ship's crew of 12 men have provision for 5
months ; how many months will it last 5 men ?
4. A man gained $14 by selling a watch for If
times what it cost him ; how much did it cost him ?
5. There is a pole, i of its length is under water,
and 9 feet out ; how long is the pole ? , ,^^ ^ ,
6. A pole is standing in the water, so that 15 teet
is above the water, which is f of the whole length of
the pole ; how long is the pole ?
7. If t be 2 what will 2 be ?
8. If 8 horses can in 1 day eat 4 bushels of oats,
in how many days can 1 horse eat 1 bushel ?
9. If 3 heroes can in 1 day eat If bushels of oats,
how many bushels can 1 horse eat in 4 days ?
10. If 1 horse in 2 days can eat 6 buBhels of corn,
how many bushels will 4 horses eat in 3 days ?
,
COMPOUND PROPORTION.
109
11. If 4 horses eat 16 bushels of grain in 2 days,
how many bushels will 3 horses eat in 12 days ?
12. How many tons of hay will 3 horses consume
in 4 days, if 4 horses in ^ of a day consume |^ of a
ton ?
13. How many hundred weight of hay can 3 horses
consume in 25 days, if 2 horses in i of a day consume
-=^1— of a hundred weight ?
400
14. In how many days can 4 men cut 16 cords of
wood, if 1 man in 1 day cut i of a cord ?
15. How many men will be required to earn 20
dimes in 4 days, if 4 men in 2f days. earn 11 dimes ?
16. If it require 6 days for 2 men to lay 36 rods
of wall, how many men can in \ of the time build 72
rods of similar wall ?
17. If in 4 days 3 men accomplish a certain piece
of work, how many men will be required to perform
a piece of work 4 times as large in 2 days ?
18. If 4 men in 8 days perform a certain piece of
work, how many men will be required to accomplish
3 times as much work in f of a day ?
19. If 1 horse eat 1 bushel of oats in 4 days, in
how many days would 6 horses eat 48 bushels ?
20. If f of 6 be 3, what will \ of 40 be ?
21. If 3bef of6,whatwill^of40be?^
22. If 2 men in i of a day earn ^^ of a dollar, in
how many days can 3 men earn f of a dollar ?
2S. If it require i of a bushel of oats to feed 4
horses ^ of a day, how many horses would it require
to consume 9 bushels in f of a day ?
Jj;^" Suggestion. — li£view unless the pupils thoroughly un-
derstand the preceding Chapters, ^gj
The study of Chapter VII- may be omitted until the class
has learned Chapter VIII., ^Ci ceptiog the miflcellaneous quesj
tioDS.) , ,
110
QUESTIONS
CHAPTER VII.
Iiesson I.
1. $24 is f of twice aa much as a cask of wine
cost ; what did the wine cost ?
2. Bought 30 barrels of flour, and f of the num-
ber of barrels, equalled i as many dollars as they all
cost ; what did 1 barrel cost ?
3. 35 is f of how many times f of 4 ?
4. A farmer, being asked how many sheep he had,
answered, that 160 was | of 10 times his number ;
how many sheep had he ?
^ 5. Mr. B, being asked the value of his horse, said,
$54 is -5^ of 3 times its value ; what is the value of
his horse 1
6. 72 is f of how many times f of 12 ?
7. 36 is f of how many times f of 12 ?
8. 48 is f of how many times i of 18 ?
9. ^6 is f of how many times i of 8 ?
10. 60 is f of how many times | of 16 ?
11. 84 is V^ of how many times i of 25 ?
12. A spent $60, which was f of 4 times aa much
as he was worth ; how much was he worth ?
13. B sold 9 sheep, which was -^^ times ^ of his
whole flock ; how many sheep had he remaining ?
14. D, at a game of cards, lost $20, which was f
times I of all the money he had ; how much had
he?
15. C found $45, which was f of 3 times as much
as he already had ; how much more did he find than
he had at first ?
16. A boy lost 9 marbles, which was f of twice as
many as he had at first ; how many had he left ?
17. A boy gave away 8 apples, which was f of
t
]
t
I
t
QUESTIONS.
Ill
twice as many as he had left ; how manv had he at
first ?
18. 12 is f times } of what number?
19. 86 is y\ times § of how many times f of 13^-?
20. Jeremiah is 18 years old, and his age is f times
I of his father's age ; how old is his father ?
21. Mary ^ve 6 cents for a comb, which was f
times i of all her money ; how many cents had she ?
22. Martha gave 8 cents for a pine-apple, which
was f times | of all her money ; how many apples
could she have bought with the money she had re-
maining, at 2 cents apiece ?
23. Henry had 20 marbles, which was f of twice
as many as Harry had ; how many had Harry ?
24. Margaret is 16 years old, and her age is f of 3
times Martha's age ; how old is Martha ?
25. f is f of twice as much as what number ?
26. A man bought a horse foi $60, which was ^ of
twice as much as he sold him for ; how much did he
gain by the bargain ?
27. A horse was sold for $40, which was ^ times
f of what he was worth ; what was the value of the
horse ?
28. A man when he was married, was 20 years of
age, which was | times f of the age of his wife ; how
old was she ?
29. Shepherd was worth $160, which was f times
■^ of his father's fortune ; what was the father's
fortune ?
30. A and B were playing cards, B lost $14 which
was -j^o times f as much as A then had ; and when
they commenced f of A's money equalled f of B's.
How much had each when they began to play ?
31. A and B were playing cards, A lost $20 which
was ^ of the number of dollars B then had more
1 1 i-
iii was J-'- Limes as mucn as
than A ; provided this su ^ ^
A had at first ; how much had each when thev beffan
to play? " ^
112
<iU£STIONS.
Xiesson II.
rt„\" 1^ ''°^: "'*" "P™^*"? i of all his money, found
af =ir,^|<,| z^ Zrs^^'tA, tit. Tn-
This by the condition of the question is 16 cents JflnfJ'
money he had at first is 16 ce^nts. i of i\ il Vof 6 cent! wh ch
Solution 2d -He spent f of his money ; therefore he had
IfiTnT^.^ '^'*; which equals 16 cents. ^If ^ of Ws money's
16 cents, he must have had 40 cents. ^
2. Euth, after losing f of all her roses, had only 8
remaining ; how many had she at first ? ^
3. Jane gave f of all her flowers to Ann, and had
4 remaining ; how many did she give to Ann ?
4. George, after eating ^^3. of all his oranges, had
only 8 oranges remaining ; how many had he at first ?
if 'n , i'^ expended ^ of his money for a pie, ^ fop
a ball, i for a to^, and had 6 cents remaining • how
many cents had he at first ? ^ '
6. In a certain school i of the scholars study gram-
mar, 3 study antiemetic, and the remainder, which is
lU study geography ; how many scholars in all, and
how many attending to each study ?
7. A third part of an army was killed, i part taken
thTarr^"^ ^^^ '''"^'^' ^'^ ^""^^«« ^^^^^
8. If from my age you subtract i and | of my age
the remainder is 2 years ; how old am I ? ^ ^
.Ja f?' ? v°5 ^^H^ }'''^ ^^°y Paeons he caught,
said, that If to f of the number, 36 were added, the
hHalch ? ^"^ ^""'"^ *^^ '''''''^'''- ^°^ "^^^^ ^^^
QUESTIONS.
113
10. If to f of the cost of B's horse you add $100.
the sum will be twice the cost of the horse ; what was
the cost of the horse ?
11. A gentleman, after spending ^ of his fortune
and 2, of the remainder, had $2400 remainin*^: what
was his fortune ? °
12. A gambler lost ? of all his money, and the
next night he won f as much as he lost the night
before; he then had $90: how much had he at
first?
13. John had stolen from him -f of his money, and
the thief was not caught until he had spent f of it ;
the remainder, which was $iO less than John had
remaining, was given back ; how much money had
John at first ? ^
14. A traveler had stolen from him | of all his
money, and the thief was not caughb until he had
spent i of it, the remainder ($100)" was given back:
how much had he at first ?
J;^- I^ *o i of the cost of A's watch you add
^10, the sum will be $21 ; what was the cost of his
watch ?
IQ. If to f of B's age you add 15 years, the sum
would be 39 years ; how old is B ?
y?'.J^ ^''°^^^ ^^^°^ ^®^®^ ^^°^ "^^^y s^^^P ^6 liad,
said, if to i of my flock you add the number 9^ the
sum will be 99.^ ; how many sheep had he ?
-lol?* ^ ^^ *^^® length of a pole is in the water, and
12 feet in the air ; how long is the pole ?
19. If to I of A's age you add 16 years, the sum
will be 1 L times his age ; how old is he ?
20. A man, being asked how manv pigeons he
caught, replied, if to f of the number I caught you
add 20, the sum would lack 4 of being equal to IJ
times the number ; how many did he catch I
114
PARTNERSHIP.
M I
Lesson III.
1. Divide the number 36 into two parts, wliich
shall be to each other as 7 to 2.
SoLLriON.-Sinre the two parts are to be to ench other as 7
IhZfT'^ '^r^^ ^' '"^^ ^ -^ 2, which are 9 equal par s
fir«f n mhoA . ^' """^ ^ ^^''^ ^ '''^^'^ *, which are 28 fthe
hrst number,) and .;. are 2 times 4, which are 8 (the other num
Mf:l ?'' 'V'^" '""^' P^''* «f the solution, say : ^of 86 is ps'
the hrst number; and | of 36 is 8, the other number. '
2. Two men hired a pasture for $72; one put in 7
horses and the other 2 horses ; what ought each^to pay ?
d. AandB hired a pasture for $14; A nut in 4
cows and B put in 3 cows ; what ought eath^top^y ?
4. A aiid B bought a lottery ticket for $5 ; A paid
S3, and B paid $2. They drew a prize of $60 ; wh^t
was each one's share ? '
5. Two men bought 40 mules : the first paid $5 as
tf r'ece" e'' '''^^ ^'' ^^^^ "^^ ^^^^ 4ht tch
6. Mary and Elizabeth went to school SO davs
and as often as Mary went 3 days, Elizabeth weufs
days ; how many days did each go ?
r^.-A Ti?i!'^'' ^^^ ^ ^'^^^^^ ^"d ^^ake 4 cents; they
e^afh ?o :e'::i:r^ '^''' ^PP^- ^ ^- --/oughl
firs^t D^idT2T ^'''^^* ?i°*^'y *^^^^* ^^^ $^2 ; the
first pnid $2, the second $7, and the third $3. They
drew a prize of $240 ; what was each man's share ? ^
in 2 hnria T"" ^''^^/ P^'*"'® ^°^ ^24 5 the first put
Dut inThn ""' 'f """^ P^f ^^ ^ ^°^«^«' ^^^ tbe third
put in 4 horses ; how much ought each to pay ?
on}v'^tfT''At}'''i ^" ^^^^^«««' ^^« able to pay
only I of his debts ; how much will that man receive
to whom he owes $90 ? receive
11. A man, meeting an equal number of poor wo-
PARTNJIRSHIP.
Ud
men and boys, gave to each woman 7 dimes, and to
each boy 2 -dimes ; and to them all he gave $9: how
many women and boys were there respectively ?
12. Two men bought a barrel of fish for l$9 ; the
first paid ^4, the second !$5 , what part of the barrel
belongs to each ?
13. A farmer gave 35 bushels of rye to two of his
poor neighbors ; to the first he gave 1 bushel as often
as to the other | of a bushel ; how many bushels did
each receive ?
14. Three men hired a pasture for $36 ; the first
put in 3 horses, the second 2 horses, and the third 4
horses ; how much ought each to pay ?
15. Two men hired a pasture for $60 ; the first
put in 4 horses, for 2 weeks, and the socond put in 3
horses for 4 weeks. How much ought each to pay ?
16. Three men hired a pasture for $15 ; the first
put in 4 sheep for 5 weeks, the second put in 8 sheep
for 5 weeks, and the third put in 10 sheep for 9 weeks.
How much ought each to pay ?
17. Two men entered into partnership ; the first
put in $40 for 10 months, and the second put in $80
for 5 months ; they gained $95 : what was each man's
share of the gain ?
18. A and B agreed to cut a field of wheat for $20 ;
A sent 6 men for 4 days, and B sent 3 men for 10
days ; how much ought each to receive ?
19. Divide $56 between A and B, giving to A $1
as often as to B f of a dollar.
20. A and B hired a pasture for $24 ; A put in 4
sheep for 10 weeks, and B put in 2 horses for 10
weeks ; w^hat ought each to pay provided 2 sheep in
1 week eat as much as a horse in the same time?
21., Simpson, Bomer, and Eyer, enter into a joint
speculation by which they clear $460. Simpson
claims to have furnished f ; Domer, J ; and Eyer, ^
of the entire capital. Bow much according to these
calculations ought each to receive ?
116
ALGEBRAIC QUJ33TIONS.
er
u
Lesson IV.
l.«h? \^ ^ *PP^®^, ^^""^ *^«» ^' and they togeth
had 14 ; how mauy had each ? ^ ^
hlvlofiJL A . ^ "P^^"' ' ^" ^^^<^^» «^^ A'8 Dumber, and we
uer equals 14 — 4, Oi' 10; and once ha numbei' eauals A nf in
or 5 apples. And B's number is 5 + 4 = 9 apples * '
Knfi; ?^"'S^ ^"l" ^ ^°°^'' '"^^^ *b»^ Handford, and
both have 26 ; how many has each ?
Knfi; r ot^""? ^ '"^'■^^^' "^^^« t^a^ Richard, and
A ^r® ^ ' ^^"^ "'^^y ^^»« each ?
hnv^ 2l^'{ ^""^ ^ '""'f '^^'^ *^^^ ^a^t^a, and both
have 24i ; how many has each ?
5. Alice has 7 pins more than Abner, and both have
2i) ; how many has each ?
^' I 0^ I is A of what number f
.nl; .^^^^'^^^ of two numbers is 36, and their differ-
ence is 16 ; what are the two numbers ?
^ V • ^?y,^o"g^<= f of a melon for 8^ cents : how
much IS that apiece ? '
hpfn?"""®!^"^ ■^^''?^^ '"''^^ ^°^g^t an equal num.
mnrfj^'^'^'V °\*^"^^ ^^^^ hoSe Hannah had 4
ITv&^htV^^ '^^^ ^^^-^^-^^^24; how
onpt Jr ^/' ^^'^ ?^^ ^"^ ^^^^^ "^«^^e^ of block.;
n A ^ ' ^""^ ^any had each at first ?
much i.-r^? ""f '°M ^^^ ^1^^^ ^^icJ^ ^as f as
^9 as it cost ; what did it cost ?
ffene' un^T^^^f ^'^l'^ • \^^^^ strawberries a,. Eu-
gene, and both Um. 18 pints ; how many had each ?
Tro Au^''' ''''- ""^^0 than twice as many as
Ira,^and both had 36 ; how many had each ? ^
-^* ^.usaahuu^ as many cents as Sarah; Sarah
ALOEBRAIC QUESTIONS.
117
as
lost 10 of hers ; then together they bad 60 ; how
many had each at first ?
15. Thomas was returning from market with twice
as many eggs as Timothy ; Thomas broke 4 of his
and Timothy 6 of his ; they then liad 50 eggs remain-
ing. How many had each at first ?
16. A of a number + 14 = 44,; what is that
number ?
17. A boy being asked his age, replied, :{ times my
age -7 years are 23 years. How old was he ?
18. A, being asked how much money he had, re-
plied, twice what I have + $60, is four times $400 ;
now much money had A ?
19. Two boys had 49 marbles, but the first has 7
the most ; how many has each ?
«^n^* i^ *"^^ bought a sheep, a cow, and a horse for
WiO; the cow cost $10 more than the sheep, and the
horse cost $20 more than the cow. What was the
cost of each ?
21. A man bought a melon for 18f cents, which
was only f as much as his dinner cost ; what was the
cost of his dinner?
4.U ^\'^ gentleman bought a watch and chain for $80 ;
the Cham cost i as much as the watch ; what was the
cost of each ?
23. A farmer bought a plow, a harness, and a
horse for $58 ; for the harness he gave $6 more than
tor the plow, and for the horse $34 more than for the
harness. How much did he give for each.?
24. A boy bought twice as many oranges as lemons,
and on his way home ate 4 oranges and gave six away ;
and was surprised to find he had only 14 orauges re-
maining. How many of each kind did he buy ?
25. 5 times a certain number— 12 is 48 ; what is
that number ?
26. f of a certain number— 5 is 40 : what is that
number ?
Ill
118
ALGEBRVIC (QUESTIONS.
27. A boj, being asked hia age, replied, U years
j^. •^Y^^^'i'^^^gasked how many sheep his father
29 A boy bought IS lemons ;— for ^ of thpm l.n
paid Scents for 2, and for th. rematder he pa^d 3
cents a piece; for what must he sell them a piece to
gam 10 cents on the whole ? ^ ^
30. James, John, and Joseph together have qfl
peaches 5 James has 2 more than John, and Jo ephh.s
as^many as both James and John / how many hL
pafd2fe?t7f.!!.T^^^.^T.°^''^ ^°^* °^*^«^ ^^
2 and sold^ of th' "I t' ^^"^^'^^er, 3 cents for
I'/fiT ^ f ^''"'' ''^ *^^ ^^<^^ of 2 cents for 3
and the remnuuier, at 3 cents for 2. How much did
he gain by so doing ? ^" "^^
Ijesson V.
1. If a man can do a certain piece of work in 12
days, what part of it can he do in 1 day ^
wi ; 'i^'i'? '^^'^ '^"' "^^ '"^ ^^^^^1 «f beer in 20 weeL s
what part of it can he drink in I week ? '
oft ol^il''^''''f I" • ^'^ t° '"'P'^ '^ ^^««^^ ^^J^at part
or It can be emptied m 1 hour ? 7 t-oiu
4. If a family consume a barrel of pork in 30 dava
what part of a barrel do they daily consume ? •' '
nev wL Z'^T't ^^ ^T '" P"""'"™ " certain jour-
ney, wha. part of it can be performed in 1 day?
indR L if? t " *'"'''''" P'^'=« °*' ^■o'-'^ w 8 days,
^an el'So'inVdXr^ '^ '^ '^"--^ -^^' P-' o/S
couM^d?*'""'^ "°- "r'f '° '^?'''*'" ^ '5''^^' ""^dD
<-i.ma ao ..,= ,.,uiu lu G days; what part of it could
ALGEERAIC QUESTIONS.
119
each do in a day, and how much could they together
do in a day ?
8. If C and D can, in 1 day, mow -^^ of a field, how
long would it take them to mow the whole field ?
9. How many days would it take to perform a cer-
tain piece of work, if -^ of it can be performed in 1
day?
10. If George can do a certain piece of work in 3
days, and Granvil in 6 days ; how long will it take
them together to do the work ?
11. If James can eat a bushel of apples in 10 days,
and Eud in 12 days ; how long would 1 bushel last
both ?
12. A can cut a field of wheat in 12 days, and B
can do the same in 20 days ; how loug would it take
them to cut the field when they work together ?
13. A merchant bought a hogshead of molasses for
$20, 10 gallons of which leaked out; how must he
sell the remainder a gallon to gain $6.50 ?
14. f of a barrel of flour cost $4|, what will |. of a
barrel cost 1
15. A and B can build a boat in 20 days, and with
the assistance of C, th<^y can build it in 8 days. How
long would it take C to do it alone 1
36. A farmer and his sou can do a piece of work in
6 days ; the son can do the same in 27 days. How
long would it take the father to do the work ?
17. Three pipes. A, B, and C can fill a cistern in 2
hours, A and B can fill it in 4 hours, and A and C can
fill it in 3 hours. How long would it take each to fill it ?
18. If a barrel of beer would last a man 35 days,
and the man and his son 20 days ; how long would it
last the son alone 1
19. A box of tea, usually, lasted a man and his
wife 9 months ; when the man was absent it would
1
fU,
oaf; . ..„
10
lasted the man alone ?
XT
xxuw
iOilg
u ould it have
120
ALGEBRAIC QUESTIONS.
li'l
<3a, '; anHla I'd" ' 'T"^ " ,'"^^' °' ^^^^ - 24
I of thiTtt^-Te^rea* ''^r/' ^^ ^^^^
each arid thereby gaLd"o;t''.„f '"" "J ^ "^"t^
bought How ^„»oh"d1^ 4 ^or pirf "'""^^
4J; f :rehr'h:a:tTr;.^ °^-°* ■•-^ °^
c^a h^tLTeaThe%%rA:j'r"^^''-^°^a
^b. Isaac can make a pair of boots in 2 ^c .
themtoeut a cord thjll ''°/ '"""''^ '' t«ke
28 if •■' nP„! ' 1 ° *°®y worked together?
of an appfel:t"/"P'^ '=°^' * "^ ^ -"^. -ha' will |
can A and B ^ow in a^dal "haf6 ^ ''°" ""•=" '"'"■«
« bear oa^ it t1° iliVuZ'JV "'^ '"'"^''"^
take them together to rnr«,l,?' "^ 1"°^''''"''' '*
^fter the wol? harbe^t^rn'ri TanTotI ' '''''
ALCEBRAIC QUESTIONS.
121
Lesson VI.
1 'Lewis, meeting some beggars, gave each of them
2 cents, and had 12 cents remaining ; if he had given
them 4 cents each, it would have taken all the money
he had. How many beggars were there.
Solution.— By the last condition of the question, he gave
each beggar 2 cents more than by the first, and to them all 12
cents mure than by the first condition. Therefore there must
have been as many beggars as 2 is contained times in 12, which
are 6 beggars.
2. A boy gave to each of his playmates 3 cents, and
had 24 cents remaining ; If he had given them each
7 cents, it would have taken all the money he had.
How many playmates had he ?
3. Mary gave each of her playmates 5 apples ; if
she had given them each 7 apples it would have taken
12 apples more ; how many playmates had she ?
4. A certain number of persons gave me 10 cents
each ; had they given me 12 cents each it would have
amounted to 20 cents more. How many persons
were there ?
5. i of $100 is ^^ of I times the salary of the
President of the United States. What is his salary ?
6. $40 is f of Jq of the salary of the Vice Presi-
dent of the United States. What is his salary ?
7. Divide 35 oranges between James and Joseph,
so that James may have 15 more than Joseph.
8. A cask of wine was sold for $96, which was | of
twice as much as it cost ; how much did it cost ?
9. By selling a quantity of cotton for $560, I gain-
ed f of what it cost ; how much did it cost f
10. A and B are 187 miles apart, and are traveling
towards each other ; one at the rate of 8 miles an
hour, and the other, 9 miles an hour; how many
hours before they will meet ?
122
ALGEBRAIC QUESTIONS.
her 20 dimea^more hoT' /"'"'^ "7°"^^ '"'^'^ cost
contain ? ' ^""^ """"y y^fds did the piece
oranU T/het„7ht th"ose ' a^ 2''eenr^- r"'"- "^
hare had no money left -Ld h t ' ?"=''' "^^ ^™uld
cents each he would havrwant^^ \T^^ *'"°^«' ^' 3
iave paid for them wlt ^" "^^o*^ «ore to
quired to buy ? ^°* "^^^ °'''"'?« was he re-
ofmu3lt;iCtre%1nr^'"-«^^^
yard, and some at 12 cenf« « i""?r "* ^ «ents a
that at 12 cents a yard ?t wo^f ^""^ '^' ^^^en
more than the other kind W ^"^ '"'"' ^6 cents
wish to buy? "^'^ '""''• HowmanyyardsdiJshe
niw ofTou'&:;:Lt%rnri/°h \"^ \-^'-
atScentsanounW l,o^ ij? ' " "o bought beef
but if he bZht Jork Ifs . T ^^ ''^"*^ remaining;
have only 6 f^ts rematbri'" T"^' ^' ^""'d
was he sent ? '«'"aming. Por how much meat
time's- tl^slTnu^X^'Xt Th 't^ '' T- ^''^ '
16. A boy being askedftg tid T I?"'' '
IS 24 years more than 2 timea m v ^! , 'T^ ""^ age
17. A boy, beine askerf 1,.^^ ="' '"''^ "'^ was he?
he had saidf 4 timfs tt ie7>7l\'7'^ "^P^P^"
tunes the number • hnwll^ i .'^ ^^ '^ss than 7
., 18. AperZ ;ishi^"t?{!^''*«°fP«Porhadhe?
f he bought that which fa, 10^.'''"' ''""'='•• ^"nd,
have 20c?ents reml-nLg but if h': t ^TS^^ '^°"W
was 12 cents a pound he wo, W 1 ^"i'f *" "'"* which
"-'> "^ vvuuid have $20
ALGEBRAIC QUESTIONS.
123
remaining; but if he gave .1^5 a head he would lack
^^0 of having money enough to pav for them. How
many sheep did be wish to buy ? *
,20. A, B, and C, talking of their ages; says A to B,
I am 4 times as old as you ; savs B to C I am ^ as
old as you, but says A to C, I am 40 years older than
yoa. liequired the ages of each ?
Lesson VII.
1. A laborer agreed to work 40 days upon this con-
aition ; that for every day be worked he should
receive |2, and for every day he was idle he should
pay $1 for his board. At the expiration of the time,
he received $50. How many days did he work ?
^ • ""T^n r^^ H ^'^"^ ^^^°^^^ ^'^« ^'^ole time, he would have
received 40 times $2, or $80. But he received only ^50 : he
therefore, lost by his idleness $80 - $50. or $30. For ever^
day he was idle he lost $2 (his daily wages) + $1 (the cost of
his board) which are |3 If in 1 day he^se $3 ; he will lose
$1 in j of a day, and $30 in 30 times I of a day, or 10 days.
Therefore he was idle 10 days, and worked 40 — 10 days or
60 days. "^ '
2. A man agreed to work 60 days on this condi-
tion ; that for every day he worked he should receive
^1^, and for every day he was idle he should pay Si
for his board. At the expiration of the time he re-
ceived $68. How many days did be work ?
3. A man w^as hired for 80 days on this condition ;
that for every day he worked he should receive 6
dimes, and for every day he was idle, he should forfeit
4 dimes. At the expiration of the time he received
140. How many days did he work ?
4. How many times | of 12 is | of 40 ?
_ ?; ;^ and B bought a quantity of flour for $50 ; A
paiu ^i as oiten as B f of a dollar ; what part of the
flour belongs to each ?
124
ALGEBRAIC QUESTIONS.
6. A, B, and C built a house, which cost $500, of
which B paid $1/^0 more than A, and C paid as mucli
as A and B both ; how much did each pay ?
7. A merchant sold a quantity of cloth for $84, and
thereby lost % of what it cost ; what did it cost ?
8. T-^is 2i times % of how many times IJ?
9. A farmer having in his employ an equal number
of men and boys ; to each boy he gave $4, to each
man $8 ; and to them all he gave $84^ ; how many
men were there ?
10. Two men hired a pasture for $35 ; one put in
3 cows, and the other put in 4 j how much ought
each to pay ?
11. A man sold an equal number of ducks and
turkeys for 20 dimes ; the ducks, at 2 dimes each, and
the turkeys at 3 dimes each ; how many did he oell
in all ?
12. A farmer sold an equal number of ducks and
turkeys ; the ducks at 4 dimes each, the turkeys at
7 dimes each ; and for the turkeys he received $3
more than for the ducks ; how many of each kind did
he sell ? . ^ ,
13. There are two baskets, contammg 37 apples ;
in one of which there are 17 more than in the other ;
how many apples are there in each ?
14. Charles and Henry together have 49 marbles,
and Charles has 7 more than twice as many as Henry :
how many has each ?
15. Philip has 20 apples more than Philo ; and to-
gether they have 92 ; how many has each ?
16. Three boys has 47 lemons ; the first has 3
more than the second, and the second has 7 more
than the third ? how many has each ?
17. A boy was hired for 20 days, on this condition,
that foe every day he labored, he should receive
3 dimes, and for every day he was idle, should
pay 2 dimes for his board. At ths expiratioa
ALGEBRAIC QUESTIONS.
125
of the time he received only $1. How many days
was he idle ? , . i j
18. A boy bought a whistle, a whip, and a drum
for 70 cents. For the whip h gave twice as much as
for the drum, and for the drum, twice as much as for
the whistle ; how much did he give for each ?
19. The sum of 3 numbers is 54. The first is
twice, and the third 3 times the second ; what are
those numbers ?
20. Sarah's age is | of Susan's, and the sum ot their
ages is 25 ; what is the age of each ? ^
21. f of an army were killed, f of the remainder
taken prisoners, and 400 escaped. How many were
there in the army ?
Lesson VIII.
1. A fishing rod, the length of which was 14 feet,
wasbroken into two pieces. The shorter piece was f
of the length of the longer. "What was the length ot
each piece ?
Solution.— I of the length of the longer piece, which is the
length of the shorter,+t (the length of the longer)- I of the
length of the longer, which is *he length of both, or 14 feet.
If I of the longer is 14 feet, i is ^ of 14 feet, which is 2 feet,
and 4 (which is the length of the longer) are 4 times 2 feet, or 8
feet. 14—8 = 6 feet, the length of the shorter piece.
2. A pole, the length of which is 20 feet, is in the
air and water, f of the length in the air equals the
length in the water ; what is the length in the air and
water respectively ? i j ^ ^
3. If in 2 days a man traveled 160 miles, and ^ ot
the distance he traveled the first day, equals the dis-
+o««n V.O frnvplpd thft second day : how far did he
travel each day ?
126
ALGEBRAIC QUESTIONS.
4. B and C togetlier have 40 marbles ; how many
has each, provided % of B's minibor is equal to C's ?
5. From New York City to Eedhook is 100 miles,
and I of the distance from New York to Ehinebeck,
equals the distance from Ehinebeck to Eedhook. How
far from Ehinebeck to New York, and how far from
Ehinebeck to Eedhook ?
6. If a horse and a colt were worth $90, and the
horse was worth 1 3- times as much as the colt ; what
was the value of each ?
7. A boy paid 70 cents for a slate and a book ; how
much did he pay for each, provided the book cost 1|
times as much as the slate ?
8. If a traveler pay $1.20 for his breakfast and
dinner ; how much did he pay for each, provided his
dinner cost f as much as his breakfast ?
9. A pole, the length of which is 67 feet, is in the
air and water ; f of the length in the air + 7 feet
equals the length in the water. Required the length
in the air, and in the water ?
10. Divide the number 108 into two such parts,
that ^ of the first + 8 shall equal the second.
11. Divide the number 97 into two such parts, that
-f- of the first + 7 shall equal the second ?
12. There is a fish the length of which is 18 feet ;
its tail is 4 feet, and f the length of the body, equals
the length of the head. "What is the length of the
head and body respectively ?
13. There is a fish the weight of which is 11
pounds, and -^- of the weight of the head 4- 8 pounds
equals the weight of the body ; what is the weight of
each?
14. A ship-mast 51 feet in length, was broken ofl"
in a storm, and f of the length broken off, equaled f
of the length remaining ; how much was broken off,
*luu uuW mucn remuiiieu :
15. A boy being asked how many apples and
ALGEBRAIC QUESTIONS.
127
oranges he had, answered, in all I have 36, and, f of
the number of apples, equals I of the number of
oranges ; how many of each kind had he ?
16. I of one number equals -} of another, and their
sum is 57 ; what are the two numbers ?
17. A farmer has 290 sheep in two difiVrent fields ;
and f of the number in the first field, equals f of the
number in the second ; how many are there in each
field ?
18. A market woman was requested to buy 33
fowls, consisting of two kinds ; i of the number of the
first kind, was to equal f of the number of the second ;
how many of each kind must she buy ?
19. A person, being asked the time of day, said, the
time past noon is i of the time past midnight ; what
was the hour ?
Remark. — Since the time past noon is | of the time past
midnight, the time from midnight to noon, which is 12 hours,
must be f of the time past midnight.
. 20. A person, being asked the hour of the day,^ said,
the time past noon, is l of the time past midnight ;
whiit was the hour ?
"■' . A person, being aaked the hour of the day, said,
T .1 past noon, is ^ of the time from now to mid-
ni-: "hat was the hour?
SoLurroN — From now to midnight is f, and i added (the time
past noon) is f. Consequently from noon to midnight (which is
12 hours) is f of the time it lacked of being midnight; and ^ of
the time, is i of 12, which is 3 hours, the time past noon.
22. What is the time of day, provided f of the time
from now to midnight equals the time past noon ? ^
23. A man, being asked the hour of the day, said,
f of the time past noon, equals | of the time from now
to midnight ; what was the time ?
24. A pole, the length of which was 68 feet was in
the air anu water ; ^ oi tuu it;ugtu m mc au, equaicu
128
ALGEBRAIC QUESTIONS.
^ of the length in the water. What was the length
in the air, and in the water respectively ?
25. The sum of two numhers is 176, and f of the
first + 4i equals J of the second ; required the num-
bers ?
20. A person, being asked the time of day, said f
of the time past midnight equals -j'^o of the time from
now to midnight again ; what o'clock is it ?
27. Provided the time past 10 o'clock, A.M., equals
f of the time to midnight ; what c 'clock is it?
28. Says A to B, | of my age + 4 years equals f
of yours, and the sum of our ages is 74 years. What
is each of their ages ?
29. A person, being asked the hour of the day, re-
plied, f of the time past noon, equals | of the time
from now to midnight +| hours ; what was the time ?
30. A pole, the length of which is 78 feet, is in the
air and water ; f of the length in the air + 12 feet,
equals 1|^ times the length in the water. What is the
length in the air and water respectively ?
Lesson IX.
«
1. There is a fish the head of which is 4 inches
long, and whose tail is as long as its head + -^^ of its
body, and whose body is an long as its head and tail j
whai is the length of the fish ?
Solution. — By a condition of the question, ^ of the length
of body + 4 inches, is the length of tail; to which add 4
inches, (the length of the head ), and we have i of the length of
the body + 8 inches = f, or the lengtli of the body. There-
fore, f— J, or i of the length of the body, equals 8 inches ; and
f , or twice the length of the body, which is the length of the
fish, equals 4 times 8 inches, or 82 inches.
2. Th
long as its head 4- i of its body, and the body is as
ALGEBRAIC QUESTIONS.
129
long as the head and tail together ; what ia the length
of the fish ?
3. The head of a fish ia 12 inchea long, the tail ia
na long aa the head + i of the body, and the body ia
as long aa the head and tail ; what ia the length of
the fish ?
4. The head of a fish weighs 10 pounds, the tail
weighs aa much aa the head -f I as much aa the
body ; and the body weigha as much aa the head and
tail ; what ia the weight of the tail ?
5. -5- of a certain number equals f- of the same num-
ber + 10 ; what ia that number?
6. A boy, being asked his age, replied, f of my
age exceeded ^ of my age by 4 years ; how old was
he?
7. Jamea, being asked how many arithmetical ques-
tions he had answered correctly during the week, re-
plied, I of the number is 3 more than f of the num-
ber ; how many questions had he answered ?
8. A farmer after selling | of 1-^ times as much
grain as he had, had 80 bushels remaining ; how much
had he at first ?
9. An individual, after spending |- of all his money,
and I of what then remained, had only $12| remain-
ing ; how much had he at first ?
10. If f of a ship be worth | of her cargo, which
is valued at 300 eagles ; what is the value of the
ship?
11. Dick being asked how much money he had,
said, its -J exceeded its i by $2 ; how much had he ?
12. A tree by falling, was broken into three pieces;
the top part was 10 feet long, the bottom part was as
long as the top + f of the middle, and the middle
part was as long as the other two ; what was the
length of the tree, and of each piece ?
13. A man boii'^ht a hat, a coatj and a vvateh : the
bat cost $6, the watch cost as much as the hat + f of
130
ALGEBRAIC (iUESTIONS.
tho cost of the coat, and the coat coat as much as the
nM "■'' """^ ^- "'■ " '^"'-^ °'' 1« i^ -^ of what
17. If from a certain number you take its i and its
^-. the remamder w,ll be ]3|. wh'at is that nuXr '
18. After spending -| of ,ny money, I earned »„<■
muen as I spent, and then had onf; «20 Jess Aan
what I had at first ; how much had I'at first/
tt let^tt^^ the^fifh? - "'« '-" -^ *ail? What'
20. The head of a fish is 12 inches lone- its tail i,
10 inches longer than its head increS'bv 1 the
ength of the body ; and its body is 20 inches longer
of theth?' '"^' ''^" '°="''"'-- ''^^' - t^e l-fth
Lesson X.
1. James is 20 years old, and John is 4 years old
dd a?jr Vr^l 1" .J--%-^- - -w I tt^aes as
oia as John, be only twice as old ?
2. Sarah is 10 years old, and Sallv is 4 • in >,««.
many years will Sally be J 'as old asljnhV " ''"^
d. Jacob IS 40 years old, and Alfred is 2 • in how
many years will Alfred be i as old as Jacob? ^""^
6 K ;^ ^^*i'? *'l":d °f e- «hat win the i of 20 be ?
o- li i or lii oe lu, what will f of 10 be ?
ALGEBRAIC QUESTIONS.
131
7. Divide the number 85 into two parts, that shall
be to each other as -^ to |.
^ 8. When A was married, he was 3 times aa old as
his wife, but when they had been married 15 years,
he was only twice as old as she; how old was each
when they were married ?
Remaek.— The conditioue of tho above question elvo tlie fol-
lowing: .
9. Three times a certain number + 15 equals twice
the same number + 30 ; what is that number, and
what is 3 times the same number?
10. Once a certain number + 15 equals f of the
same number + 30 ; what is that number, and what
is 3- of the same number ?
11. "When I first met Mr. A, I was ^ as old as he
was, and in 12 years after that, I was | as old as he
was ; what was each of our ages when we first met ?
12. There are two numbers, one of which is 4 times
the other ; but if to each 20 were added, one will be
double the other ; what are these numbers ?
13. When B was married he was 3 times as old as
his wife ; but after they had been married 60 years,
J of his age equalled hers ; what was the age of each
when they were married ^
14. A hound takes 3 leaps to a fox 4, and 3 of the
hound's leaps are equal to 6 of the fox's ; how manv
leaps must the hound take to gain 1 on the fox ? '
15. If tho hound takes li leaps to gain 1, on the
fox ; how many must he take to gain 20 on the fox ?
16. A hare is 20 leaps before a hound, and takes 4
leaps to the hound 3 ; and 3 of the hound's leaps are
equal to 6 of the hare's. How many leaps must the
hound take to catch the hare ?
17. A fox is 60 leaps before a hound, and takes 5
leaps to ^he^:.ound 2; and 4 of the hound's leaps
equala 12 of the fox's. How many leaps must the
hound take to catch the fox ?
132
ALGEBRAIC QUESTIONS.
18. Alfred is GO steps before Silas, and takes 9
steps to Silas 6; and 3 of Silas's steps equals 7 of
t\ u '!• ?u "^ "^^^^ '*^P'' ^* *^is ra^e> will each
take betore they will be together ?
12/ iTma^'b^.^ *"'' '''^^^'''' ''''''^'''''' ^^ square feet, or as near-
19. How many panes of glass in a box, provided
they are 6, by 8 inches ?
Remaek.— Flud the area of a pane of glass by reducino- fhp
inches to parts of a foot, and then multiply these PtsSer
The urea of a pane 6 by 8 inches is i of a equare foot. 5w
mamder may be solved as follows : i"ere-
SoLUTioN.-If to make | of a square foot it require 1 pane
to make f or 1 square foot, it will require 3 times Cs
panes ; and to make 50 square feet, (1 box,) it will require 50
times 3 panes, which are 150 panes. ^ ^
20. How many panes of glass in a box, provided
they are 8, by 10 inches ? proviaea
21. How many panes of glass in a box, provided
they are 10, by 12 inches ? ^
22. How many panes of glass in a box, provided
they are 8, by 12 inches ? F'oviaea
i\.?' ^?o u ^ vl P^^'f ' °^ S^^'^^ ^" a bo^' provided
they are 12, by 15 inches ?
Lesson XI.
1. What number is that, to which if its h be added,
the sum will be 15 ? '
2. What number is that, to which if its i be added,
the sum will be 24 / *
3. What number is that, to which if its i be added,
the sum will be 40 ? «ucu,
4. What number is that, to which if its i be added,
the sum will be 30 ? «uucu,
o. „ j^ j^uj^j^^ ^Q ^^^^^^ ^|. added,
the sum will be 88 ? ^ auucu,
ALGEBRAIC QUESTIONS.
133
6. How old is that man, to whose age if you add
its i and its f , the sum will be 104 years ^
7. What number is that, which being increased hv
itsi, its 'h and 18 more, will be doubled ?
8. A. man, being asked his age, said, my a^^e in-
creased by Its I and 20 more, is double mj age.
W hat was his age ? "^ °
9. Suppose I buy a certain number of boxes of but-
ter, at $2 a box, and as many more at U a box ; and
much ?"" ^ ' '^'' ^ ^''''' °' ^°'"' ^^^ ^°^
^,9- f .l'^.^' ^eing asked how many oranges he had.
replied, if my number were increased by its ^ its ^
and 42 more, the sum would equal 3 times my num*-
ber. How many had he ? j ^
J 1. Suppose 1 buy a certain number of melons •
sonie at 10 cents each, and as many more at 40 cents
each ; and sell them all, at 30 cents apiece ; how
much do I gain on each melon ?
12. If by selling 1 apple I lose ^ of a cent, how
many apples, at this rate, must I sell to lose 6 cents ^
1^. A boy bought a certain number of lemons, at
^f^*^/ piece, and as many more, at 4 cents apiece;
and sold them, at the rate of 3 for 5 cents- did he
gain or lose, and how much ?
14. A woman bought a certain number of apples
at the rate ot 2 for a cent, as many more at the rate
ot 3 tor a cent ; and sold them all at the rate of 5 for
Tf"' and b^^^o doing lost 4 cents. How many of
each kind did she buy ? ^
15. A woman bought a certain number of effffs, at
the rate of 3 for a cent, and as many more, at 4 for a
cent ; and sold them out, at the rate of 8 for 3 cents
she bu ^? ^^'""^^ ^ '^^''*'* -^"""^ ""^""^ ®^S^ ^'^
.. « , "~ •• "&^^^'^ «■'-' f^^aro ^uxu lu tne propor-
tion ot 2, f , and i ; how much must each receive ?
134
AEGEBRAIC QUESTIONS.
18. The difference of 2 numbers is 15, which is
more, at the rate of 5 for $1 and !nl/?h "' T°^
geraee of 10 yards Zfs] ^nd ttoeW Lf$f
How many yards did he buy ? ^ * '
theratfof rfor°sf t V*"° """''^^ of melons, at
in / ., n"^ *^' *°'^ ^ Many more at the rate of
10 for $1; and sold them all at the rate of 8 for $2
and thereby gamed $6. How many melons dM t'
Lesson XII.
4 t^XlariTbTw^a^^t^fhT''' «-^
tJc'eSlTtheVf '° ' ^"""^ P*''^ ^^''^ "- ^hall be
3. Divide 21 oranges between two bova so iUf nr.o
may have twice as many as the othLr ^ '* "''"
4. ±raukhn and Francis together have 15 nn«rfo
to|tht'|:y;rar|;Lr^^^^^^^^^^^^^^ -
7. Harriet 13 twice as old as Ellen, and the sum of
TT7JbJ''^^'- T'"''^ ""eageofeachT"^
o. A ana ±J are 36 rods aT^n^^f «v,Jj ^ i x ,
i.^- •-* «iiu i/iuvei cowards
ALGEBRAIC QUESTIONS.
135
apples
h and
1
all he
1
it one
^^B
uarts
V
ncis.
1
aud
1
shall
1
mof
1
ards
1
each other ; how far will each travel before they meet
provided A travel twice as fast as B ? "«/^eet
9. What number must be added to twice if^plf
that the sum will be 57? ®^^'
10. A, after spending i of all his money and -I of
tVhTaTh:UTrsn' '^' ^^^^ ''' ^^-^--^^ ^ ^-
one Vha^t1'o\%ro'tL'^ ^^*° *^° ^"^^ P^^*«' *^^*
12. In a certain school, there are 8 times as many
boys as girls and in all there are 52 pupils ; how
many boys and how many girls in the school ?
13 James and Jackson together have 45 marbles,
has eachT °^ ^ ""' "^^""^ ^' ^^''^'°'' ' ^"""^ °*^^^
14. A man and his son together earned $280 in a
year ; how much does each earn, provided the boy
earns only i as much as his father ? ^
15. A boy bought a melon and a citron for $1;
how much did each cost, provided the melon cost only
i as much as the citron ? ^
+1, ^^' j^,"^^" bought a horse and a saddle for |;120:
the saddle cost only x as much as the horse ; what
was the cost of each ?
17. A man, being asked the cost of his oxen, said
my oxen and waggon together cost $240, and the oxen
of each r ^' "''' ""' *^^ '^^^^'''' ' ^^^^ ^^^ *^® ^^«*
18 A man bought a sheep,a hog, and a cow for $42,
tor the hog he gave twice as much as for the sheep,
and for the cow, 3 times as mucb as for the sheep.
How much did he give for each ?
19. A farmer and his two sons earned $560 in 1
year ; the father earned twice as much as his elder son,
and the elder son earned twice as much as the younffer
son. How mufth diH t^nnh oo«« o ^ &
v^i« v,t.ll.ii
20. A, B, aud C together, in 1 day, can dig 105
136
ALGEBRAIC QUESTIONS.
day" "' ^- ^°^ '"^"y bu^l'els can each dig in a
fj,f fl" "^ """ ''°"Sht three pieces of cloth for «lf!0.
the first p:ece oulv cost ^ •!« mn^l, „» I '? '^ '
the second, only /as much ^thAv f^ 'lr'°'"^' "'^'^
did each piece cost" ^"'''- "°*' "«'='>•
asii^trwrdTdtTri^rd'rd'rt'"^'
iyely -^ ' ^"""'^ed, and unhurt respect-
= ^e'-D' °^ ^'^' ■*: * °'' S's money equals S5500 • nr„l
i of B'a money is 4 times i of A '= w ' ,
money has each ? ' '^^ ^- ^o'' "^'-ich
and B.^f"'*" ""^^ ^y™° *°ge*«'' have 60 blocks •
hafete °™«*'«»-yas Herman; how mty'
bet e^ro&"t"r -*° 2 parts, that shall
theUorlionTf'*^"^!^;:*" ^'"" ". "PP'^ ^
receive ? " * »» 3 5 bow many o^g^t ^^^[^ .^^
yefr^'. w'Z °^ ^r^ and Hezebiah's age is 25
Is old as Mary r ' ^'■°"'''' ''^^^''''"' '^ ""'^ *
oatfi'nf^''^ ?** his father can thrash 35 bushels of
th Lhes oSv ^T ""7 '^V ''"^ thrash, i? Henry
OQ A 7 "■ "^ """"h as his father ? •'^
•^». A pole, whose length is 70 fpof ;= ;„ n
and water; how much ;<. i n tu • j ' '° *''^ air
ivelv if' ^ptu 1 il ^".^^airandwaterreapeet-
tKteH " ''"^* '" "^^ «'^ ^^-^^'^ "'« 'e"gthTn
beTo-eStV^ra"sTt'oT '°'° ''^'^ "^^'^- "^^ ^'-"
be to eSh otfcu^' '' '"^° ' '''''' ">^' ^''^U
ALGEBRAIC QUESTMNS.
137
*S4if!?™"wriS'.ij7"»''
QQ A 1.' , "iuiJii oejonors to each ^
twf • i^ ""'^ ^^'?S'^^ ^^^** ^^200'to be divided be
tween his son and daughter, in the propo t on of 1
Jl How much ought each to receive }
twt J^s^^^^^cr;^^^^ ^^r%
each kind was there ? ^ ^"^ ' ^°^ ^'^^^ ^^
35. A man bought a cow and a hor-^P fn». ^qr 4.i
each? quarts, ho^ nianj belongs to
BbairbfSci':trarx^^"'° ^'^^ p^^*^- *»-'
equalled the distance he wa^lealThen^W Sei'
How far did the fox run, and how far In advene! of
the hound was be when the chase commenced?
is to he I'T t'^o numbers is 140, and the larger
beJs? ' as 1 to f, what are the two num'
40. A and B together owe $69, but B owes onlv
^41 Thtr ^ ''. Tr r'='^ '"'^ -•'h owe/' °°'^
41. Ihomas and Thornton found $240 but ronM
not agree about the division of it thp^' tl f
threw it on the floor and each got ;hat h'e could fi
TWrrV'"' ^'r.^^ sol only Vas much a
inornton. How much did each get?
th^Z: ^% J?"''"'" """"""l consisting of 48 puoils
boys and htw "'' "' "r? ^°y' "^ gS-ls : how^many
ooys, and how many girls m the school ? ^
«160-, if i::''.^„.:f !Lr*iy- "ought for
gold one ; how much was tUc-o^oFe^crr" " ''''
138
ALGEBRAIC QUESTIONS.
44. Divide the number 17 into two parts, that shall
be to each other as f to f . ■ ^ ' **" ''"^^
45. A farmer had 180 sheep in two fields, and i of
the number in the first field equalled i of ihe num-
ber in the second ; how many in each field ^
othtr afi'^t^^^^ '''^'' *''''' ^""'^^ ^^""^ '^^^^ ^" *° ^^^^
47. I of the distance a hare ran after a ■ 1 start
edm pursuit equalled the distance she ... ,8 before
the hound when they started ; how far did the hare
snin/ r ^''^.^^^''"ght, provided the hound ran
SO rods to overtake her ?
in tt ^ *"i^ started from the same point, and ran
in the same direction ; B ran 60 rods ; tnen X of the
T'T^^ ^i^ ™" e<J>'«"ed the distance A was
60 rods ? "'"''' ^''^ ^ S"'" °'' ^ '° ^"•^"'"g
. 49. A fishing-rod the length of which is 24 feet, is
in two parts ; f of the longer part equals the lenetli
°f*^e shorter. How long is each part ? ^
50. A hound ran 90 rods before he caught a deer-
the deer ran 44 times as far as it was ahfad of the
Howl r f 7.1^^1^^' ^'^°'' it ^"^ overtaken!
Sretmtencel?"^ ''"^' ^^^ *'^« ^-- ^^^^ *•>«
emtVJm^? """'"''■ °/''''"P + f of B's number,
equals 900 ; how many sheep has each, provided | of
B s number is twice f of A's number ?
Lesson XIII.
1. A person had two silver cups, and onlv one
cover for both. The first cup weighed 6 oz If the
theVeco^n^/ ^r/fi " ^'"' 7«gh twice as much as
tue second, but if tliA 5Jpf»r»r.ri «,,^ u^ i •.
, - - — — ^ t^t^vvixva vup uQ uuvered It will
ALGEBRAIC QUESTIONS.
13a
Zl'^}, ^/J,™'' ""^ T""^' «' *^® fi^«t- What is the
weight of the second cup and cover ?
Solution— By the last condition of tlie Question S t.'m^a «
oz the weight of the first cup, or 18 ounces^ equal \heweS.?
cove;weir.h isT?"' ''''''' , PT'^^^^-^'y '^« two cupsT d
covei weigh 18+6 ounces, which are 24 ounces And hv fho
first condition, the first cup and cover weigh twi'ce as mu^h n!
the second cup. Therefore' the 21 ouncerS.u X diXt to
two par s which are to each other as 2 to 1. One of th" e
parts will be the weight of the second cup, and 2 the weLht of
the first cup and cover, &q. ^ weignt ot
fJl t}^'^l}''l^'''^ ^^^^^'' ^"P"' ^'^^ only one cover
Jorboth. Tde Srst cup weighs 8 ounces. The first
cup and cover weigh 3 times as much as the second
cup ; and the second cup and cover 4 times as much
as the first cup What is the weight of the second
cup and cover ? «^^tfiiu
3. A man bought a hat, a coat, and a vest for $40.
The hat cost $6 ; the hat and coat cost 9 times as
much as the vest. What was the cost of each P
4. A boy bought a squirrel, a rabbit, and a bird,
ihe squirrel cost 15 cents. The squirrel and rabbit
cost twice as much as the bird ; and the rabbit and
Dircl cost 3 times as much as the squirrel. What
was the cost of the bird and rabbit respectively ?
5. A farmer bought a cow, an ox, and a horse r
the cow cost $20. The cow and ox together cost 3
times as much as the horse ; the ox and horse
together cost 4 times as much as the cow. What
was the cost of the ox and horse respectively ?
6. A man bought two horses and a saddle. The
younger horse cost $40. The saddle cost -} as much
as both horses ; ana ihe younger horse cost i as much
as the other horse and saddle together. What did
tbe saddle and older horse cost respectivelv ?
7. A man traveled three successive days. The
tirst day he traveled 30 miles, which was 4- of fh^ ,!,•«,
tance he traveled the other two days ; and 4 times
140
ALGEBRAIC QUESTIONS.
t^ie distance he trnv^laA *i,
di.ta„co he travS e tltZ7\J"{ T'''^^ the
fer did he travel each day ? "'' *"''^ <Jaj8. How
8- A la worth $1000 iin<l B j ^
"-orth 9 times as much a" A » . n ^°^'*^'' »re
.^3^^?^4T^ ^- «- -hlfB^^^dTtjrtt
°f tw vest equalled the cos? oV h ..^ '"""' "'^ «°«t
What was the cost of hfs v«f ° ]^^"l ""''" ^^^ hat-
10. B's harness cost SI2n 1?^''^' respectively?
of his horse audseth* and th.h '''''* °^ '''« <'°«*
together cost twice as ^^1? *''\hameas and horse
•""cl, did the horse and sS ^n f*""* '^''^^- Ho^
11- A tree in falling k^i ?'™«P««t'''ely?
pieces. The top piece L^«/ Z"?*" *'^'^« "^^^^al
of the length of the othe?tw« • ^°°^' '''''''h '^as •
length of the bottom dL*" ^'Tll ""'' ^ times thi
other two pieces. How lo^X %*.'" J'"Sth of the
long was each pieee^ ^ "^"^ *® tree, and how
A ?«^20^fels'oldTndtlf ;fj."'^ ^- "^^ ^"owing that
iB 4 timers A's age Id tW «.'"■" °^ ^ """d C's age
of A and B's agl ' ^ **"** ^^ ''ge is i of the sum
13. Find the fortunes of j\ Ti n rw t,
know.ns that A is worth «9n' L^^' ^' "^d P, by
B andC are wort" aTd thaf r ^^'"^ f * «^ »"eh al
A and B , and, also That if 10 /' '^°' "^ * "^ •»"«*' as
f d C's fortun'e were d t ded int: *' ^"™-°^^' ^^
h and i it would i-oo^o I- , . t"® proport on of -a
and^i ^f P>s fortun7 '*"''^^ ^^' * "^ »•«, ^ of E's
gcd;ed w'shilt|s'rro°d'':n1 B*f f^^'r «"^- ^
-ttow many rods diW ooli;^- "'^ ^ shiJlmffs a rod
«S0? Ins'f duf oP-?^'d«d each^ei^d
NoTp P J , g ^'^^ rods, and B 62i
^o..-Co„s.der ,ie above a Pe„, „, ^. ;„„,,,„„ ''^-
REDUCTION.
141
CHAPTER VIII.
Lesson I.
this, matbematSlyVeakinl win „„,'" "l" ''""■• Although,
a /ear^'^"*" ^ ^"^' """^ ^ ""''">'« *" ^^e fraction of
monlUave4S;l wWchL ;„Vl t"^" n"' "»'' *
how many thirds! lu one t ere I'r! a* n^f'- i".^*y«-"-s
remainder. (>^n equentlv Te '^^^^^^ <jf«o«.»a<or, without,
oontinne to divide gSthe^ea J m.^h^^'^'/'""' """^ ^"' *>«. to
numerator and denominator withon ' „ "' " '?"t''''"'' ■■" '"'"»
fraction i, reduced to il^s lowe.rterms. "" ' """' '""
yef;. ^'^""' ^ ^""" "'"' ^ ""°"*''= *» the fraction of a
a year^"''"''' ^ ^""■' """^ ^ '"°'^'''« *° *''« f™«on of
a ytar^"^""' *^*''" ""'' ^" ™°"*^ *" t^e fraction of
a /ear^"^""^ '' ^""'' """^ " "°"*'=« *" 'l-e fraction of
a ylr^"''"'" ^ ^'''"■' ^""^ ^ '"°"*''« '" the fraction of
of a yS"-^ ^^ ^'"' ""■* ^ """"'hs to the fraction
8- Eeduce 11 years and 11 mnnffcp *„ *i.. f„_.- _
of a year. ' » -"^ •"= iiatiion
142
REDUCTION.
a yt^'""' ' y^-- -d 6 months eo the fraction of
oUyef:''"'' "^ y''"' ""-^ 8 months to the fraction
fracL"":' r;eaV"" ' "'""''^ -d ^5 days to the
1 v!»r n •■;' '■''■•" ?•■"•' of a year *T , """"■• ** ""o-'l'^,
I ^f ^r- ""fpforo 1 month is 1 If, ''"^ "^ ' 2 months in
* of t\, wh cb is J, „f „ '' 7^ "' " y"'"'. and J of a month S
ye«.', 9 halves are^^l t"ml^ 4,f "t ''*»'" ■"""»>' " X „V a
yoars, eqnal V» years ' ^^' '''"'•'' "^ A or S of a ye". 2*
fri^'S^a/"" ' ■"-*''^ -d 6 days to the
fraction'':f'r:e'ar^^ ' ■"-">« -d 18 days to the
fr.ltio^otV.r'' ' --*''« -d 18 da,s to the
fracL^1r;ea/-" ' "'-^'^^ -d 6 da,s to the
ha,^"--0--"i". t.. intermediate steps in the analysis we
years equal M
fraction olry'ef/'""'' ' ''''»'*''^ ""^d C days to the
fraction of a'yearf ^"' * ""'"*''■ '^d 24 days to the
fra|;S"a year--^ ' "'-*''^ -d 18 days to the
fraction of ryear*""" ^^ "'"""^^ «°d 6 days to the
^^^tftioZu%iT' '<> ""'"*''« ''°d"l2 days to
PERCENTAGE AND INTEREST. 143
Lesson II.
which is regulated by law ''''' P®'' *'«"^- P^r anuum,
* or ,y of the p,.l„oi,,al eqS ,he ""iere™"- " " •'"""'-
When „o time is specified lyeaMsu.d.«t„„d.
the intretr' "'"'- '''"'* P"' "' t^« Pri"cipal equals
per cent, ^ of the prinSpt^^^s :L\Z'; J''"'""- "• *
the "inferestT ''''"•' ^'^''* ?"* "^ *''« P^eipal equals
the infere' ?r ''"*" """^ P*"* °^ *»>« P^^P"' equals
fue ■interlPr"''"" ^"""'P"' "^ ^l^^ P^^^Pal equals
the iutestT ''*'*•' ^'"'* P*'* "f "■« Pri'-^^-p"! equals
gain/' ^^^ P'' '''°*- ^''''* P«' °f *e "ost equals the
the\wT ''"*•' ''''''* P'"'^* of the principal equals
gait ?^^ ^^ P"" ""''*•' '=«* P-'rt of *e cost equals the
gain ?^' ^^ P'' '^°*-' '''"'* P"'* of the cost equals the
per cenM"' " '^' ^'^^'* of «80 for 1 year, at 15-
the IXI^Z ot^0Um'!t],Zit:,l *' P"""'?"' »<!"«''
per LI?"' ^ '^' ''''''''' °f *i2af<,r 1 year, at 25
144
PER CENT.
12. What is tho iuterest of §510 for 1 year, at 20
per cent. ?
13. What is the interest of $750 for 1 year, at 24
per cent. ?
14. A man paid $120 for a waggon and sold it, at a
gain of 30 per cent.; ho v much was his gain ?
Solution.— If he gained 8i per cent, he gained ^^^, or -^ of
the cost. -^ of $120 is |36, the gain.
15. A tailor sold a coat that cost him $25 at a gain
of 32 per cent. ; how much did he gain ?
16. A man sold a quantity of goods that cost him
$840, at a gain of 75 per cent. ; how much did he
gain ?
17. Edward spent 85 per cent, of $120 for a suit
of clothes. How much did his clothes cost him.
18. Henry's watch cost $180, he sold it at a loss of
15 per cent. ; how much did he receive for it ?
19. A boy sold a quantity of candies that cost him
60 cents, at a gain of 120 per cent. ; how much did
he receive for them ?
20. Jacob sold a horse that cost him $240, at a loss
of 25 per cent. ; how much did he receive for the horse"?
Lesson III.
Remark. — The principal or cost is always 100 per cent.
1. If ^\ of the principal equals the interest, what
is the rate per cent.
Solution 1st. — If -^xs of the principal equals the interest, the
rate per cent, is -^ of 100 per cent, which is 6 per ceut.
Solution 2d. — If the interest of 1 cent is 3% of a cent, the in-
terest of 100 cents is 100 times 3^^, or ^%o, or 6 cents. There-
fore, it is 6 per cent.
2. If gV of *^® principal equals the interest, what
is the rate per cent. %
3. If A- of the principal equals the interest, what
is the ra^ per cent. ?
PER CENT.
145
4. It' -80- oF tho cost equals the gain, what is the
rate per cent ?
5. If a^y of tho coat equals the gain, what is the
rate per cent?
(>. If aV of the principal equals the interest, what
Is the rate per cent ?
7. If ^- of the cost equals the gain, what is the
rate per cent ?
8. If the interest of 844 for 1 year is $4, what is
tho rate per cent. ?
SoLtjTiox.— If the interest of i?44 is $4, ,\, or ^\ of the
principal equals the interest. Therefore, the rate per cent.
13 ^^ of 100 per cent, which is 9^j per cent.
9. If the interest of $72 for 1 year is $6, what is
the rate per cent. ?
10. If the interest of 396 for 1 year is $12, what is
the rate per cent. ?
11. B bought a horse for $100 and sold it for $109,
how much did he gain per cent. ?
12. A woman bought a quantity of oranges for 75
cents and sold them for '^vl cents ; how much did she
gain per cent. ?
13. A merchant bought a quantity of books for
$200, and sold them for $228 ; how much did he gain
per cent. ?
14. If by laying out $37, I gain a sum equal to |
of it, what do I gain per cent. ?
15. Harvey bought a hogshead of molasses for $25
and sold it for $3H > how much did he gain per cent. ?
16. Bought a knife for 37 cents and sold it for 57J
cents J what was the gain per cent. ?
17. A stationer sold a quantity of paper for |- of
what it cost him ; how much did he gain per cent. ?
18. James received for his horse ^ of what it cost
him ; how much did he gain per cent. ?
I
I
t
145 FIR CENT.
19. A man sold a barrel of pork for f J^ of what it
cost him ; how much did he gain per cent. ?
20. The interest of $500 for 4 years is $240 ; what-
is the rate per cent. ?
SonffioN.— If the interest of $500 for 4 years is $240, for 1
year it is i of $240, or $60. Therefore, 3^, or ^ of the pnn-
?ipal equals the interest. L the interest of $1 for 1 year is
IX the interest of $100 is 100 times $^S. or %%o^ or $12.
TErefore, it is 12 per cent.
21. A man, being asked, at what per cent, his money
was on interest, replied, I receive $120 interest m 10
years for $24K) ; what was his rate per cent . ?
22. A bought a horse for $150 and sold it for $100 ;
what was his gain per cent. ?
23. Elisha bought 10 horses for $800, and sold 8
of them for what they all cost ; what v\ras his gain per
24. VV of t^e money C paid for books, is ^ of what
he gained by selling them. How much did he gain
per cent. 1 . . , > a i.-
25. -i-K of the money I have on interest, is 4 times
the yearly interest received. What is the rate per
26 ' i| of the cost of A's merchandise, is ^ of what
he gained when he sold it. What was his gain per
27.*!;^ of the cost of B's wagon, is f of what he
gained by selling it. What did he gain per cent. ?
28. A book was sold for | of f of what it cost.
What was the loss per cent. ?
29. i of i of the cost of a sleigh, was what it was
80ld for. What was the gain per cent. ?
30. A merchant bought a quantity of goods for
I860 and sold them for $1075 ; how much did he gam
Por PAirfc. f
PERCENTAGE.
147
Lesson IV-
1. At 5 per cent, for 4 years, what part of the prin-
cipal equals the interest ?
Solution— If the interest of $1 for 1 year is 5 cents, for 4
years it is 4 times 5 cents, or 20 cents. Therefore, t%%, or i of
the principal equals the interest.
2. At 6 per cent, for 5 years, what part of the prin-
cipal equals the interest ?
3. At 3 per cent, for 2 years, what part of the prin-
cipal the interest ?
4. At 4 per cent, for 3 years, what part of the prin-
cipal equals the interest ?
5. At 6 per cent, for 3 years, what part of the prin-
cipal equals the interest ?
6. At 4 per cent, for 3 years, what part of the prin-
cipal equals the interest ?
7. At 9 per cent, for 6 years, what part of the prin-
cipal equals the interest ?
8. At 8 per cent, for 5 years, what part of the prin-
cipal equals the interest 'I
9. At 4 per cent, for 6 years, what part of the prin-
cipal equals the interest?
10. At 6 per cent, for 5 years, what part of the
principal equals the interest ?
11. At 10 per cent, for 5 years, what part of the
principal equals the interest ?
12. At 6 per cent, for 4 years and 8 months, what
part of the principal equals the interest ?
Remark.— It is expected that pupils thoroughly understand
every lesson they have been over ; and are, therefore, prepared
to arrive at results, understandingly, without giving the entire
analysis of all paits of the question.
SoLUTioN.~8 months is ^\, or § of a year. 4? years equal
y years. If the interest of $1 for 1 year js 6 cents, for^^r*
years it Is V* i-"^'-''* ^ cents, or 28 cents. Therefore, j^iOr
^'. of the principal equals the interest.
148
INTEREST.
11 I I
13. At 4i per cent, for 6 years and 6 months^ what
part of the principal equals the interest ?
14. At 6 per cent, for 5 years and 4 months, what
part of the principal equals the interest ?
15. At 10| per cent, for 1 year and 6 months, what
part of the principal equals the interest ?
16. At 4!j- per cent, for 9 years, what part of the
principal equals the interest?
17. At 3 J percent, for 2 years and 2 months, what
part of the principal equals the interest ?
18. At 61- per cent, for 4 months and 24 days, what
part of the principal equals the interest ?
19. At 7 l per cent, for 10 months, what part of
the principal equals the interest ?
20. At 3^% per cent, for 2 years, 4 months and 15
days, what part of the principal equals the interest ?
Lesson V.
1. "What is the interest of $50 for 4 years, at 6 p.c.
Solution lsT.~Tbe interest of $1 for 4 years, at 6 per cent.
is 24 cents ; and for $50 it is 50 times 24 cents, or $12.
Solution 2nd.— The interest of $1 for 4 years, at G per cent.
ia 24 cents. Therefore, -rVu. or u% of the principal equals the
interest, ^"g of |50 is $12, the interest.
2. What is the interest of $10 for 2 years, at 5 p.c. ?
3. What is the interest of $48 for 6 years, at 5 p.c. t
4. What is the interest of $70 for 7 years, at 5 p.c. ?
5. What is the interest of $68 for 5 years, at 6 p.c. ?
6. What is the interest of S70 for 2 years, at 5 p.c. ?
7. What is the interest of $75 for 5 years, at 3 p.c. ?
INTEREST.
149
8. What is the interest of $120 for S years, at 5
per cent. ?
9. What is the interest of $100 for 10 years, at 6
per cent. ?
10. What is the interest of $140 for 12 years, at 5
per cent. ?
11 What is the interest of $150 for 5 years, at 3
per cent. ?
12. What is the interest of $145 for 6 years, at 5
per cent. ?
13. What is the interest of $200 for 10 years, at S
per cent. ?
14. What is the interest of $250 for 3 years, at 8
per cent. ?
15. What is the interest of $220 for 11 years, at
10 per cent. ?
16. What is the interest of $500 for 9 years, at 8
per cent. ?
17. What is the interest of $250 for 12 years, at 6
per cent. 1
18. What is the interest of $500 for 8 years, at 12
per cent. ?
19. What is the interest of $200 for 9 years, at 3
per cent. ?
20. What is the interest of $405 for 10 years, at 8
per cent. ?
21. What is the interest of $50 for 2 years and 2
months, at 6 per cent. ?
Solution.— 2 menths is ^ of a year. 2^ years equals ^
years, If the interest of $1 for 1 year is 6 cents, for V ye*"
it is l^ times 6 cents, or 13 cents. Therefore, ^ of the prin-
cipal equals the interest Von «f $60 is iJ, or |6.50, the in-
terest,
22. What is the interest of $25 for 4 years and 3
months, at 4 per cent. ?
23. What is the interest of $80 for 5 years and 5
months, at 6 per cent. ;
Ijl
ti'.
150
INTEREST.
24. "What is the interest of $60 for 8 years and 6
months, at 6 per cent. ?
25. What is the interest of $240 for 3 years and
9 months, at 6 per cent. ?
26. What is the interest of $75 for 4 years and 8
months, at 9 per cent. ?
27. What is the interest of $50 for 2 years and 9
months, at 6 per cent. ?
28. What is the interest of $80 for 12 years and
10 months, at 6 per cent. ?
29. What is the interest of $69 for 8 years and 4
months, at 2 per cent. 1
30. What is the interest of $60 for 4 years and 8
months, at 3 per cent. ?
31. What is the interest of $600 for 2 years 4
months and 15 days, at 4 per cent. 1
Solution.— 15 days is i of a month. 4^ months equab f
months. | months equals ^^, or § of a year. 2^ years equal
V years. If the interest of |1 for 1 year is 4 cents, for V
year it is V ti^^a 4 cents, or ^ cents. Therefore, ^^^ of the
principal equals the interest. ^^% of $600 is $57, the interest^
32. What is the interest of $300 for 5 years 9
months and 18 days, at 5 per cent. ?
33. What is the interest of $550 for 4 years 7
months and 6 days, at 10 per cent. ?
34. What is the interest of $500 for 1 year 7
months and 18 days, at per cent. ?
35. What is the interest of $250 for 3 years 7
months and 6 days, at 4 per cent. ?
36. What is the interest of $250 for 3 years 3
months and 6 days, at 6 per cent. ?
37. What is the interest of $50 for 6 years 4
months and 24 days, at 5 percent. ?
38. What is the interest of $75 for 2 years 11
months and 6 days, at 15 per cent. ?
QQ TxrViof ia fhA infpr*i9f. of iftl.^Ofor 2 vears 10
months and 12 day s, at 15 per cent. ?
n
INTBRKST-
151
40 What is the interest of 8300 for 2 years 9
„,ontbs and 18 days, at 1| per cent. ?
Lesson VI.
1. What is the amount of $75 for 2 years, at 6 per
cent. ? 1 „f «i fnr 1 year is 6 cents, for 2
SoLtT.os.-If the interest of *1 for 1^ ^ ^ f
vears it is 2 times 6 cents, or 12 ««™- ,i»5 jj |9, the int«eet;
C principal ^f ''''/^^J^'an^d^we have $84, the amount,
to which add $76, the principal, anu ^
2. What is the amount of $90 wr d yea .
■^ t What is the amount of $100 for 4 years, at 5 per '
't'Whatisthe amount of $160 for 10 years, at 5
P's" WhL is the amount of $160 for 8 years, at 5
P%: Wklt is the amount of $200 for 12 years, at 5
^'r Wiat is the amount of $210 for 2 years and 6
•" t Whttls'Ae'mUnt of $250 for 4 years and 3
"t Whttl'the 'amVuut of $240 for 4 years and 2
■To' mat Tthf amount of $500 for 3 years 3
nt\tt%11Cnnf-|200for5 years 4
„,onthsand24days,at5percent.?
Lesson VII.
1 What principal wiU in 4 years, at 6 per c»nt..
give $12 »teref ^^ ^^^ ^ ^^^^ ,, , .^nts. for *
152
INTEREST.
years it ifl 4 times 6 eents, or 24 cents. Therefore, ^Ver or VV o^
the principal equals the intereet which is $12. If ^ of the
principal is $12, ^ of the principal is | of $12, or $2 ; and 1+;
or the principal, is 26 times $2, or $50.
2. What principal will in 6 years, at 4 per cent.,
give $36 interest ?
3. What principal will in 4 years, at 5 per cent.,
give $30 interest 1
4. What principal will in 8 years, at 7 per cent.,
give $42 interest ?
5. What principal will in 10 years, at 7 per cent.,
give $140 interest ?
6. What principal will in 4 years and 6 months, at
6 per cent., give $54 interest?
7. What principal will in 4 years and 3 months, at
5 per cent., give $102 interest ?
8. Wb ..; principal will in 4 years, and 3 months,
at 8 per cent., give $51 interest ?
9. How much money has that man on interest, who,
at the expiration of 4 years and 4 months, at 6 per
cent., receives $260 interest?
10. At the expiration of 2 years and 4 months, at
6 per cent., a man received $49 interest. H^w much
money had he on interest ?
11. A is worth twice as much as B, and the in-
terest of their united fortunes for 4 years and 2
months, at 6 per cent., is $600. How much is each
worth ?
12. The interest on the cost of B's store and house,
for 1 year and 6 months, at 4 per cent., would be $270.
What was the cost of each, provided the store cost i
as much as the house ?
13. If the money B paid for a sheep, a cow, and
horse* was put on interest for 4 years and 6 months,
at 4 per cent., it would give $18 interest. What was
the cost of all, and of each respectively, provided the
sheep cost J as much as the cow, and the cow, I m
much as the horse ?
INTEREST.
15S
Lesson VIII-
1 . What pvineipal will itt 4 years, at 5 per cent.,
amount to 8360 1
SoLCTioN—If the intevest of $1 for 1 jear is 6 «"">'*
;t 1. i HmM 5 cents, or 20 cents. Therefore, -ff^, or J ol
rorta pa ™q«al°re interest; to which add J, the principal
the principal mi „_i.„:t,al eaual to the amount, $360. IC
r„'f te prin\ pal s*8™ 4 of thi principal is i.of«»60 which
|-s $«0, anA>e principal), i. 6 times PO, ^hich are $800.
2. What principal will in 3 years, at 6 per cent.,
"TwKrtocipal will in 6 years, at 10 per cent.,
'TwKrinlipal wUl in 4 years, at 5 per cent.,
"Tt is°worth 4 as much as B ; and the interest on
their united fortunes for 2 years, at 5 per cent., is
$880. AVhat is each of their fortunes •
7. A merchant sold a q"''"''*? ?/ "^^Vt-hP IriJ
=md thereby gained 7 per cent. What did the cloth
"°t. What principal will in 2 years, at 7 per cent.,
''TwKrtacipal will in 10 years and 8 months,
at 9 per cent., amount to $490 ? , . , , , , ^_ „,,
lof The amount due on a note, ^l"«li '^''"f =°;"
interest 6 years and 2 months, at 6 per cent., was
$274. "What was the face of the note .
11. What principal will in 12 years and 9 months,
at 4 per cent., amount to $302 ?
12 If * of A's fortune for 4 years and months
at 6 per cint., amounts to §127 ; what is bis whole
fortune? ^ _ , . „„i. ,,„ 4„fo%.ttaf. fnr
13. If ii of B'8 tortune, being pui- on xuu....«
154
INTEREST.
3 years 3 months and 6 days, at 15 per cent., amount
to $149 ; what is his whole fortune ?
14. Mary, being asked how much money she had
on interest, and at what per cent., replied : the prin-
cipal and rate per cent, are such that in 5 years hhe
amount would be $750, and in 7 years, $8iO ; what
was the principal and the rate per cent. ?
15. A man sold two horses for $240, losing on the
first 20 per cent., gaining on the other 20 per cent. ;
what was the value of each horse, provided he received
for the second 3 times as much as for the first ?
IG. The amount of Eobert*s capital for a certain
time, at 4 per cent, is $360, and for the same time,
at 7 per cent, it is $405 ; required his capital and the
time.
I
Lesson IX.
1. In what time will $40, at 6 per cent., give $12
interest ?
Solution.— If the interest of $40 is $12, ^, or ^^ of the
principal equals the i-iterest. If the interest of $1 for 1 year
is 3% of a dolhir, of $100, it is 100 times $j% or |30. If it re-
quire 1 year for $100 to give $6 interest, to give $30 interest it
\vill require as many years as $6 is contained times in $80, or
5 years.
2. In what time will $60, at 5 per cent., give $18
interest ?
3. In what time will $90, at 7 per cent., give $27
interest ?
4. In what time will $100, at 6 per cent., give $10
interest ?
5. In what time will $120, at 10 per cent., give
$120 interest?
6. In what time will $250, at 6 per cent., give $20
interest ?
PER CENT.
155
7. In what time will »40, at 7 per cent., give *8.40
'T'ln Ihat time, at 8 per cent., will $80 give $9.00
'"Klhat time, at 6 per cent., will $10 give $2.40
'''tain what time, at 4 per cent., will $20 give
$5.60 interest ?
Lesson X.
1. At what percent., will $50, in 1 year and fi
months, or (li years), give $6 interest ?
SoLOTios.-If the interest of |60 for U, or f years is $6, for
X of a ve™ it is i of t6, or $2 ; <mi for ?, or 1 year, .t is 2 times
I2! 0? IT Therefore: A. «' A of ""« ^^TIT ot^iwO
nual interest. If tlie interest of *1 for 1 year is 85V ot il'J".
hTs iSo times $^^. or $8. Therefore, it is 8 per cent.
2. At what per cent., will $40 annually give $2
'" t'tft what per cent., will $80 annually give $3.20
'"tlVwhat per cent., will $120 annually give $12
'"I'lVwhat per cent., will $120 in 4 years, give
*^6.' tntat per cent., will $100 in 3 years, give
^'?.^U whal per cent., will $5 iu 14 years, give $7
'"T iVwhat per cent., will $25 in 1 year and 9
T^^VX-l^r^'n *S0 in 5 years and 8
•"TrAtThf Jirt^t! will $500 in 7 years and C
months, give $15 interest ?
15G
PER CENT.
11. At what per cent., will $600 in 2 years 4- months
and 15 days, give $57 interest?
Lesson XI.
1. At what per cent., will $10 in 4 years, amount
to $12 ?
Remark. — From the amount substract the principal, and the
remainder will be the interest. Then proceed as in the pre-
ceding lesson.
2. At what per cent., will $12 in 3 years, amount
to 313.44 ?
3. At what per cent., will $20 in 6 years, amount
to $26 ?
4. -At what per cent., will $24 in 10 years, amount
to $36 ?
5. At what per cent., will $30 in 7 years, amount
to $30.30 ?
i\ At what per cent., will §50 in 10 years, amount
to $75 ?
7. At what per cent., will $36 in 5 years, amount
to $39.80 ?
8. At what per cent., will a given principal double
itself, in 20 vears ?
Sou .xON. — A i^iven principal will double ifself in 1 year, at
100 per cent.; and in 20 years, at ^o of 100 per cent, or 5
per cent.
9. At what per cent., will a given principal double
itself, in 4 years ?
10. At what per cent., will a given principal double
itself, in S years ?
11. At what per cent., will a given principal double
itself, in 5 years ?
12. At what per cent., will $80 in 7 years give $80
interest ?
PER O^NT.
15'
13. At what per cent., will «640 in 6 years give
^^^4. 'm whit per cent,, will 25 cents in 8 years give
'>fi ofints interest ? . ..^^
15 At\.hat per cent., will S97 in 9 years give S97
'" iTlt what per cent., will S372 in 23 years give
*1?/ At Thai per cent., will $1 in 30 years give SI
'° irlt what per nant., will «15 in 12i years givo
*^19°Tt'wh;t per cent., will 842 in 141- years give
**20° Tt'what per cent., will 5 cents in 16J year,
aive 5 cents interest ?
Lesson XII.
1. In wbalJ time will a given principal double itsell,
fit 5 ner cent, ?
., ,L„^ _A Biven principal will double iUelf m 100 yea™.
.tTperC^irt I per -.t, in -| of 100 years, wl„ol> >s
'" 2!Tn what time will a given principal double itself,
'''3.^1" :ttLe will $25, at 3 per cent., give S25
^°*nn what time will $27.5, at 6 per cent., give §275
'"*!.' U what time will a given principal double itself,
"■^ I ^11 :tt time will 54, .t 7 per cent , give S4 in-
'TVn -..hat time will S94, at 9 per cent., give 894
interest ?
158
PER CENT.
8. In what time will 6 cents, at 8 percent., give 6
cents interest ?
9. In what time will 33 J at 10 per cent., give 33i
interest ? o »
give
10. In what time will 1 dime, at 12i per cent.,
^e 1 dime interest ?
Lesson XIII.
1. Bought a bushel of grass-seed, for $5 and sold
it for $7 ; what was the gain per cent. ?
Solution.— Since it was bought for $5 and sold for $1, the
gain must have been $7— $5, which is $2. Therefore, * of the
cost equals the gain. If on $1 I gain |J. on $100 I will gain
100 times ^, or $40. Therefore, the gain is 40 per cent
2. A book was bought for $2, and sold for $3 ; what
was the gain per cent. ?
3. A shawl cost $5, and was sold for $8 ; what was
the gain per cent. ?
4. A cow was bought for $20, and sold for $25 ;
what was the gain per cent. ?
5. A merchant bought a hogshead of molasses for
$80, and sold it for $95 ; what did he gain per cent. ?
6. A barrel of pork cost $12, and was sold for $11 ;
what was the loss per cent. ?
7. A horse was bought for $140, and sold for $60 ;
what was the loss per cent. ?
8. Bought au orange for 4 cents, and sold it for 6
cents ; what was the gain per cent. ?
9. Bought a melon for 15 cents, and sold it for 20
cents ; what was the gain per cent. ?
10. Bought a book for 5 dimes, and sold it for 8
dimes ; what was the gain per cent. ?
11. Bought a quantity of silk for $120, and sold it
for $200 ; what was the gain per cent. ?
12. A boy sold melons, at the rate of 10 cents
PERCENTAGE.
159
apiece, \ of which equaled his gain ; how much would
he have gained per cent., if he had sold them, at 12
cents apiece ? ^ , i j
13. A merchant sold sugar, for $80 a hogshead,
and thereby cleared ^ of his money ; if he had sold
it, at $92 a hogshead, what would he have gained per
cent. ? 1 p di or» 1
14. A quantity of cloth was bought for $3G, and
sold for $43 ; what was the gain per cent. ?
15. A horse was bought for $100, and sold for $95,
what was the loss per cent. ? wi i.
16. A man sold a horse for $120, and thereby
cleared V of its cost ; how much would he have lost
.' .,.1 1 _j __i.i u:w> *• — (ttQA 9
Of ^ 18
per cent., if he had sold him for $80 ?
17. What per cent, of
"3 ^^ C
Of 4 is
1 ?
^V?*0ffis|1 Offisf? Of2^is|? Of3^is2^V'?
18. i of $6 is what per cent, of J of $100 ?
19. 4 of $28 is % of what per cent, of -} of $300 ?
20. Walter sold a horse for 120, and thereby
cleared ^ of its cost ; what would he have lost per
cent., by selling it ^r $80 ?
Lesson XIV.
1. A man bought a cow for $20 ; for what must he
sell her, to gain 5 per cent, on the cost ?
Solution.— If he gains 6 per cent, he gains ^go.* ^^ 20 °^ ^^^^
cost. ^V of $20 is $1, the gain. Therefore, to gam o per cent.
he must sell the cow for $20+$l, or $21.
2. A man bought a yoke of oxen for $100 ; how
must he sell them, to gain 6 per cent, on the cost f
3. A man bought a barrel of rum for $10 ; tor what
must he sell it, to gain 10 per cent, on the cost ?
4. A gallon of wine was bought for 20 dimes ; how
mi
cost?
"f ;f L anl/l fl nint. to srain 20 per cent, on the
lao
DISCOUNT.
5. A hogshead of molases cost $20; for what
ought it to be sold a gallon, to gain 40 per cent, on
the cost ?
6. B bought a horse for $80, and by selling it, lost
5 per cent, on the cost ; for what did he sell it ?
7. A wagon cost $140, and was sold for 5 per cent,
less than it cost ; for w^hat was it sold ?
8. A merchant, by selling 40 yards of cloth for
1164, lost 20 per cent, on the cost. What did it
cost per yard ?
9. If a quart of brandy cost 50 cents, how must it
be sold a gill, to lose 4 per cent. ?
10. B lost 5 per cent, by selling a gallon of rum,
which cost 80 cents ; for what did he sell it a ffailon ?
Lesson XV.
1. What principal will, in 4 years, at 5 per cent.,
amount to $60 ?
t
Solution.— If the interest of $1 for 1 year is 5 cents, for 4
yearc it is 4 times 5 cents, or 20 cents. Therefore, -j%% or -V
of the principal equals the interest ; to which add -|, the prin-
cipal, and we have & of the principal equal to the amount, or
|60. If I of the principal is $60, | of the principal is -^ of S60.
■which is S;10; and |,(the principal), is 6 times $10, which arc
$50.
2. What principal will, in 3 years, at per cent.,
amount to $118 ?
3. What principal will, in 5 years, at 6 per cent.,
amount to §130.
4. What principal will, in 7 years, at 5 per cent.,
amount to $81 ?
b. What principal will, in 9 years, at 8 per cent.,
amount to $86 ?
6. What principal will, in 8| years, at 8 per cent.,
amount to $260 ? "
DISCOUNT.
161
r what
tent, on
it, lost
t?
?r cent.
oth for
t did it
must it
►f ram.
?ailon ?
cent.,
t8, for 4
he prin-
ount, or
i^ofseo,
liich are
' cent.,
' cent.,
' cent.,
cent.,
cent.»
7. What principal will, in 4| years, at G per cent.,
amount to $640 ?
8. What principal will, in 5-f- years, at 7 per cent.,
amount to $42 ?
9. What principal will, in 6f years, at / per cent.,
amount to $b7 ?
10. What principal will, in 8f years, at 6 per cent.,
amount to $76 .''
Remark.— The present worth of a debt payable at some fu-
ture time, without interest, is such a sum, as will in the given
time, and at the given rate per cent., amount to the debt. Hence,
the present worth of any sum of money, payable it some future
time without interest, may be found in the same way that we
found the principal, when we had given the amount, time, and
mte per cent.
See the above solution.
11. What is the present worth of $26, due 5 years
hence, at 6 per cent. ? ^^«- j?20.
12. What is the present worth of $14, due 8 years
hence, at 5 per cent. ? , ^ ., , ^ . ^
13. What is the present worth of $110, due 5 years
hence, at 5 per cent. ?
14. What is the piesent worth of $86, due 8 years
bende, at 9 per cent. ? ^.,^^« i «
15. What is the present worth of !ibl02, due 9 years
hence, at 4 per cent. ? , .^^ , a
16. What is the present worth of S72, due 4 years
hence, at 5 per cent. ? , « i
17. What is the discount on $46, due 3 years hence,
at 5 per cent. ?
Remark.— 2Vie discount equals the amount minus the presetU
worth,
18. What is the discount on $54, due 5 years hence,
at 7 per cent. ? , . i. ^«
19: What is the discount on $65, due 5 years hence,
"" 20rWhat is the discount on $93, due 3 years hence,
at 8 per cent. ?
e
162
PERCENTAGE.
21. What is the present worth of $186, due 44
years hence, at 5 per cent. ?
22. What is the present worth of $66, due 5| years
hence, at 6 per oent. ?
23. What is the present worth of $128, due 4t
years hence, at 6 per cent. ?
Lesson XVI.
1. If I sell cloth, at $2.50 a yard, and thereby gain
25 per cent. ; what did it cost a yard ?
Shlution.— If I gain 25 per cent. I gain J of the cost ; to
which add f, the cost, and I have f of the cost equal to $2.50
If f of what I gave for it, is |2.50, i of the cost is 4 of $2 50
of 50 cents ; and ^ (the cost) is is 4 times 50 cents, which are
200 cents, or $2.
2. A horse was sold for $38, which was at a loss
of 5 per cent. What did the horse cost ?
3. If I sell cloth, at $2.50 a yard, and thereby gain
25 per tent., how must I sell it a yard, to lose 20 per
cent. ?
4. If I sell cloth, at $4.40 a yard, and thereby gain
10 per cent., how ought I to sell it, to to loose 25 per
cent. ? ^
5. If by selling a piece ot cloth for $46, I gain 15
per cent., how ought 1 to have sold it, to have lost 30
per cent. ?
6. A sold his horse for $105, and thereby gained 5
per cent, on the cost ; for what ought he to have sold
it, to have lost 10 per cent. ?
7. Afarm was sold for $495, which was 10 per cent,
less than what it was worth ; for what ought it to have
been sold, to have received 40 per cent.inore than its
value ?
8. A mechanic lost 20 per cent, on the cost of a
Wfio-ornn h
1-
1 I
"CT QAlllVirv ■• 1- ■»j-\'M Hf /I f ft _ A-^^ . 1_ _ j_ 1 i ■* .
J --.^liiu^ XV iu'i >ff-x\j i luv vvijiic ougnt ic CO
nave been sold, to have gained 30 per cent. ?
PERCENTAGE.
163
h due4|
) 5| years
i, due 4|
reby gaia
be cost ; to
tl to $2.50.
f of $2.50,
which are
at a loss
^eby gain
se 20 per
eby gain
se 25 per
gain 15
e lost 30
9. A horse was sold for $90, which was 10 per
<;ent. less than its value ; what would have been the
gain per cent, if it had been sold for $120 ?
10. A farm was sold for $690, which was 8 per
cent, less than its value ; what would have been the
gain per cent, if it had been sold for $850 ?
11. A book was sold for 90 cents, which was 10
per cent, less than its value ; what would have been
the gain per cent, if it had been sold for $1.50 ?
12. A man sold two watches, at $12 each ; on one
he gained 50 per cent., and on the other he lost 50
per cent. Did he gain or lose by the bargain, and
how much ?
13. An individual sold two gold pencils, at $6
apiece ; on one he gained 20 per cent., and on the
other he lost 20 per cent. Did he gain or lose, and
how much ?
14. A farmer sold two horses at $210 apiece ; for
one he received 25 per cent, more than its value, and
for the other 25 per cent, less than its value. Did
he gain or lose by the bargain, and how much ?
15. A merchant sold a quantity of cloth for $280,
and by so doing lost 60 per cant. ; he then sold an-
other quantity for $80, and thereby gained 60 per
cent. Did he gain or lose by the operation, and how
much ?
gained 5
I'ave sold
per cent.
; to have
than its
3st of a
fnt it to
Lesson XVII.
1. An individual was ordered to collect $190, and
his own fee, which is to be 5 per cent, on all the
money collected. How much should he receive ?
SoLUTioN.—He ia to receive 5 per cent, or j^ or ^V:, of all
he collects, fg, all he collects, minus A-. his fee, equals ii of
ail he collects, or $190, the amount he fs^to pay his "employer.
If 4§ of what he collects equals $190, ^V is -^^ of $190, which
164
MISCELLANEOUS QUESTIONS.
i8$10; and f§ (what he collects) k 20 times flO nr t>mn
Therefore he must receive $200 - $190 J= $lo.
.J'J^'''' ""r^ ""^^^^ ^ *^ ^^^^^^^^ ^'or collecting $90
and his own fee, of 10 per cent, on all he collect^s ?
a debt n • trT!l^^ "''^n ^-^ ^'^^ ^' ^"^^^^^"t ^« Pa-
a debt ol $38 and the collector's fee, which is 5 ner
cent, on all the money collected ? ^
4. How much cider must that man make to brine
away 15 barrels after the owner of the mill rece ves
16| per cent, of all he has made ?
5. How much grain must a farmer take to mill, that
he may bring away the flour of 1 bushel, after the
miller has taken 10 per cent, of all he took there '
Miscellaneous Questions.
1. At 5 per cent, for 4 years, what oart of th**
principal equals the interest ? ^ ^
T..;^' •^''i*''''^' '"''''^ ^^^""^^ "* ^ per cent., will a given
n pL c'ent""' '' *'' ''"^' '' '' "^^^ '^ ' /««'«^
8. At what per cent, will a given principal in 14
'^^ntvahi"^^ ?™' ^°' ^ y^"^' ""•"""ted to
J^i^l M , ^''"* P*"" <=«'^*- did he annually re-
ceive on the value of his farm* <^M,y le
pefcltf " **" ^^""^ °^ ^''^^ ^°' 5J years, at 6
give SntSf' "'" '° '^ y^"^' "* « P- -*•'
mo'nu'I to" »S55 r^ "'"■ •" *^ y^«-- «* 3 V» cent..
MISCELLANEOUS QUESTIONS.
165
or $200.
tin^ $90
lects ?
it to pa^
is 5 per
to brincr
receives
lill, that
fter the
lere?
of the
a given
! years,
1, in 14
2 years
:, what
ited to
Uy re-
9, at 6
cent.,
cent.,.
.. ^-4* Y^^^ P^'" ^^"^•» "^'^^ ^ Siven principal double
itself, m 12 i years ?
10. The interest of A.'s and B's fortune, for 8 years
at 5 per cent., is IJ420. What is the fortune of each'
provided A'a fortune is twice B's ? '
11. The interest of j of A's aud ^i of B's fortune.
for 7 years at 5 per cent., is $2100. AVhat is each
of their i-ortunes, provided f of A's fortune equals i
of B s ? ^ *
12. B sold his horse, for ^ of U times what it cost,
what did he lose per cent. ?
13. What is the interest of $540 for 4 years, at 5
per cent. ?
14. What is the interest of §180, for 5 years and
9 months, at 6 -| per cent. ?
15. What principal will in 4 years 7 months and
6 days, at 6^ per cent., amount to $412 ?
16. The interest of the cost of B's horse, sleigh
»nd wagon, for 6 years, at 5 per cent., is $69. What
IS the cost of each, provided their prices are to each
other respectively, as h I and i ?
17. What principal will, in 8 years and 8 months,
at 7f per cent., amount to $419 ?
18. What principal will, in 5 years 9 months and
18 days at 10 per cent., give $116 interest ?
^19, In what time, will $420, at 5 per cent,, give
$147 interest ? f », b
20. -If the interest of $200, for 1 year and 6 months,
13 $18, what is the rate per cent ?
2J. At what per cent., will $500, in 4 years and 9
months, give $190 interest r
22. At what per cent., will $500, in 22 years and
6 days, amount to $1821 /*
23. At what per cent., will a given principal double
itself, in 20 years ?
24. In what time will a given principal double
itself, at 12| per cent. ?
166
MISCELLANEOUS QUESTIONS.
25. At what per cent, will
ipal double
., ,^ . ^ X -- - given pri
Itself, in 6 years and 8 months ?
26. A horse was bought for $60, and sold for $90;
what was the gain per cent. ?
27. A basket containing 39 oranges, cost $1.20 •
oJ^tIK^^^^' ^^ '?^^ ^P^e^^e to gain 30 per cent. ? '
,nnlf -f i Tr* °n «,^^°^Pag^e cost 40 cents, how
must it be sold a gill to gam 20 per cent. ?
29. What is the present worth of $68, due 10
years hence, at 7 per cent. ?
30 What is the discount on $162, due 10 years
and 4 months heiice, at 6 per cent. ?
31. What is the present worth of $87, due 3^ years
hence, at 5 per cent. ? ^ y ^'■^
.Jh'ln^ hogshead ot; molasses containing 84 gallons
cost $30; how must it be sold a gallon, to gain 40
per cent, r
33. The money I have on interest, in 9 years, at
ci alT amounts to $190; what is the prin-
^dm* ^I'r ?°"®; "^^'^ "^^^^^^ ^ P^^ ^e^*^ ' I 'nought
$400 worth of goods ? 6 months afterwards I sold
them, and gamed 10 per cent, on the cost. How
much did I gain .^ j,^^^ ^23^
^&. A speculator bought a horse for $36, and sold
It tor 25 per cent, more than he gave for it ; which
however was 10 per cent, less than what he asked
Qu x^ ^"^^ ^^^ ^® ^^^^ ^0^ *be horse ?
^6. A gentleman being asked how much money he
had on interest, replied, that if instead of 6 per cent,
he should receive 10 per cent , he would receive $268
mterest more than he did then. How much money
had he on interest ? "^
37. A meTchant bought broadcloth for $1.20 a vard
and sold It for 331 per cent, more than he g^vrs for
It ; which, however, was 33i per cent, less than bis
marxied ^jvice lor it. How much was his marked
price per yard ?
sipal double
)ldfor $90;
Jost $1.20 ;
)er cent. ?
cents, how
?
!8, due 10
3 10 years
le 3^ years
84 gallons
to gain 40
' years, at
i the priu-
, I bought
ds I sold
sfc. How
s. $28.
, and sold
t; which,
he asked
3?
money he
per cent.
eive $268
jh money
20 a yard
giiTQ for
than bis
I marked
MISCELLANEOUS QUESTIONS.
167
38. A merchant sold a quantity of cloth for $120
and by so domg gained 50 per cent. He then sold
another quaiitity, for $120, and thereby lost 50 per
much ? ^''" "' ^''' ^^ '^' ^"''S"^^» ^^^ ^^^
39. B sold a horse for $60, and gained 20 per cent.
He then sold another horse for $60, and lost 60 per
^ A rS . ® ^^'"^ °'' ^°«®' »»^ ^«w much ?
40. Ihe interest on 1^ times A's, and 4 of B's for-
tune, lor 8 years, at 5 per cent., is $520. What is
firi\* ^ f ^,'' J^'*"°^ ^^^«d *o f of E's, which is 3
times ^ of D s bemg put on interest for 8 years, at 5
of each ?' ^''''' ^^^^ '''^^'''*- ^^^* '' *^^ ^°^*^^^
42. The interest of A's, B's, and C's fortune, for 5
years, at 8 per cent., is $1040. What is the fortune of
h Pmr"^^? *^®^ ^""^ *^ ^^«^^ «*^e^ as i, i, and i ?
43. The interest of A's, B's, and C's fortune, for
53 years at 6 per cent, is $800. What is each of
their fortunes, provided B's, is twice A's ; and B's
and C's are equal ?
44 A's fortune added to | of B's, which is to A's
as Z to S, being put on interest for 6 years, at 4 per
eaeh ? ^"'''''"^' ^"^ ^^^^' "^^^^ ^^ ^^e fortune of
45. D's money added to 4 times E's, which is equal
to 1) s, being on interest for 10 years, at 5 per cent.,
amounts to $3000. What was each of their fortunes ^
46 The sum of f of A's + ^ of B's money, being
Sinn 'p ^^'1 ^ TT^,^^ ^ P^^ ^^"^' a^o«^t« to
piOO. Provided i of B's money is twice i of A's ;
now much money has each ?
47. I of tt^g ^og^ Qf ^,g j^^^g^^ increased by -^ of the
coat "r Ina fayryi V.^,'^._^1 J . • . ,«•'-?
_^ ,_ ..,^ ,«xm, vciijg piuufu on interest lor 10 years,
at 7 per cent , amounts to $17000. What is the cost
168
MISCELLANEOUS QUESTIONS.
of each* if | of the cost of the house is only 1 of -|
of the codt of the farm ?
48. If f of A's fortune in 2 years and 4 months, at
6 per cent., amounts to $570; what is his whole
fortune ?
49. The sum of A's, and B's fortune in 4 years and
S mouths, at 6 per cent., amounts to $256. What
was each of their fortunes, provided \ of A's fortune
equals B'a ?
60. The interest for 6 years, at 6 per cent., on \ of
the money Morgan owes is $180; and the interest for
the same time and rate per cent., on ^ of the money
due him is $120. How much has Morgan after pay-
ing his debts ?
51. The money John paid for a sheep, a cow, and
a horse, in 8 years, at 10 per cent., would give such
an interest, as would in J as long, at ^ as great a per
cent., amount to $104 ; how much did he pay for each,
provided the shoep cost -J- as much as the cow, and
the cow \ as much as the horse ?
52. The interest of the sum of \ of Simpson's, -f of
Eyer*s, and -^ of Domer's fortune for3 years 7 months
and 6 days, at 10 per cent, is such as will in the same
time, at \ the rate per cent., amount to $531. What
is the foj'tune ot each, provided \\ times Domer's part
of the principal equals f of Eyer's, ai ! -^ of Eyer's
part of the principal equals \ of Simpson's ?
53. The interest of the sum of \ of A's, and | of
B'a fortune, for a certain time, at 2 per cent., was to
thi% sum as 9 to 250. And the amount of this interest
for 25 times as long, at 10 times as great a per cent.,
was $180. What was each of their fortunes, provided,
A's fortune was to B!s as 1 to 3 ? And how long was
the first on interest ?
Remahk. — Since the interest was to the principal as 9 to 250.
^fp of the principal equals the interest. Hence, 1 year 9 months
and 18 days is the time required, tfcc.
nly -1 of I
months, at
hia whole
! years and
I. What
.'s fortune
t., on I of
Qterest for
;he money
after pay-
i cow, and
give such
reat a per
Y for each,
I cow, and
3on's, ^ of
1 7 months
L the same
II. What
Iter's part
of Eyer*s
and I of
t., was to
is interest
per cent.,
provided,
long was
IS 9 to 250.
vr 9 months
QUESTIONS, QUERIES AND PUZZLES,
FOR
PUPILS AT HOME.
w.l: ;^r,i'°'}^^ '!^ ^° J^"^^^^^ ^^ ^ ^^^ that is lO rods ahead of
him, and t^/»/g the hound runs 10 rods the fox runs 1 rod
^; ti.'^nf .V .' ?°;''^^ T' ,'^^,f ^''^^ ^^^i^n^^. the fox runs one-
venth of that distance.) Will the hound overtake the fox ?
The conditions remaining the same, what is the greatest dig-
•Kance they can run ? & wiw
^^ t Jji°''? V '^}^ P/''^'^ °^ ^ ^''^ ^^*^^ '^ t^" rods ahead of
kim and while the fox runs 1 rod the hound runs 10 rods.
, far will the hound run before he overtakes the fox ?
3. Place four 5 s in such a position that they shall equal 6^
4. A boy was sent to a spring with a 5, and a 3 quart
measure to procure exactly 4 quarts of water. How did he
measure it? '
5. What is the difference between twice 25, and twice 6
and 20 ? J w
6. A man had 9 pigs and put them in four pens, with an
«ld number of pigs m each pen. How did he divide them ?
7. Two men have an 8 gallon cask full of wijie, which they
tlesire to divide equally between them. How can they effect
this division, provided the only measures they have arc a 5
gallon cask and a 3 gallon cask?
e uaM?° ^^^^ ^'^ ^^ ^^^^ ^ manner that they shall exactly
9. Place 9 apples in 10 rows so that each row shall contain
.1 apples.
10, A squirrel finding 9 ears of corn in a box, took from it
ciflijy 8 ears; how many days was he in removing the com
rrom the box ?
»# y^: ^y^^^J^^ y^u take iX, and from IX you take ten : and
vT fifty from forty be taken, there will then just half a dozen
1,1!
no
qUESTIONS AND PUZZLES.
60 apples an/Lld 'hem'^ff ^ ' f. If ^ Vh''' ' ^^^^ ^^^
120 apples and sold thorn, at th^ raL^ ..f «' f o'"" '''°^^°' ^^'^^
iather's aon." What relation wn^.L .?' ' '' "'■ 's mv
14. A man havtng ^C^™^,^'™'>'■'•'"•°''''=l'^™""'•'■
clC8irou8 Otero Jns\ river' He^foihn.f '"f '^ <•■»■•''' ^«''
» time, and if he lelt tl,7fn; „11. '' '"'" »"'>' <"'^ ■'•"oss at
««,,tLe foxwitldln °.l^-i:S3'°Z'iS M f,^'r" '"^ '<'™
oorn, the goose would oaf t°tmT„' '"'' °''''''^' •'"=S»3cancl
.II skfely ScrossThe river ' '"• "°" ''"•''" ''«?<'' ^^<""
tJ..' day H cnS 5 fcen:!' •:,]:"",-» [-,? '» '-S'u : during
Ho» .nany days .oulTll uI'ef'L"^!^,,- Z "'"■' "'^hS
cbin-t ^To'hiff^S'-prfo?.^'" ^Xei^' T^ r^^ ^''^ --
mak. thechan.'e, ?ent timl, ni */ ? "<'"'"'i" hoing unable to
then gave the ^aChot^'iM^^.e fe^°V * I""]"'"' J""
the purchaser of the hat tiad^o),. t„ , ^,''* '"'°1'«''' »««"
oonnterfeit, and therefor ret?Suto7hf ""*', "'° ^'"'^'^^
cemd $60 good money. Ilow .™oh , W foT'"""' '"'^ «"
tkeopwation? '"""""^"'"tt "lomcrchant iosebr
leaVfeJ'npo'ntrjhM'V f"' .*''^''' "■■"'■^ °"» over t„o
ten peLies SmtJyVn'ylrp'', "ef ;r f"'"?" ""^ """' ^^
»»«. How man^ po'n'drdTdtot'jf iJ^t*^, °"'"' " '"'■'^'■="' -"
feet everfjL" ' Howmtv"- ^ ™" '' ''"' *^1'' "^eonds a
20. A drove?'beint »?^-^7>,''™'" """"' '^^ ""« '» get »ut V
" ify horses to^?Le? have twlf ''"? '""'f"' '"= ''^'°' ■■"PlM :
horses had he ? '"^^"'^ ^'""^ '"=gs." How many
t. be 1^"" ^^ '" '""' " """ner, that you can show i(s half
32. " I am constrained to plant a grove
To please the lady that I lov!
Th,s ample grove is to compose
K?rtres*r„i\i".-'-:?'!' -- ;
JJive trees in each row i m.f-t
Or I shall nover see her face."'
iCC.
QUESTIONS AND PUZZLE.s.
171
2S.. Do the wabrs of the Mississippi river tlow up hill v
same in each column, whether added
pcrpendicularlj, horizontally, diagon-
ally, or taking any fourof the numbers
m the form of a square.
1
II
14
ir.
r,
O
16
la
Magio Squams-An East India Poms^
the figures" from ! o 05 ^"I'" ''-"' !•"""» '^ 25,_^rite
horizontallT or diaironnllv .h? "'"'.added perpendicularly,
one-mh ofVe\'u3ti^ler e\"?ntt™n'?/'ir"*X'
of the numbers 7, 9, 11 etc ""^"Ders, i to 2o,— andso
position of th^e "^'aa e ust ZZ ^T'^'l' "^^^^^"^ ^« '^^
upward to the nX nVj?l ' ^'''' \ ^'■°^*^^*^ diag-onally
011 the 1 iL fde^of ;^/^" '?" °^^ ^^ this go to the^quari
the ri^ht or Lt ifnfnhi^ '^"'3°^^^^ "^ ^^^^ "«^t line at
the sqCelm^di^tely bew'^" '' "'" ^'" "°* ^^ ""^> ^^^^
These figures can be varied in
at least four different ways. If
the number 1 bo taken, they can
hQ varied .u; different ways ; if
Jff .•^"' ^^''^ ^^'' ^^° ^-a^ied
jJiorc,
• perhaDs
17
23
4
10
11
24
1
7
18
8
14
20
21
o
15
16
22
3
5
G
X^
10
25
18
»
Tomovro : ^m^rm by ro^riL a^d on^, to'^^e street
u
l )*
El t
I
Canadian Editions.
PBIOB BACH
Bullion's Aualytical and Practical Eng-
lish Grammar 50 Cts.
Introduction to ditto 25 "
Stoddard's Juvenile Mental Arithmetic, 13 "
Intellectual do. 20 "
Carpenter's Spelling Book 10
Mayor's do. . . » 10
Walker's Dictionary 30 "
Catechism of the History of England. . 10 "
-_— Bible and Gospel History 10 "
LOVELL'S SERIES OF
Stationery of every description.
^The Trade Supplied at very Low Prices,
ADAM MILLER,
62 King Street Eastj Toronto.
L
.<«r^SS\