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1
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Si" " "■ ~
•s,^ irC^^:A 0.^^^/^^^^.^
r"'-
THIS COURSE GMBRACBS
THREE DIVISIONS ■
THE ELEMENTARY. INTE?IMEDIATE AND HIGHER.
ARITHMETIC
ELEMENTARY tOURSl;.
NEW HKRIEH
VY IHK
Brothers of the Christian Schools.
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MONTH EAL,
50 COXTE ST"
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THE E
A
E
B
THIS COURSE EMBRACES
TRRKB DtTISIO.VS :
THE ELEMENTARY, INTERMEDIATE AND HIGHER.
ARITHMETIC
ELEMENTARY COURSE
NEW SERIES
BT THC
Brothers of the Christian Schools
•■ „
MONTREAL,
30 9OTTE ST
A
''I
ENTERED according to Act of the Parliament of Canada, in
the year of our Lord, 1893, by
JEAN ROUTHIBR,
in the Office of the Minister of Agriculture and Statistics,
at Ottawa.
1. Aritli
2. A Nui
; 3. A Uni
eomparpd, w!
A unit ma
4. A Qui
o street, the j
5. The g
I 3 Denominai
I 6. Aniui
AFracti
two-thirds, th
A Denoi
of coutiuuoui-
7. Arith
8. ArithuK
is called Nuv
9. Xumc
them when e;
10. Each
one, two, thrt
tEach of th(
rder. They a
formed of c
f Canada, in
»d Statistics,
"vV
ARITHMETIC.
ELEMENTARY COURSE.
Introclnctioii.
!■ Arithmetic is the science of numbers.
2. A Number is a unit or a collection of units.
3. A Unit is the quantity to which n quantity of the same kind is
isompared, when it is desired to measure it.
A unit may also be defined to be a single thing or one.
4. A Quantity is any thing tlmt can me measured. Ex.: </w length of
a strtett the population of a city, the surface of a body, etc.
5. The general classes of numbers are: 1 Integers, 2 Fractions,
8 Denominate numbers.
6. An Integer is a number of integral units ; as, four, six, etc.
A Fraction is a number of the equal divisions of a unit ; as, one-half
two-thirds, three -fourths, etc.
A Denominate number is a number in which the unit is a measure
of continuous quantity; as, three yards, two pound . '^vefeet, etc.
ARITHMETICAL LANOUAGB.
7. Aritlimetical Language is the method of expressing numbers.
8. Arithmetical Language may be either oral or written. The former
is called Numeration, the latter Notation.
9. Numeration is the method of naming numbers and of reading
them when expressed by characters. It is the oral expreseion of numbere.
NUMERATION.
10. Each of the first nine numbers has received a separate name ; thus,
one, two, three, four, five, six, seven, eight, nine.
Each of these nine numbers express simple units or units of the fir»t
)rder. Tbey are formed by adding one to the preceding number, thus : two
•*" formed of one aud one, three of two and one
KUMERATION.
The number after nine is colled ten.
Ten !• the unit of second order and is equal to ten vnits of the first
order. Tens may be counted or read just as the simple numbers ; thus,
one Un, two Una, three Unt nine tens / but usage has replaced these
words by the following : Un, twenty, thirty, forty, fifty, tixty, uveiUy,
eighty, ninety. .
The numbers intervening between two tens are formed by joining tUe
names of the first nine figures to each of the above tens. Thus lwe;Uy
one, twenty-two, twenty-three, till twenty-nine. However instead of saying
Un-one, Un-two, etc., usage has adopted the expressions eleven, twelve,
thirUen, fourUen, fifteen, sixteen, seventeen, eighteen, nineteen.
Tiie number following ninety-nine or teu-tcns is called hundred.
Hundred is the unit of the third order.
Hundreds are counted just as units are ; thus, one hundred, tvo
hundred, .... nine hundred.
The group of the" first three orders of units forais the first ixjriod or class
of units.
The number following nine hundred and ninety-nine or ten hundreds
is called thousand.
Thousand is the unit of the second period. The second period or
class of units comprises units, tens and hundreds, just as the first period.
The number after nine hundred and ninety-nine thousand nine
hundred and ninety-nine or a thousand thousands is called million.
Million is the unit of the third order. The fourth group of a thousand
millions is called a billion ; the fifth group a trillion, etc. Each of
these periods comprises three orders : units, tens and hundreds.
11. Remark.— Ten units of any order forms a unit of the ordrr
immediately above it. A thousand units of any period forms a unit of the
corresjtouding class in the period next above it.
Numeration table.
TllICI) l-F.l.li
First period
Second period
)■ First order Units.
.; Second " Tens.
Third " Hundreds.
(•Fourth " Thousands.
J Fifth " Ten-thousands.
(.Sixth " Hundred-thousands.
FoUllTH Htll
12. Notll
in three w,
letters (Romu
13. To rep
1 2
one, tw
Tlie first n
a value ; the
Hgure ; it ma
Willi ting.
14. Ppin(
two following
1.— When
I riglitrepresei
' thousands ; tl
I 2.— The ter
\ 15, Every
Simple Vs
alone, the Ix
\ any other pla
In the nuni
5, its local va
second figure i
16. How
reprei
written succ*
first, zeros are
figures
The numbe
representing f
thirty is writt
ts of the firflt
umbers ; thus,
replaced tliese
sixty, seventy,
by joining tliH
Thus twe;Uy-
istead of saying
eleven, twelve,
teen.
hundred.
le hundred, two
it period or class
r teu hundreds
econd period or
the first period,
thousand nine
1 million.
up of a thousand
I, etc. Each of
idreds.
it of the ordrr
rms a unit of the
is.
isands.
l-thousands.
Kl .Ml;|t.\riiJN. g
r Seventh •' Millions
Tnira. i-KMn,, \ Eijjhth •' Teu-millions.
I
'^^'''"tl' " Hundred-millions.
( '''*»th " Uillions.
KouuTH Htuion .'l Klevnith " Ten-biUions.
I
'^ Tuilltli " lluiidit'd-billions.
NOTATION
12. Notation is tinj^ method ol writing numbers. This mny be done
in three ways : ] By xoords, 2 By figures, (Arabic Method), 3 By
letters (Komm Method).
13. To represent numbers ten figures are used. These are ;
12 3 4 5 6 7 8 9
one, two, three, four, five, s'lx. seven, eight, nine, zero
-in a ^ 1 ""^ naught.
1 he first nine figures are said to be significant, because they re,)resent
a value ; the tenth, zero, represents nothing by itself, it is an auxiliary
figure ; it may iiold the place of a unit of any order when this unit i.
wanting.
14. Principles. All number may be represented by means of the
two following principles :
l.-When sevenl figures are written one after the other, the first to the
right represents units ; the .econd. tens ; the third, hundreds ; the fourth
thousands ; the fifth, ten-thousands. '
2.-The tero is put in the place of any order of units that may be want ne
15. Every figure has two values; a «m;,fe and a /ocai value, 'lu^
Simple Value of a figure is the number it expresses when it stands
alone, the Local Value of a figure is the number it expresses when in
any other place than units place.
In the number 6,604, the simple value of the first figure to the left is
5, Its local value is 5 units of thousands ; so also the simple value of the
second figure is 6. its local value is 6 hundreds, etc.
16. How to writeanumber.-To represent a number the
figures representing the hundreds, tens and units of each period are
written successively from left to right ; the highest periods are written
first, zeros are used to take the place of missing orders
The number three hundred and eight is written 308 ; and the number
representing forty million five hundred and twenty-seven thousand and
thirty IS written : 40,627,030.
4 Nl'MF.RATION. ^
17. How to l'eiUlauuniber.--To read a number written in
figures, it is divided, at least mentally, into periods of three figures, going
from right to left ; then the groups are successively read commencing to
the left, and giving to each one the name of the period it represents. If
an order of units or even un entire class were wanting, it should
not be mentioned.
Thus 37,409,000,265 would read : thirty-seven billion four hundred
and nine million two hundred and sixty-five.
Roman Figures.
18. To write numbers tiie Kouiaiis used the following characters :
J, V, X, L, C, D, M.
•whose values were : 1, f, 10, 50, 100, 500, 1000.
19. Priuciplcs.— 1. The letters placed to the right of another, add
tluir value to Dial of t/ie other if less than it or equal to it.
Thus the numbers : III, XV, ^ XXVll, CLXl, MDCCXVI
are re|id . 3, 15, 27, 161, 1716.
2. Any letter placed to the left of another should be deducted for tlie
value of this number if less than it.
Th3 numbers : IV, XXIX, XL, XCI, CDXIX.
are read : 4, 29, 40, 91, 419.
3. A dash over an expression increases its value a thousandfold. Thus
Vlll denotes eight thousan I.
EXERCISES IN NUMERATION.
Read the following iiumberM :
1.
10
15
17
24
26
29
81
2.
35
40
48
49
53
08
69
3.
62
72
80
86
98
99
OK
4.
100
101
040
160
169
406
768
5.
004
050
505
523
006
796
801
6.
1 027
1
060
1
090
1
126
2
002
3
019
5 404
7.
11 Oil
11
101
4
046
111
010
10
409
12
002
15 040
8.
116 096
273
459
430
590
246
689
386
211
406
804
679 43-2
Express tbe following numbers In flgiires :
9. Ten, eleven, thirteen, eighteen, twenty-one, twenty-four.
10. Twenty-eight, thirty-four, thirty-seven, forty-three.
11. Forty-eight, fifty, sixty-four, sixty-nine.
12. Eighty-eight, uiuuty-five, one hundred.
13. One hundred and three, one hundred and eight, one hundred and
ten, one hundred and twenty-three.
1
■f
33
1
34
1
35.
36.
;
37.
38.
'4
39.
1
40.
41.
;i
42.
63.
1
64.
55.
56.
57.
1
68.
1
\/
NL'MKllATION.
5
nber written in
>ree figures, going
i commencing to
it represents. If
anting, it sliould
ion four hundred
ving characters :
D, M.
500, 1000.
of another, add
, MDCCXVI
1716.
deducted for tlie
CDXIX.
419.
uandfold. Thus
'N.
29
08
99
406
796
3 019
12 002
06 804
arcs:
ty-four.
le.
81
69
09
768
801
5 404
15 040
679 43-2
14. One hundred and lifty-scven, one liuudred an.l sixty-eic-ht, two
hundred and eleven. °
15. Three hundred and twelve, four hundred and thirteen, fivu hundred
and fourteen.
16. Six hundred and fifteen, eight hundred and seventeen, one hundred
and nineteen.
17. Seven hundred and twenty, one hundred and tweuty-one, tiuee
hundred and three.
IS. Two hundred and ninety-eight, five hundred and nineteen.
19. Nine hundred and sixty-eight, four hundred and seventy-four.
20. Seven hundred and ninety-seven, eight hundred and eighty.
21. Two thousand and five, four thousand and twenty-four, one
thousand and seven.
22. Ten thousand and eight, twcnty-four thousand and teen.
23. Three hundred thousand raid twenty-seven, seventy diousand and
three.
24. Two million one thousand and nine, fifteen million five thousand.
25. Four hundred and six million nine thousand and fifty-six.
26. Six hundred and six million sixty thousand six hundred and six.
27. Twenty billion seventeen million one thousand and forty
28. One hundred and fifty billion forty-five thousand three hundred
and one.
29. Fifty-six million ten thousand and eight.
30. Three hundred and thirty-three million eighty-one thousand.
81. Nine million seventy-seven thousand and fifteen.
32. Five billion thirteen milUon two thousand and twelve.
KzprcM In flvures the fol lowing numbers t
33.
34.
35.
36.
37.
38.
89.
40.
41.
42.
VII
IX
XIV
XV
XXI
XXfX
XXXIV
XLIII
LIX
LXXXVI
53.
54.
55.
56.
43. XC
44. XCVII
46. XCIX
46. cxcviri
47. ODXXIX
48. DLXXXVI
49. DCDLXXVII
60. MCCXXXV
61. MDCLXXII
62. MDCCLXLIII
Expresi. ||.« foUowingr numbers In Homnn fiff.ires :
I 13 16 19 25 31
» «2 69 76 83 89
95
500
98
540
101
650
212
811
319
842
me hundred audi 57. 1 000 1 019 1 146 1 237 1 328
347
955
44
90
418
963
58. 1 800 1 824
1 848
1 556 1 666
1 859 1 883 1 900 2
OOU
/
I
m
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
Vo.
71.
72.
73.
74.
75.
76.
77.
78,
79.
80.
81.
82
ADDITION.
Oral exercises.
What is a unit ? Name the dilFerent kinds of numbers.
"V^hat is an integer? Define a fraction.
In how many ways may numbers be expressed ?
Name the orders of units in the first period. — In the second — In
the third.
How mauy values has every figure ?
What is the local value of 7 in 75 ?
What is the value of the Roman figur_ps V, X, L, C, D ?
What is the use of the figure zero ?
How many figures are required to write a hundred units ?
How many figures are required to write a thousand units ?
How many tens are required to make a thousand ?
How many figures are required to write ten-thousand units ? — a
hundred-thousand ? — a million ?
How many (hundreds in ten-thousand ?
How many ten-thousands in a million ?
How many hundred j in a hundred-thousand ?
In a million how many thousands are there ? How many hundreds ?
How many units in a hundred 1 How many tens ?
How many tens in a thousand ?
How many hundred-thousands in p. million ?
How many thousands in a billion ?
How mauy figures are required to write a number whose highest
unit is a thousand ?
What is the highest unit in a number of five figures ?
What is the highest unit in a number of eight figures ?
How many periods are required to write a number of twelve figures ?
1
FUNDAMENTAL OPERATIONS.
ADDITION.
21. Addition is the process of finding the sum of two or
more numbers of the same nature.
The result of addition is called the sum or total.
22. Ni
same del
15 doUari
they are 1
23. Ad
addition <
118+65.
24. To
thorough!
the sum o
and
and
and
and
and
and
1 and
1 and
1 and
1 and
1
1
1
1
1
1
2 and
2 and
2 and
2 and ,
2 and
2 and
2 and
2 and '
2 and (
2 and i
3
3
3
3
3
3
and
and
and
and
and
and
3 and
8 and
3 and 8
3 and 9
>.A>
'S.
e second — In
its?
lits ?
md units ? — a
fiuy hundreds 1
whose highest
twelve figures ?
)NS.
m of two ov
tal.
ADDITION'. 7
22. Numbers of the same nature are those which are of the
same denomination or name. Ex. 25 dollars, 6 dollars,
15 dollars, are numbers which have the same denomination ;
they are then of the same nature.
23. Addition is expressed by the sign -f-, called plus. The
addition of the numbers 132,118 and 65 is marked • 1324-
118+65.
24. To solve any addition with ease, it is necessary to be
thoroughly familiar with the addition table. This table gives
the sum of any two figures.
Addition Table.
1 and are 1
I and 1 are 2
I and 2 are 3
1 and 3 are 4
1 and 4 are 5
1 and 5 are 6
1 and 6 are 7
1 and 7 are 8
1 and 8 are 9
1 and 9 are 10
2 and are
2
2 and 1 are
3
2 and 2 are
4
2 aud 3 are
5
2 and 4 are
a
2 and 5 are
7
2 aud 6 are
8
2 and 7 are
9
2 and 8 are
10
2 and 9 are
11
and
and
and
and
and
and
and
and
and
and
are
1 are
2 are
3 are
4 are
5 are
6 are
7 are
8 are
9 are
4
5
6
7
8
9
10
11
12
13
3 and are 3
3 aud 1 arc 4
3 and 2 are 5
3 and 3 are
3 and 4 are 7
3 and 5 are 8
3 aud 6 are 9
8 aud 7 are 10
3 aud 8 ore 11
3 and 9 are 12
aud are
7 and are
7
7 aud 1 are
8
7 and 2 are
9
7 aud 3 are
10
7 aud 4 are
11
7 and 5 are
12
7 and 6 are
13
7 and 7 are
14
7 and 8 are
la
7 aud 9 are
16
and
and
and
and
and
1 are
2 are
3 are
4 arc
.') are
and 6 are
and 7 are
aud 8 are
and 9 are
5
6
7
8
9
10
11
12
13
14
are
6 and
6 aud
6 and
6 aud
6 and
5 and
6 and 6 are
6 and
6 ami
are
are
are
are
are
are
.ire
6 aud 9 are
6
7
8
9
10
11
12
13
14
15
8 and are 8
8 and 1 are 9
8 and 2 are 10
8 and 3 are 11
8 aud 4 are 12
8 and 5 are 13
8 and 6 are 14
8 aud 7 are 15
8 aud 8 are 16
8 aud 9 are 17
9 and
9 and
9 and
9 and
9 and
9 and 5
9 and 6
9 aud 7
9 aud 8
9 aud 9
are
are
are
are
are
are
are
are
are
are
9
10
11
12
13
14
15
16
17
18
iiii
"J ADDITION.
PROBLEM.
25. WhcU ia the sum of 748, 695 and 874.
Solution. — The numbers are written so that the Opkbation
terms of the same order stand in the same column, units 748
under units, tens under tens, etc ; begin at the right to 695
add: 4 and 5 are 9, 9 and 8 are 17, or 1 ten and 7 874
units ; 7 is written under the column of units and the ten
is added to tlie column of tens : 1 and 7 are 8, and 9 are Total 2317
17, and 4 are 21 ; 1 ten and 2 hundreds ; write the 1 under the column
of tens and add the 2 to the column of hundreds. 2 and 8 are 10, and 6
are 16, and 7 are 23 ; 3 hundreds and 2 thousands, write the 3 under the
column of the hundreds and place the 2 to the left in the place of thousands.
Hence the sum of the numbers is 2,317.
26 Remark. —In pn.ctice the operation is performed thus:
4 and 5. . . . 9 and 8 . . . . 17 write 7 and carry 1 ;
1 and 1 .... 8 and 9 . . . . 17 and 4 .... 21 write 1 and carry 2 ;
2 and 8..;. 10 and 6.... 16 and 7 .... 23 which is written.
27. Rule. — /. Wrile the numbers so that the units of the
same order stand in the same column, and draw a line
beneath.
II, Begin at the units, add the number of each column
separately, and write the number under it, if less than ten.
III, 1/ the sum of any column is m,ore than ten write the
units only underneath the column and add the tens with the
next column.
IV, Write the entire sum of the last column.
28. PrOOfofaddition.— Find the sum of 1543
the figures in each column commencing at the 678
^p, the total found should be the sum as that 482
found in the first operation. 1074 3783
29. Secondmethod.— Theproof ofanad- 2156
dition compi'ising several lines may be made as 1354
follows : the numbers are added in groups of 769
five or six, and the sum of these different totals 802
is afterwards foumd, this sum should equal that 1G78 GSOi a
already found. 10582 10582
exb:
83.
84.
An!«
Ans
8.5.
Ans. ..
86, 4(
Ans. . .
99. /
100.
101.
102.
103.
104.
105.
106.
107.
loS.
109.
110.^
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.'
124.
ADDnnioN.
Opeuation
748
695
874
Total 2317
ier the column
8 are 1 0, and 6
the 3 under the
ice of thousands.
1 thus :
1 and carry 2 ;
is written.
e units of the
' draw a line
each column
than ten.
ten write the
tens with the
1543
678
482
1074
3783
2156
1364
709
802
1G78
EXERCISES IN NUMERATION AND ADDITION.
Alia ihc rullowiiiir nuinberM :
83.
84.
85.
Ans.
Anfl.
412
325
514
342
87.
748
28.')
An
3.
i
Ans.
86.
6976
827845
535694
405789
6854
76768
6304
10582 10582
88.
89.
7<i.'.
.\ns.
Ans.
90.
Ans.
671079
567765
875449
996898
3824
745+223
148+750
632+243
475+204
557+227
789+209
575+405
545+429
574+219
486+297
596+279
489+257
345+456
4.57+754
896+944
897+409
609+769
707+797
779+776
744+659
575579+426145
973476+595649
898423 + 769579
574615 + 697470
674907+575799
477424+648695
91.
!»2.
Ai S.
8r..]4'.4
90727!)
576r)07
447279
95
Ans.
93.
Ans.
94.
6823
9S9'347
724839
4927
98896
679589
Ans.
125.
126.
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
160,
Ans.
96.
£76721
464934
853799
764581
Ans. . . ,
97.
Ans.
98.
357047
79879
€^49754
452372
9694
877783
Ans.
475670+694957 -
727519+844619 '
995676+576644
789476+617094
547764+350097
597091+447089
895467+301959
709987+605304
794691+657784
829651+728577 "
789107+695999 H
894575+876934
759544^-877409
657897+794976
707809+976437
856437+934579
576279+495176
882354+576937'*
650769+775678
765097+975985
578467+854359
307450+850967
7456744-.^02966
980079+395891
807406+360706
805464+890316
/
10
ADDITION.
151. 217904+548254-679yt)4
152. 897452+920672+746794
153. 904525+876577+9283i)5
154. 987864+64247+809456
155. 741854+7465+3978
loti. 327410+7689+456351
157. 59827+747365+984576
15.S. 677491+5887+976642
15lt. 854947+967876+7897t)7
KiO. 654576+976787+898694
161. 654789+773212+564342
lti2. 495837+72224+795477
ir;). 676976+799884+685544
1(>4. 834905+976827+895795
165. 954653+497974+68939D
166. 5276+576423+760554
167. 654957+78786+547679
168. 7809+356377+254594
169. 34827+376956+798898
170. 87851+676724+375697
171. 78947+364705+495827
172. 676+456694+972397
173. 4.')0017+696459+807576
174. 576895752+495847967+9954634
176. 376457897+453376586+547684794
176. 654234654+568976456+876889999
177. 667954+862945677+452789654
178. 587654927+674987634+486856858
179. 576795984+687987877+793676785
180. 376452677+7546984+678667646
181. 476796675+764579889+507687964
182. 467676324+6847987+689698798
183. 74234654+986876497+747987854
184. 354796452+477689376+766876889
185. 4347651+865755561+447675384
186. 645606997+2754884+567875776
187. 745676462+356789584+789898976
188. 7652927+535746795+676898888
189. 798652450+7987987+956896789
190. 650475875+6984989+889796854
191. 74678432+7465374+847963459
192. 7660342+974376457+83085768
193. 794217476+6964307+954307
194. 66276454+367796709+6719187+577485S55
195. 576450079+94196376+65438+560898275
196. 57874089+4786774+875697897+965665
197. 789894607+6546754+73836454287948
198. 6798954+452679687+7665+777423749
199. 56884569+677958888+3735894+469962
200. 7847976+46964624+74548935+3856907
201. 7692762+79764276+736577423 + 4798234
?02.
203.
204.
205.
206.
213.
214.
215.
216.
217.
218.
222.
223.
224.
225.
226.
2:27.
228.
229.
230.
231. Fifty
232. Si.\ty
233. Five
units, uiiie
234. Sev
teeu units.
235. Foil
thousnud ai
236. Eig
eight, two 1
237. Fou
s^iven huudi
238. Thii
six hundred
ADDITION.
78;54254+086«7637^+54476+77664986r
/ 808+8867666644-834251+977407307
796487825+4754954+92236+47623564'>
452376824+1364795+898987885+856676
746834232+988978345+75576+89452372
^i"f*+^^7976469+89547978+97997807
96577+476784896+7929654+856934701
70542+653476+764589985+579698794
97334+989296857-^97576854+32677496
^o^J«fe^+^^^^^*'^^+3«"576376+489236579
78476854+5995876+889689+979375487
4809675+307685494 + 96972+807574676
475879+674275827+7454+3976798
«^i?i?^^^+^^'^S^ + ^57684754+9767896984.76i5.;
676401888+765465854+654754976+i89894±j8j? 7 . 7
507427+834236454+766687935+94879+476372'tH4
75685378+837456+24359876 + 507876934+89^432
*.l^^?i-/'^^^^^«+«»''76+876247689+797685764
'^f^?I«^50+56437+874954653 + 6788K2+4976569
476850+79643279 + 898767984^ 87678797+7709 47^ ^08 156
95673987+549637709+34907+9871036L+q87%7J?3?8g^
Kxpress (he rollowinir numbers aiul flnu their finni :
^ T'^'^t" ""'''' "'»«^yfi^« "«»■<*. seventy-eightunrts.
.3-. Sixty-three unit,, eighty-nine units., seventy-seven u„i/,.
-33 Five hundred and sixty-five units, four hundred and thirtv-six
units, nine hundred and eighty-five units. ^
teen LS"" '"'""""'"""'"•""" ""■^*' "'"^^^^^ "-■^'. »"-
235. Four thousand and nine, sixteen thousand and fifty-four three
thousand and one. ten thousand and thirty-three
.if ^^'f*!l""f '''/"'* thirty-aiue. three h mdred and twenty-
eight, two hundred and eighty-three, . ^
237 Four hundred and stventyuine, eight hundred and fifty-six
soven hundred and nineteen. •' '
• ^f ■ J^?*''^ *^°"''"^ ''°"'" ^""^''^^ «»d eleven, sixty-one thousand
8.x hundred and sixteen, three hundred and seventy-eight!
11
?02.
203.
204.
205.
206.
207.
208.
209.'
210.
^12.
213.
214.
215.
216.
217.
218.
219.
220.
221.
222.
223.
224.
225.
226.
227.
228.
229.
230.
/
i/
ii!
WA
12
ADDITION.
239. Thirty thousnnd and ninety-six, seventy-eight thouHand and
seven, eighteen thousnnd six hundred and nine, twenty-two thousand
nine hundred and seventy.
240. Five hundred and ten, eighteen hundred and forty-four, three
thousand eight hundred and ninety-five, six hundred and three, one
thousand and thirty-three, nine hundred and ninety-on».
241. Fifteen thousand three hundred and nineteen, eleven hundred
and seventy-six, seven hundred and two, three hundred and thirty-five,
thirteen hundred and fourteen.
242. Eight hundred and sixty-three thousand four hundred and fifty-
five, three hundred and eighty tliousand four hundred and sixty-weven,
nine hundred and three v.housund six hundred and eighty-two, one
hundred and forty six thousand three hundred and seventy.
Oral Exrirciaes In Numeration and Addition.
243. How many tens in 1783 units ?
244. How mflny hundreds in 18860 ?
245. How many ten thousands in 52465346 ?
246. What order of units represents : 1°
3" hundred-thousands ?
247. What order of units represents : 1° ten-thoui
3' ten-millions ?
248. How many zeros to the right of a hgtire representing
2' thousands, 3° hundreds, 4° millions ?
249. In what order and period are : 1' tens, 2* hundred-millions,
30 thousands, 4" ten-thousands, 5" millions, 6" ten-millions, 7"
huntlreds ?
250. What is the sum of: 1.— 4-f6+5 ; 2.-3+7+9; 8.— 10+6+
4 ; 4._8+l3+6 ; 5.-12+10+9 ; 6.-15+7+14 ; 7.-16+12+9 ?
251. ^Vhatis the sum of: 1.— 11+6+7 ; 2.— 10+8+6+7 ; 3.-34+
25 ; 4.-35+52 ; 5.— 40+30+6 ; 6.— 46+31 ; 7.-34+25+8 ?
252. What is the sum of: 1.— 19 + 12-1-8 ; 2.-72+60+4 j 3.-48+
10+30 ; 4.— 13+254 7 ; 5.-29+24+30 ; 6.-33+28+7+35 ?
253. What is the sum of: 1.-64+40+9 ; 2.— 29+17+12 ; 3.-7+
37+26 ; 4.— 14+394-4 ; 5.-48+31+9 ; 6.— 56+41+10 ; 7.-75+60+
22?
254. What change is made in the sum of several numbers : 1. When
one of the numbers is increased ; 2. When one of the numbers is
diminished ?
255. What change is made in the sum of several numbers : 1. When one
of the numbers is omitted ; 2. When one of the numbei-s is doubled ?
tens, 2<=
•lids.
simple units,
2" hundreds,
1» tens,
I
Note,
Thus, th(
dollars.
being sep
$25.36 is
In wri
together,
the colui
there be
zeros.
256. Hei
257. A p
age?
258. Wh
259. Cha
i. years ; in w
I 260. Ji'li
I 261. Mos
|of 120 years
262. A b(
other ; how
263. The
their sum ?
264. One
both receive
265. A ba
Tuesday; he
266. A ba
uring a spc(
267. In a
ing ; how mt
268. How
n class ?
269. What
through one ]
270. Henr
lore; how lu
%
M
thouiiand and
y-Uro thousand
"orty-four, three
and three, one
eleven hundred
and thirty-five,
iidred and fifiy-
ind sixty-seven,
ighty-two, one
lion.
' simple units,
}, 2' hundreds,
nting : 1° tens,
ndred-milHons,
jn-raillious, 7"
9; 3.— 10+«+
16+12-1-9?
-6+7; 3.— 34+
25+8?
iO+4; 3.-48+
7+35 ?
7+12 ; 3.-7+
0; 7.-75+60+
iberg: 1. When
the numbers is
rs : 1. When one
s is doubled 1
ADPITIOV.
PRACTICAL PROBLEMS.
13
i -ru : ''^° ^' ""''""^ ^'^■■« * ""•"^"'- Signifies dollar..
) Ihus. the expression $120 is read one hundred and twnit,,
I dollars. Dollars and cents may be written together, the cents
I bemgseparated from the dollars by a point, thus, the expression
. S-5.36 IS read twenty-fice dollars and thirt>,.six cents.
I In writing sums containing dollars and cents to be added
I ogether, care must be taken that the cents be written under
I he cohimn of cents and the dollars under dollars ; should
, there be no cents in any amount, they are replaced by two
■ zeros. ' ■^
256. Henry is twelve years old ; hcv old will he be ,n 27 yoars?A
^^^257. A person was bom in 1792 ; ,„ wbat yey will he be 50 years of
258. What number is formed by adding 15 to 57 ?
259. Champlain was born .„ 1570, his career covered t'.e space of 65
., years ; in what year did he die ?
j 260. Jvlius was bom in 1808 ; .„ what year was he 27 years old ?
I 261. Moses was bo n 2373 year, a'-r the ci^afon, he died at the ««.
I of 120 years, in what year did he die ? ^
I 262. A bookbinder delivered 75 volumes at one time and 149 at an-
I other ; how many volumes did he deliver in all '
ithrsul'f '"""'' '"° """'"^ •'^ ''' '''' '""^ g'*"*^^ 362 ; what i,
ibothtc^:::r'"" ^"^ ''' ^"' ^^« ^^'^^^^^^ »>- -^h do they
265. A baker receives 20 barrels or flour on Monday and 18 barrels on
Tuesday ; how many did he receive on both days f ■/
266. A baker left 45 loaves of bread during one trip and 19 loave,
iunng a second trip, how many loaves did he deliver ?
267. In a battle 8945 cartridges were fired, there are 12450 remain
png ; how many were there before the battle »
In !£sf ""^ """^ ^"^"' '" " '^'^' '^'' "' *^««»* «">«» the« are 29 .till
I 269 What is the capaaity of a tun which is to receive 45 gallon,
■thronsrh onA niru» anA QIC *i u _„QiL . ganom
270. Henry placed §12.50 in a bank
uore ; how miiuh has he in bank ?
at one time, then $17.60
14
ADDITIOW.
^271. What is the amount of a bill of $5.25 for sugar and 80 centi for
preserves !
272. How long did it take a man to clear a piece of land knowing
that a first time he worked 75 dnys and a second time 49 days.
273. James received $42 from his father and $19 from his mother ;
how much has he 1
274. What is the length of a piece of cloth, if after selling 45 yards
there remain 27 yards ?
275. A merchant bought goods for $164, for how much must he sell
them to gain $24 >.
276. A person bought a house for $15160, he spent $1575 in
reparations ; fo. how much should he sell it to gain $2t)00 ?
277. Peter spent $123 and has remaining $20 more than he spent ;
h' .V much has he now f How much had he at first ?
278. A merchant made three sales during the day : the first was of $45,
the second $65 and the -third $97 ; what did he receive ?
279. $24 w«re taken from a drawer containing money, then $45, and
there remain $79 ; how much money was in the drawer ?
280. In an orchard there are 395 apple-trees, 247 plum-trees and 197
pear-treris ; how many trees in all ?
281. A servant spent $18 for provisions and $23 for wood ; what was
the amount spent ?
282. After paying a debt of $845 ; 1 have $179 remaining; how much
hSl?
283. On a certain number of oranges 1 ate 27 and have remaining 15
more than I ate ; how many had I at first ?
284. A man cut down in a forest, 445 maple-trees, 514 ash-trees, 423
cherry-trees and 536 pine-trees ; how many trees were hewed down ?
285. A family's expenses for a day were : for milk 8 cents, bread
32 cents, meat 28 cents, vegetables 15 cents, cofTee 10 cents, tea 6 cents
and sugar 12 cents. What were the total expenses ?
286. What is the weight of four oxen, the first of which weighs 860
pounds, the second 1082, the third 1238 and the fourth 1148 ?
287. A person bought furniture for $225, linen for $187.50, cloth
for $168.00 and provisions for $288. How much did he spend ?
288. How many men in a regiment of four batallions : the first of
which comprises 1209 men, the second 1075, the third 976 and the fourth
987?
289. A grocer received 4 boxes of soap : the first weighed 250 poundi
the second 150, the third 294 and the fpurtb 214. What was the weigh!
of the soap received ?
290. Ow
: llaminl of
J for $1.15,
■ How much
" 291. A
I $1.75 n da]
I 90 cents nii
it nil for a da
i 292. Wfi
J ],J5 yii lions
I 293, WIi
for $405.50,
294. A II
of pants, $1
ihe s))eiul ?
295. Onii
liorses, 105
296. Inv
ilied at the i
297. At tl
ye are now i
298. To I
>ank note of
lents. How
299. Hai
low much di
300. Whai
owing sums
197.60, and 1
301. A per
mount of $
lined $540.;
302. A mei
85.76 from
ount of 1
fore?
303. A ma
960.75 for
tiaritable pur
804. A coi
AnniTioK.
IS
of land knowing
9 days.
from his mother ;
selling 45 yards
inch must he sell
spent $1576 in
00?
than he spent ;
and 80 cent, for 290. Owen bought « Grammar for 35 cents, a Geography for r.5 cents „
• or r 5 ^'"'»»-^-/- accents, an Algebra for 4o'ce'ts. a gZ 'ry
I hL '. "" tr'*'^'"«^° f" ^5 ""'«. " History of Canada for 30 cents '^
1 How much did he spend ? ^ • ov ecu is.
I $1^ a davTr ^"' 'Z. T" ''"' '" ''"'' "' '^"«^^ = to tf'^ ft«t
'oft ? , '"""'^ ^'•°'^' ''^ t'^^ ^hird, 81.20; to the fourth WL
I In ;::r ::^r "" ''''-''''' '' ""^- "°^ ^-^ ^- "« p^^^^^-
I 292. What is the capacit, of four casks of wine, if the first contains .
I h,5 gnllons. the second 135. the third 120 and the fourth 90 ?
Ifo.'L'o^'Io'!.""" Tl^ ^'"^ '"'■ ^°"' "°**"'= ♦''•-• fir^t of which is
I of ? • "'' TL^ *"'■'"• ''»« ^''"•d S576 and the fourth §179.:5? "
, r^r * '' '"'. " '"'• ^'' ''' "» °^'^'-"t' «^^ 25 for a pair
i. al.75 fnr » rano an.) CK ra c .. __ ■ .,
i.e first wasof J(45,
I?
ey, then $45, and
lum-trees and 197
wood ; what was
ining ; how much
lave remaining 15
514 ash-trees, 423
hewed down ?
: 8 cents, bread
cents, tea 6 cents
which weighs 860
ii 1148 ■(
"or $137.50, cloth
le spend ?
lions : the first oil
J76 and the fourth
lighed 250 poutflA
liat was the weigh^
How much did
f , 4 £,, _ V - -- ■- , v»u lui iiii overcoai
|ol pants, $1.75 for a cane and $6.50 for a pair of boots
|he si)end ?
%^ mZ^'^H ''" "'"' "'' V'' ^'"''' ''' ^"^^"' ''' o«". 86 /
^lorses, 106 pigs. How many animals were soltl ?
296 In what year before Christ was Alexander the Great born, if he
pied at the age of 32 yeai-s, in the year 324 before Christ ? ^
-^ 297. At the birth of Our Lord the world had been created 4004 years ^
298. To p,iy for a certain quantity of merchandise, I have given a.
Nuts. How much did the goods cost ? v^
I ^^^" ?!i^!!'f '''*"^''* * """*«' ^"'" «^<>' » "Change it for a horsTv.
rirt^^ ' ^I '" '^^ '"''''' '' ' «'- ««5 -«h besides 1 '^
I 300. What sum does it require to pay 5 clerks who have earned the fol
I ^"^-Z r.T.L^?^''' * **'"'' ^"^ *"50 ; he made r.parations to the
'rd"$6to.'3o?-''- '-' ''^ -'-' ''' '^ -" ^^' ^"-^"« t.;:tt
302 A merchant wishing tc purchase some cheap goods, borrows
385.76 from one of his. friends, $76.95 from another one ; wha was 1
nou^nt of his purchase, knowing that he had .^47.35 in his pocket
Sflfio'rf r\!:"^' ^^ T'"'"' *^''*^ ^'' »'»« education of youth.
8960.75 for the poor. $960.80 to the church. $7,506 for other
Imntable purposes ; what is the amount of these legacies ?
1804. A contractor baa received for tne construction of a school :
>«
ADDITION .
\i
I
l" 13643, 2^ $3529, ;" $2675; he has still to receive $1,0825. What
#«l the price of the contract?
30^ An army composed of 6875 m ;i received 3 re-enforcemeuts : the
first of 1680 men ; the second, 1500 men, and the third, 2050. What
is the total number of the army at present 1
T306. A person will be 40 years old in 1894. What age shall his
father have who is 30 years older than he i& '
807. What is the total length of 4 streets which are : the first 342
yards long, the second 1425 yards, the third 718 yards, and the fourth
866 yards ?
308. A shoe factory turns out the following work during a week : On
Monday 178 pairs, Tuesday 205 pairs, Wednesday 217 pairs, Thursday
245 pairs, Friday 256 pairs, Saturday 262 pairs. How many pairs were
made during the week ?
309. The number of pupils attending the schools of the Brothers of
the Christian Schools, on the 31st of December 1892, was: in Europe,
253280 ; in Asia, 6879 ; in Africa, 4586 ; m America, 40735. Find
ho^rmauy pupils in all ?
310. The population of Bonaventure county is 18908 ; that of Gasp*
county, 25001 ; that of Rimouski county, 33791 ; that of Temiscouala
county, 25484 and that of Kamouraska county, 22181. What is the
population of these five counties ?
311. A woman currying eggs to the market, bi-eaks 36 of them, she
sells 120 on her way, gives 8 to the poor, and when she arrived had
665 remaining. How many eggs had she when she left home ?
312. What is the revenue of a man who spends $160 for food, $120
for rent, $125 for clothing, $34 for sundry items ; he gives $12.38 to the
poor, and has $150.62 remaining ?
313. I bought 647 yards of cloth for $2375.40 ; 765 yards of linen
for $1036.25 ; 86 yards of ribbon for $126.30, aud 30 yards of calico for
$12. How many yards of goods did I buy and what did all uoit ?
314. A workman received $60, another received $20 mor'. thin i«
first and a third as much as the two others. What did ear'. ' ■ .o 't^ .
815. If 1 could get $41.10, I would want only $2.10 MOio to donble|
my money. How much have I i
"f^^^
30. Sut
tekon from
The roaui
31. Sunt
J If 37 w«
IpcprossuJ b
4 fmm
|0 froni
I 1 1
1 fron
21
lo from
31
? from
41
from
51
'0 from
61
|0 from
71
40 from
8 1(
from
9 1.
1 from
11(
1 from
2 If
1 from
3 1e
1 from
4 1<>
1 from
5 1p
1 from
6 1e
i from
71e
from
8 1e
from
9 1e,-
from
Oier
from
2 1m
from
3 lea
from
4 1m
from
6 lea
from
6 lea
from
7 lea
from
Blea
from
Hea
from 10 leai
from 11 leai
g $10825. A^'hat
SULTnACTION,
17
iforcemcuts : the
rd, 2050. What
SUHTKACTIOX.
.hat age .hall his ^^O. Subtraction is . process by which one number is
.... .he first 342 ^ ^JZh:^^^^''' '''''''''' ^^'^''^
is, and the fourth J ,'''"'' "' '^'' subtraction is called the difference.
J 3^SuuMaction is expressed by the sign-, read minus.
ring a week: On ^" ^' '''''^ to betaken from 78, the operation would be
pairs. Thursday l^pios.sed by writing: 78 —37,
.itanir nnira ivnrtt
many pairs were
of the Brothers of
was : in Europe,
a, 40735. Find
Subtraction Table.
8 ; that of Gaspe
at of Temiscouata
)l. What is the
s 36 of them, she
1 she arrived had
t home ?
150 for food, $120
ives 112.38 to the
^55 yards of lincu
yards of calico for
lall .o;t?
^20 moi'. thin the
ear", n :.' ieotivii '
10 hioiii to double
flODl
from
from
from
from
from
|0 from
|0 from
40 from
.0 from
-4
leaves
1 lenvbs 1
2 leaves 2
3 leaves 3
4 leaves 4
6 lenvi's 5
6 leaves 6
7 leaves 7
8 leaves 8
9 leavt's 9
4 from
4 lioin
4 from
4 from
4 from
4 from
4 from
4 from
4 from
4 from
4 leave
5 leave
6 leave
7 leave
8 leave
9 leave
10 leave
11 leave
12 leave
13 leave
1
2
3
4
5
6
7
8
9
1 leaves
2 leaves 1
3 leaves 2
4 leaves 3
5 leaves 4
6 leaves 5
7 leaves 6
8 leaves 7
9 leivt'S 8
'eaves 9
2 leave
3 leave
4 leave
6 leave
6 leave
7 leave
8 leave
'om 9 leave 7
rom 10 leave 8
rem 11 leave 9 | 6 from
6 fiom
6 from
6 from
6 from
6 leave
7 leave
8 leave
9 leave
6 from 10 leave
6 from 11 leave
6 fiom 12 leave 6
6 from ]3 le.ive 7
6 from 14 leave 8
15 leave 9
8 from 8 leave
8 from 9 leave 1
8 from 10 leave 2
8 from 11 leave 3
8 from 12 leave 4
8 from 13 leave 5
8 from 14 leave 6
8 from 15 leave 7
8 from 16 leave 8
8 fr, m 17 leave 9
9 from 9 leave
9 from 10 leave I
9 from 1 1 leave 2
9 from 12 leave 3
9 from 13 leave 4
9 from 14 leave 5
9 from 15 leave 6
9 from 16 leave 7
9 from 17 leave 8
9 from 18 leave 9
10 from 10 leave
10 from 11 leave 1
10 from 12 leave 2
10 from 13 leave 3
10 from 14 leave 4
10 ♦rom 15 leave 5
10 irom le leave 6
10 from 17 leave 7
10 from 18 leave 8
10 from 19 leave 9
10
i!i
»;l!(fll!
3 from
8 from
3 from
from
from
from
from
3 leave
4 leave
f) leave
6 leave
7 leave
8 leave
9 leave
from 10 leave
from 11 leave
3 from 12 leave
8UBTBACTI0N.
from 7 leave
from 3 leave
from 9 leave
from 10 leave
from 11 leave
from 12 leave
from 13 leave
from 14 leave
from 15 leave
from 16 leave
The preceding
table should be
mastered t h o -
roughly before
taking up the ex-
ercises in sub-
traction.
OPr.UATION.
4795
3582
1213
PROBLEMS.
32. Case I.— To subtract ichen no term of the smalJ't
number is greater than the corresponding term of the laryn
number.
Ex. : Subtract 3582 from 4795.
Solution: Write the smaller number or suUralieitd under tli
larger one or minuend, placing the terms of the same order in the saiiij
oolurau, and( begin at the right to subtract. 2 units
from 5 units leave 3 units, which is written under the
units ; 8 tens from 9 tens leave 1 ten, which is written
under the tens ; 5 hundreds from 7 hundreds leave 2
hundreds, which is written under the hundreds ; 3
thousands from 4 thousands leave 1 thousand. There-
lore the difference is 1213.
33. Case II. — To subtract when one or more terms of tk
smaller number is greater than the corresponding terms < |
the larger number.
Ex. : Subtract 3867 from 45073.
Solution : Write the subtrahend under the minuend, and begin
the right to subtract.
7 units cannot be taken from 3 units, therefore add
10 units to the 3 units, making 13 units, 7 units from
13 units leave 6 units, now since 10 units or 1 ten were
added to the minuend the remainder will be 10 units or
1 ten too large ; hence to obtain the correct remainder add
1 ten to the subtrahend, 6 tens plus 1 ten are 7 tens ;
7 tens from 7 tens leave tens. 8 hundreds cannot be
taken from ; therefore add 1 hundreds to the minuend ; 8 hundrcl
from 10 hundreds leave 2 ; now since 10 hundreds or 1 thousand wf
added to the minuend the remainder will be 1 thousand too large ; henci|
thousand must be added to the subtrahend. 8 thousands and 1 thousa;^
Operation
45073
3867
412U6
ire 4 thou^
phere are ii
thousands
34. No
7 from
1 and 6
8 from
1 and 3
from
35. Ru
mtmber ph
i-ind draw i
//. Ben
\iiimber f\
fcriting the
III If
torrespond
md then s\
IV. Adi
yroceed as
An$
Ana,
SUBTKACTIOV.
19
The preceding
ible should be
lastered t h o -
nighly before
iking up thf ex-
rcises in sub-
raction.
% of the small t
\rm of the largn
trahend under tli
;e order in the saiii-
lits
OPnilATION.
4795
3582
1213
the
ten
-e2
; 3
sre-
lore terms of th
ponding terms
lucnd, and begin .
Operation
45073
8867
41206
add
rom
vere
I or
add
ns ;
the
inuend ; 8 hundrc|
or 1 thousand wtj
d too large ; henal
nds and 1 thousa
Ire 4 thousands ; 4 thousands from 5 thousands leave 1 thousand. As
^here are no ten-thousands to take from 4 ten-thousands, write 4 ten-
^liousands Tlicrefore tiie difference is 41206.
34. Note :— Iq practiou the procesi* is as follows :
I 7 from 13 leave 6 and carry 1
1 "'"I 6 7 7 from 7 leave
8 from 10 leave 2 and carry 1
1 a»*l 3 4 4 from 5 leave 1
from 4 ler.ves 4.
35. Rule :— /. Write the smaller number under the larger
humhcr placing the terms of the same order in the same column
tind draw a line beneath.
II. Begin at the right and subtract each term of the smaller
\iumher from the corresponding term of the larger number,
writing the remainder beneath.
Ill If any term of the smaller number is greater than the
corresponding term of the larger nvmber, add 10 to the latter
md then subtract.
IV. Add 1 to the next term of the smaller number and
proceed as before.
Examples for Practice.
NO
Ml.
42.
149.
150.
151.
152.
153.
154.
Ans.
729
417
925
619
Ans,
454565
7347
A71S.
748-534
969-733
767-548
451-323
855-548
745-254
617-429
343.
344.
345.
356.
357.
358.
3.09.
360.
361.
362.
454565
7347
1346.
Ans.
487654
298047
Ans.
454500166
8893287
Ans.
347. 542600741
66725746
780705
90877
Ans
An>
348. 274000300
92129405
Ans.
749-573
683-494
698 - 299
784-395
400-245
800-501
545-484
363.
364.
365.
36(J.
367.
368.
369.
476-297
754-264
745-359
976-495
874-199
741-174
842-376
./
hi;"
ll'll
iHiii \
20
SUBTHACTION
370.
476 —
287
399.
769 400 007
371.
426 542 —
179 127
400.1* 879 766 833
372.
457 421 —
178 175
401.
705 454 377
373.
847 457 —
457 424
402.
879 457 651
374.
375 147 —
196 078
403.
457 893 453
375.
455 310 —
8 474
404.
104 007 852
376.
459 435 —
88 578
405.
678 476 501
377.
547 422 —
268 657
406.
405 234 542
378.
256 456 —
74 179
407.
587 847 007
379.
789 852 —
49 776
408.
657 462 024
380,
458 075 —
75 497
409.
867 491 234
381.
357 117 —
87 779
410.^/
645 479 846
382.
134 207 —
70 709
411.
875 674 745
383.
740 070 —
471 097
412.
745 874 320
384.
870 050 —
757 147
413.
874 807 790
385.
357 074 —
196 407
414.
997 007 001
386.
645 444 —
452 079
415.
847 653 454
387.
704 555 —
375 697
416.
546 807 575
388.
455 606 —
375 697
417.
956 753 764
389.
359 854 —
204 905
418.
950 076 074
390.
897 954 —
541 378
419.
477 275 759
391.
654 087 —
87 659
420.
876 007 064
392.
854 087 —
98 498
421.
564 079 768
393.
256 895 454 —
4 947 872
422.
400 076 646
394.
754 674 790 —
64 834 799
423.
460 007 646
395.
764 675 790 —
275 987 899
424.
650 079 059
396.
461 900 797 —
7 191 989
425.
837 040 064
397.
810 847 066 —
614 896 874
426.
974 600 700
898.
418 030 450 —
27 740 761
427.
846 977 606
71 900 747
19 837 692
7 792 19S
97 780 07S
9 594 327
72 876 194
89 497 354
53 912 47f
94 958 09S
79 834 01 ,-
91 374 92:
493 791. 7!*;
94 789 82:i
97 905 4,s:)
65 910 o-i:
45 124 37;
74 375 57u
277 451 79),
678 404 951
475 207 Ui
298 345 84;'
798 435 49;.
285 187 g?*)
93 457 89;
40 079 452
479 084 764
4 134 66;
93 236 94r
7 884 m
Ex|»i . MH in flKares and anbtraet the ftollowlny nnmben i
428. Fiud the difference between four hundred and sixty-six and throi
hundred and fifty.
429. Diminish eight hundred and ninety-six by fifty-five.
430. How much greater is seventy-five thousand eight hundred anc
lorty-three than sixty-seven thousand and nine ?
431. Find the remainder when two hundred and sixty-nine thousand
seven hundred and fifty-seven is diminished by one hundred and thirteei
thousand and twenty. ^
432. Subtract one million seventy-eight thousand nine hundred aJ
three from nine million three hundred and twenty-seven thousand sii
hundred and eighty-one.
433. What remains if three hundred and two be diminished by sevci
hundred and fifty-eight ?
434. From two million five hundred aud uiuety-l wo thousand cigbij
\ hundred
I hundred t
I 435. T(
I thousand
I *36. H
1 six than r
I 437. W
f and one m
f 438. H«
I seven thoi
I 439. Fi
i thousand
thirty-sev<
440. I
441. I
442. (
443. (
444. (
446. (
446. (
447. (
448. (
449. (
450. All
ttwcd him ?
451. w:
452. A i
ell knowin.
453. Fin(
454. On I
455. The
eater.
466. A bi
if there still
457. Ap€
lie still owe
SUBTRACTION.
21
007 —
71 900 747
833 —
19 837 692
377 —
7 792 19-
651 —
97 780 07f'
453 —
9 594 32?
852 —
72 876 HH
501 —
89 497 354
542 —
53 912 47('
007 —
94 958 09.^
024 —
79 834 01 .■
234 —
91 374 92:
846 —
493 791,7!';
745 —
94 789 82?
320 —
97 905 4S:i
790 —
65 910 o-j;
001 —
45 124 3-i
454 —
74 375 5/1
575 —
277 451 79i
764 —
678 404 95)
074 —
475 207 45)
759 —
298 345 84:'
054 —
798 435 49;,
758 —
285 187 97*i
546 —
93 457 89;
546 —
40 079 452
059 —
479 084 764
054 —
4 134 56;
700 —
93 235 94;
606 —
7 884 m
Inv nnmben t
I sixty-
sixandthrcf '
ty-five.
1
. eight hundred anc
lixty-nine thousaiiii i
andred aud thirteei |
i nine :
hundred ancl
■seven i
thousand aiiM
minished by sevoS
I wo thousand ci<'liil
^tdtda:/twl^:^"^ '-'- ''- '-'-' -^ --^ ^^--^ three
thot'and'tdtTo.*'"^"' '^ '""^^••^' ^"^ seventeen fro. fourteen
six'than"n1n 7"^ T"^ '' "^°'*y-°"' *'^°"'«'"^ three hundred and
.S w^ ! "? / ""'^ '°' '''""^""^ «'^ J^""dred and two ?
437. What ,8 the difference between nine hundred thousand and twc
and one milhon nme hundred and fifty thousand and twenty-eight »
L^^'J^"^ T. u" f'"''^-'"'^ ''^""^'^'^^ ^"^ t^« «^«««d seventy-
I seven thousand two hundred and two ?
439. Find the difference between one hundred and one million ten
hn °":,'"°'^f/"^ «-.-<! nine million seven hundred at;
I thirty-seven thousand three hundred and fifty-one ?
Exercise, in Addition and Sabtractlon.
440. (1207+352) — 1548.
441. (2713+1065) — 2466.
442. (21672+67023)— 80471.
443. (87641— 72320)+4537.
444. (112796— 10683)+97042.
445. (71889+13562)-75262.
446. (87003— 27509)+23709.
447. (4603+705+3518)-6034.
448. (7323+687+9346) - (812+5006).
449. (4503 - 706) — (8003 - 7125).
PBACTICAL PROBLEMS.
How much more is^
450. A laborer earned $76 ; he has received $55.
|owtd him ?
451. What number must be added to 67 to make it 201 ?
452. A gardener had 345 melons in his waggon ; how many did he
ell knowing he has 79 remaining? ^
Ta' n""^ k!;^ "."^^'' ''"** '""'* ^' ''^^''^ *° 138 to make it 450 ?
454. On a bill of $4217 a man p»ys $427. Find the balance due.
455. The sum ot two numbers is 1052 ; the smaller is 358. Find the
t'ttTr!"''V"'V*^'''' '^'''" n^ucl^ has it been diminished
in^TS atiii fciuain due $4278 ?
person owing a sum of $16384, paid $
lie still ow« f
how much does
• / '/
>
::l
23
BUBTBACTION.
i; ilii
I
Mllll
ii!
liii
458. A person after travelling 9 days, ends his journey 6a the 24th of
the month. On what date did he start ?
469. A woman goes to market with $14.30 and returns with $6.75 ;
How much did phe spend ?
460. Two men working together perform 427 yards of work ; if one
has done 174 yards, how mmiy did the second do '(
461. I had ,$628.75. I bought a farm for $410.90 ; how much money
have I left ?
462. A scholar has 345 lines to recite ; he knows 257. How many
more must he learn ?
463. Having $2128.25, I intend to buy a house worth $3000 ; how
much more do I rer[uire to pny for it ?
464. A voyage is to last 87 days ; how many days is it begun if there
are 49 days more to travel ?
1(r466. The age of a father and his son together is 127 years. The father
iS/83 years old, how old is the son ?
466. A prisoner is in for 270 days ; he has served 187 days. How
many more days must he pass in prison ?
467. The first Crusade was in 1096, and the seventh and last ended in
1270. How many yeais did these expeditions last?
468. A merchant bought cloth for $6364. He sold part of it for
$3977.40. Find the value of the remainder ?
469. Columbus was 51 years old when he discovered America in 1492 ;
in what year was he born ?
470. A grocer sold sugar for $870.45 and by so doing gained $75.60.
What did the sugar cost him ?
471. Potatoes were introduced into Europe in 1586, and coffee in 1644.
For how many years were potatoes in use when coffee was introduced ?
472. I want $420.45 to be able to pay a debt of $746.20. How much
have I ?
473. An army numbering 40300 men lost 7850 in a campaign. How-
many men are left ?
PROBLEMS IN ADDITION AND SUBTRACTION.
474. Find the total weight of 6 waggons, weighing respectively : 4524
pounds, 9425, 7217, 3425, 2027, and 1875 ?
475. Charlemagne ascended the throne in 768 and died in 814. His
son Louis, ascended the throne on his father's death and died in 840.
Which of the two sovereigns reigned the lon/crw '
476. A
nesdny $]
$17429,0;
477. A
478. C(
ninny yea
479. Ill
62446. ]
480. W
I bureau wo
J 481. A
lowe?
I 482. Pa
I Andrew tl
I 483. Tv
Jthe shai-e (
I 484. M(
|63090 and
I 485. Th
iliabitants
|l 488535?
I 486. Ha
iK^'ods cost
I 487. A (
^till owe ?
483. A h
luch must
489. A I
55400 to r
»oor. Fim
490. I be
:ain?
491. Fine
492. A m
'ards, 85 yt
493. The
father is 92 ;
494. Thei
09078 in P
495. A w
|n<i 608 pagt
rney 6a the 24 th of
eturns with $6.75 ;
ds of work ; if one
how much money
? 257. How many
worth $3000 ; how
is it begun if there
years. The father
d 187 days. How
k and last ended in
sold part of it for
America in 1492 ;
ing gained $75.60.
and coffee in 1644.
pvas introduced ?
1.20. How much
i campaign. How
TRACTION.
•espectively : 4524
died in 814. His
ii and died in 840.
SUBTRACTION. 23
476. A banker received on Monday $2426. Tue&dav «472S ii Wo^
$1/ 429.07 ; how much did he receive during the week » ^
I 477. A farmer had 345 sheep. Haviui? s..lH 9io j, . .
17a n». * «avuig sold J49 how manv remain t
478. Cannons were invented in 1346. and guns in 1430 ^orhoJ
many year, are each of these pieces of ordinance if „se? "
Liul' I a!. *'•' P^'P"'"*'"" «f Quebec was 59699; i„ 1881 it was
'80 w!!l "•"■"" •'f P«P"l«t-» for that decade ;f year
480. What sum is owed a .abinet-maker for a desk worth S!?^ 'in .
[bureau worth $48.25 and a table worth $7 ? * ' *
JSl. A man owes $4567 and pays $3789.65; how much does he still
uZJZt^r-'"' ""^^^^ '''''■''-' ^- -eh mo. has
ih:iJ:;i^::s^^" - ''-'' -'''''' ' '^- ''-^^^^^^- ^i-^
I 484. Montreal has a population of 220650. Toronto 18190ft n u
|63090and Ottawa 44154 F,„H rJ,. i. ^""o^to 181220. Quebec
I 48R Tl.a V *"'«tlie population of tliese four cities?
J 485. The population of Ontario is 2114321 • hn,„ "^ ""<'8 f
|.ubitants has it than the Province of Outh ' 7 """"^ """^ ''^•
|l488535 ? province of Quebec, whose population is
486. Having sold goods for $8795, 1 mined «17i «i u . j-. .
foods cost me ? *«'•'. i gained $374.84 ; what did the
487. A debtor who owes $7887.75 nava SSaos o*: . v.
i|till owe ? * o'./o pays $995.95 ; how much does he
»or. Fiud the sh»te of the poor ? ^"""" "'" "-"■"'ler to the
m. I hough. . vm. !„ nsm ^^ „« u fo. nm,. wh.. i, „,
«5. A work comprir ,i " , ' " '"" "'"'™"™ '" P»P"'«"'» '
M 50, ^ .. h.„L„; ;.';::- r'rs:? '''- "'• '"-
24
MULTIPLICATION.
i! i
496. A father dying bequeaths his fortune to his three sons as follows :
to the eldest he gives $15750 ; to the second, $13800 and to the youngest
$11760. What was his fortune ?
497. In a Ist class there are 38 jiupils ; in the 2nd, 65 ; in the 3rd,
78 ; in the 4th, 85 ; and in the 5th, 95. How many pupils attend the
school ?
498. I had $14.20 ; I bought a hat for $3.35, and a pair of boots for
$5 40. The remainder I gave for a prayer book. Required the cost of
the book ?
499. Louis has $18930 ; how much has John knov/ing his sum to be
greater than Louis' by $5980 ?
500. I owe my butcher $29.44; my baker $18.75 ; my shoemaker,
$33.10 ; my tailor, $67.18 ; my milAmau, $12.30 and my grocer $47.36.
How much do I want to cover my expenses knowing that 1 have only
$180.85 ?
501. A merchant has 18547 yds of calico ; he sold at different times
760 yds., 200 yds., 567 yds., and 125 yds. How many yards remain 1
502. A fartaer has three pieces of land which yielded 4500 bushels of
oats. The first yielded 1333 bushels and the second 1428. How many
bushels did the third yield 1
503. A workman should receive $45.75 for 5 weeks' steady work, but
$8.95 were deducted for time lost. How much did he receive ?
604. A servant spent $1.25 for linen, 90 cents for butter, 60 cents for
cheese, $1.05 for vegetables and $2.35 for sugar. How much must she
return to her master on $6 65 ?
To in
written :
1 timt
1 time
I time
1 time
1 time
1 time
1 time
1 time
1 time
1 time
2
2
2
2
2
2
2
time!
times
time!
times
time!"
time.«
times
2 times
2 times
2 times
III
ee sons as follows :
ad to the youngest
iJ, 65 ; in the 3rd,
' pupils attend the
a pair of boots for
equired the cost of
iving his sunt to be
5 ; my shoemaker,
my grocer $47.36.
ig that 1 have only
1 at different times
ly yards remain ?
led 4500 bushels of
1428. How many
s' steady work, but
receive ?
3Utter, 60 cents for
w much must she
HULTIPLICATION.
MULTIPLICATION.
25
36 Multiplication is the process of taking one number,
called multiplicand, as mmy times as there are units in
another, called multiplier.
The Product is the result obtained by the multiplication,
rhe Multiplicand is the number to be multiplied : the
Multiplier, the number by which we multiply.
the' Ldtt^"^*'^"''''^ ^""^ Multiplier are called Factors of
38^ The sign of multiplication is X which is read : multi-
plied by, times, or into. . .
JLn^^7xl. *^'' "'"''^P^'^^'^^^ °^ " ^y ^' t'^° ^"'"bers are
Multiplication Table.
1 time is
1 time I is
1 time 2 is
time 3 is
4 is
5 is
1 time
1 time
1 time 6 is
1 time 7 is
1 time 8 is
1 time 9 is
1
2
3
4
5
6
7
8
9
4
4
4
4
4
4
4
4
4
4
2 times
2 times
2 times
2 times
2 times
2 times
2 times
2 times
2 times
2 times
are
1 are
2 are
3 are
4 are
5 are 10
6 are 12
7 are 14
8 are 16
9 are 18
times
times
times
times
times
times
times
times
times
times
are
1 are 4
2 are 8
3 are 12
4 are 1 6
6 are 20
6 are 24
7 are 28
8 are 32
9 are 36
5
5
6
5
5
5
5
5
5
5
tira^
times 1
times 2
times 3
times 4
times 5
times 6
times 7
timi-s 8
times 9
are
are 5
are 10
are 15
are 20
are 25
are 30
are 35
arc 40
are 45
7
7
7
7
7
7
7
7
7
7
times
timas
times
times
times
times
times
times
times
times
are
1 are 7
2 are 14
3 are 21
4 are 28
5 are 35
6 are 42
7 are 49
8 are 56
9 are 63
times
times
times
times
times
times
times
times
times
times
are
1 are 8
2 are 16
3 are 24
4 are 32
5 are 40
6 are 48
7 are 56
8 are 64
9 are 72
lid!
26
MCLTIPLIOATIOW.
times
times 1
tiniPM '2
times 3
timi'S 4
times 5
times 6
times 7
times 8
times 9
are
are 3
are 6
are 9
are 12
are 15
are 18
arc 21
are 24
are 27
6 times
6 times
6 times
6 times
6 times
6 times
6 times
6 times
6 times
6 times
are
1 are 6
2 are 12
3 are 18
4 are 24
5 nre 30
6 nre 36
7 are 42
8 are 46
9 are 54
9 timeft
9 times
9 times
9 tim s
9 times
9 times
9 times
times
times
limes
9
9
9
Oare
1 are 9
2 are 18
3 are 27
4 are 36
5 are 45
6 are 64
7 are 63
8 are 72
9 are 81
PROBLEMS.
39. Case l.—To multiphj when the multiplier is not
greater than teji.
Example.— Multiply 654 by 9.
Solution.- In this example 654 must be taken 9 Operation.
times. Begin at the right and multiply ; 9 times 4 units are 654
36 units, 3 tens and 6 units. Write 6 in the units place and 9
cany 3 tens ; '9 times 5 tens are 45 tens plus the 3 tens 53^
carried equal 48 tens or 4 hundreds and 8 tens. W^ite 8 in the .tens
place and carry 4 hundreds; 9 times 6 hundreds are 54 hundreds plus
the 4 hundreds earned equal 58 hundreds which is written down. There-
fore the product is 6886.
Note.— In practice the process is as follows :
9 times 4 30 write 6 and carry 3
9time85 45 and 3 48 write 8 and carry 4
9time86 54^nd4 68 write 58.
40. 'RMle.—'-Begin at the right and muUiplu each term of
the mHltiplic'and by the multiplier, carrying as in add.tion.
Case U.—When the multiplier is greater than 10.
Example.— Multiply 3527 by 382.
Multiply by the units as in case * Opejiatiok.
I, then by the tens placing the
fii-st product under the tens
column. Multiply the hundreds
in like manner placing the first
product under the hundreds col-
umn. Take the sum of the partial
products. The total product is
1347314.
3527
382
7054
28216
10581
1347314
u.
product by
units
((
<<
tens
«
«
hundreds
Total
product.
timeS
Limes 1
times 2
tim s 3
times 4
times 5
times 6
times 7
times 8
limes 9
are
are 9
nre 18
are 27
are 36
are 45
are 64
are 63
are 72
are 81
MUtTIPMCATIOK.
27
Itiplicr is not
n 9 Opeuation.
are 654
and 9
tens 5_38p
j;ite 8 in "the ,tens
54 hundreds plus
tten down, "fhere-
I :
irry 4
)hj each term of
i in addition,
kan 10.
42. Rule. — /. Bef/in at the right and multiply the multi-
plicand hy each term of the multiplier, writing the first term
of each product under the term of the midtijtlier ichich pro-
duces it.
II. Add these partial products and their sum icill he the
entire product.
ArraniT.iiicnt mf work.
uct by units
I •« tens
« hundreds
,1 prodnet.
. 8527
_382
7054
28216
10581
1347314
65437
.'•)3040
26T7480
196311
327185
3470778480
Example : Multiply 109080 by 36050.
Begin the opi ration by placing a Operation'.
in the units place there being no 109080
units. Then multiply by 5 say. 36050
ing : 6 times are ; write this 5454000
to the left of the first that is in the 654480
tens place. Continue : 5 times 8 327240
are 40 ; write the and carry 4 ; 5 3932334000
times ai-e 0, plus 4 equal 4, etc. .
Omitting the occupying the hundreds place take 6 saying : 6 times are
0, which is to be placed in the same column as the 6 it being of the
same order, thousands, etc. The product of the multiplicand by 3 must oc-
cupy the place of ten-thousands as it expresses by itself ten-thousanda.
I The product is therefore 3932334000.
Note ;— I. The product of the tens is advanced one place to the left,
that of the hundreds two places, etc , because the first figure of each
partial product is of the same orde/as the figure of the multiplier.
, II. When ciphers occur between the figures of the multiplier omit
I them and multiply by the next significant figure.
III. To multiply a number by 10, 100, 1000,
I add one, two, three ciphers to the multiplicand.
[Ex. 75X100=7500. Also if there are ciphers
jat the right of one or both factors, multiply by
Jthe significant figures and annex as many 312000
ciphers to the result as there are ciphers to the right of both factors.
B05.
•'•OS.
510.
5J1.
5 J 2.
513.
5J4.
2S
'^- Proof . AT , '"''"^"^"^'^-^o^.
'"' i»»-actit.©.
- / r,jQ
8642076 „
515.
5Je,
5 Jr.
5/8.
5I».
5-'0.
r>2i.
523.
524.
525.
526,
527.
528.
529.
5ao.
531.
532.
533.
534.
535.
53C.
537,
538.
539.
540.
541.
542.
543.
S45.
546
547.
5i8.
Tx 6
t'^X 4
'^^X 5
566X 8
40iX 7
436^ 3
i«4X 6
28 -^ ^
I't^ 2
5'5X 5
476X 7
873X 4
li^X 9
576X 7
8760 i
t^^507X 2
»24654 V I
&51847Q I
547854 V I
864753O I
J^^«27X f
?5«r6P 2
''45«78y
S64207V ^
«2<025v I
«47989P ^
4569070
»07075V
»74834 V o
: f^
529X14
540X17
'54X19
359X21
669X25
mxso
f»7X34
is^xse
fPX'^1
605X45
625X48
1^^X53
^57X58
S76X62
964X67
854X70
674X74
S57X80
^S7X8J
667X84
457X87
657X91
»37X93
978X96
5f«X36
7070430 ;| ^
«%?^|,^
978007X It
,7«WX27
786795X 20
^53477^ 32
609834V «|
«27454X 3«
f 7070^ i*
60774J^ is
74fiS24X S ^
6770079, 47
79645nv !:
^^»X48 / la^^-
jg /»6450X 48
" «^e854X tf?
j Wx el
678967^ fl
^»5437X 7/f •
674874X if
f6&4Q7\^^J^
*'^74B9X70S
4
' '«t^« same a« the
>93.
95.
96.
>7.
S.
9.
). •
ll^X 83
ro795^P fi
'76753$ l;
ff«075< 5»
i6854X 63
^275><e; .
'yx 4
967X 72
854X 74
<37X 75 '
7fiX 7»
'?X257
5X618
»xroff
(537.
638.
«39.
640#
641.
642.
643,
644.
645.
646.
647.
648.
173.
674.
675.
6/'6.
677.
678.
679.
680.
681.
682.
683.
684.
686.
887.
688.
689.
690.-
691.
692.
693.
694.
695.
696.
697.
698.
699.
foo.
701.
702.
' 703.
704.
706.
706.
707.
708.
709.
♦710.
.978457X346
876574X457
457974X640
853473X703
957456X854
824956X387
347653X457
456824X654
976489X877
970546X200
457834X456
827669X623
MULTIPLICATIOK.
«49. 747898X^07
650.^ 647I>59X183
651. 834706X370
652. 900897X405
653. 986007X726
654. 837454X947
655. 967827X125
656. 678984X345
657. 730064X500
658. 984765X756
659. 947876X842
660. 689834X943
849654X -f'W I 711
747876X 7487 712!
457854X J»768 I 713.
679456X 1304 714
895775X 3726 715.
70(I789X 1425 716.
476895X 4070 717.
469889X 2004 718.
6y6489X 5360 719.
987824X 1076 720.
987684X 4567 721.
643956X 9475 722
8347.'53X 2475 723."
690790X 5709 724.
674825X 8907 725.
807405X 4937 726.
457670087X 4564 727.
,„546876X 94347 728.
475087654X 7498 729.
^^„764276X 47839 730.
679009675X 6689 731.
759364X 27895 732.
847664857X 9874 733.
674307X 42765 734.
764897695X 8007 73.5.
470076X 742-'4 736.
475795834X 2076 737.
786789X 69864 738.
95376947oX 8421 739.
476843X 85654 740.
815456789X 3575 741
764854X 37654 742^
464879456X 8419 743.
966433X 77807 744.
654476S8SX 4739 746.
897466X 87493 746.
866674987X 6321 747
876452X 70809 748."
99
661. 946634X236
662. 769487X426
663. 69.')844X575
664./ 654266X429
665. 346854X537
666. 650079X935
667. 965789X327
668. 697896X938
669. 157679X937
670. 747876X945
671. 789379X849
672. 874119X927
497364956X 8470
867453X 96207
487847207X 2460
987407X 9S307
689047207X 2460
654857X 80076
877986755X 6790
854307X 67084
540090X 6900
780000X 4000
604000X702000
990000X 3490
940000X 7600
670000X 47600
875400X 96600
987400X 7000
8571O0X 1900
914400X 7200
977700X 4900
742800X 47000
890000X 98400
648700000X 47000
699400000X834000
927540000X896600
642570000X 69400
764600000X629000
600301000X400700
975007000X457600
845004000X700040 f
795654000X 84700-^-
648745601X474257
789407672X587648
457465478X459876
786745056X954378
956543576X376894
976432758X976432
669754007X649876
796030407X87600'
«
7
•r
t!
w
1
80
1
749.
760.
761.
762.
• ii
763.
754,
.' !
766.
, f
756.
■!
757.
, :•}
768.
iii
769.
m
Ex
MUI.TIPMOATIOX.
938321676X^68076
47rt7-12074y3781»74
flo7007428v«8l>073
678098789X795409
75S507961X146279
674907461X307824
879421702X376548
855807607X976866
757489007X900(176
879407854X678765
787375634X894757
760.
761.
762.
763.
764.
765.
766.
767.
768.
769.
770.
695769452X976801
876454876Xtil5U8u
*875849064X76797'I
987453970X64581!
995296307X48792;)
796753769X84968 J
794037254X97847'!
759097895X760061
754827939X477231
674396856X28567!*
674007906X78456;i ;
ExprcBM the rollowinir nnmber* In figure* and solve
Itae mnltlpllcntion.
771. "What is the product of one thousand two hundred and thrc
units by thirty-two ?
772. Multiply three thousand one hundred and twenty-one by tliirty-
four?
773. What; product is obtained by multiplying three hundred and
twenty-four by two hundred and twelve ?
774. Find the product of eleven thousand two hundred and twenty
three by forty-one.
775. Take four hundred and tweuty-fonr times the number twelve'
thousand and twenty.
776. What is the product of two thousand and twenty-one by ninety
five ?
777. Give the result of one hundred and three thousand two hundred]
and seven multiplied by five hundred and forty-three,
778. What number is obtained by multiplying thirty thousand and '
seventy-six by five thousand three hundred and forty-two ?
779. Find the product of nine hundred eighty-four thousand and
eighty-six by seventy-eight thousand three hundred and twenty-one.
780. Find the product of one thousand three hundred and two by forty
three units.
Or.il Exercises In Aaditlon, Anbtractton and SInKiplieallon.
783. D
<|it:»ntity 1
hubtracte(
784. T(
answer bo
785. H
786. H
another n'
787. W
times lai'g
788. W
iii^jer than
789. Ho
'45; 76— 2i
790. Ho
|5); 29-10
791. Ho
[«X2X7;e
792. Ho
I); 93 -(6:
793. Hoi
') ; 47-10
794. Hoi
0X6 ; 7X
795. Hov
; 52-22-j-
796. Hov
2xn-(ic
1st by adding the smaller number of a sub-
2nd by taking away the ditference from tli
781. What is obtained
traction to the difference ^
larger number ?
782, What change takes place in the difference of two numbers : 1° ill
the larger number is increased ; 2" if the larger niimber is diminished |
8' if the smaller number is increased ; 4" if the smaller number
dimiuished ?
Note.-
iteger th(
[hvays be '
797. How
798. How
\n each bencl
799. How
[20 shots in (
800. A fan
6t»r)7fl9452XP7fl8'^t
87«-J5-187«Xt'l5l^8n
*8758490fl4X767»7'l
987453970X64581:)
995296307X4871*1'!
796753709X849681
794037254X97847'!
759097895X760051
754827939X47723 1
67439«856X2856rn
674007906X7846611
MCLTIPMCATION.
tl
«• and tolv*
hundred and tliiet!
?enty-one by tliirtj
three hundred ami
lundred and twenty-
the number twelve
snty-one by ninety-
lusand two hundred
t
thirty thousand am
-two ?
-four thoiinand ant
md twenty-one.
ed and two by fort\ •
MiiltlpllenSioii.
iv number of a 8ul)-|
difference from tluj
;wo numbers : 1° ill
iber is diminisheii
smaller number
»
783, Does the difference of two numbers change : l._if the sama
.,n.>t.ty be added tcTeach of the two numbers ; 2.-if fhe same au^.tit"Te
iMibtracted Irom each of the two numbers ? ^
784. To add 12 times the same number, in what other way may the
|answer be found besides by addition ? ^
786. How do you call the number that is to be multiplied »
786. How do you call the number that indicates how many time,
another number is to be taken ?
tiJeJ'C? " ''' --"'S of the expressions: twice smaller, three
WlZnZnt rt[i '" '-n'^ "•"" ^"«" ''^"" ' ' 2-12 times
789 Hw ' T T """"'-■'■ "'"" ^^ ' ^-^ """^^ «°«'">" than 24 ?
/89. How much are: 39-27 ; 43-32; 29-17 ; 53-23 • 61-21 • 67
;o.'~u' '' "-'' ' ''-'' ■• ''-'' ■• ^^-22 ; 55-25/ ' '~
790. How much are: 25-lOf 5; 26~(10-4): 28-10-4-2 -27 /in l
15) ;^9 10 + 6 ; 32-(I0+8, ; 34-10+7^ M^-^S V,l'l~''
Px:x7";™i:7x:s: '^:^: • '^'^ ' ^x^x« ^^-^^s .
;"-^;:;?:^iS:t^^^ ■' ^X-+^-X6) ; loxio-dix
/93. Howmuchare : 35—10+4 • 37— /104-7\ • qa in , o «/^
795. How much are : ..t6-20+6 ; 47-20+8 ; 47-(37+4i -49 lo .
; 62 22+10 ; 54-(34+n) ; 56-46+7 ; 17-27 + 1^4^6 1 ar+^M
796. How much are : 6X2+(2X9+3)-(3X10) • 14+114-8 ritZ
2X11-(10X7) J 8X16-(7X?3-f llT ? ^ ll+8-(?X4) ;
PRACTICAL PROBLEMS.
Note -When Dollars and Cents are multinlied by any
teger the point to separate the Dollars and Cents must
|hvays be worked after the lii^t two figures to the right.
798' HoT Z7 ^"' "' ?"■' '° ' '^«^ ''■''''' ^«« <=°»tail ?.47 t
In el "Ih r '' "" '^ "^^^' °" ^^ '^"^^^^ ^^ ^^- - « Pl«ces
»ri"?:.""'^^'.''*^ '^'^^^ ^-" fi»«^ o« i« -X hours at the rate of
|20 shots in one hour ?
800. A
family sj,e,id. f 1,3? a da^ ; how mucl, will it spend
inl6^
32
MtJLTirLICATION.
801. A train is composed of 27 cars each weighing 4800 pounds. What
is the weight of the entire train ?
802. What is the price of 490 pounds of mercury at $2.80 a pound I
803. How many hours are there in a month of 30 days?
804. How many hours are there in a year of 365 days ?
805. A man gains $45 a month ; what is his annual income t
806 What number is 37 times larger than 4015 ?
807. An acre of land costs $72.50 ; how much would you have to pay
for 18 acres ? , , u a'a
808. Twenty-seven children received 15 cents each, how much did
they all receive ? > i. v
809. It requires 38500 slabs to cover a street ; how much must bo
paid if each one cost 49 cents ?
Problems In Addition, Subtraction and Multiplication.
810. On a tree there are 942 apples ; how many remain if 579 are
gathered ? ., .- 4.1. j
811. How many apples on a tree, knowing that if 345 are gathered,
there remain 407 ? , j n« j
812. Bought 72 pounds of coffee at 34 cents a pound, and 95 pounds
of sugar at 7 cents ; how much must be paid for all ?
813. What is the number of oranges contained in two boxes if the
first contains 345 and the second 367 ?
814. A box of oranges contains 345 oranges ; another coutams 642
oranges ; if 47 be taken from the second and placed in the first, how
many will each box then contain 1
815. A servant receives $12.85 a month,. what are his yearly wages?
816. A box contains 476 oranges, another contains 504 ; how many
must be put in the fiist box so as to equal the number in the second box ?
817. A merchant receives four orders each for 450 bottles of beer; he
sends'on two occasions 370 bottles each time.^ How many botUes must
he still send ? ' v u
818. A man bought 12 reams of paper at 15 cents a quire, how much
must he pay if there are 20 quires in a ream 1
819 How many travellers can a train of three cars transport, if there
are in the 2nd class car 36 places, in the Ist class 40, and in the parlor;
car 20 ? , ., *u
820. How many pupils are absent in a class of 76 places, if those
presfiiit are seated on 8 tables of 9 places each ?
821. What is the number of boards iu two loads the first containing
240 and the second 275 'i _
MUtTIPLICATION. 33
S.'"; It, °'°* °"'" "^ '"'" '° " "■"• """"S i-fng 20 d.,. ..
.wfy's^l ""*"" ""'" "' ''"■■''" "<" ""!' «°»ta •"- '"king
J2«.^How many fig, a„ ,h.„ ;„ „ ^^^^^ each c..,dm.g 125
mel'LI?" " "■" '"™ '""• «'• «ee,.f9„».„ crry,„g45«
..i"'™;™7 "^ ""' " ■"""' '» ° """"-■•"' »' «^ - •» "
830. Wli»t iBthe totalmiiiiberofyearsinthe.m.rfj,„.~™ •
«y. .,e «... w„g «. .He .».. '«. .,. :;^T; l\';:x„: ;
minutes iu an hour » '*°"'' '" "■ ^"^ ""^ «»
840. A basket contains U6 1
many ftre there in it now ?
eggs ; 17 dozen were^ added to it, how
«■-•. ; '
34
MULTIPLICATION.
■*;■'!
841. What is gained by selling at 35 cents a pound, 60 pounds of.
goods that cost 28 cents a pound ?
842. What is the number of men in an army composed of 14700
iijfantrjs 3800 cavalry, 2160 artillery and 1140 huicers?
343. In thrnshing wheat with a flail a man strikes 37 times a minute ;
how.many limi's will he strike in a day of 10 hours I
844. If a pile of sheaves give an average of 32 gallons of wheat,
Kow many gallons will 95 piles give ?
845. A man earns 75 cents a day, what will he receive for the work of
the five, last mouths of the year allowing 25 days for Sundays and sick-
ness 1
8^6. A city pays annually $1345600 for butter and $5498060 for fish ;
by iiow much does the amount paid for fish exceed that paid for butter ?
847. The area of Prince Edward Island is 2133 square miles ; that of
Nova Scotia, 20907 square miles; New Brunswick, 27174 square miles;
Quebec, 188688 square miles; Ontario, 101733 square miles; British
Columbia, 341305 square miles ; Manitoba, 123200 square miles ; the
Territories; 2665252 square miles. What is the area of the Dominion 1
. 848. A workman saves 40 cents a day ; how much can he save in 3
years of 305 working-days each ?
849. Bought 12 yards of cloth at $4.30 a yard and 31 yards at $5.50 a
yard. I sokUhe whole at $6.80. Did I gain or lose and how much ?
850. There are 15780 slates placed on a roof ; and the slaters say that
they want 29 times as much to complete it ; how many slates will there
be on the roof ?
851. In a hospital containing 156 persons, they distribvte yearly 5
shirts and 3 pair of stockings ; how many shirts and pairs of stocking
will there be distributed in 4 years ?
852. How much does a man earn yearly, if he spends $212.50 and
saves $140?
853. A man was born in 1796 and died in 1882, how many months
did he live ?
854. A work ^ composed of 5 volumes, each volume contains 220
png«s, each page contains 32 lines and each line 11 words. How many
wokIh in the whole work ?
855. If a man breathes 20 times a minute ; how many times will he
breathe from the first of March to the first of September a i^riod of 184
days ? .
856. A merchant bought 486 dozeu pf oranges at 2 cents apiece ; ho\|r
much must he pay ?
MULTIPLICATION.
s»
imes a minute ;
Ions of wheat,
867. An overseer has 20 men under liim, he pays them $1.25 a day
How much must he pay them for 50 days' work ?
858. How many hours are there in 11 years and 20 days?
859. What sum is required to maintain 34 sick persons during a year
of 365 days at an average of 3 cents each hour ?
860. A father of a family earns $2.50 a day and spends $1.60 ; how
much money will he have remaining at the end of a year if he abstained
Irom working during 52 Sundays and 9 Feast-days ?
861. How many days are there in 34 years, if 27 are of 365 and the
remainder of 366 dnys ?
862. In a workshop there are 33 workmen, 11 of whom earn $1.30 a
day ; 12 others $1.50, and the remainder $1.75 ; what sum is required to
pay them for a year if they did not work on Sundays and on 9 festivals «
863. Six baskets of apples contain 15 dozen each, what is the total
contents of these baskets ?
864. 10 baskets containing 125 dozen of figs each were bought for 2
cents a fig ; what was the amount paid ?
865. An army of 49854 men received reenforcemeuts after which the
army numbered 65878 men. What was the number of the reenforcement »
866. A man received 3690 boxes each containing 1350 pens at 2 cents
a lien. Require the cost.
867. Six boxes, containing 24 dozen of knives each, were boucht for
45 c. ,.ts a knife ; what was the total cost ?
868. A merchant sold 645 plates : he delivered 340 the first time and
1 ^8 the second time. How many are stUl to be delivered f
869. In 8 building there are 85 windows having 24 panes of glass each •
the glazier received 15 cents for each pane : how much did he receive fo^
ail !
870. What must be paid for 2 boxes of soap the first box containing
242 pounds and the second 191 pounds, at 6 cents a pound ?
871. In selling 30 yards of cloth for $180 I gained 90 cents on a yard
what did the cloth cost me ? ■
872. What would be the gain on 50 pounds of tobacco that were sold
lor 40 cents and bought for 33 cents ?
873. A man bought 36 yards of silk at $2. 60 a yard, 64 pounds of salt
at 3 cents a pound 15 gallons of oil at 42 cents a gallon, and 26 cords of
wood at $3.70 a cord. How much must he pay for all ?
874. A contractor has three workmen, by the first he gains 46 cent,
perday. by the second 30 cents, by the third 25 cents ; what wiU be his
entire gain at the end of 3 weeks, omitting Sundays ?
86
DIVISION.
I I
!!«
DIVISION.
44. Division is the process of finding how many times a
number call divisor is contained in another number called
dividend.
45. The result of the division is called quotient.
46. Division is indicated by the sign -v- or : which reads
divided by, or by a line placed between the dividend and the
divisor.
Thus to indicate the division of 21 by 3, it is written 21-^3
or V.
Note.— The quotient of a division may be obtained by subtraction.
Tlius, to find the quotient of 16 by 5 ; subtract 5 from 16, this gives 11
for remainder ; then 5 from 11 give 6 for remainder ; 5 from 6 leave 1
for remainder. Another subtraction being imposiiible it is seen that 16
contains 5 three times with 1 for remainder.
This means of fiudiug the quotient of two numbers requires too much
time and would not be practical in many cases ; a shorter method of
solving division is therefore necessary.
pivision Table.
Ex. 20-i-6=3, r. 2. Read 20 divided by 6 equal 3 remain-
der 2.
=1
=l,r. 1
=1, r. 2
=1, r. 3
=2
=2, r 1
=:2, r. 2
=:2, r. 3
=3
=3, r. 1
=3, r. 2
=3, r. 3
=4, r. 1
=4, r. 2
=4, f. 3
l-f-l=l
17--2=8, r. 1
15-5-3=5
4-
.4
2-^-2=1
18-=-2=9
16^3=5, r. 1
5-
—4
3-^2=1, r. 1
19-5-2=9, r. 1
17h-3=5, r. 2
6-
-4
4-r-2=2
18-f-3=6
7-
—4
6^-2=2, r. 1
3-5-3=1
19-5-3=6, r. 1
8-
-4
6-=-2=3
4-5-3=1, r. 1
20-5-3=6, r. 2
9-
-4
7-f-2=3, r. 1
5-5-3=1, r. 2
21^3=7
10-
-4
8-5-2=4
6-5-3=2
22-5-3=7, r. 1
11-
—4
9 .-2=4, r. 1
7h-3=2, r. )
23-5-3=7, r. 2
12-
- 4
10-:-2=5
8-5-3=2, r. 2
24-5-3=8
13-
-4
11-8-2=5, r. 1
9--3=3
25-5-3=8, r. 1
14-
-4
12-*-2=6
10-5-3=3, r. 1
26^3=8, r. 2
15-
-4
13-h2^6, r. 1
llH-3=3, r. 2
27^3=9
16-
-4
14-!-2=7
12-1-3=4
28-f-3=9, r. 1
17-5-4
15-1-2=7, r. 1
18-5-3=4, r. 1
29-r-3=9, r. 2
IS -4
ie-f-2=8
14-5-8=4, r. 2
19-^
■-4.
6^5=
6-^5=
7-1-5=
8-5-5=
9-5-5=
10-5-6=
11-^5=
12-^.5=
13-5-6=
14^6=
15-5-6=
16-5-6=
17--6=
18-5-6=
19-5-6=;
20h-5=
21-h6=.
22-5-5='
23-;-5=<
24-f-5=<
25-5-5=i
26--6=i
27-5-6=£
28-5-5=£
29-5-5=5
30-^6=fi
31-f-5=e
32-^5=6
33-5-6=6
34-5-5=6
w many times a
r number called
tient.
r : which reads
ividend and the
is written 21-^3
led by subtraction.
n 16, this gives 11
5 from 6 leave 1
I it is seen that 16
requires too much
shorter method of
equal 3 remain-
DIVISION.
12-
13-r-4::
14-T-4::
15-4-4^
16^4^
17-4-4=
IS -4=
19^4=
6-7-4=
■4=
8--4=
9h-4=
10-f-4=
11-h4=
4=
:l
:l,r. 1
:1, r. 2
:1, r. 3
:2
:2, r 1
:2, r. 2
-2, r, 3
:3
;3, r. 1
^3, r. 2
-Z, r. 3
^4, r. 1
:4, r. 2
:4, f. 3
20
21
22
4
-f-4
-r-4^5
23-J-4:
24-^4:
25
26-=-4:
27-?-4:
28
29-f-4:
30-f-4:
31-r-4.
32-f-4:
33-^ 4 1
34-
35-
36^^
37-=-
38
89
^5
=5. r. 1
4=
4=
:5, r. 2
:5, r. 3
:6
:6, r. 1
:6, r. 2
:6, r. 3
:7
-7. r. 1
=7, r. 2
=7, r. 3
=8
-8, r. 1
=8, r. 2
=8, r. 3
.9
:9, r. 1
:9, r. 2
:9, r. 3
5--5
6-J-5
7--5
8-f-6
9-^5
10-^6
11h-5
12-1-6;
13-f-6:
14^6:
15-5-6:
16 4-6:
17^6=
l8-f-6=
l9-f-6:
20-i-O:
21-f-6=
22-i-5=
23^6
24-J-5
25H-5
26-^-6:
27-^5:
28-f-5:
29-5-6:
30-5-5=
=1, r. 1
:1, r. 2
i=l, r. 3
=1, r. 4
=2
=2, r. 1
=2, r. 2
=2, r. 3
=2, r. 4
=3
=3, r. 1
=3, r. 2
=3, r. 3
:3, r. 4
:4
4, r. 1
4, r. 2
=4, r. 3
=4, r. 4
=5
=5, r. 1
=5, r. 2
=5, r. 3
:6, r. 4
:6
31-=-5=6, r. 1
32h-5=6, r. 2
33-5-6=6, r. 3
34--6=6, r. 4
35-=-5=r7
36-5^7, r. 1
37-5=7, r. 2
38--5=7, r. 3
39--5=7, r, 4
40^5-=8
41-T-5=8 r. 1
42---5.T.8, r. 2
43-5-5-^8, r. 3
44-5-5-=:8, r. 4
45-5-5=9
46-5-5=9, r. 1
47-^5=9, r. 2
48-5-5=9, r. 3
49^5=9, r. 4
6h-6
7-5-6
8-5-6
9-5-6
10^-6
n--6
12-5-6
13-=-6
14-5-6
15^6
16H-6
17^6.
18-5-6:
19-H6:
20^6
21-5-6:
22-!-6.
23-H6:
24-4-6=
25-5-6=
26-T-6z
27^6=
28-H6
29-H6
30-^6
31H-6
32-f-6=
33-4-6=
34-4-6=
35-4-6=
38-5-6
=1
--1, r. 1
i=l, r. 2
■ :1, r. 3
:1. r. 4
i=l, r. 5
't
-2, r. 1
=2, r. 2
=2, r. 3
=2, r. 4
=2. r. 5
-.A
.3, r. 1
=3, r, 2
:3, r. 3
:3, r. 4
:3, r. 6
:4
:4
=4,
r. 1
:4, r. 2
:4, r. 3
i, r. 4
:4, r. 5
:5
:5, r. 1
:5, r. 2
6, r. 3
5, r. 4
:6, r. 6
:6
37-4-6=6, r. 1
38H-6=6, r. 2
39-4-6=6, r. 8
•11 ; 6
4 2 --6
43-f-6:
44-5-6:
45-5-6;
46^6:
47H-6:
48^-6=
49-5-6r
50-5-6=
51-5-6=
52h-6=
63-^6^
54-5-6=
55 .-6 =
56-5-6=
57^6 =
58 5-6 =
59-5-6=
=6, r. 5
=7
=7, r. 1
=7, r. 2
'-'~7, r. 3
=7, r. 4
=7, r. 5
=8
=8, r. 1
:8, r. 2
:8, r. 3
:8, r. 4
8, r. 5
:9
9, r. ]
9, r. 2
9, r. 3
9, r. 4
9, r. 5
7-5-7
8-5-7
9-=-7
lO-r-7
11^7
12-5-7
13-7
14--7
154-7
16-5-7
17^7
18-5-7^
19 4-7:
20-5-7:
21-5-7:
22-5-7=
23-5-7=
24-5-7=
25-4-7=
26-5-7=
27-5-7=
23-5-7=
29-5-7=
30-5-7=
31-4-7=
32-5-7=
33
'=1
=1. r. 1
:], r. 2
1, r. 3
=1, r. 4
=1, r. 5
=1,4. 6
=2
=2, r. ]
=2, r. 2
=2, r. 3
=2, r. 4
=2, r. 6
=2, r. 6
=3
=3, r. 1
=3, r. 2
=3, r. 3
=3, r. 4
=3, r. 5
i3, r. 6
:4
:4, r. 1
:4, r. 2
:4, r. 3
4, r. 4
7=4, r. 5
34-5-7=4, r. 6
35--7=5
36-5-7=6, r. 1
38-5-7
39-f-7
40-5-7
41-5-7
42-5-7
43-5-7
44-4-7.
45-5-7:
46--7:
47--7:
48-7:
49-5-7
504-7:
51-5-7:
52--7=
53-^7:
64-7=
55-4-7=
56h-7=
57-5-7=
58-7=
59-5-7=
60-4-7=
61h-7=
62-4-7=
634-7=
644-7=
60 4-7=
66-5-7=
67-5-7=
684-7=
69-5-7=1
37
:5, r. 3
:5, r. 4
=5, r. 5
=.5, r. 6
=6
=6, r. 1
=6, r. 2
=6, r. 3
=6, r. 4
=6, r. 5
=6, r. 6
=7
=7, r. 1
=7. r. 2
=7, r. 3
=7, r. 4
=7, r. 5
=7, r. 6
=8
=8, r. 1
=8, r. 2
=8, r. 3
:8, r. 4
:8, r. 5
:8, r. 6
:9
:9, r. 1
:9, r. 2
:9, r. 3
:9, r. 4
:9, r. 5
:9, r, 6
8-5-8=1
9-8=1, r. 1
10-8=1, r. 2
11-4-8=1, r. 3
12-5-8=1, r. 4
13-5-8=1, r. 5
14 4-8=1, r. 6
15-8=1, r. 7
16-5-8=-^2
17-5-8=2, r. 1
18-5-8=2, r. 2
19-5-8=2, r, 8
20-4-8=2, r. 4
21-5-8=2, r. 5
22-5-8=2, r. 6
23-4-8=2, r. 7
24-4-8=3
40^6=6, r. 4 | 37-5-7=6, t. 2 | 26-1-8=3, r. 1
;/
m Hi 1
i; ri^
88
DIVISION.
26
27
28
29-f-8
30
31^8
32
33
34
35^8
36
37---8.
38-V-8:
39h-8=
.8=
8=
40.
41-
42-f-8=
43h-8.
44-h8=
45^-8=
46-
47-
48.^8
49-^8
50-5-8
51-^8=
52-f-8.
53h-8.
54^8=
55^8=
56
58
59
8-
8_
57-r-8 =
:3, r. 2
-3, r. 3
-3, r. 4
:3, r. r.
-3, r.
=3, r. 7
.4
:4. r. 1
:4, r. 2
.4, r. 3
:4, r. 4
-A, r. 5
■4, r. 6
:4, r. 7
:5
:5, r. 1
:5, r. 2
:5, r. 3
:5, V. 4
:5, r. 5
:5, r, 6
:5, r: 7
:6
=6, r. 1
:6, r. 2
:6, r. 3
:6, r. 4
:6, r. 5
:6, r. 6
:6, r. 7
:7
:7, r. 1
:7, r. 2
:7, r. 3
8=
60-4-8
61-f-8
62-f-8
63-4-8
64-f-8
66-r-8
66 --8
67-^8
68--8
69-r-8
70^8
71-r-8
72-^-8
73 --8
74f-8
75-5-8
76-=-8
77^8
78^-8
79-5-8
^7, r. 4
=7, r. 5
=7, r. 6
=7, r. 7
=8
=8, r. 1
=8, r. 2
=8, r, 3
=8, r. 4
=8. r. 5
=8, r. 6
=8, r. 7
-^9
=9, r. 1
^9, r. 2
=9, r. 3
=9, r. 4
=9, r. 5
=9, r. 6
=9, r. 7
9-5-9.^1
10-5-9^=1, r. 1
11-5-9=1, r. 2
12^9=1, r. 3
13-5-9=1, r. 4
14-5-9=1, r. 5
16^9=1, r. 6
16-5-9=1, r. 7
17-^9=1, r. 8
18-5-9=2
19^9=2, r. 1
20-5-9=2, r, 2
21-5-9=2, r. 3
22^9=
23.
24_:-9
25.
26.
27^9=
28-^9:
29-^9=
30^9^
31^9=
32^9-
33
34-1-9=:
35
36-f-9.^
37-5-9^
38.
42
44.
45-5-9
46
48
49
50-5-9:
61-f-9r
52-5-9;
53-5-9.
54^-9
554-9
.9=
.9=
.9^
39--9=
40--9.
41^9=
43--9=
■9.
47--9=i
:2, r. 4
-2, r. 5
:2, r. 6
^2. r. 7
=2, r. 8
=3
:3, r. 1
:3, r. 2
:3, r. 3
-3, r. 4
:3, r. 6
:3, r, 6
:3, r. 7
:3, r. 8
-A
A, r. 1
:4, r. 2
■A, r. 3
:4, r. 4
:4, r. 5
:4, r. 6
:4, r. 7
:4, r. 8
:5
:5, r. 1
:5, r. 2
:5, r. 3
:5, r. 4
.5, r. 5
-.5, r. 6
:5, r. 7
:5, r. 8
:6
=6, r. 1
•9=
9=
9=
Difi'erent Gases of Division.
56-5-9=
67-4-9
58-5-9
59-=-9
60-4-9
61-5-9
62-5-9
63H-9
64^9
65-r-9
66-5-9
67-4-9
68-4-9
69H-9
70-4-9:
71H-9:
72-5-9
73-H9:
74-5-9^
76-^-9
76^9:
77-4-9
78-5-9:
79^9
80-t-9:
81-^-9:
82^9:
834-9:
844-9
85-5-9
86 5-9
87-5-9
884-9
89^9
=6, r. 2
-6, r. 3
:6, r. 4
'.Q, r. 5
:6, r. 6
=6, r. 7
=6, r. 8
=7
-7,
r. 1
—7. r." 2
=7, r. 3
=7, r. 4
=7. r. 5
=7, r.
=7. r.
=7, r.
7, r.
=7, r. 6
=7, r.: 7
=7, r. 8
=8
=8, r. 1
=8, r. 2
=8, r. 3
=8, r. 4
=8, r. 5
=8, r. 6
=8, r. 7
=8, r. 8
:9 ■
:9, r. 1 I
:9, r. 2 \
-.9, r. 3 ^
=9, r. 4
:9, r. r.
:9, r. 6
=9, r. 7
:9, r. 8
48. Case I. — The divisor in let's than 10. In this case the,
qiiotient may be easily fouud by the nmltiplication table.
Ex.\MPLE. — Divide 51 by 6.
Ill the multiplication table it is seen that 51 is greater OPEiiATloy,;
than 6X8, and smaller than 6X9 ; therefore 8 is the 6) 51
quotient with a lemainder of 3. 8 R. Sl
Example 2.— Divide 8754 by 8.
Solution. — 8 is contained in 8 thousands 1 OPKitATioyr
thousand times, with uo remainder ; 8 into 7 8 )8754
hundred is contained hundred times. Annex 1094 — 2
5 tens, '
9 for qu(
34 units
The quol
49. (
figure.
Find
Solut
with a 1
horizouta
42 is 1
there are
tliousand
thousand
thousands
hundreds
liuodred 1
3 hundred
tens, a cip
units. 42
which sub
The quo
50. N
[the subti
divisor is
[Thus 3 tin
3 tin
Kemaind
51. Ri
same line.
]/iorizuntai
II. Fir.
iffures Oj
\lii:isor ; f
ill M
roductfr
\he follow.
56-i-9=
67-5-9:
68H-9:
59-^-9:
60-^-9:
61-4-9:
62-4-9:
63-=-9:
64^9
65^9
66-4-9^
67-r-9
68-4-9:
69-4-9^
70-4-9:
71-4-9=
72-4-9
73-h9=
74-4-9=
76-4-9:
76-4-9=
77-4-9=
78-4-9=
79-5-9=
80-4-9=
81-5-9:
82-4-9=
834-9:
84^9:
85-4-9;
86 4-9:
87^9:
88-4-9:
89 4-9:
=6, r. 2
-:6, r. 3
:6, r. 4
-Q, r. 5
:6, r, 6
=6, r. 7
:6, r.' 8
=7
-7, r. 1
=7, r: 2
=7, r. 3
=7, r. 4
=7, r. 5
-7, r. 6
=7, r.: 7
=7, r. 8
=8
=8, r. 1
=8, r. 2
=8, r. 3
=8, r. 4
=8. r. 5
=8, r. 6
=8, r. 7
=8, r. 8
:9 '
=9, r. 1
=9, r. 2
=9, r. 3
=9, r. 4
=9, r. r.
=9, r. «
=9, r. 7
=9, r. 8
DIVISION.
39
Opkkation.
12945 |42
^26 3U8
345
336
9— Rem.
n.
In this case the
[cation table.
reater Opeuation,
is the 6) 5 1
8 JR. S|
OPERATTOJf,
8 )8764
1094—2
5 tens, 7 hundreds and 5 tens are 75 tens, which divided bv 8 gives
9 for quotient and a remainder of 3 tens. 3 tens annexed to 4 unit^ are
34 units which divided by 8 gives a quotient of 4 and a remainder of 2
Ihe quotient then is 1094 and a remainder of 2 units.
49. Case II. — When the divisor contains more than one
figure.
Find how many times 42 is contained in 12945.
Solution. -V/rite tlie dividend and the divisor on the same line
with a vertical line between them and draw a
horizontal line beneath the divisor.
42 is not contained in 1 ten-thousand hence
there are no ten-thousands in the quotient ; 1 ten-
thousand and 2 thousands are 12 thousands ; 12
thousand does not contain 42, hence there are no
thousands in tiie quotient ; 12 thousands and 9
hnndreds are 129 hundreds. 41 is contained 3 hundred times in 129 3
hundred times 42 are 126 hundreds, which subtracted from 129 leave
3 hundreds which with 4 tens are 34 tens. 42 is not contained in 34
tens, a cipher is written in the quotient. 34 tens with 5 units are 345
units 42 is contained 8 units times in 345. 8 units times 42 are 336
which subtracted from 345 leave a remainder of 9 units.
The quotient then is 308 with a remainder of 9.
50. Note I.— It ia not necessary to write the number 12G
the subtraction may be made mentally after the figure of the
divisor IS multiplied by the quotient : - . .
Thus 3 times 2.... 6 from 9 leave 3 •
3 times 4. . .. 12 from 12 leave
Remainder 3 hundreds, add 4 tens .... 34. Proceed as above.
51. Rule.—/. Write the dividend and the divisor on the
same line, separating them bi:] a vertical line and drawing a
horizontal line under the divisor. . ,
//. Find hoxo many times the number expressed by thd first
'guns of the dividend contmns the highest units of the
tlivtsor; place this figure in the quotient.
Ill Multiply the divisor by this figure, and subtract the
•oductfrom the partial dividend. To the remainder anr^x
nefollowtug figure of the dividend.
i/
. i
% i
!
11
I
11"
40
DIVISION.
Example.
6|00 ) 97180
16—180 B.
IV. Proceed as be/ore till all the terms of the dividend
have been used.
V. If any partial dividend will not comain the divisor
plate a cipher in the quotient and annex the following figure
of the dividend and proceed as above.
52. Note. — I. When the divisor has but one figure. The
quotient is written under the dividend without writing down
the remainder as shown in Case I.
II. When there are ciphers to the right
of the divisor, they are cut off from the di-
visor and as many figures from the right of
the dividend. Then divide the remaining
figures as usual ; prefix the remainder to
the figures «ut off.
III. To divide by 10, 100, 1000 it suffices to cut off one,
two, three figures to the right of the dividend.
63. Proof. — Multiply the quotient by the divisor and add
the remainder, if any, to the product; if the work is correct the
result will equal the dividend.
54. Proof of multiplication.— Divide the product by
the multiplier ; the c^uotient will equal the multiplicand if the
work is correct. There should be no remainder.
Examples for Fraotioe.
Divide
87S.
870.
877.
878.
879.
880.
881.
882.
883.
834.
885.
886.
887.
889.
468-r-2
963-i-3
624-f-4
970-i-6
672-r-6
434H-7
■ 672-H8
405-5-9
621-r-9
207-V-9
42047-.-5-2
407630^5
342009-f-9
492630-^6
644013-^3
890.
891.
892.
898.
894.
895.
S96.
897.
898.
899.
900.
901.
902.
903.
904.
333006-i-6
870120-5-9
540764-5-4
761002-5-7
432536-5-8
478353-5-3
981006H-6
453607-5-7
600702-5-8
604430-5-5
650016-5-8
450U09-5-9
674108^4
894609^-7
874224-5-4
905.
906'
907.
908.
909.
910.
911.
912.
91 J.
914.
915.
916.
917.
918.
919.
920.
921.
922.
923.
924.
92.'i.
926.
927.
928.
929.
930.
931.
932.
933.
934.
935.
936.
937.
938.
939.
940.
941.
942.
943.
944.
945.
946.
947.
948.
949.
960.*
951.
952.
963.
954.
955.
DIVISION.
of the dividend
cain the divisor
following figure
lue figure. The
It writing down
EXAMPLK.
i|00 ) 97180
16—180 R.
ces to out off one,
lend.
divisor and add
)rk is correct the
the product by
ultiplicand if the
ler.
833006-H6
870120-5-9
640764-^4
761002-i-7
432536-f-8
478353-5-3
981006-^6
453607^7
600702-^3
604430-r-5
650016-(-8
460U09h-V>
674108-4-4
894509H-7
874224-!-4>
905.
906'
907.
908.
909.
910.
911,
912.
91 J.
911.
915.
916.
917.
918.
919.
920.
921.
922.
923.
924.
92.'5.
926.
927.
928.
929.
930.
931.
932.
933.
934.
935.
936.
937.
938.
939.
940.
941.
942.
943.
944.
945.
946.
947.
948.
949.
950.*
951.
952.
963.
954.
965.
41
4596ri5^:- 9
354-f-ll
407--12
984-f-14
649--2()
895 ^--J.J
780^25
354--2fi
197 -T 28
425 -:-33
407-34
654 f ;i5
954 - ;J9
201 ^43
426^46
999^46
864 --50
9G4 V 63
975-r-54
5^3288-f-12
90,-)765-r-17
405680-t-20
652.';47-=-23
743240 ■?- 25
793751-5-26
704900-5-29
805909-5-33
847216-5-36
487804-5-38
497999-5-40
659415-5-43
710756^46
926404-5-49
845001-5-53
858415-5-67
867010-5-69
984824-5-Gl
694115-5-64
699999-5-66
840026-5-68
600010-5-72
430074-5-76
605407-f-78
604905-5-81
806404-5-85
676477-H86
934376^89
297049-5-91
977046-5-93
674246 -=-96
306423-5-99
9.')6.
9.^7.
953.
959.
!<(J0.
961.
902.
9«3.
9'i4.
9fi5.
960.
967.
968.
969.
970.
971.
972.
973.
974.
975.
970.
977.
978.
979.
980.
981.
982.
983.
984.
985.
986.
987.
988.
989.
990.
991.
992.
993.
994.
995.
996.
997.
998.
999.
1000.
1001.
1002.
1003.
1004.
1005.
1006.
800715-i- 36
640072-5- 69
695425-5- 97
78!)(»16h- 84
42b'432-5- 67
6941 20-T- 68
94327 4 -r- 62
796425-5- 75
843255-5- 87
169400 5- 78
345895 ^ 85
474050-T- 470
654207-^ 147
674604-^ 341
805940-5- 276
606825-5- 376
646079H- 346
654054-H 897
907850-i- 307
612904-f- 761
576452-i- 384
764805-T- 359
975450-+- 970
389807-*- 778
676402-*- 876
672070-H 462
908406-*- 607
454026-f- 247
430020-*- 7£9
874984-*- 789
678761-*- 290
904868-*- 207
767766-*- 461
896876-*- 675
845790-*- 475
664327-*- 147
842364-*- 915
846618-*- 964
846618-*- 854
809456-i- 942
654827-*- 835
676464-*- 807
466872-*- 867
660017-5- 466
976460-5- 749
845872-5- 948
470878-5- 548
765484-»- 654
452878-*- 874
829742-»- 764
840742-5- 842
42
DIVISION.
t li
'M
ll' I
1007.
1008.
1009.
1010.
1011.
1012.
1013.
1014.
.1015.
1016.
1017.
1018.
1019.
1020.
1021.
1022.
1023.
1024.
1025.
1026.
1027.
1028.
1029.
ao3o,
1031.
1032.
3033.
1034.
1035.
1Q36.
1037.
ao3P..
1039.
1040.
1041.
1042.-
1043.
1044.
1045^
1046;
1047.
1048.
1049.
1060.
1061.
106?.
1053.
1054.
1055.
1066.
1057.
459066+
739874+
605427+
605207-;
437878 +
859049 +
754754301+
178935421+
351978432+
794325069+
459457853+
373765007+
394756809+
947450207+
517486809+
929452907+
465027897+
167047096+
757807953+
847695876+
954761827+
807436587+
604876554+
874256084+
749657822+
397458701+
907009471+
642324529+
453873201+
940079009+,
675423804+.
fl432l7876+
987745878+
876495688+
347006921+
740080008+
942367460+
547084372+
827453671+
467009840+
254866763+
176870009+
784256862+
67007 "407+
496807904+
696807904+
• 104856009+
647607007+
664600070+
794827954+
607824087+
774
819
742
78!)
871'
847
247
247
668
895
704
405
749
345
621
347
634
296
196
341
684
659
896
647
346
499
742
674
642
,679
.779
476
740
677
846
540
875
976
197
742
475
497
746
857
357
678
595
457
.598
547
.679
10.^8.
1059.
1060.
lo^a.
1002.
1063.
1064.
1065.
1066.
1067.
1068.
1069.
1070.
1071.
1072.
107S.
1074.
1075.
1076.
1077.
1078.
10". 9.
1080.
1081.
1082.
1083.
1084.
1085.
1086.
1087.
1088.
1089.
1090.
1091.
1092.
1093.
1094.
1095.
1096.
1097.
1098.
1089.
1100.
1101.
1102.
1103.
1104.
1105.
1106.
1107.
1108.
345676407+ 287
809596433+ 876
576827462+ 634
852025044+- 297
654307854+ 387
745653842+ 977
300457089+.897
534875706+ 676
679854374+ 447
546894325+ 470
746876381+ 279
674237452+8907
743215908+3427
678332572+4086
674834207+6954
543207509+4987
743207008+2076
642396987+6430
453837954+6534
898754321+9784
47'940815+4110
907008752+1941
547927952+8432
764106347+B043
684124206+5398
541307650+4766
673454807+7,964
470075334+8107
807077927+9067
456374204+6760
■407854274+1749
742960864+0765
,674075847+2471
746820049+1986
787455654+9876
537658470+7407
876432574+1784
345653027+'4864
476845904+1664
875454807+2769
307452806+8745
746854954+2975
453347907+2794
787654927+4789
874642874+1743
546874957+2987
174854957^4789
678907854+0875
847942671+7421
742626834+1466 j
874089458+2989 1
1100.
1110.
nil.
1112.
1113.
1114.
]!15.
IIIU.
1117.
ni8.
1119.
1120.
1121.
1122.
1123.
1124.
1125.
1126.
1127,
1128.
1129.
1130.
1131.
346676407-f- 287
809596433H- 876
676827462-!- 634
862025044-+- 297
654307854-r- 387
745653842-f- 977
300457089-f-.897
634875706->- 676
679854374-^- 447
546894325-f- 470
746876381-!- 279
674237452--8907
743215908 -;-3427
578332572-r-4086
674834207-r-6964
543207509-r-4987
743207008-7-2076
542396987-^6430
453837954-!-6534
898754321-4-9784
47' 940815-4-4110
907008752-4-1941
547927952-4-8432
764106347-4-B943
684124206-4-6398
541307650-4-4765
673464807-4-7,964
470075334-4.SI07
807077927-4-9067
466374204-4.6760
407864274^1749
742960854-4.0766
.674075847-S-2471
746820049-4*1985
787455654^-9876
537658470-4.7407
876432574-4-1784
345653027-4-.4854
476846904-4-1664
876454807-4.2769
307462805-H8745
746854954-4.2975
453347907-4-2794
787664927-4.4789
874642874-4-1743
546874957-4-2987
174854957^4789
678907854-4-8875
347942671^7421
742525834-*.1466
374089458^2989
DIVISION.
1109.
1110.
nil.
1112.
1113.
1114.
1115.
1116.
1117.
1118.
1119.
1120.
1121.
1122.
1123.
1124.
1125.
1126.
1127.
1128
1129.
1130.
1131.
004087605-=-2984
741233479-!-4876
476807462-4-1627
600109729^6079
370230510-4-2798
874337452-4-2663
761045817-4-2352
216116076-!-8234
742676207-;-2694
904007369-4-2747
709478927^9079
294076927-4-7609
660076927-4-2476
346074837-4-1074
745674854.4-8790
174800976-5-1009
6524 75856-!- 78 46
895405974-4-8495
. 170079450-4-4560
900076466-!-3217
650074605-4-6541
654800077-4-7045
964757754-4-8794
43
1132.
1133.
1134.
1136.
1136.
1137.
1138.
1139.
1140.
1141.
1142.
1143.
1144.
1145.
1146.
1147.
1148.
1149.
11. 10.
1151.
11.52.
1153.
1154.
790078456
653070089
487094070
701874417
794854376-
230456876-
347606854
806423135-
636426976-
560079452-
766876342-
907880077-f
560079076-f
340058952-4-
646068095-4
647610023-4
647607432-i-
604653752^
243072654-4-
604224012-H
894007965-4-
654006795-^
670074027-!-,
4-2347
-4-6097
-4-6076
-4-1011
-4-4561
4-8741
-4-8479
4-4689
4-8941
4-8974
^9784
f-2769
-4985
-4794
9765
4706
8423
8423
7981
7654
1765
9871
3799
E«l»r*« the rollowlnir nnmber. in llsares and «,ive Ihe
Problems.
1- 56. What 18 the quotient of one hundred and twenty-one thousand
|uo Jiuudrcd and forty-seven by seven ? mousana
I 1156. The product of a multiplication is two hundred and thirty-eight •
nd the .^.Itiplier is twelve. What is the multiplicand ? ' ^ '
],,"/■ ^''' """^ ''°''' '" *'""y =<'«t'^i'»ed iu twenty thousand and
1158 How many times is three hundred and twelve contained in
ven tlionsand four hundred and eighty-eight T
1 1169. If four thousand one hundred and sizty-six be multiplied by an
.known number, and if the product be fifty thousand and forty what
I the unknown number ? «»"'iy, wnat
t!'Jl!^ *'""'"''' """ ''*'°""*' ^'' hundred and forty, tea
11161. What will be the resujt of twenty-five thousand made one
lousand times smaller J maae one
Tfit^rtT^' f""'" '*" '^' °"'^^^' ""« thousand eight hundred
r^
44
DIVISIOK.
1165 hZ ^ ''""'••••^'•« are there in 8602 units ?
1170. When is the nuotipnf • i
greater than the divided 3 •r/'"f'^^ ^^"^ *•»•" dividend ; 2.-
, nn. Having divide^Vn^-ierb; r^: "^ = ^--^^^^
dcnd contain the quotient ? ^ ' """"^ "'"'"' d«°» the divi-
1172. In dividing a number hv o u
contain the dividend ? ^ ' ^""^ '"'"^ ""^«« does the quotient
1173. How many times are • l k i o
«+4. in 60. in 70 ; 3.- 94-2 in flT- t; '°"*"'»^'i i" 21, i„ 35 ; 2.-
1174. Howman;arc: .- " 1^1 ' ^T/' "'^^ ^^' - ^
.-3^!?rT'^:r^3^iv^;rrf"-^^
30; 6.--29-4inl3r-12- 6-26 « f.r'' *- 18-12 in 9oJ
119A w ' — ■'o— 8 lu 140— 32?
J 176. How many times aw 1 le "* >
J5X7; 3.- 21. in 12X7 ; r.'lr'''"^^ '" 'X^' 2.- 5. in
(10-6)1 '^'' ^-».'"3X(21+9); 6.- 5. i„ 7^1' ^^
1177. What is the .luotieut • 1 „«• r , «
.178. H.„ „„„, „ T,._ ^8 ,;*.„, +8-3X5^10 ,
-3X^-^6; 4.—
1
I
ol t)-|-i5-jlxi2-M0 ?■
1190. H
1191. W
• nst 1138 ?
1192. B}
1193. A
many montl
1194. W]
348X60 T
1195. A c
lt)« the value
1196. A SI
was the valu
1197. In !
wnounted to
DIVISIOK.
10" six hundred and
iiltiplioand u twen-
ier ?
?
!•; 2.— of the 6th
the same number,
^t, what change is
iplicand ; 2.— the
■ 1. —having the
2 — having the
dividend ; 2
less than one T
'8 does the divj.
B8 the quotient
21, in 35 ; 2
>+9, in 63-f9f
15X12-1 (20X
-S, iu 107—7;
18-12 in 80-
15
2; 2 — 5, in
5. in 7X154-
; 2.^ of4-f.
:5-h10 ?
l«X9-(13X
- of 9-f-7_
-7 ?
2.-of9-f
<12--10?"
I
I
result ? ^ ' ^^ ^" ^'^ **»« remainder ; what is the
«l..t i. the ,L' " ' """'""' "' «• «"' 20 .0 .he product ,
product ! ' ■ ^ ''' ""' ""'"P'S »y 11 i what „ th,
Vraolcal Problcma in MKIUw
•..t 11881 "^ ^"''' " °'"'« »''. <"""■ 3(5 bottiM
z. i'z'rz:'zit z::^ '»»''-»3.„,u,t.„.,
■nauy nouth. „«, he paid ! ' '"' '"' "«""' '''C f" how
1194. What number multinlv hw 0-7 •
348X60 ? P^ ^y "' S'^«' the same product a,
1196. A city of 43872 inhabitants uaid SR-^rma ,•„ * .
be the value paid by each, if in equal'plmf ""'' ' "'''* "^^^*»
11 W. A sum of $7300 is made nn nf q«k • .
was the value of a piece f ^ ^''°''' °^ ^'^'''^ ^*I«« J what
J 197. In a nrnvinna *!,» - - .""■'
-»«.ed .0 f ua.;;ioT ;sr,r;,s;;:* :;t' '"''°* " '•"-
T'f"'*i-fiiifcVi" '■'-^■^•■^^ >'^^'H
h
III
46
DIVISION.
1198. How many 5 cent-pieces must I give in exchange for 45790
fifty cent-pieces ?
1199. How many days would be required for a writer to copy a book
of 720 pages if he copies 3 pages an hour and works 12 hours a day ?
1200. A horse-dealer bought horses for ?7990 and iu selling them for
$8466 he gains $28.00 on each horse. How many horses did he buy t
REVIEW PROBLEMS.
he pays $380.00, how much does he
1201. A debtor owes $4,050
still owe ?
. 1202. A person has in his safe $9260.00, if he deposits $750.00 more
at one time and then $250.00 ; what sum has he in his safe ?
1203. In an arsenal there are 92 piles of shot, each pile contains
3400 bullets ; what is the number of bullets ?
1204. The Carlovingian dynasty commenced in 752 and occupied the
throne 235 years. In what year did it end ?
1205. A decorator received $25.20 for his salary of six days' work of 12
hours each ; What did he gain each hour ?
1206. A printer bought paper at $2.50, $2.75 and $3.00 a ream ; he
had the same number of reams of each quality and he spent $330.00.
How many reams of each sort has he ?
• 1207. On the eve of a battle an army consisted of 80,000 men, on the
next day it had but 60785 ; how many men did the army lose ?
1208. I bought 75 yards of velvet at $9.20 a yard. In payment I gave an
equal number of pieces of $5, of 50 cents and 25 cents. How many did I
give of each 1
, 1209. I bought 96 reams of paper for the sum of $124.80. What is
the cost of each sheet knowing that a ream contains 20 quires and each
quire 25 sheets ?
1210. How many vessels will be required to carry 6840 men, if one
vessel carries 1368 men ?
, 1211. If 6 horses cost $1500, what will 16 cost ?
1212. I pay 75 cents for 25 steel pens, how many can I buy for $30 ?
, 1213. Patrick was 7 years old when he went to school, if he remains 2
years in the 3rd class, one year in the 2nd class, and 4 years in the 1st ;
at what age will he leave school ? *
1214. A man earns $25.20 in 9 days. What will he earn in 40 days ?
,1215. From a certain sum 172 persons received $18 each and there are
$16 remaining ; what was the sum ? ^
1216. If 90 dozen of eggs cost $4.50 j feow many eggs can be bad
for $12.50? ^ 99 . ^
DIVISION.
47
change for 45790
V much does he
40 men, if one
1217. A father was 35 years old at the birth of his son ; how old will
the son be when the father is 77 ?
1218. Nicholas was 23 years old in 1860 ; how old was he in 1851 f *
1219. A man spent 8260 in 6 months ; at that rate what would he
spend in 3 years ?
1220. A person has an annual revenue of $2021, how much can he
spend a day after placing $743.60 in bank ?
1221. Owen Kearney was born in 1870, how many years after 1892
will he be 47 years old ?
1222. A grocer received 308 pounds of sugar for $21 ,56 ; he wishes to
gam $6.16, What price will he ask for a pound ?
1223. The deluge took place 3308 years before Christ ; how many years
elap.sed from that event to the death of Champlain 1635 after Christ ?
1224. The siege of a city lasted 45 days, and the besiegers fired 13365
bombs into the city, how many bombs did they fire on an average per day t
1225. What number multiplied by 341 gives 443641 for product ?
1226. How many years in 10512000 minutes ? (365 days to the year)
1227. A bookbinder had 640 volumes to bind at the rate of 16 cents
per book ; if he completes the work in 41 days, what will he earn a day ?
1228. A general distributes 116000 cartridges among 5 batallions each
comprising 650 men ; how many cartridges will each soldier receive ?
1229. A vestibule is paved with marble tiles and is divided into 44
parts the whole number of squares is 148852, how many squares in
each part t
1230. Peter owes $168, he pays $62. then $63 ; how much remains due f
1231. A butcher buys 28 oxen for $1200 ; he sells them and gains $10
on each ox. What is his entire gain ?
1232. A grocer receives 6 cases containing 1500 pounds of cheese •
what did each case contain, and what will be the cost of a pound know'
ing that he 'aid $189 for the 6 cases ?
1233. Ernest received 40 cents to buy 6 pounds of bread at 4 cents a
pound and 2 candles at 3 cents apiece. How much money did he spend ?
1234. What is the weight of a case which contains 85 packages of
• aiidles each package containing 4 pounds, knowing that the case when
empty weighs 24 pounds f
1235. A hundred volumes cost $75.00, what will be the cost of one
volume, and for what will I have to sell them to gain $5.00 on all ?
1236. A contractor engaged 10 workmen at $1.20 ; 15, at $1 00 • 20
ai 80 ots., and 25 at 60 cts. What 8um ot money will he require each
week to pay th« workmen f
48
sivieiov.
;!l!.
li
1287. A father when dying left §3500 to each of his 4 sons and |6600
to each of his 2 daughters. What was his fortune ?
' 1238. A hundred eggs cost f2.00, how many can you purchase for
$15.00? ;
1239. 135 pages of 15 lines each were written by 46 pupils ; how
many lines did each pupil write ?
1240. How many pages can be written by 55 pupils, if each pupil
writei 4 pages of 18 lines each I
1241. A remnant of cloth cost $126.00 and in selling it for $155.25 I
gain $2.25 a yard ; how many yards were contained in the remnant f
1242. A man said that in 16 years he would be 49 years old and his
son would be 23 ; what are the ages of father and sou I
1243. A rosary contains 70 grains ; how many grains will be wquired
for 3 docen of rosaries t
1244. A hone and harness cost $170.00, the horse without the harness
cost $76.00 ; how much does the price of the bMmess exceed that of the
horse t
1245 George's overcoat cost 3 times as much is Andrew's shoes which
cost $6.50 ; what is th« cost of the overcoat ?
1246. A work lasted 18 days; on what day was it begun if it was
finished on the 23rd of May and there were two Sundays in that time !
1247. A person says that with $72.46 more he would double his
money and have $24.46 over ; how much has he ?
1248. A workman started his day at 4 o'clock A. M. and left work 10
hours after ; what o'clock was it ? "
1249. A servant receives $182.60 » year ; if he loses 78 days how
much less will h» receive I
1260. A man spends $1.35 a day ; how much does he save a day if he
gets a salary of $7.80 ?
1251. I am to receive $7424 in three payments: thvinrstwill be
$1 704, the second $4026 ; what will be the amount of the third T
1252. A miller wants $84 in order to pay for 125 barrels of flour at $4
a barrel. How much has he !
1268. Along a road trees are planted every 12 yards ; how many trees
will there be in a distance of 3660 yards i
1264. A subscription was taken up in a church on different occasions :
the first collection realized $37.00, the second $9 mora than the fint, the
third $52.00, and the fourth as much as the 1st and the 2nd ; what was
the amount of the subscription ?
1265. I pay $4.60 a yard for a certain work ; how many yards should
a workman do to receive $90.00 ?
DivisroN.
49
drew's shoes which
; how many trees
How many days
nauy yards should
1256. A workman received 342.50 for 17 days work,
will he work for ?1487.50 ?
1257. A house has 28 windows each containing 12 panes ; how much
will the glazier be paid at 15 cents a pane ?
1258. Peter has ^570, Paul has $60.00 more than Peter, and John
has as much as the other two together less $45.00. How much have
Paul and John ?
1259. A tailor has a piece of cloth worth $189.00. he made 4 pairs of
pants at $3.50 and 8 coats at $35.00 ; how much did he receive for it?
1260. A man having $12300 gave $8900 to an hospital and divided
the remainder among his 5 sons, what did each receive ?
1261. 1 bought 12 books at 52 cents each and I received 13 books free •
how much did each book actuully cost me ?
1262. A scholar had to recite 250 lines ; but having recited only 125
hnes, he has to write 2 lines for every line not recited ; how many pages
has he to write, if each page c ^ ;os 25 lines ?
1263. A squadron is coir < ,( 6 corvettes and 2 frigates. The
vessels carry each 400 me. and the frigates 350 men ; what is the
number of mm in the squadron ?
1264. A man spends 65 cents on Monday, 90 cents on Tuesday, 65
cents on Wednesday, $1.04 on Thui-sday. 75 cents on Friday and $1.64
on Saturday ; how much has he left if he had $4.00 on Sunday ?
1265. Three gamblers made a common purse, John gained $76.00 but
1 eter and Charley lost each $27.00. What is their gain ?
1260. A gentleman having an annual revenue of $3560, pays $56 00
for tajces and other expenses ; what can he spend daily after paying
1267. The city of Constantinople was 2540 years in existence in 1882 •
what 18 the date of Its foundation, and how many years after the creation
was It built ?
1268. Four gambler., have a common purse ; the 1st loses $40.00 ; the
2nd, $7.00 .ess than the first : and the 3rd gains $15.00 and the 4th
«25.00 ; what is their net loss ?
1269. A boatman made 4 voyages a day, he carried 80 persons each
time at 30 cents each ; what does he gain eveiy day, his daily expenses
oouig $33.00 I
1270. A man having no children ; left half of his goods to his four
nephews and the other half to his six cousins ; how much does each
receive, the fortune beiug $20640 !
,v.i»'«»'W.<n<0'.j,H'
t''\
A"' ,1
00
nivrsioN.
1271. I bought a certtin auiouut of goods for $620 ; if I had sold them
for $56 moip 1 would Imve gained half the cost price ; how much should
I hnve sold 'lem for ?
1272. Fred had $1500 before borrowing $850, if he pays a debt of $1860,
how much money has he left ?
1278. A workman gains $730 a year ; and spends $1.25 a day ; what
sum does he possess at the end of the year I
1274. A merchant has a revenue of $6935 ; what can he spend daily ;
1275. St Louis reigned from 1226 to 1270 and Louis XII from 1498 to
1615, how many years more did St Louis i-cign than Louis XII?
1276. A sailor buys silk for 30 cents, thread for 25 cents, needles for
8 cents and cotton for 6 cents, after paying these amounts he had 55tts.
remaining, 'iow much had he at fii-st ?
1277. Of three individuals ; the first receives twice as much as the
second plus $55, and the third as much as the other two minus $120 ;
how much has the third knowing that the first had 66 times $2.50 ?
1278. Thornl'ey went out with $1.30 ; how much money should he
bring back to his mother after paying . 40 cents for sugar, 26 cents
for coffee, 18 cents for butter and 8 cents for milk ?
1279. On an avenue there are 36 trees 15 yards from each other ; if 5
trees more were added ; what would be the distance between the fii-st and
the lost tr^ t
1280. Frank walks from the city to the village twice a day during I
three years, knowing that the village is 5800 yards from the city, how
many y^rds did jie cover ?
1281. How many seconds in 15 hours and 6 minutes ?
1282. With $540 more than I have, 1 could pay $1800 and have $28 j
remaining ; how much money have I ?
1283. Twenty-five men worked 60 days at $1.25 a day ; what surnj
will they receive ?
1284. A postman has 60 unpaid letters to distribute, among the
number thei-e are 23 at 3 cents and the remainder at 6 cents ; how mucli
will he collect in all ?
1285. A merchant has $12000 cash, he gains 3 times $580, and 5 times!
9805 ; how much money has he ?
1286. A man gains 1 cent on every pencil sold ; how many pencils did
he sell knowing that he received $13.80 for what cost him $11.04 ?
1.287. A dozen of omnges cost 60 cents ; what will 36 oranges cost f
DIVI8I0X.
61
ys a debt of SI 860,
1.25a day ; whnt
$580, and 5 times I
llft;.lLlti\'' T' *''*" ^^'^ ^«*'*'^« third half of the first 4«^
i9«i aV ^'"^ *^"" ^^"^ ^^'^ ' ^'•^^ ^"^ »1^« ««» divided f
1289^ A dozen of copies cost 42 cents ; how much would a person
ga.n who would sell 108 of these copies, at the ^te of 4 cents a coj"
.o.rgafnrorthrw:o;:r ''' ' '- --' -'^-^^^ ^
ini'jL'td rZthsf *^ '' '' -'-' ^" "^""^^ '' ^^^* -'' ^« --
1292. I have bought 48 dozen of pencils for the sum of $11.52. I wish
S Tr* "" '"'\ ^""' • '" ^^^* '^"^* ' ««" them a dozen 1
9 < Af TT "°^7' ^^ ^'''"'""' ''^ '^' '^^' °f 80 cents a day for
1294. Howmany hours in a journey which begins Monday at 7 o'clock
A. M. and finishes on Wednesday at 8 o'clock P. M.?
1295. A man having an income of $1328.25, has .saved $3225.00 in 15
years ; how much did he spend a day ?
1296 The quotient of a division is 102215. the divisor 342 and the
remainder is 341 ; what is the dividend ? •
tK.T^* "^IW^^T ^"^"'^ """'^'^ ^'"' ^« ^''y' "°«'^«<1 »« ; one of
amount did each receive ?
J^lL^'^f ^\ ^^l f ** ^**"' that a journey began knowing it took
86 hours and was finished on Saturday at 11 o'clock AMI
1299. A workman from whom $7.50 were retained, received $42 as his
I salary for 18 days' work ; how much did he gain a day ?
i ^r°" J° t ^r"^ **"' '"*^" eains $56 a month, the mother $2 70 a
yeaM * * "" **"-^' " ^'" ' ^°^ '""'^^ '^'•^ they all gain I
h ^^??-i/T"^*'*"''P''^2^^*^^»"<^^«««fhayfrom4acre8, which
I he sells $30 a hundred. How much did he get from each acre »
13U2 A child being sick the doctor came to see him 15 times. The first
tranh?H*\'"* *'•''; f ' *'^ ^'"^ ''''"''' °^*^« ''t^- visits knorg.
I that the doctor received $9.25 in all ? ""i"B
1303. If I had 25 $5-bills, 45 $2.bills and sixty 50.cent pieces, I could
pay my debts and have $7.60 remaining ; what do I owe ?
1':
j'i'i
ill
! i
r i
62
MENTibl. ABITHMETIO.
MENTAL ARITHMETIC.
55. Mental Arithmetic is the art of calculating with-
out writing the numbers. A pupil acquainted with writtenwork
only, will not readily detect an error by the absurdity of the
result obtained. He, who is in the habit of calculating men-
tally, will, on the contrary, immediately detect such errors,
and will seek to correct his work.
Rules for Addition.
56. To add a small number add the tern successively and
then the units.
Example.— To add 37 to 44, first add 3 tens to 44, thus : 54, 64,
74 ; tbeu add 7 units and the result gives : 74-j-7=81.
57. To add, a number^ it may be decomposed into parts and
then added successirelij.
Example.— To add 324 to 475 ; decompose it into parts as : 300-f
20+4, then 475+300=776 ; 776+20=795 ; 795+4=Au8. 799.
58. It is sometimes more advantageous to add a larger
number than that given, and then subtract the difference.
Example.— To add 92 to 446, first add 100 and then subtract 8,
since 92=100—8 ; thus 446+100=546 ; 546— 8=An8. 638.
59. When the numbers to be added end «» the same number
of ciphers, add the aignificant figures, and annex the number
of ciphers in either number.
Example.— To add 1200, 600 and 900, first add 12, 6 and 9 : 12+
6=18+9=27 ; then annex two ciphers, 2700.
Problems in Addition.
1304. I bought $7 worth of bread, $4 of butter and $6 of wheat ; how
much did I spend t
1305. A piece of clcth cost J70, another $80 ; find the total cost !
1306. A school consists of two classes : in the 1st there are 30 pupils,
in the 2nd 45 ; how many pupils in the school ?
1307. How many minutes in one hour and a hi\lf t
1308. Paul was born in 1874 ; in what year was he 11 years old !
1809. What is the perimeter of a room 9 yards long and ? yards wide?
(There are 2 lengths and 2 breadths in the perimeter.)
MENTAL ARITHMETIC.
«8
J of wheat ; how
To pay he offers
Biiles for Subtraction.
60. Two processes are us 1 to solve questions in subtmction :
Tim first process w to subtract successively the mils of the
smaller number from the iarger.
T1»U8 to snbtrnct 3 from 15, say : 15—1=14 • H-l=]3 • l3_i=3
12 Ans. Or, 15-1=14 ; 15-2=13 ; 15-3=12.
The second method is to add to the smaller number the units
required to equal the larger number.
Example.— To subtract 4 from 9.
4 ami 1 make 5 and 1 make 6 and 1 make 7 and 1 make 8 and 1 make
9. Tints 5 units are required to have 4 equal 9. The practice of addi-
tion enables the pupil to resume these operations in a si-jgle one. Thus
4 and 6 make 9. The answer is 5 units.
Problems In Subtraction.
1310. A person buys meat for |4, vegetable for |2.
I n $10 bill ; what change will he receive ?
1311. I sold goods for $75 and gained $12 ; how much did I
pay for it ?
1312. I'eter is 15 years old and Paul 29. How many years older is
Paul ?
1313. A man was 30 years at the birth of his son. How old is the
I son now the father being 77 ?
1314. One traveller walked 47 miles and a second 22 miles. How
I many miles did the first one walk more than the second *
Rules for Multiplication.
61. When the multiplier is n or U, the multljjUcation can
I he solved as by one number.
Example. — 97085
12
1165020
I Thus : 12 times 5«60, write and cany 6 ; 12 times 8=96 and 6
make 102, write 2 and carry 10 ; 12 times 0=0 and 10 make 10, write
and carry one ; 12 times 7 are 84 and 1 are 85, write 5 and cany 8 • 12
times 9 are 108 and 8 make 116. Write 116 ; the product U 1166020.
64
MENTAL ARITHMETIC.
62. The product does not change if one factor is multiplied
and the other factor divided by the aame number.
Example.— Multiply 24 by 5. *
Multiply 5 by 2 to have the factor 10 and divide 24 by 2 this gives 12
which multiplied by 10 will give 120.
63. To multiidy a number by 20 it can be doubled and then
multiplied by 10.
Example.— Multiply 42X20
42X2=84 ; 84X10=840.
64. To multiply a number by 50 it can be multipliec^ by 100
and then half of the product talen.
Example.— Multiply 36x50
36X100=36 hundreds ; 36 hundreds -4- 2=1800.
65. To multiply a number by 25 we can multiply it by
100 and divide the product by 4.
Example.— Multiply 56X25
56X100=56 hi^dieds ; 56-r-4=14 hundreds =1400.
Problens In Bfnltlplicatlon.
1315. I bought 40 yards of cloth at $4 a yard. How much did I pay t
1316. What will be the cost of 100 yards of cloth at $5.50 a yard t
1317. What will 40 registers cost at 50 cents apiece t
1318. What is the price of 50 chairs at 60 cents each !
^ Rules for Division.
66. To divide a number by 10, by 100, etc., make the number
10 times, 100 times smaller by cutting off one, two or more
figures.
1st Example.— 275-5-100=2.75 or 2 with a remainder of 75.
2nd «« 12451-7-000=1.245 or 1 and a remainder of 245.
\ Problema in Division.
1319. Six persons share $54 ; what part does each receive f
1320. If you divide $130 among 5 persons what will be the share
of each ?
1321. I bought 5 dozen of eggs for 60 cents. What is the price of a
dozen ?
1322. Divide $5 among 20 children. What is each one's share T
1323. Twenty men earn $46. What is one man's wages t
MENTAL AniTHMEriC.
65
the price of a
" Problems In Mental Arithmetle.
H«w"* ^"f ^u\^ """* °^ ^"''"^ *«» ^' ' »»• •>«» « ™"« to ftnUh.
How many has he done f
now f * '^°**"'' ^"^ ^* '°'"'^''' ' ?' ''°" ^ ™°"- "'*' °^^y »»«« he
1326. Owen hud 25 pens in a box ; he lost 7 of them. How many
had he remaining T '
1327 James had 60 cents, his father gave him 40 cents and his aunt
60 cents. How much has he now ?
1328. Louis had |80 in bank, his uncle gave him $15. How much
has he not? ! •»•»«"
1329. Add 260 to 150.
1330. What is the sum of 360 and 140 ?
1331. My uuclo had 15 hens; he bought 2 others and gave me 4.
How many has he remaining ? o « ».
1332. Alfred had 15 cents ; he buys a pen for 1 cent and 2 copy-books
at 3 cents each. How much has he remaining 1
1833. How many hats must I sell at §3,00 ench to recoive «30 ?
1334. Walter received 18 pieces of candy ; he gives 3 to each of hi,
companions and keeps 8 for him.self. What was the number of his
companions ?
1835. Louis gains 60 cents a day ; how many days will it take him to
gam 90 I
1336. Philip has arranged his pens in several piles ; the Ist contains
25 the 2nd 35. the 3rd 40, and the 4th 70. How ma'ny pens h^t T
1337. John buys oil for 12 cents, ink for 15 cents and coffee for 6
cents. What sum did he spend ?
1338. A merchant sold 150 newspapers in the morning and 130 at
night. How many has he sold in his day ?
1339. What is the product of 4 by 7 ?
1340. Henry has 35 apples, his brother 25 and his sister 40. How
many have they together ?
1341. A man owes $15 to the grocer. $25 to the baker and $20 to the
butcher. How much does he owe them all ?
1342. Leo had 37 apples ; he gave 4 of them to each of his four
comiMuions. How many has he rtmaining ?
1343. A husband earns 80 cents a day, his wife 40 cents, his son 60
cents and his daughter 20 cents. How much do they save if thev
spend 11.40? '
M
MKNTAL AHITUME'l'lC.
184«. Joseph received 60 cents from his father, 40 cents from his
nude nnd $2 from his god-mother. How much did he receive in all t
1345. James bought a horse for 9450 and sold it for $200. How
much did he lose T
1346. If I hod $4 more I would hnve |29. What is my fortune T
1347. Charles bought a cupboard for |50 and sold it for |68. Hdt^
much has he giiined ?
1348. If Peter had 7 cents less, he would have 27 cents. How much
has he ?
1349. A barrel contains 220 qunrts of wine ; 4 quarts are dn^wn every
day during 20 days. How many quarU reinniti in the barrel ?
1350. Paul obtained 7 goyl notes a day d^'riag 4 days. How many
has he now knowing that he had 14 olready ?
1861. How many pair of boots at $1.50 » pair can be bouglit for f 6 ?
1352. If a boy drawd 4 quarts of oil out of a barrel that contains 32
quarts, how many will be remaining at the end of 8 days f
1353. I had $75 t I have given |5 to the poor and placed $50 in
the Savings Bank. How much have I remaining 1
1354. Alphonsis had 45 marbles ; he lost 15 and gained 20 ; how
many has he now ?
1355. A flock is composed of 730 sheep ; 1 00 are sold every day during
7 days. How many sheep remain ?
1866. Felix's father spends 4 cents a day for tobacco. How much dees
he spend weekly T
,J^1367. A family eats 8 pounds of brtad a day. How long will it take
to eat 72 pounds T
1858. Leo gained 8 good notes a day during 5 days ; how many has
he now knowing that he had 14 to start with t
1359. Thomas had 24 apples ; he ate 8 a day. How long did his
provisions last f
1860. A fruit-seller offers me 9 plums for a cent. I bought some and
ho gave me only 50 for 6 cents. How many are missing ?
* 1361. How many 10 cent-pieces will it take to pay $1.20 t
1362. A gardener plants 144 cabbages in a piece of land in which only
12 can be planted on the width. How many rows will he be obliged to
make t
1868. How many months in 15 years t
1364. Eugene is 12 years old, his younger sister is 7, his father 85 aad
his mother 29. What will be their agci in 12 years f
MBMTAt ABITHMITIO.
W
1M5. A 1MB booght 100 egg, on the market. He broke 4 In couiln^
home. How many dozen ha. he remaining to sell T ^
6^1\ll "^fT"" P™'^""'" ^^^ "PP^""- The proprietor gives 8
dc^en away and keep, the «„t for himself. How ma'y do«n'did h!
^«7.^At 18 cent, a dozen for eggs, how many eggs could I buy for
oe„\?!' t ^^ij""*"" "'^'^"' " ^"'°'»- 'J^i^J* »>« «e"B at « gain of 15
cents each. How much did he gain ? ^
per' doL^fr" '''""^^* "^ '«»' *" "**"* •"'^ "''"- them for 20 cents
870 ir/ "'' '"'" f *'•'"*' ''«- ^'^"^ •"»«* he receive »
Jr AvVr//"*" "•"'"'^ • "'I"*" K*''^^" *ho«e side is 13 yards
long. What distance did he go ? uo ib lo yaras
o J"^'u'? * ^'''"*** containing 25 needles, 3 are broken, 5 are rustv 3
18^ Ho:l' m "^ ""'• ""^^' ™^»^ -^'- «- '-old?'
1372. How much do I owe for 8 umbrellas bought for »1.40 each f
1373. How many buttons are ther« in 15 dozen ?
money ha'e I J ' """ ' ""^^ '''' * ^''^^ ^"'^^ *2«- How much
Jef-H?kr.i'l8''f''f •"":;• "• ^^" " *" *-h ofh---
com^de. , "^ " '" ''""^'- «°^ -»y •'•^ »>« «- to hi.
8o'c'ent« f"^ "^' """"^ **' "•"**" '* " «"**• * ^«^«-' ««H ^e had for
the ™t oT,^*.*2^;r1a^r ""^^^ "^ '^^"-^ *° ^^ ^« -^- «*
1379. Maurice was 16 years old when his sistor was born Wh.t „ni
1385. Andrew disuosed .Ifln fr«»men*s Af -^n« • -c -
-__ .V . * . : o'"eB,s 01 =ionc ui iS pues. How
father 86 and | '*""* *«" there in each pile ?
1^6. I bought 18 eggs at
many
themt
eggs at 18 cent, per do,en. What must I give for
M
MBMTAL ARITHMETIC.
1887. Eugene will be 18 yean old in 11 yearn. How old is he now t
1388. John's father receive); $9 for 4 days work. What will he get for
20 xya work, t
1389. ^Vilfrid changed forty-five 5 cent-pieces for twenty -five cent-
pieces. How many did he receiv'< ?
1890. A ream of paper contains 20 quires and each quire 24 sheets.
How many sheets in a half quire T
1391. Charles gains $15 per month. What is his annual gain t
1892. Adolphus was born in 1864. How old was he in 1885 f
1393. In adding $3 to what I have ac^iallyt aud in doubling the sum
obtained, I find I have |14. What is my money ?
1394. Joseph's mother paid f21 for three pair of sheets. What ab the
price of one pairt
1895. Stanislas was 8 years old the first of March 1893 in what year
was he half this age T
1398. If the sum of money I have were tripled I would have |46,
what is this sum ? ,
1397. I had 50 plums. I gave 32 to my brother ; iind after eating a
part I fined that I have 18 remaining. How many plums did I eat 1
1393. I met three poor persons and to the first I gave two cents. How
much did I give in all knowing that to the others I tripled the amount
given the first t
1899. Edgar bought 45 yards of cloth for $27. He sold 15 yards at
eost price. JIow many yards remain and what is he to receive for the
part sold f
1400. I give $14.60 to my baker and this sum is only half of what I
owe. What credit did he give me f
1401. If the sum I had were four times greater I would have |32.
What is the sum T
1402. Four brothers have each 25 marbles : The 3 older give what
they have to their youngest brother. How many marbles has the
youngest brother ?
1403. Ferdinand divides his pictures he has into 4 parts and gives
one of these parts to «ach of his companions. Counting those that
remain he has 35. How many had he at first t .
1404.^ If James's pictures were multiplied by five he j^;Quld rh^ve 7& ;
how many has he !
1 405. Andrew's father received $35 for tan (^ays* work. How much
would he have received had he worked only 7 days ?
1406. Seven times my money would be sufficient to purchase 6 yard*
of silk at $7 a yard. How much have I !
MENTAL AniTHMETIC.
59
forT? '' ""**" °' "'''"" '""' ^'•''- ""^^' '"'"'^ y"'^^ ^"^ ^ «-i^«
1409 Louis gave one-half Lis money to th« poor and hi, father multi-
centi now , ' " '' *"•"• "•"•' ™"«'» '^^ ''« "^^ ^-t if he has 24
1410. Half a certain sum equals 24. What is four times this sum ?
1411 I received three tunes a certain amount wheu T H.„;rht 1 would
receive four times the amount. How much did I .c ei. t,^ Z J
a., .cpated. if the double of what 1 received equah. $n7 " '
1412. Alfred's money was doubled three time . a., he nov has SI40
How much had he at first ? *^"*
1413. William arrived home on the 28 of Februarv .r »., oK
15 days. When did he leave home f " "'^^^'^^'^^ '"»» "I'^^nceof
1«4. My mother is 5 yeara younger than my father. What is th,. «„«
1«8 A grocer .old a tub of butter for «I0, and a box of chee» tor «li
""bT;:;™'" '»'""■""»- «'«»»• »»«-; »«. h^ ^ri^S;
"19. If • iKwnd of coffee coets 31 cent.. How much will ■ 1 .
l«n«d. coat J s._ 7 pounds : 3.- 8 pound, I ' " '
U20. How much will be paid for 6 pounds of boiler., i-i™.
l«.u»d, and 4 i»nnda of sugar at 8 cent, a jound ! ""'' *
u.uoMid ill*'," '° ""•* "* •= " "'•■^ '"^ -" '"- '» »»»• How
lioq A 1 , ^''^"" ' 2— 72 cents ; 3.-^ 90 cents ?
*m H Z T ^''"'^^ ^°'' *^« ''' «»« t™« ; '^ second time for
$130 Having sold them for «2. how much did he gain ?
1424. A man having been married 49 years dies at theaaeof 77
What age was he when he was married ? * "*
1425 At 18 cents a yaid what cost : 1.- 6 yards of calico • 2 7
yards ; 8.— 9 yards ? "'^ ' * — ^
i
I
4
\
\
60
MENTAL ABITHMKTIO.
1426. A farmer sells 14 sheep at $4 each and 10 lambs at |2 each.
How much did bo receive for all t \
1427. What is the sum of: 1.-9+12+6—7 ; 2.-36410—12;
3.— 14+10+12—24 ?
1428. A mau walks 25 miles per day : how many miles will he walk :
1. — in 10 days ; 2. — in 12 days ; 3. — in 15 days ?
1 42d. John has 1 6 marbles, and Leo has 4 times as ma;iy as John.
How many have both together ?
1430. What is the result of the following combinations : 1. — 43+
37—20 ; 2.— 9+12+15—26 ; 3.— 26+15+7—18 ; 4.— 27+23—
20—2 ; 5.— 33+28+9—30+15 ; 6.— 16+12+9+6—34+7 ; 7—
44—20+11-12 ; 8.— 16+26—30+15 ?
1431. By how many does the number 58 exceed 31+19 f
1432. What cost 12 pounds of butter : 1. — at 15 cents per pound ;
2.— at 18 cents ; 3.— at 20 cents ?
1433. I have ^Ol 1 buy a coat for $15 a veat for $5 and a bat for $4.
How mnch will I have remaining t
1434. Joseph bought 12 oranges for 3 cents each ; 8 melons for 4 cents
each aud five pen holders at 2 cents. How much did he spend t
1435. A child bought 16 apples from one stand, 18 from another ; he
at)! 6 and lost 5. How many has he remaining T
1436. At 66 cents a pound for tea what will be paid for: 1. — 9 pounds ;
2. — 7 pounds ; 3. — 10 pounds ; 4.-8 pounds ; 5. — 12 pounds ?
1437. Henry has 48 cents in 3 boxes : the first contains 16 cents, the
second 19 ; how many arc in the third ?
1438. A merchant employs a mau and his son, he pays the father $1.80
a day and the son 80 cents. How much will he owe them : 1. — in 7 days ;
2.— in 10 days ; 8 in 12 days ?
14R9. Jack had 12 marblc!*: one of his comrades gave
10 ; a third comrade gave him enough marbles to mi
did the third give him ?
1440. If a railroad train runs at !ie rate of 24 mi
will it run : 1.— in 7 hours ; 2.— in 9 hours ; 8.— i
hours ; 6.— in 16 hours ?
1441. Francis who is 17 years old is 8 yean older
12 yean younger ilxan Leander. What are the
Leander f
1442. At the ra* ■ of 30 eenta a hushil, what cost
potatoes ; 2.— 7 bushels ; 3.— 9 bushels !
im 8, another
how many
hour, how far
lun ; 4.— in 12
Louis, who is
of Louis and
5 bushcla of
)s at |2 each.
6 bnshcla of
MENTAL ARITHMETIC. *gi
Of IJll'lJt'^'T "'"" •ndahalfofegg,for20ce«t.; one bushel
the ::t o'AragLf '"" ^^' ^"^^ ^^"^^ ^^ *^- ^^ ^- ^^^^ i-
Klivef fot r"^ T ^"^' ' ^"* ^°' *^' '^ P"' of ^oot'* for $8, a pair of
gloves lor «2, and an umbrella for Si H« .mV *u i
...;:^-.u'';4" niX'; '"^ °""°' "'" "'^ «"" '-'» *
Michael ? '"'''^ ^'^ •^«''«"^e tjained than
at $16 each, for 8 calves at $9 each ? ^ *^
les^'foua'rr'H*''' ' 'T?/ '*'"^'-' ^"""^ ^''''^S times as many
lesa quarts. How many did Frank pick ?
ceT'.'^tZ'^'"T^r''^'"'^''''^ ' '^'^'»''^y»'' '^ have 82 '
Lt^Jha. th^tlirb;? " '"*' "'^^" ^'^^^^^ ^- ^« --." How
the'^ki^irh-r^;^^^^^^^^^^ .t r • ""-"^" '^-^^ ^ ^^^' -
I ?if^]f ^"^ ^'^ " ^ '""'' * PO""*^ *»d pork 9 cents : what will
b. the difference in cost of 9 pounds of each ? "
J«6. What is the difference between 7 times 18. and 8
wii^bl?" ^ * *'"" ^ P'"""' •'^'^ H-'^'y 8 «»- 8. How many
1469. What wiU 6 lemons cost at 3 for 12 oents f
timfts Or,
'S
62
MEKTAL ARITHMETIC.
m !
1460. If 4 peaches are worth 8 cents, what will be the cdstof 8
jwachcs ; of 18 peaches ; of 27 ^waches ?
1461. If 7 pounds of meat cost 42 cents what will be the cost of 9
pounds ; of 13 pounds ; 17 pounds ?
1462. What will 11 barrels of flour cost at the rate of 5 ',rTrelsfor$30 ?
1463. A man walks a distance of 36 miles in 4 days. What distance
will lie wnliv in 12 ; in 15 days ; in 20 days ?
1464. What will be paid for 5 turkeys at the rate of 120 cents for 3
turkeys !
1465. William gave 10 cents for apples at the rate of 3 apples for 9
cents ; how many did he get ?
1466. If 6 men can mow 12 acres of land in one day. How much will
15 men do ?
1467. Six cooks use a chest cf laa in 12 days ; what time will 4 chests
last T
1468. If 5 workmen can do a certain amount of work io 16 days. In
wliat time would 20 men do the same work '(
1469. How many men would be required to build a yacht in 6 days, if
3 men can build it in 12 days !
1470. Maurice paid 8 cents for a ball. How many balls of the Lame
kind can he buy for 32 cents ; 56 cents ; 80 cents ; 96 cents ; 104 cents t
1471. If 4 pounds of butter cost 60 cents, what will 6 pounds cost f
1472. If 9 dozen of eggs cost 81 cents ; what will 1 dozen cost ?
1473. If 6 pen holdei-s cost 12 cents ; what will be the cost of 7 pen
holders ; 10 pen holders ?
1474. When beefsteak cost 10 cents a pound, how many pounds can
be had for 70 cents ; 90 cents ; |1.20 ; |3.00 ; $5.50 I
1475. If a child reads 7 pages per day, how many days will he require
to read 49 pages ; 77 pages ; 98 pages ?
1476. If a horse goes 42 miles in 7 hours ; what distance will he go
in 11 hours ?
1477. What will 9 pon Is of coffee cost if 3 pound*-«o8t 27 cents ?
1.478. If 6 barrels of flour cost $54 ; how much will 8 barrels cost ?
1479. If 15 yards of cloth cost $75. What will be the cost of 12
yards ; 16 yards ?
1480. When melons are sold at the rate of 3 for 60 cents, how many
can I buy : l.-for$1.20 ; 2. -for $1.60 ; 8.— for $2.40 f
1481. If 9 yards of muslin cost $1.08, what will be the cost : l.-of
5 yards ; 2. —8 yards ; 3,-10 yards ; 4. =18 y-wds ?
1482. A fruit-dealer gives 3 apples for 4 ceuts, how many will he give
for: 1.-24 cents ; 2. -40 cents : 3.-56 ceotr '.
MENTAL ARITHMETIC. gg
.•.".■-63*;., V 45°'"?" f .' """^ '■°' "■"' -" ^<"' ""J'
oo cenis , 2.-45 cents ; 3. -$1.08 ?
»,«r! Jte ir ;i ;err "'°"'" '° "^ '- ' "»»«"■ «-
..." r!; :''..iirrir.' i "r :• ^t "-^ °"*' -'^ ^""
1491 I h.»ll " ' • 2— 3b chestnuts ; 3.- 48 chestnuts ?
Howich S'j: r '' ' '-' '' -' ^"^ ' -'' *^- ^* « ^o'«7.
.uuiris Iff 'J.*'''' 'l^'""^' °^ ^"S^^ ^'' ' P""""^'' of butter ; how
UOi w. ^? ^'''*^- ^''^^ 's the price of 1 yard of the cloth ?
1 494. When wheat is worth $1 for 5 bushels Hnw .«„ V , ,
would be required to buv s .n J "r o ousnels. How many bushels
1 iQK IP ; 1 , , ^ °'^'^^ °*^ '''°°'* "t ^^ a cord ?
buheL/r^^'^^*^''' '*'•'' ^^^"'^l^ bushels of corn; how many
bushels of corn equal 10 bushels of wheat ? ^
1497. A man bought 14 barrels of cider for $56 ; he dvel 5 barrel,
for a certain number of yards of clofh at ao . 7 « * "^®"
1498. Five men buy a mowing machine for 8120 Th.„ u a -. , ■
^^ ,. per „ee. .„d .,Ua. .u'r j:;v:?r2
Srf for 7« aato ! ' ■ ■" '"' *' 'PP'"' i 2nd for 60 .ppl„ j
; *ll1:
64
COMMON VRACTIOKS.
1501. If one bushel of corn equals 2 bushels of oats, and one bushel
of wheat equals 2 of corn, how many bushels of wlieat will equal 20
bashels of oats ?
IBOi,. Jf it require 8 days for 10 men to build a wall. How many men
would it take to build it in 5 days ?
1503. Justin gave 7 aiyples for 21 chestnuts ; at this rate how many
chestnuts can he have for 8 apples ?
1504. 1 gave 8 yards of merino for 6 pints of syrup : what will a pint
of syrup cost, if 4 yards of merino cost 48 cents ?
1505. Felix bought 7 yards of cloth for $21, and he gave 4 yards of
this cloth in exchange for apples worth $2 a barrel. How many barrels
of apples did he receive ?
^ COMMON FRACTIONS.
67. A fraotiidn is ono or more of the equal parts of a unit;
as, one-ha^ff tvco'thirds,
If we divide a unit into 5 equal parts, we can take one of these
parts and have one-fifth. If three parts were teken then the
part would be three-fifths ; one-fifth and three-fift} - are
fractions.
68. A fraction is represented by means of two nuvabers
placed one over the other and separated by a dash. For
example the fraction three-fifths is written |.
The number above the line is called numerator. It denote^
the number of equal parts which is taken.
The number below the line is called denominator. It
denotes the number of parts into which the unit is divided.
69. To read a fraction the numerator is called first, then the
denominator. Example : f is read three-fourths.
The fractions J, §, |, |, |^, are read, one-half, two-thirds^
three-fourths, four-fifths, five-sixths.
70. The numerator can be greater or less than the deno* .
nator, or it can be equal to it.
When the numerator is smaller than the denominacot a
have a proper fraction, that is to say, a value less than Sk
unit. Ex. : ^.
4
i
i
COMMON FRACTIONS. ^
When the numerator is greater than the denominator it is
unitT^Ex^T *°'^' *^'' '' *° '^y * ^^^"« S^«^t«^ t^a^i
When the numerator is equal to the denominator the fraction
equals unity. Ex : f , |, |g.. "<»cuon
bv'^?vfd1^°^®''® • v^'"''' '^'" ^'^^^ °^ ^^^<^t^"°«« to the pupils
board n/ T'."'^'' ''''^"^ *^"" ' ^^'^^^« ^^ ^he Mack-
Doard, an apple, etc.
EXBROISES.
1. Bead the rollowinjr fraction*
§
i
i
I*
fi
I?
It
II. Write in fflgnreB the f»lIowln9 fraction*
nZ^TJ" ^^T :?r'°"^''^"*^ Thirtee^-fourteenth,
oLe hif j!^«-t«°ths Th«e.fifteenth8 Seven-eighteenths
Jwj'Srds Sr T^ Four-sevenths Ninteen-Lntieths
iwo thirds Eight-nmths Four-twentiethi "-ven-twenty-filths
Seven.e.ghts Four-elevenths Six-ninteenths . - ..ty-seve'-Seths
III. What fraction is obtained by dlTldinff a unit
Ans..J
1.— Into 2 equal parts
4
8
12
16
20
24
2d
1.— Into 5 equal parts
7
AUS...J
11
15
19
23
27
81
II
II
II
II
II
II
IT. int. how many e,nal part, mnst a nnlt be divided to obtain :
I tia1«*An a
1 — halves
fourths
sixths
tenths
Ans. into 2
fifteenths
eighteenths
twentieths
twentjr.fiftbs
f • • • f .
. • * . f n
• f f ft
'• ; i i
[Hi
UK
'ili
m
66
2.— thirds
fifths
sevenths
elevenths
COMMON iT.ACTIONS.
Ans. into 3
seventeenths
thirteenths
eighteenths
thirtieths
^V. lExiirei** In the form of a fractlCMs
1 . Five numbers smaller than xtnity.
2. Five numbers greater than unity.
?,. Five numbsvs pqwal to ur.ity.
VI. Willi* arc . 2se r«»f !'»wii!jg expressloiiia In relation to a maiiSt
9
I
i
I
i
tV
H
H
REDUCTION OP FRACTIONS.
71. Reduction of fractions is the several operations
to 'vhich the terms of a fraction may he suhmitted without
chan^in" or altering the value of the fraction.
There arc four principal reductions of fractions,
72. To reduce a whole or mixed number to an
improper fraction.
1 .— Let it be required to reduce 4 to fifths.
A unit equals 5 fifths = |, 4 units will equal 4 times f or ^«.
2.— Let it be required lo reduce 6 units § to an improper fraction.
A unit equals 3 thirds= |, 6 units will equal ^ : adding f we have
Y4-i=V- Therefore 6-|-i=or ^=^°-.
73. Rule.— To reduce a whole or mixed number . v..
improper fraction, m.l Ay the given denomin.. i" the
whole number and add ;..; numerator of the /rac * > cny.
I. Red
130vS.
J509.
» h-jlO
1511. I
II. RC4
1518.
1519.
1520.
15'21.
1522.
1523.
74. Ti
ormiz<
1.— Le
expressio
One u
the fractio
therefore ^
2.— Lei
ex] issioi
Oneun
the remaiud
75. Ru
improper i
the quotiei
COMMON FIIAOIJONS.
67
I
u
il operations
tted without
ber to an
jer fraction,
iiug f we have
imber . ,-/
ti.:;" ' the
'^iuya i^ any.
EXERCISES.
I. Redncetoan ImproiMr rracllon
1506.
1507.
130S.
1509.
1510
1511.
units to halves Ans, §
" thirds
" halves
" fourths
" thirds
" fourths
1512. 6
1513. 8
1514. 9
1515. 10
1516. 11
1517. 12
units to fifths
sixths
Ans. ^jO-
sevenths
eights
sixths
ninths
II. Beduoe .he following numbers to Improper fraction.
1518. 4^
1519. 5^
1520. 8 J
1521. 9^
1522. 6^
1523. 9g
s. 8
1524.
24
1525.
n
1526.
6|
1527.
n
1528.
H
1529.
8s
Ans. >^
1530. 7f
1531. 4g
1532. lot
1533. 141
1534. 17i
1535. 21|
Ans. Jyi
74. Ta reduce an improper fraction to a whole
or mixed number.
l.-Let it be required to find the units contained in the
expression V.
th. ,°";.""'';f'l"''I^ ^ f°"rths or |. As often as 4 is contained in 12,
the fraction then contains one unit. The quotient of 12 by 4 is 3'
therefore ^=3 units. * "j' » is o ,
2.-Let it be required to find the units contained in the
ex] ssion HK •
One units contains 8 eights = |. The quotient of 1 47 by 8 in 18 and
the remainder is 3, thefore A|i=18+| or ISf. ■
75. Rule.— To find the number of units containfld m an
improper fraction divide the numerator by the denominator •
the quotient is ihe number of units.
\y-4
C8
COMUON FRACTIONS.
EXERCISES.
Find the nnlta contained In the followlnfr nninbera
1636.
s
Ans. 3
1542.
¥-
Ans. 3i
1548.
¥
1537.
^4*
• • • •
1543.
•V"-
1549.
V
1538.
V-
• • > •
1544.
■V-
1650.
-V
1639.
¥
1545.
V
1551.
1640.
¥
• • ■ *
1546.
¥
l.')52.
¥
1541.
V
. • . •
1547.
V
....
15.'i3.
¥
Ans. 3^
To reduce a fraction to its lowest terms.
76. To simplify a fraction is to represent it by its lowest
terms. The fraction || simpliiied could be written ^ or |. These
are obtained by dividing by 2 and then by 3.
To reduce a fniction to its lowest terms is to represent
it by the smallest numbers possible.
1. — Let it be required to reduce to its lowest terms the
fraction U.
Divide both terms by 2 and we have ^^ ; divide again both terms of
the new fraction by 2 and we have |, of which both terms may be
divided by 3 and the quotient=i. } is the lowest term of '^J.
2. — Let it be required to reduce to its lowest terms the
fraction IB.
Divide saccessively both terms by 10 and by 6 and we have § as the
lowest terms of ^f ^.
76. Rule. — To reduce a fraction to its lowest terms, divide
both terms of the fraction by the same number, and repeat
this operation with each new fraction until a fraction is
obtained whose terms will contain no common factor.
EXERCISES.
Bcdnce the foUowlns fmetlona to their lowest terms
1654.
t
Ans. §
1560.
if
Ans. 1
1566.
M
Ans. H
1566.
i
t • • •
1561.
H
1567.
fi
1556.
Xi.
1562.
ii
1568.
13 cj?r
1667.
H
• • • •
1563.
iS
1569.
m
1658.
1669.
A
«
• • • •
t • • •
1664.
1666.
1670.
1671.
1444
COMMON FnACTIOVS.
99
To reduce fractions to a common denominator.
Fractions have a common denominator when both
have the same number for denominator.
1 — To reduce two fractions | and ^ to a common denomi-
nator.
Ol'KUATION.
3
3X8
24
—
:=!
5
5 X 8
40
7
7 X 5
35
8
8 X 5
40
Multiply both terms of the first
by 8, and both terms of the second
by 5, and we obtain J^, JJ.
77. Rule. — To reduce two fractions to a common denomi-
nator muUiply both terms of each by the denominator of the
other.
2.— To reduce more than two fractions to a common denom^
nator. Ex.--J,|andf
Oi'EnATioy.
2_2 X 6X7 70
3 3X6X7~105
*_* X 8 X 7 84
6 6 X 3 X 7 ~ 105
« « X 8 X 5 90
7 7X8X6 105
Multiply both terms of the first
by 5 and 7, then both terms of the
second by 3 and 7, and both terns
of the tKird by 3 and 6. We
thu8obtain^j,^5^,^^V
78. Rule.— To reduce more t jrn two fractions to a common
denominator, multiply both i,,ma of each fraction by the
product of the denominators of the other fractions.
70
ABDiTioa OF r V A . IONS.
BXBBOISES.
Bednce the followliiit rrnetioiM to n cnminon denominator
1672.
i i.
1673.
i. h
1674.
hh
1676.
?. h
1676.
i h
1677.
^ 3-
1678.
<i. i'. h
1679.
i. h a.
1680.
^ h h
Ans. f, §.
1581. §, ^ i. Aad. tii:;,18S. ^.
1682. f, ^, f ;
1683. -8, S, 4
1584. S, i f
1585. f, i, f
1586. il, I, f
1587. i, t, A
1688. I, i, T?,
1689. i, fi, T>,
ADDITION OF FRACTIONS.
79. Addition of fractions is the process of finding the
sum of two 01* more fractious.
. Example. What is the sum of f and H
Solution. Reduce the fractions
to a common denominator. ^ = }J.
andi = ^;; 20 twenty-eight' .md
7 twenty-eights are 27 tweiiiy-
eights.
OPKBATION.
f < i = U
M + A =11
80. Rule. /. — Reduce tiiii fractions to a .ommon denomin-
ator, add the numeratora and place the sum over the common
denominator.
II' — If the numerator is greater an f'e denominator
divide to find the units and annex the Mi r as a fractio,
If thereare units add them and annex t. fraciton to the result.
Note. — Before reducing to a common denominator, reduce
each fraction to its lowest terms, and also the result after
addition.
Inator
ading the
--n
denomin-
e common
\ominaior
I fractioi:
he result.
ir, reduce
lult after
SCBTRACilON OF FRACTIONS.
What ' i the Muin of the followlnv rrnctlona
71
1690.
1691.
1692.
1693.
1694.
1696.
1696.
1697.
1698.
i and f
« and i
i and f
f and jPy
» and ^
2> and 3*
3.^ and 2^
h i n»d §
h i and I
1699.
1600.
1601.
1602.
1603.
1604.
1 '^>06.
1606.
s
8 I.
18 §,
1607. 31^,
I
6i
lOj'^
40
1 M
and
and
and
and
and
and
and
and
and
i
10 J
"A
1608. John ha.) § of a fam and bought i more ; how much has he now f
1609. Louw had „ of a ton of coal, he buys i more ; how much has he
at present?
1610. Martin had |2i, he receives |5.1, how much has he ?
nil' o'^J""" ^"^ lOi acres and buys llj acre8,how many acres has he ?
1612. Prude- I receives 16i bushels from one farmer. 10^ from another,
IH from anothe • bow much has he in all ?
1613. A merch. had 107§ yards of cloth and buys 146J yards, how
many yards has he » .r g j , ««
1614. RogatiansoV 4| yards of silk and has 49i yards remaining,
how many yords ha he ? *
1616. Bernard sold 671 pr N of honey to Jack Shallow, 351 to Dan
Dufly and has 17f remaining ; . av many pounds had he at first I
CUBTRACTIOX.
■ 81. Subtraction effractions is the process of finding
the diflference b itween two fractions.
Example.— Subtract f from f
S>lution.— Reduce the fractious to a common
denominator f = f J and ^ = |f ; then 27 thi. ty.
sixths from 28 thirty-sixths leove ^. This gives
the following
OrKRATION.
I - i =
*J - H = ^f
82. Rme— Reduce the fractions to a com?non denominator
and subtract the numerators, and jplac. th^ result over the
common denominator.
72
SUHTIIACTION OF ri!A< TIONM.
// there are units avUra t the fractioiM and then auhtraet
the whole mtmbert'.
Note.— Keduce both the frnctinns, and the diflVreuce to their lowe«t
terms.
Mnlttrnct
1616.
from
f
1623.
f
from
1
1617.
from
i
1624.
/ff
from
H
1618.
from
1
1626.
«J
from
m
1619.
from
i
1626.
lou
from
nn
1620.
from
^2
1627.
2J
from
6J
1621.
from
1628.
13 J
from
21 t
162i2.
from
l^
1629.
14i
from
18 i
1630. John has | of a dollar and he gave James | of a dollar ; what
had he remaiDing !
1631. Mary has } of a pie, she gave her sister | of it ; how much
how much had she ?
1632. From I of a ton of hay a farmer sold } of a ton ; what has he
remaining ?
1633. A merchant has ^ of a ship, he then bonght \ of the ship and
afterwards sold \ of the ship ; what has hs on hand f
1684. The suui of two fractious is {, one of the fractions is f, what is
the other t
1686. Three fractions make together ^, one is \ and snother \, what
is the third t
1636. A man has ^ of a dollar he owes John \ of a dollar and Peter | ;
what will he have after paying his debts ?
1637. From 42^ pounds of butter, a man sells 10^ and 14^ pounds ;
how much has he on hand still }
1638. Joseph had 45} cords of wood, he buys 80^ cords and then sells
40^ cords ; how many cords has he now ?
1639. John has ?20 and pays $9} for a coat, $2} for a hat, and |4^ for
shoes ; how much has he remaining f
t subtract
lieir lowest
i
18 i
liar ; what
how much
lat has he
lie ship and
I ^, what is
tier \, what
ad Peter ^ ;
1} pounds ;
L then sells
and |4^ for
MUI/ni'I.tCATION or FUACTI0N8.
MULTIPLICATION OF FRACTIONS.
71
Multiplication effractions is tlio process of multi-
plying wlieu one or both tc-nn.s are fractions.
Case L—To mnlHplu a /ruction by a whole number.
Exainple._Miiltii)ly g by 6.
Solution.— 6 times %=,^, which reduced to
its lowest terms equals ',".
QPEHATION.
84. R\iie.—Mul{i/,h/ the numerator by the whole number
and reduce the remit to its lowed terms.
Unit I ply
1640.
1641.
1642.
1643.
^s X 7
I X 6
« X 10
if X 12
1044.
1645.
1646.
1647.
if X 22
§ X 18
i X 86
* X H
1648. John has | of an acre aud Louis has 10 tim.s as much ; how
many acres has Louis ?
Case II.— 7*0 multiply a fraction by a fraction.
Example-Multiply j by f. OPEiiATioy.
Solution.— Multiply the numerators together i X J == H
for a new numerator, and the denominators for a iJ = |
new denominator. Keduce the result to its lowest terms.
86. Rule.— Multiply the numerators together for the numer-
ator, and the denominators together for tho, denominator of
the product.
NotC—l. If there are units in one of the factors reduce to an
improper fraction before multiplying. Ex. 2i multiplied by 81. 24—
i and Z\=x^ • iX¥=!i=7/^. y i i-
2. Reduce the result to its lowest terms.
»■•■
74
DIVISION OF FKACriONS.
What is the proflnct or
1649.
1660.
1651..
1652.
1653.
f by ^ ?
f by n
^ by
by
T5
?
T?
if by
3. 7
1664. i? by ft
1655. 2\ by 3i ?
1656. 7 J by lOf ?
1657. 18 1 by | I
1658. 40^ by sj?
165&. John has f of f tons of hay, Peter has 4J tons more ; how many
tons has Peter ?
1660. "What remains after selling the | of 10 J pounds of honey ?
1661. Find the cost of 9| yards of cotton at 11 J cents a yard ?
1662. John pays for 14| pounds of coffee at 15^ cents a pound, how
much did he spend ?
1663. What will 9 tons of coal cost at $6| a ton ?
' 1664. A fanner sells 14| pounds of butter at 21 1 cents a pound ; what
does he receive ?
1665. Martin has | of a load of hay, Tobias has ^ as much plus 3}
tons ; how much has Tobias ?
1666. I have $25, I buy 6^ pounds of tea at 60 cents a pound, and 4
teapots at $3| apiece ; what have I remaining ?
1667. At $3J a yard what will 9| yards of cloth cost ?
1668. A man pays $10^ for a coat and | as much for a rest ; what
will both cost ?
1669. In a room containing 56 persons, ^ are boys, g are girls, how many
remain ?
1670. A dozen of eggs cost $^ ; what will 25 dozen cost ?
1671. Find the cost of 20J^ pounds of cheese at llf cents a pound.
DIVISION OF FRACTIONS.
86. Division of fractions is the process of dividing
when one or both of the terras are fractions.
Case I. — To divide when the dividend is a fraction.
Example.— Divide || by 4.
Solution. — {} divided by 4=^^. When the numer- Operation
ator will not contain the divisor, multiply the deuomin*
ator by that numlii . , {^ -j- 4=/^
87. Rule- — Divide the numerator or multiply the denomi-
nator by the divisor.
MENTAL EXKliCIsnS IN REDUCTION.
75
i?
V
f ?
how many
ney ?
i?
ound, how
md ; what
ich plus 3 1
ind, aud 4
est ; what
how many
Mund.
Divide.
1672.
1673.
1674.
1675.
t%
I
by
by
by
by
3
6
12
11
1676.
1677.
1678.
1679.
HI
V-
by
by
by
by
6
9
10
12
1680. 1 gave $5^ to 8 little boys, what did each receive ?
Case n. — To divide lohen the divisor is a fraction.
Solution, f divided by 1 equals «. Hence f di- Opkkation.
vided by i equals 4 times f, and f divided by | equal 4^3^
4 of 4 times f or f times § which give ^ or V. Hence 5 v i-*" nr .1 a
we see that the divisor becomes inverted. » A *— r s or 5
88. BmIq.— Invert the divisor and multiply the dividend
by the restdting fraction.
Divide.
1681.
1682.
1683.
1684.
1685.
I
i
if
by
by
by
by
by
I
*
12
11
1686. fl
1687. 4 J
1688. 7^
1689. 12|
1690. 15|
by
by
by
by
by
i
I
1691. How many pounds of butter at ^ can b" had for |2.i ?
1692. At .$7 1 per ton how much coal can be had for$5o ?
1693. Oiviue ?;156 among a group giving each $10^ ; how mai.v persons
can be paid ? - i
1694. I had 1200 and spent $96>, how many acres of land can 1 buy
with the remainder at |15§ an acre ?
dividing
on.
RATION
^4=^
denomi-
MENTAL EXERCISES IN REDUCTION.
1695. If an apple is divided into two equal parts, what do you call :
1 — One of these pnrts ; 2.— Two of these parts ?
1696. What is the half: of 8 ; of 12 ; of 16 ; of 28 ?
1697. If a pound of butter cost 18 cents ; how mnch will half a
pound cost ?
1698. Thomas bought 24 sheep ; in selling half of them, how many
does he sell? , ' /
76
UEXTAIi EXERCISES IN SEDUCTION.
m
1699. If I divide an apple into three equal parts, how do you call :
1. — One of these parts, 2. — 2, and 3 of these purts.
1700. What is the third : of 6 ; of 12 ; of 18 ; of 21 ?
1701. Henry had 30 cents, and he lost the third ; how many cents
did he lose t
1702. How many thirds are there in : 3 units ; 5 units; 8 units ?
1703. Louis having 42 marbles, gave the third of them to Edwnrd ;
how nuny had he remaining ?
1704. What are the two-thirds ; of 9 ; of 15 ; of 24 ; of 30 ; of 27 ;
of 33 ?
1705. How many thirds in : 1.— 4S ; 2.— SJ ; 3.— 2f ; 4.— 6§ ?
1706. Joseph had 21 cents ; he gave § of them to his sister. How
many cents did she receive ?
1707. John lost the § of $36 ; how much has he remaining 1
1708. How many units in : 1— f ; 2.— \o ; 3.— ^ ; 4.— J/ ^
1709. If an apple is divided into four equal parts, what do you call :
1.— One of these parts ; 2. — Two of these parts ; 3.— Three of these
parts?
nir^. What is the fourth : of 12 ; of 20 ; of 32 ; of 48 ?
1711. What are the two-fourths : of 16 ; of 40 ; of 24 ; of 36 ?
1712. What are the three-fourths . of 20 ; of 24 ; of 16 ; of 12 ?
1713. If a yard of cloth cost $16, how much will the | of a yard cost ?
1714. James gave his brother the | and his sister the £ of 28 oranges ;
how many did each receive ?
1715. How many fourths : in 5 ; in 7 ; in 4| ?
1716. How many units : in f ; in ^^ ; in \^ ; in \* t
1717. Victor is 24 years old and Alfred is f as old ; what is Alfred's age 1
1718. If you divide an orange into 5 equal parts, what do you call 1,
2, 3 and 4 of these parts I '
1719. What is a fifth?
1720. What isthelifth: of 25; of 10; of 15:
J721 . What are the two-fiftl. : of 15 ; of 30 ; of 45 ; of 50 ?
J722. What are the three-fifths : of 10 ; of 30 ; of 25 ; of 65 !
J 723. What are th.- four-fifths ; of 55 ; of 35 ; of 40 ; of 50 ?
1724. James has 15 oranges and Maurus has g of this number; how
many oranges has Maurus ?
1726. Julia it. 25 years old and her sister is | of her age ; how old is
her sister ?
ImV. M-Vvt luauy 1111,113 : ;u u ; n. a ; :u 'ig ; Uj :
1727. Andrew is 86 years old and his wife is ^ of his age ; what i> her
age?
of 30*?
1728,
3, 4 and
1729.
1730.
1731.
1732.
1733.
1734.
less 4 ; i
1735.
the I ; 1
1736.
bought f
1737.
iu 23 ?
1738.
1739.
1740.
1741. :
4, 5 and
1742.
1743. '
1744. '
1745.
1746.
1747.
1748.
1749.
1760.
in If?
1751. i
1752. B
1763. A
was the loi
1754. If
yards cost
1765. If
fif these pa
1766. Vi
J767. W
MENTAL EXEnciSES IN KEDUCTION
1728. If you divide a melon into 6 equal parts, what do you rail
3, 4 and 5 of these parts ?
1729. What are the two-sixths ; of 24 ; of 18 ; of 36 ; of 60 ?
1730. What are the five-sixths : of 18 ; of 54 ; of 24 ; of 72 ; of
77
1.2.
36?
'■ rate(
laya
1731. What will the f of 36 yards of cloth cost, at
1/32. How many sixths : in 5 ; in 2J ; in 4J ?
1733. How many units : in V ; in ^ ; iu V ; in J ?
1734. Alfred had 12 tops, and Louis had only the § of this number
less 4 ; how many tops had Louis ?
♦.,^?V'^"'' ^"""^ ^^ plums; he gave Jane J of them, and Charles
tne f ; how many had he remaining ?
1736. If a yard of cloth cost ^ of 50 cents ; ho^v many yards can be
bought for 60 cents ?
• o?I' ""'"^ ""^"^ '' ^—fourths in 21 ; 2.- Fifths in 24 ; 3.-Sixths
111 Zo f
1738. How many dollars in $ ?/ !
1739. Express in whole numbers : 1.— 2fi ; 2.— f f ; 3.— "5 ■?
1740. What are the relation of the following fractious to unity • 1 -4 •
2— i%;3.-|; 4.-J;5.-9? , ^' ' *'
1741. If you divide a melon into 7 equal parts, how do you call 1 o 3
4, 5 and 6 of these parts ? - f . »
1 742. What is the seventh : of 21
1743. What are the two-sevenths :
1744. What are the three-sevenths ,
1745. What are the four-sevenths : of 70
1746. What are the five-sevenths : of 77 ;
1747. What are the six-sevenths : of 35 ; of 42 ; of 49
1748. How many sevenths in 9^ pounds I
1749. What are the lowest terms : of f f ; of f J ; of || ?
What is required to complete the unity' : in i ; in f ; in | ;
of 28 ;
of 28;
of 14
of 42 ; of 56 ?
of 49 ; of 63 ; of 70 ?
; of 49 ; of 49 ?
of 63 ; of 84'
of 42 ; of 28 ?
of 140?
; of 35
of 77;
of 91;
1750.
inH?
1751.
1752.
1753.
Express in cents : 1.- the | of a dollar ; 2— the f of $1.50.
How roiny bushels of potatoes in Sj^ of a bushel ?
A watch which cost $70 was sold for the f of its cost. What
was the loss ?
1754. If the half of 10 yards of cloth cost $10, what will l of 6
yards cost ? a "■ «
^ 1755. If you div. i. . aything into 8 equal parts, how do you call one
fii ihese parts ?
1766. What is th. >-vhth : of 24 ; of 48 ; of 72 ; of 88 ?
J767. What are the three-eights : of 16 ; of ^ j of 80 ; of 96 f
1 2
78
MENTAL EXERCISES IN REDUCTION.
1768. What are the fivo-eights : of 8 ; of 24 ; of 48 ; of 64?
1759. How many times : Three in § of 24 ; 5 in § of 40 ; 8 in | of 80 ;
7 in § of 56 ; 12 in f of 64 ; 3 in i of 72 ?
1760. How many fourths : in 2i ; in 7| ?
1761. How many sevenths: in 5j ; in 3^?
1762 How many sixths : in 7f ; in 3| ?
176?-. How many eighths : in 7| ; in 5| ?
1764. Reduce § to 12ths. | to 30ths.
1765. " i tol6ths. ji to 36 ths.
1766. '« ^% to 20ths. I to Slsts.
1767. How many units : in -'5* ; in J| ; in '5* ; m 'j* ; in Y ; in V >
in V; V?
1768. What must be added to the following fractious to complete 2
units: 1.-^; 2.-| ; 3.-^; 4.-3 ?
1769. If you divide an orange into 9 equal parts what part of the
orange would you obtain if you take 1, 2, 3, 4, 5, 6, 7, 8, and 9 of these
parts ?
1770. What are the | : of 18 ; of 27 ; of 45 ; of 36 ?
of 9 ; of 36; of 54 ; of 81?
of 54 ; of 72; of 63 ; of27 1
of 18; of 99 ; of 27 ; of 108?
1774. What are the lowest terms: of }S ; of j^V of \^ ; o( ^^ ;
of|§; Hiofll; H?
1775. What is the sum of: 1.— 8 times 6 and § of 6 ; 2.— 4 times 12
and I of 12 ; 3.— 5 times 10 and ? of 10 ; 4.— 5 times 7 and 4 of 7 ; 5.
— 9 times 8 and J of 8 ?
1776. Louis bought 15 horses and after selling 6, found that he
required 4 to have 20. How many had he at first ?
1777. How much should you pay for a case of soap, if the J of a case
cost $15 ?
1778. If the I of a yard of cloth cost $6, what will a yard cost?
1779. If 5 yards of cloth cost $2.50, how miichwill 6 yards cost ?
1780. What must you pay for 10 peaches, if 3 peaches cost 4J cents ?
1781. 2 apples cost f cents, what will 5 apples cost ?
1782. What is the cost of 9 lamps, if 5 lamps cost $ -'^ ?
1783. Of what number is ; 1 . — 6, three times its J ; 2. — 8, twice its ^ ;
3.-16, four times its ^ ; 4.-9, three times its J ?
1784. Frank's coat cost $10 which sum equals J of 6 times the price of
1771. WHatarethe*
1772. What are the ^
1773. What are the I :
J785, Of what nul^ber is : 9 the f ; 6 the |, 10 the f ; 12 the ^?
WRITTEN EXERCISES 79
nil' T"* r"i ^ ^,r° '^ •'^^^ "^^ ''^ 18^ ''^'^ « dozen ?
1 7R0* T r f ''"^ '"'* * ^' ^^''* ^'» 6 '°*ds cost ?
^^789, Tobias purchased 6 pair of shoes for J18|. what did they cost a
for'eSluL?"' '' '''°'' '''* ^ '' '' "°*^' '^"^^ ""^"y y"d« -» be had
1791. How often do the | of 32 contain the J of 12 f
1792. How often do the | of 56 contain the ^ of 42 ?
1/3. How often do the § of 27 contain the | of 12 ?
tulst !t '"'"■'°" ''*'''"« '^P'*^ ^^ b"«h«l «f °«ts, sells J to Michael and
th I of the remainder to Bernard, how niany bu. '.els hat he S
Jch did's"Cveray't '' '''''^" '' " ^^'^ ^^ « ^ *« «- ' ^o^
Im 7T IV/'J^'. '' '''''' •="'*' ^^ * «f •* y"d cost «6 »
bleu ,^ '''"'"'' *''P^'^^^''"'«2'^- -"^'^ -^' ^' paid for 3
JyJJ" M ?' * "-^ V*"^' ''^ '^''^^'°'' «3^' ^°^ """ch will 9 yards cost ?
WRITTEN EXERCISES.
1800. Reduce f and ^ to tlie same deuomi.mtor ? '
1801. Which is the greater of tl>€ two fractions § and A ?
1802. Joseph empties f of a tun in 8 hours; Louis empties the U in
tlie same iime. Which is the more active ? ^^
1803. How many sixths : in J ; in | ; S ?
1804. How many eighths : in i ; in ^ ; f ?
1805. How many twelfths ; in f ; in | • ai I.
1806. Reduce §, f, and | tc twelfths.
1807. Reduce i and | to a common deno^iriai ^r
1808. If 2i y.rds of lace ..ost 13 cents wh t will 3 yar-ls cost?
1809. Low many fourths in J, |, ^j, iq,
1810. Whatmustyouaddtoorsubstract /:om the followin<r
ainiiH i-n Imiro 1 i.
.J
3
V'» 6
expres-
Mil. How many fifteenths : in § , iu ^ ; in | ; in f f
80
WaiTTRN EXEBCI8E8.
'I':
1812. Seduce the following fractions to a common denominator : ^, §,
1818. Eugene lost 20 roses which were | of all his number. How
many had he ?
1814. Write in order of their value §, f, f, J.
1816. How many sixths : in |§ ; ^j ; in § ; in ^Sj t
1816. Reduce: ^% to fifths; ^ to fourths ; ^^ to halves; ^j to
foiirUis ; f to thirds ; ^^ to sixths ; ^j to sevenths ; || to nineths.
1817. If 8 is I of a number, what is the J of twice that number ?
1318. Two boys buy coffee at 30 cents a pound, one buys 3^ pounds
the second ^i pounds. Who spends the more ?
1819. Reduce to a common denominator : 1. — § and |, 2. — i and ^
3.— i and ^ ; 4.— § and | ; 5.— f and f ; 6 | and ^g.
1820. Reduce to a common denominator ; 1.— J, i, i ; 2.— f, i, i
3.-*, i, i; 4.-ia.i»5-
1821. Joseph found 60 cents which equals f of i of what he then had
how much had he at first ?
1822. Paul said to Arthur ; " Would you prefer to receive the | or the
§ of my money and why " ?
1823. Reduce the following fractions to their lowest terms : ^f ; |J ;
1824. Four times 50 years is 10 years less than 10 times Philip's age.
What is Philip's age ?
1825. How many lemons would be required to pay 7 oranges, if 6
lemons equal 4| oranges.
1826. Which is the smallest of the following fractions : i, f, ^Sj, f ?
1827. What will 3 J pounds of sugar cost if 2i pounds cost 25 cents?
1828. A horseman can travel 21 miles in 3^ hours, how fat will he
travel in 5^ hours ?
1829. Henry gives 16 conts to a beggar and John gives ^ of a dollar.
Who was the more generous and by how much ?
1830. Reduce to their lowest terms : ^Sj, ^j and |f ; and then reduce
to a common denominator.
1831. if it requires 83 yards of cloth for 2 coats, how many yards will
9 coats require f
1832. f of 48 oranges cost 40 cents, what will | of 12 oranges cost ?
1833. It requires ^ days for 6 men to build a boat ; how loiig will it
take 3 men to build it !
1834. Reduce to an improper fraction :— 2| ; 5J ; 6)^ ; 4J ; 5J ; 2i ;
8f 5 8| ; 4i ; 6} ; 5J ; 9* ; 7|; Si , eg , 9J ; 7f ; 8i; 6| j 91-
1835. A
1836. ^\
1837. H
nineths in
1838. A]
in the othe
1839. Lo
Louis still ]
1840. W
X1841. Wl
1842. Ap
1843. A)
\1844. At
.1845. At
1846. A f
1847. As
how many y
1848. Tw(
T849. Ah
is 6 mouths I
1850. Johi
how many pi
1851. Am
many bushels
1862. Hon
for $18|.
^ 1853. I sol
much is due j
1854. How
1855. 1 spe
did I buy ?
1866, Thej
other ?
1857. Theq
dividend ?
1858. Byw
1859. Byw
1860. If^o
1861. What
taace is 108 mi
1835. A man
WRITTEN EXERCIHE8.
81
1836. mat sS''^'"'"^^'''"^^'""^^-"''^
1837. How many : eights iu A, U
earn in 5 days ?
a man pay for 8 barrels of apples at $3 J a barrel T
fifth
nineths in H, |^ rtent^L'i/^^^^/'^n '" "' ^' ' ^"^"^^^ *?' ^ '
Lors;iJrr:;t-\^r^^
u'a!?' wk'! '°n '' °'""S'' ^'^ °^* ^«"t «««h »
1849 , f ^"'"y°" P*y f«r 16| yards of calico at 9* cents a yard ?
8 3 a'' ""?.'* ^^•' '"^^^ ' ^^'^''^ -•" b« P-<i for Srbarrels t
.845. A bntcher buys sheep at |8 a he.ul. how many will he get for m ?
846. A farmer has 14| tons of hay and sells 9J tons, whaf remls
how i^Shiri!:^ "^^ -^^ "'• ^'-' ^« ^"- -i --=;
1848. Two fractions together ffivp a eiimnf 18 «« • < , .
^ 1849. A bov earn, «i of! I T ^^'°°^ '* ^' ''*>''* '« ^^^ °"»er ?
is 6 months ? ^ ^ '"'"*'' '"'^ 'P^"*^' «^2|. what will h. have
how ly;t?r„dtr ' ''' ^^"""^ '"'^^^ -' '- ^^1 --^'^"«.
manyL1;er::m:i:r'"""^*'^'^*'^*^ bushels of oata ; how
for «18|."" ""' '"'^ "' ^"""^ ^* ^ «^ « '^°"- a y,rd can be bought
jrisdrf '''^"""'^"^-^^r^^^^i-*-"^ -ived ,5. how
1854. How many sheep at 08* per head can a man buy for $200^ ]
did I buy r* ''■''' '" "^^* '' ''' ''^'^ ^ P-"'^' ^- many pounds
otJeM ' '''' ''°'"'^' '' *"° ''"""^^ ^« «' -« °f ^^- - i. what is the
divMend?' '"""' °' *"' ^""'^'•^ " * ^ *^« <^-- » i -hat is the
1858. By what number must you multiply J to got 13i ?
1859. By what number must 3^ be divided to get | ?
1860. If ^ of an arrp nf ^anA ^r^*^ ooa „.i. . .,, _
--_.„...., .. ^._..j-^ uiiUv vviii o &ci*cs cost?
82
DKKOMINATK MUMBKR8.
1862. If } of a farm cost $120, what would 8 similar farms cost I
1863. A barrel of flour costs J18, what will § of a barrel cost ?
1664. If j of a barrel of flour cost |12, what will f of n bairel cost t
1865. Louis had $1240 he spends f of it and then 2 of the remainder,
how much has he now ?
DENOMINATE NUMBERS.
104. A Denominate number is a concrete number in which
the unit is a measure ; as, 5 pounds, 6 yards, 3 minutes.
105; Reduction is the process of changing a number from
one denomination to another, without changing its value.
It may be either ascending or descending.
CURRENCY.
106. Money is the measure by which we estimate the
value of thingd.
Gurrency is money used ab a circulatinj^ medium.
Table.
(m) equal
10
10
10
mills
cents
dimes
«
1
1
1
cent
dime
dollar
et.
d.
$.
107. Coins are made either of copper, silver or gold :
The 60 cts, 25 cts, 10 cts, and 5 cts, are made of silver.
The 1 ct, and 2 cts, of copper.
Exercises.
1866. How many cents in $3^ ?
1866. How many 10 cent-pieces : 1. — in 50 cts ; 2.— in §1 ; 3.-
12.30 ; 4.— in $3.80 ?
1867. How many 5 cent-pieces would be required for : 1. — 65 cts ;
2.— 90 cts ; 3.— $1.70 ; 4.— $5.25 ?
1868. How many 26 cent-pieces : 1.— in $4.25 ; 2. — in |6.50 ; 8.—
in 17.75 ?
1869. I owed Henry $4.20 ; I gave him 60 five-cent pieces. How
much do I still owe him ?
in
1870. I
many dolli
1871. H
5.-$i; (
1872. V
108. E
4 fart
12
pen
20 shil
21
shil
Note.-
5 shillings.
1873.
Ho
1874.
Ho
1876.
Ho^
1876.
Ho^
187^
Bed
lP/8.
In)
109. Tr(
jewels, &c.
24 graini
20 })enn]
12 ouQoe
COBtt
stT
rel cost T
remainder,
ir in which
les.
Bber from
ralue.
bimate the
n.
Id:
iilver.
DENOMIHATB NDMBERB. (g
Jnl'^; n ^^"^ I ^''''' °^ ^^ ''"*'• ""^ 3 piece, of 26 cents. How
many dollars and cents have I?
1871. How many cents in : 1— «i : 2.— «i • 8 _ «a • i •!
1872. What port of 8 cents is the f of 10 cents!
ENGLISH MONEY.
108. English money ia the money of Great Britain.
Table.
equal
i<
M
<«
1 penny ^^
1 shilling g^
1 pound or sovereign jg.
1 guinea ^
4 farthings (/ar.)
12 pence
20 shillings
21 shillings
5 sWUin^'s""^^^ ^°"°*^ " sovereign is worth «4.866. A crown is worth
Exerelaea.
1873. How many farthings in 10 d. and 3 far. f
1874. How many pence in 16s. and 9 d. ?
1876. How many farthings in ^ 16 6s. 3d. I
1876. How many shillings in 900 far. t
187^ Reduce 3178 pence to pounds ?
lP/8. In 9760 farthings, how many lounds I
51 ; 3.— in
. — 65 cts ;
16.60 ; 8.—
ieces. How
MEASURES OF WEICJHT.
Troy.
109. Troy weight k used in weighing gold, silver,
jewels, &c. *
24 grains (gr.)
20 jH'nnyweights
12 ounces
Table.
equal
M
1 pennyweight pwt.
: I oniice ox.
|po\iBd lb.
r
84
DEI^OlilKATB kCMDERS.
Exercises.
How many :
1879. Grains in 4 oz. 5 pwt f 1882. Pennyweights in 2 lb. 3 oz ?
1880. Pounds in 7365 grs ? 1883. Oz., and pwt., in 4170 grs ?
1881. Grains in 3 lb. 4 oz. 6 pwt? 1884. lb.,oz., and pwt. in 10302 grs?
Apothecaries*.
110. Apothecaries' weight is used in measuring
medecines.
Table.
20 grains (gr.)
equal
1 scruple
ser.
8 scruples
II
1 dram
dr.
8 drams
It
1 ounce
oz^
12 ounces
Exerclsrs.
1 pound
lb.
How many :
1886. Grains in 3 oz, i <■!
1888. Pounds and oz. in 239 drams ?
1886. Drams in 2 lb. ,..i? , £ ds" ? 1889, Oz. in 4800 grains ?
1887. Drams in 960 gr i 1890. Pounds, &c., in 91304 gr I
AVOIRDUPOIS WEIGHT.
111. Avoirdupois weight is used in weighing all
tfAxnmon goods.
table.
16 ounces (pz.)
100 pounds
20 hundred-weight
equal
II
II
1 pound n,
1 hundred- weight ewt.
1 ton T,
■fiTote. A quarter is one-fourth of a hundred-weight.
Exercises.
How many :
1891. Oz, in 3cwt!
1892. Pounds in 6 T 10 ewt I
1893. Pounds in 976 ozt
1894, Cwtin 1000 oz'.
1895, T in 15630 oz f
1896, Ounces in 20 owt 16 lbs 6 oz?
DENOMINATE NUMBEHS.
85
1897. How inniiy ounces in : 1.— 3 lbs ; 2.— 6 lbs ; 8.— 8^ f
1898. If I pay 33 ceuts for 6 ounces of soda, how much will I nov
for : 1.- 2 lbs j 2.- 6 lbs ; 3.- 6 lbs j 4.- 7i lbs ?
1899. For 4 ounces of camphor I pay 14 cents ; how rany ounces
cnu bo bought for : 1.- 21 cents ; 2.- 36 cents ; 3.- 42 cents ?
icr.
dr.
oz.
lb.
39 drams ?
34 gr?
MEASURE OF LENGTH.
112. Measure of length or long measure ia used
in measuring length, breadth, depth, etc.
Table.
12 inches (in.)
8 feet
• 6 J yards or 16 J ft
320 rods
8 miles
equal
foot
yard
rod
mile
league
yd.
rd.
mi.
I.
Xote.— lu the old tables 40 rod8=l furlong and 8 furlong8=l mile.
I KxerolBes.
1900. How many inches in : 1 3 ft.; 2.— 4 yds 6 ft ?
1901. How many inches in : 1.— 4 rd. 5 yds. ; 2. - 6 yds. 2 ft. 4 in.l
1902. How many miles in ; 1.- 13720 feet ; 2.— 870 rods ?
1903. How many yards in : 1.— 376 inches ; 2.— 97 ft. 5 in.?
1904. How many inches between Mont al and Quebec if the distance
is 180 miles?
II.
SURFACE OR SQUARE MEASURE.
113. Surface or Square measure is used in measur-
ing purfaces; as, loards, lands, etc.
Table.
144 square inches (sg'. in.) equal 1 square foot ^q./t.
9 square feet ^ « i Bquare yard ya
m square yards ^ « , i perch or square rod P.
160 perches «« i ac^e j
•*^ «wrei I. I square mUo tq. mi.
M
^
.^^>
IMAGE EVALUATION
TEST TARGET (MT-3)
fe
1.0
I.I
11.25
2.5
lii|2B
US
ja |2|2 12.2
I li& |2.0
U |K6
Hiotogiaphic
^Sciences
Corporation
«
23 WfST MAIN STRKT
WfBSTIR.N.Y. I4SM
(716) •73-4S03
^^ a\. ^rS
?
„v
A
^\5^
86
DKKOMINATR KI7MBKU*.
ExerclMM.
How many :
Square in. in 3 sq. yds.
1905.
7 sq. ft ?
t sq. It i
1906. Perches in 9760 sq. tt t
1907. Square feet in 3 '
6 sq. yds I
A 4 P.
1908. Square ft. in 3 P. 8 sq. yds.
3 sq. ft ?
1909. Acres in 120460 sq. ft f
1910. Acres in 35670 squars
yards T
CUBIC OR SOLID MEASURE.
lU. Cubic or Solid measure is used in measuring
things which have length, breadth and thickness.
Talile.
1728
cubic inches (cu. in.
equal 1 cubic foot
cu.ft.
27
cubic feet
*• 1 cubic yard
eu, yd.
16
cubic feet
" 1 cord foot
ed. it.
8
128
cord feet or
cubic feet
" 1 cord of wood
ed.
Sxerelmes.
How many :
1911. Cu. in. in 6 cu. yds. 6 cu. 1913. Cu. ft. iu 9 cords of wood T
ft. 4 cu. in }
1912. Cubic yardsin 24560 cu. in.T 1914 Cords in 8766 oo. ft.t
LIQUID MEASURE.
115. Liquid measure is used in measuring nearly all
kinds of liquids.
Tabl«.
equal
4 gills (i/O
2 pints
4 quarts
31 i gallons
63 gallons
1 pint
1 quart
1 gallon
1 barrel
ft.
qt.
gal.
bbl.
1 hogshead hhd.
Exercises.
Ho\V many :
10]S, Gills in 6 quarts 4 pints ; in 5 gals ; in 4 qu.irt9 !
Idld. Quarts, in 1 barrel ; in 16 gals ; in 2 hhds t
1917. Gallons in 56D pints ; Hhds iu 1000 quarts ; bbla. in 760 giJi t
'. 8 sq. yds.
Kq. ft T
ro squaro
noasurmg
eu.fl.
«. yd.
cd. Jt.
ed.
a of wood ?
, ft.t
learly all
pt.
It.
il.
I.
\d.
DEKOKiyATE MUUBEU,
DRY MEASURE.
87
116. Dry measure is used in measuring dry substances :
as, grain, fruit, salt, &c.
Tnble.
2 pints (pt)
8 quarts
4 jiecks
eqnal
It
«
1 qaart.
1 peck.
1 busheV
qt.
pk.
bu.
Kxerelaes.
1918. In 170 pints how many pecks ; how many bushels in 200 qnartst
1919. How many pints in 2 bushels ; in S pecks 2 quarts t
1920. What part of 3 pecks ».re 6 pinto t
1921. At ]0 cents a peck, how many bushels of com can I bay for |8 I
1922 I gave 5 quarts of s^lt at 15 cento a pint, for potatoes at 60 cento
» bushel ; how many bushels of potatoes will I receive I
MEASURE OP TIME.
117. Measures of time are those used to maasore
periods of duration.
The unit of the measura of time is the day.
Minor diTlslona of the liny and year.
1 minute.
1 hour.
1 day..
1 week.
1 month.
60 seconds (see.)
60 minutes
24 hours
7 days
4 weeks
equal
«(
1 year,
1 common year.
m.
rtr.
da.
ick.
mo.
12 month or 52 weeks <<
865 days «
Wa«e.'»rtt,«tw«lTe months or «!.• yew With tbelr r«^.«cfivo
number of days.
July 31 days.
760 Ids t
January 31 days.
Feoruary 28 " (29)
Harch 31 <<
April SQ "
May 31
June 80
«
August 31
S<'pteinber 30 "
October 31 M
November 30 ••
December 31 <«
/ . '
88 DECIMAL FRACTIONf.
Exerciseii.
1923. How many seconds in : 1.— 2 minutes ; 2.— 3 minutes } 8—
6 minutes ; 4.— 1 day ?
1924. How many minutes in : 1.— 3 hours ; 2.— 4 days ; 3.— 120
seconds ?
1925. How many houra in : 1.— 2 days; 2.— 240 seconds; 3.— 1
year ?
1926. How many days in : 1.— 3 weeks ; 2.— 8 weeks ; 3.— 48 iiours ?
1927. How many minutes : in 1 year ; 2.— hours in 63,780 seconds ?
CIRCULAR MEASURE.
118. Circular measure is used to measme angles.
Table.
60 seconds (") equal
60 minutes <<
30 degrees "
12 Signs, or 360 degrees <*
,, Exereiaefi.
How many :
1928. Seconds in 5 minutes ?
1929. Alinutes in 8 degrees T
1930. Seconds in 4" 3' 2" I
1 minute.
1 degree.
1 sign.
1 circle
S
1931. Minutes in 500 seconds?
1932. Degrees in 175'' ^sconds ?
1933. Minutes in 15 .'
a
o
5
00
DECIMAL. FRACTiONS.
119. A Decimal Fraction, or simply a decimal, is a
number of the decimal divisions of a number ; that is, a
number divided into <cm, a hundred, etc. equal parts.
120. When the unit is divided into ten parts each part is a
tcuth ; if into a hundred parts, hundredths, etc.
If a line be divided into ten parts, each part will be one
tenth of the unit which is here the line, two parts will be two
tenths, etc.
:l iinii
10
nutes ; 3. —
«; 3.— 120
mds ; 3. — 1
— 48 hours ?
80 seconds ?
gles.
S
seconds ?
"yconds ?
DECIMAL FRACTIONS.
89
Should one tenth be divided into ten equal partsi each of
these parts would be a hundredth; if one hundredth be
divided into ten equal parts, each one will be a thousandth,..
Tenths are then ten times less than unity, the hundredths
ten times less than tenths, thousandths ten times less than
hundredths,
121. A decimal fraction is generally expressed by placing a
point before the numerator and omitting the denominator.
Thus, .6 represents ^n ; .06 represents jh.
The point is called th 3 decmaZjsojw/.. . .. ,
Nameratlon and notation Table.
a
o
1 I
a S
6 6
5
00
•3
o
2!
a
9
M
•3
a
p
o
a
H
-3
a
9!
a
o
H
6
i I
4
a
a • -S
►r J ^
S Eh t3
66666666
, a
S
§
Eh
a
o
&
a
a
n
CO
2 ■"
&« CO
a
09 a
a •-
.2 a
S • H
6 6
-5 -«
t» 00
I
-■■■'.;. fii*
mal, is a
that is, a
part is a
I be one
ill be two
10
EXERCISES IN NUMERATION;
Example. Read the decimal .47.
Solution. This expresses 4 tenths and? hundredths, 4 tenths equal
40 hundredths and 40 hundredths plus 7 hundredths equal 47
hundredths. Hence
122. Rule. Head the decimal as a whole number and give
it the denominator of the last term on the right ; numerate
towards the point to determine the numerator, and from the
point for the denominator.
To read a decimal number, read the wbola number and then
the decimal part to which the name of the decimal unity of the
last figure is given.
»0
VICIMAL FRACTIONS.
Thus .8
.76
.004 "
.0705 "
26.4 «
24.07 "
11.017 "
108.00012 "
is read eight Unt?u.
•• seventy-fire hundredlht.
" four thousandths.
" seven hundred and five ttn-thousandtha.
" twenty-six and four tenths.
" twenty-four and seven hundredths.
" eleven and seventeen thousandths.
one hundred and eight and twelve hutdred-thou-
tandths.
EXEBOISES.
I. Bead the rollowlng declmnl nnmbere i
1084.
.01
.001 .0001
.00001
.000001
1985.
.02
.020 .200
.0200
.002
1936.
.025
.205 .25
.250
.2005
1937.
.20050
.3008 .803
.8300
.80030
1938.
.80003
.027 .4006
.3010
.30607
1939.
.123456
.500 .00500
.00005
.10407
1940.
.36092
vii7(i .0051
.00061
.60001
1941.
.64321
.908006 .9864
.100200
.00605
1942.
.10065
.00705 .003281 .004682
.1067890
1948.
.015
.2004 .1206007 .06987
.698765
1944.
1.5
2.21
8.60
25.05
1945.
60.70
76.07
320.32
10.09
1946.
96.006
309.0870
123.987
56.6543
1947.
6701.4
6642.004
8.01045
6070.006
1948.
8965.00009 104.00186
87.010849
186.0678
1949.
12345.07
2083.0102
105.102343
24.00966
1950.
4005.005
17.0306
9.30051
8.05063
1951.
16073.2
1061,075
34.00703
145.7
1952.
231.0061
I 24.0208
439.115
5402.509
1953.
7.00075 10.01023
25.6403
198.2047
DECIMAL FRACTIONS.
ft
EXERCISES IN NOTATION.
Example. - Express 30 hundredths in the form of a decimal.
Soliitiou.d) 36 hundredths equnl 3 tentiis ni,d 6 hundreds, and this
is expressed by writing a decimal point before 36, thus .36.
Rule. Write the decimal as you iconld a whole number,
placiny the decimal point so as to give each figure its proper
place, using ciphers after the decimal point i/ necessary.
III. Express the rollnwinff decimal fractions In Hcnres.
1954. Three tenths, four hundredths, seven thoxtsandths.
1955. Six len-thoutandtlis, twelve hundred'hs, thirteen thousandth*,
1956. Seven hnndred-thousandths, eight millionths.
1957. Nine ten-milUoiUhs, fourteen ten-thousandths.
1958. Fifteen hundred-thousandths, cue hundred and twenty-four ttm-
thousandths.
1950. Two hundred and twenty-eight hundred-millionths.
1960. Four thousand four hundred ten-thotisandths.
1961. Kight hundred and fifty-six hundred-thousandths.
1962. Twenty-three thousand nine hundred millionths,
1968. One hundred and seven thousand and eighteen <«n-OTi7Wo7i/A*.
1964. Thirty thousand four hundred and seventy-two hundred-
thousandths.
1965. Seven hundred and ninety billionths.
1966. Thirty-four tenths, two thousand and thirty-five hundredths.
1967. Four hundred and twenty-seven thousand and eighteen
thousandths.
1968. Fifteen thousand three hundred and thirty-four hundredths.
1969. Three hundred and forty and five tenths.
1970. Fifty-six and sixty-five hundredths.
1971. One hundred and twenty-three and forty-eight thousandth's.
1972. Eight hundred and fifty-two dollars and fifteen cents.
1978. Sixteen and two thousand four hundred and twenty ten-
thousandths.
1974. Nine thousand eight hundred and twelve dollars and three cents.
1976. Seventy-five and thirty-two millionths.
1976. Six hundred and twenty-four dollars and ninety cents.
, n) Young pupils are sometimes helped to seize the method of writipg decimals.
Djrfacing told to call the point « unU of the m-der of the denmal num^tobi
jmMjn. Thus seven thousandths are written as one thoussDdsndflevtn-^oSr
in like manner four thousand and one millionths. wonld bs writfam aa aam
miUion four thoassnd and one=.0W001. """'""""• ^«'"'* ■• wnttwi as om
4
9i
DKCIMAt FHACTIOys.
(it
If
1977. Five hundred thousuiul and six teu-milliouths.
1978. One thonsand and four and twenty five ten-thousandths.
1979. Five cents, one hundred dollars and ten cents. "^
1980. Ninety three and fifty thousandths.
123. Principles.— 1. Chantjing the decimal jooint oneplace
towards the right multiiMes the number by \0; two places,
hy 100, etc.
2. Changing the decimal point one place towards the left
divides th& number by 10; two places, by 100, etc.
3. Placing a cipher between the decimal point and a
decimal divides the decimal by 10 ; placing tico, by 100, etc.
Thus : To multiply 67 by 10 we would write 670 ; by 100, 6700. In
like manner to divide 67 by 10 we would write 6.7 ; by 100, .67 ; adding a
cipher to .0175, changes the number to .00176 which is ten times smaller
than .0176.
124. The value of a decimal is not changed when one, two,
three, etc., zeros are written to the right of it, because after this
operation the number obtained contains ten times, one
hundred times, etc., more parts, but these parts are ten, a
hundred or a thousand times smaller than the first.
Exercises on the Method ased to make a nnmber 10, 100, 1000>
etc., times vreater or less.
1981.
Make the numbei
1982.
Make the numbei
1983.
Make the number
25
4.75
0.06
1.
10>
c
1.
10"
) ,:
1.
10^ ..
2.
100
2.
100
s
■s
2.
100
3.
^ 1000
. 1,
3.
1000
2
3.
1000
.1
4.
'lOOOO
i
4.
10000
4.
10000
5.
100000
a
5.
100000
1
5.
100000
4>
6.
1000000 J ^
6.
1000000 J
s
6.
1000000.
s
19S4.
Make the number
1985.
Make the number
1986.
Make the number
. 48946.04
3.65
137.006
1.
10-)
1.
10-^
1.
lO-v
100 8
2.
100 s
2.
100
2.
3.
1000 ! -
3.
1000
—
3.
1000 •*
4.
' 10000 '" 1
4.
10000
■• CO
4.
10000 1 1
5;.
V 100000 ,jp
6.
100000
6.
100000 H
6; -
' 1000000 ■>
' '■ 1
6.
1000000..
6.
1000000.
DECIMAL FRACTIONS.
INI
01
)■ s.
s
a
1987.
1988.
1989.
1990.
1991.
1992.
1993.
114.35.
Make the following uumbers each 10 timu greater :
1 — 47; 2.— $2.60; 3.-6.2; 4.-5.30 5.-
Make the following numbers each 100 times greater
1.- 3.18 ; 2.— 632 ; 3.— J5.39 ; 4.- 8.3 ; 6.- 0.02!5.
Make the following number* each 1000 times greater :
1. - 97 ; 2.— $24.60 ; 3.- 0.019 ; 4.- 28 ; 5— |1.05.
Make the following numbers 10 times smaller :
1.— 82; 2.-6; 3.- $518 ; 4.-0.07; 6.- f 3.00.
Make the following numbers 100 times smaller :
1.- 604 ; 2.- J5.15 ; 3.- 7.4 ; 4.- $202 ; 8.- $5.40.
Make the following numbers 1000 times smaller :
1.-1344; 2. -$33.09; 3.-14.5; 4.- 65 ; 5.- 0.0165.
Alake the number 15.04 : 1.— 10 times greater ; 2.— 1000
times smaller ; 3.— 100 times greater ; 4.— 10 times smaller ;
5 — 100000 times greater ; 6.— 100 times smaller.
Oral Exercisca.
1994. How many tenths in a unit 1 hundredths f
1995. How many tenths would be required to make a unit t
1996. How many hundred-thousandths would be required to make one
teu'thousandth ?
1997. How many thousandths in a hundredth? How many ten-
thousandths ?
.1998 What number of ten-thousandths will be required to make •
unit ?
1999. In one tenth how many thousandths !
2000. How many thousandths in a unit I
2001. In one thousandth, how many millionthst
2002. How many ten-thousandths in one tenth t
2003. To what are one hundred tenths equal? one hundred hundredths !
2004. How many thousandths in one thousand ?
2006. To write a thousandth, how many figures wil. be required ?
2006, How many to write a millionth ?
2007. How many figures in ten-milliouths ? in hundred-thousandths J
8
•* RRDUCXrOX OF PECIMAIR.
REDUCTION OF DKCIMAIii.
126. The Reduction of Decimals is tho process of
changing thoir form without changing thoir value.
There are two cases :
1. To reduce decimals to common fractions,
2. To reduce common fractions to decimals.
126. Case I. To reduce a decimal to a common fraction.
Example. Reduce .75 to a common fraction.
Solution. .75 expressed as a common fraction, is j'j*,, which
reduced to its lowest terms equals j. Hence
127. "Ryile.— Write the denominator under the decimal
omitting the decimal point, and reduce the fraction to ite
lowest terms.
■e«lnee the following a«eim«la to common ^^aetlonst
2008. .46 2013. 9.48
2009. .60 2014. 18.726
2010. .48 2016. .076
2011. .180 2016. .0826
. 2012. .0176 2017. .01026
128. Case II. To reduce a common fraction to a decimal
Example. Keduce ^ to a decimal.
Soliitiou. 8 = 4 of 8. 8 equals 80 tenths, and i of 30 tenths is 8
tenths and 6 tenths remaining. 6 tenths equal 60 hundredths^ and | of
60 hundredths is 7 liundredths and 4 hundredths remaining. 4
hundredths equal 40 thousandths, i of 40 thousandths is 6 thousandths •
therefore i=.675. Hence the
129. Rule.— 1. Annex ciphers to the numerator and divide
by the denominator ;
2. Point off as many places in the quotient as there are
ciphers annexed.
Rmlnee the followlns eommon A«etloiu «• declnuUs i
2018. i 2023. ^
S - 3024. ^^
; 2025. II
* 2020. 11
2019.
2020.
2021.
2022.
2027.
ADDITION OP DECIMAIJS.
96
Example. Required the sum of 23.04. 675 63" and
7509.857.
Opkuation.
Solution. Write the numbers so that the figures of •>.•} 04
the sauie onler stand iu the same column, and proceed as «r5 «.r»
in the a.idition of whole numbers. 75(i9.857
8208.529
130. Rule.— 1. Write the nmib^ra so that the units of tfie
tame order shall atand in the mine column ;
2. Add, as in whole numbers, placi„si the decimal point at
Its proper place in the num.
KxprriHeN.
2028.
0.8
0.2
0.4
0.01
Aus.
2029.
0.715
1.20
3.5
1.07
2030.
Ads.
4 21
0.352
2.2
0.4012
A US.
2031.
0.12015
3.022
15.0254
0.3503
Ans.
2032.
32
0.40
0.102
0.226
2033.
Ans.
0.700
0.210
0.342
12.025
Ans.
2034.
0.923 I 2035. 0.003
5.007
0.05
!.:003
An.s.
0.06009
213.4
0.1215
Ans.
2036. 0.4964-0.03+0.1816+0.074 0.18.
2037. 0.02+0.108+0.316+0.24+0.007.
2038. 0.2801+0.0034+0.0025+0.7.
2039. 0.05072+0.5072+0.072+0.65.
2040. 0.2302+0.91402+0.702+0.08.
2041. 0.1023+0.83+0.00442+0.7+0.954.
2042. 0.90086+0.121+0 21+0.12115+0.82.
2043. O.24O.2I+O.2I6+O.2OI5-O.OOO453I0.04.
2044. 0.0024+0.64121^0.0032+0.203-0.76^0.03.
2045. 12.025+4.25+4.003+218.4^57.10032^3 09
8046. 247.07+76.295+7849.089+84676.007.
96
AnniTION OF DK< IMALS.
2047. 3.0025 f 32.4053 i 313.006 tl7S. 17 f 11213.7.
204S. 23.45RO(i7f0.4()"8ft f ir.2204 ; 27,1 j-0.003.
204D. 4754 807 t 29.006 f 671*387.07 + 84690.695 + 757878.454 -f
68U374.2
7.0.
2050. 40.87 J f{75.755 -f 74781.38!) f- 897576.5 + 49854.354 +
07ti4Sl> «75.
2051. 4877tJ.37 f- 84.35 + 7409.879 + 489374.207 + 684978.054 +
97.95.
2052. 687.85 ; 078798.475 f 705875.809 + 74297.75 + 397689.876 +
79787.705.
2053. 8.45 -f 7509,875 -\ 870474.709 + 97895.395 4- 789784.7 +
895887.870.
2064. Add together 25 and 4 tenths, 1205 and 6 tenths, 9 and 52
thousandths, fifty and 19 hun.lr.Hlths. 104 and 2 hundred-thouHandths.
2055. Add 3 and 25 thousandths, 1075 and 45 hundredths. 90 and
482 thousindths.
2050. Find the sum ofl2025 and 8 tenths, 5702 and 44 thousandths.
77and HOthousundths.
2057. What 38 the total of 17 hundred-thousandths, 600 ten-thou-
saudthM 2303 thousandfh.s. 15 ten-thousandths, 37 hundredths, nineand
45 nuiidred-thousaiidths, 1 and 91008 .en-thousandths ?
2058. Find the total of 1023 ten-thousandths, 21 hundred-thousandths.
96 thousandths, 9 thousandths, and 1032 hundred-thousandths
, JJ^^'.^f*"'* " *^' '""" °^ *^ ""^ ^ hundredths, 104 and 8 tenths.
1003 and 25 thousandths, 7 and 1038 ten-thousandths ?
2000. Add 814 and 27 hundredths, 12 and 704 thousandths, 1003 and
4 tenths, and 57 and 1004 ten-thousandths.
2001. Find the sum of 113 and 25 hundredths, 12915 and 423 ten-
thousandths, and 45 and 2131 hundred-thousandths.
2002. WJiat is the sum of 507 ten-thousandths, 12 and 2131 ten-
thousivndths, 452 and 233 hundred-thousandths, 5 and 36 hundre<lths ?
50fi?r •f;-^\f"^'^'',o" """^ ^ t<-'"th8.305 and 4 ten-thousandths,
66678 milhontiis, and 12780 and 125 thoasaudths
2004. What is the total of 1130 and 42 tenths, ioo hundredth.. 10503
teu-thoHsandths. and 78 and 710003 millionths ?
2005. Find the sum of 1203 thousandths. 1003 and 70 tenths. 78I0and
845 ten-millionths. and 37 and 302 hundredths.
757878.454 I-
154.354 f
584078.064-I.
»97«89.876 +
89784.7 -f
ths, 9 nnd 52
aiiHaiKlths.
idths, 96 and
thousandths,
'00 tcii-thou-
ths, nine and
thousandths,
ths.
tnd 8 tenths,
>s, 1003 nnd
ind 423 ten-
1 2131 ten-
indredths ?
housandths,
dihs. 10563
IS, 7810 an (\
SUBTIIACTION OF DECIMALS. 97
SUBTRACTION OP DECIMALS.
Example. Subtract 73.435 from 156.78.
Sohitiou. Place tlietenuyns for the subtraction of whole 156.78
nHiiiburs so that the units of the sunic order be in the 3nme 78.43"
coiuiiin. rinco tlie decimal point 3 figures from tlie right,
nnd the dilference is 83345 thousandths or 83.346. 83.345
131. Rule.— 1. Write Me numbers so that thejignrea of the
same order stand in the same column ;
2, Sidifract as in whole numbers and place the decimal
l>oiut in its proper place in the difference.
l-'xrr<*lii<^.
2006.
764907.05
- 87929.795
2067.
240.572
— 26,372
2063.
346176.007
- 78487.878
2069.
741 7236
— 330 6126
2070."
656450. 0.';4
- 78677.09
2071.
702.432
— 601.53
2072.
376570.005
- 87745.15
2073.
9S7.5293
— 983.4193
2074.
7r.2475.754
— 89287.95
2075.
5.86196
— 5.7C006
2076.
897450.07
— 98776.C95
2077.
87.5009
— 13.916
2078.
423750.5
— 66879.75
2079.
27.72369
— 7.72138
2080.
350842.25
— 47974.745
2081.
246.72361
— 127.9506
2082.
75J754.7
- 37679.25
2083.
5.80106
— 2.59
2084.
267475.75
— 79757.975
2085.
37.52
— 18.642
2086.
764704.23
— 87957.747
2087.
27 .132086
— 19.8421
2U88.
465742.5
— 98298.25
2089.
1.3
— 1.2456
2090.
576^27.0
— 89550.957
2091.
47.006
— 46.29864
2092.
654652.5
— 73475.76
«8
sunrnACTioN of dec imals.
2098.
51.019
17.02984
2094.
• 843276.75
- 77787.985
2095.
387.
— 300.6721
2096.-
357402.5
— 69776.756
2097.
4.16019(5
4.06309
2098.
654565.5
- 78749.895
2099.
0.00831
0.0077
2100.
467517.5
- 89349.756
2101.
23.501006
9.4619
2102.
489476.376
— 4787.45
2103.
6.1
— 0.011196
2104.
467465.75
— 8234.975
2105.
0.7002
0.56203
2106.
748760.4
— 27'>429.75
2107.
112.023
— 91.90909
2108.
476435.5
— 285489.875
2109.
0.5
0.0006
2110.
378989,01
- 189471.875
2111.
37.
— 0.02345
2112.
641764.05
- 576376.476
2113.
0.00235
— 0.000139
2114.
8/0079.04
— 19878f 958
2115.
0.1
— 0.019
2116.
678576.5
— 289709.769
2117.
0.023
— 0.007412
2118.
487854.5
— 198965.428
2119.
45.00035
39.000419
2120.
745600.05
- 87740.276
2121.
477456.72
- 98748.809
2122.
789576.5
— 99767.357
2123.
742576.853
— 179407.07
2124.
754252.5
— 272189.756
2126. What must be added to eighty-three units and four thousand
cue hundred and ninety-three hundred-thousandths, to have nine
hundred and eighty-seven and fifty-two thousand nine hundred and
twenty hundred-thousandths ?
2126. Diminish three hundred units and twenty-three ten-thousandths
by twenty-seven and nine hundredths.
2127. Subtract fifty-seven and fifty-three thousandths from ouo
fine hundred and two hundred and nineteen hundred-thousandths.
2131.
2132.
2133.
2134.
2135.
2136.
2137.
2138.
2139.
2140.
2141.
2142.
2143.
2144.
2146.
Mt'LTIl'LirATION' OF DECIMALS.
M
2128. How much do three huudrod and forty-five and seventy-two
thousand three hundred and sixty-one hundred-thousandths, exceed three
hundred and forty-four and eight- thoasand two hundred and three ten-
tliousandths ?
2129. What remains when seven ty-six tenths are diminished by seventy-
six thousandths ? "
2130. How much greater are two hundred and thirty-seven and seven
hundred and two hundred-thousandths than one hundred and thirty-six
and twenty-five millionths ?
MULTIPLICATION OP DEC ^ALS.
Example. Find the product of 48.5 by 6.23.
Solution. We multiply as in whole numbers, and if the
multiplicand alone were tenths the answer would be 30215.5,
but since the multiplier is also hundredths, the product is one'
hundredth of 30215.5, which by moving the decimal point two
places to the left becomes 302.155. Hence the
48.5
8.23
1455
970
2910
302.155
I' thousand
have nine
indred and
hons^ndths
from one
Ithfl.
132. Rule.— Multij)Iy as in whole numhers andpoinloffas
many decimal places in the product as there are decimals in
both multiplicand and multiplier, prefixing ciphers if necessary.
2131.
787254
2132.
765679
2133.
794377
2134.
487789.
2135.
883749.
2136.
3548S5.
2137.
79.5678.
2138.
287407.
2139.
198793.
2140.
25490.
2141.
647y72.
2142.
47907.
2143.
774357.
2144.
567800.
2146.
980017.
.25 X
'.854 X
225 X
095 X
.005 X
.27 X
,745 X
,617 X
,001 X
005 X
829 X
853 X
907 X
004 X
004 X
Exercises.
74
2146.
78
2147.
69
2148.
57
2149.
89
2150.
459
2151.
766
2152.
897
2153.
974
2154.
678
2155.
984
2156.
685
2157.
668
2158
786
2159.
678
2160.
764527
176986
149653
239576
690523
470075
450845,
705496,
970075.
845974
943766.
345678.
745643.
645676
937004
.907 X
i.4C5 X
,805 X
003 X
414 X
237 X
74 X
855 X
08£
075
45
075
25
X
V
X
X
X
X
X
679
8479
4987
7968
47907
89423
47496
9496
79826
20327
87048
44695
84796
29.125
9.876
100
MULTIPLICATION OF PECIMALS.
2161.
674347
X 154.7
2193.
0.79646
2162.
471089
X 9-765
2194.
0.45654
2163.
345807
X 29.026
2195.
0.3747
2164.
674257
X 49.054
2196.
7.4748
2165.
647835
X 42.05
2197.
0.9876
2166.
980075
X 547.076
2198.
8.07594
2167.
975687
X 906.078
2199.
0.6632
2168.
547374
X 700.09
2200.
0.0797
2169.
856374
X 696.007
2201.
0.4356
2170.
937095
X 670^07
2202.
8.907
2171.
534624
X 53.076
2203.
5.045
2172.
950357
X 149.078
2204.
9.565
2173.
453089
X 7808
2205.
6.426
2174.
789376
X 764.576
2206.
2.6789
2175.
687009
X 87.870
2207.
4.8066
2176.
746589
X 698.765
2208.
7.6675
2177.
859407
X 524.689
2209.
4.205
2178.
975009
X 47.007
2210.
6.4765
2179.
607456
X 874.95
2211.
808954.306
2180.
670407
X 854 354
2212.
804950.075
2181.
651476
X »7.005
2213.
764205.456
2182.
542805
X 37,450
2214.
689424.760
2183.
807904
X 752.459
2215.
547485.927
2184.
0.76425
X 0.054
2216.
589770.054
2185.
0.87665
X 0.746
2217.
579745.089
2186.
0.4896
X 0.37
2218.
879476.875
2187.
0.6646
X 0.05
2219.
474606.086
2188.
0.706
X 0.89
2220.
685467.057
2189.
0.4586
X 0.07
2221.
764562.080
2190.
0.6458
X 0.03
2222.
679406.907
2191.
0.03767
X 0.024
2223.
974354.02
2192.
0.0747
X 0.145
2224.
676489.007
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X 407.
X 874.
X 307.
X ».
X 6.
X 4.
X 87.
X 47.
X 47.
X 78
X 876
X 676
X 976.
X 847.
76
495
1.405
009
004
479
40(P4
.7409
405
217
007
907
(107
975
764
7475
805
005
09
54
06
07
225
009
96
05
09
04
47
007
25
2225. What is the proauct of twenty-three by twenty-two and thirty-
five ht'udi-edtiis?
2226. Multiply twenty-five and forty-three thousandths by nine and
two h\uidred and sixty-four thousandths.
2227. What is the product of twenty-seven and five hundred and five
thousandths by seventy- two hundredths ?
2228. How much are one hundred and sixteen and one hundred and
twenty-four ten-thousandths multiplied by thirty-four thousandths?
2229. If you multiply fifty-seven thousandths by thirteen and one
hundred and sixty-seven thousandths, what will be the product ?
2230. What is the result of sixty-three teu-thousuudtha multiplied by
seventy-two hundred thousandths ?
2231. What number do you obtain by multiplying thirty-fire
Inintlredths by thirty-seven millionths ?
2232.
2233.
2234.
2235.
2236.
2237.
2238.
2239.
2240.
2241.
2242.
2243.
2244.
2246.
2246.
DIVISION OF DECIMALS.
101
0.85
9.75
4.495
0.405
7.009
0.004
0.479
9.4004
0.7409
9.405
3 217
3.007
7.907
3.007
4.975
3 764
9.7475
9.805
407.005
874.09
307.54
9.05
6.07
4.225
87.009
47.95
47.05
78.09
876.04
576.47
976.007
847.0 25
DIVISION OF DECIMALS.
ind thirty-
r nine and
:ed and fire
ndred and
idths f
1 and one
ct?
iltiplied by
thirty-fiye
Operation.
7.90(518 (3.14
628
1570
"mi
942
2198
2198
2.537
Example. Divide 7.96618 by 3.U.
Solution. Divide as in whole numbers and
the quotient is 2537 ; now since the dividend is
the product of the quotient and the divisor,
the number of decimal places in the dividend
must equal the number in the divisor and in the
quotient ; hence the number of decimals in the
quotient equals the number of places in the
dividend dimishcd by those of the divisor ;
there are then 5 less 2 = 3 decimal places in
the quotient ; the answer then is 2.537.
Hence the
133. Rule. Divide as in whole numbers^ and point off as
many decimal places in the quotient as the number of decimals
in the dividend exceeds the number in the divisor.
Note. — 1. When there are not so many decimals in the dividend as in
the divisor, annex ciphers to make the number of places equal.
2. When the number of figures in the quotient is less than the excess
of decimal places in the dividend OTer those in the divisor, prefix ciphers
to the quotient.
3. When a division has a remainder, decimals may be had in the
quotient by adding ciphers to the dividend and continuing the division.
Exercises.
2232.
76.04
-*-
8
2233.
89.026
..
_
14
2234.
74.205
_
_
25
2235.
45.255
-
-
15
2236,
84.015
-
-
30
2237.
195.3
_
_
45
2238.
87.017
-
_
50
2239.
307.50
-
_
12
2240.
550.85
-
-
40
2241.
635.85
-
_
75
2242.
673.46
_
_
72
2243.
647.96
-
-
32
2244.
716.451
-J
_
434
2245.
607.88
-J
-
550
2246.
745.801
.
!-
764
2247.
415.02
-»-
719
2248.
905.025
—
795
2249.
874.05
_
978
2250.
967.85
_
796
2251.
807.025
-
_
986
2252.
60.
_
0.08
2253.
144.
_
0.36
2254.
216.
_
0,03
2255.
525.
_
0.015
2256.
672.
_
0.0012
2257.
1280.
_
0.32
2258.
1010.
_
0.025
2259.
123.
_
_
1.20
22C0.
542.
_
2.5
2261.
464.
-J
h
6.40
102
DIVISION OF DECIMALS.
2262.
643.
22(J3.
747.
2264.
795.
2265.
875.
2266.
8945.
2267.
9764.
2268.
29754.
2269.
379745.
2270.
924807.
2271.
895476.
2272.
4205684.
2273.
7466854.
2274.
0.175
2275.
0.14
2276.
0.16
2277.
0.125
2278.
0.54
2279.
0.5406
2280.
0.3954
2281.
0.7155
2282.
0.795
2283.
0.3754
2284.
0.3217
2285.
0.5742
2286.
0..?251
2287.
0.4
2288.
0.9
2289.
0.0075
2290.
0.0025
1.60
2291.
5 2474-{- 0.72
4.5
2292.
4.7054 -
~ 0.80..
9.60
2293.
7524 -
4.0072
2.5
2294.
70 2J7 -
7.9
76.805
2295.
;Vt74 -
2.819
32.005
2296.
47 1154 -
9.007
395.125
2297.
16.017 ^
8.05
395 14
2298.
17.042 -i
9.05
79.305
2299.
54.5 -;
7.95
547.085
2300.
84.375 ^
16..^
!»87.675
2301.
97.6 -H 23.51
4761.25
2302.
157 050 -t
9.1
0.5
2303.
457.075 -J.
- 12.079
0.56
2304.
845.08 •+
47.805
0.4
2305.
509.74 -+
- 27.56
0.25
2306.
405.7 -f
79.27
0.75
2307.
817.405 -r
99.99
0.30
2308.
352.1 -^
12.812
0.25
2309.
379.035 -{-
9.009
,0.5
2310.
807.4 -f.
29.05
0.26
2311.
957.025 H-
17.005
0.032
2312.
6428.5 -L.
340.5
0.740
2313.
7467.08 -=-
154.4
0,7526
2314.
8421.51 H-
111.11
0.437
2315.
6703.01 -5-
201.1
0.2107
2316.
7507.4 -i-
107.6
0.105
2317.
8421.55 -:-
235.07
0.12
2318.
9205.04 ■+.
717.004
0.14 1
2319.
5412.02 -H
641.07
fivftf' "T^f^^'^y *™" "e 7 aud fifty.five hundredths contained in
tive thousand three hundred and fifty-five ?
2321. The product of two numbers is one hundred and eightyfive and
Z ? , 1^ ""? '^''''^•"'^ thousandths ; one number is one and four
lo*^^ ''^^*y"^'''*''°"^^''"'^'*»«^ what is the other number »
.J!;' A "":°yj'"^" '"'' y°» -«k- two and six hundredths from
lorty.two and eight hundred and sixty-four thou.sandths ?
2323 Divide forty-two and five tenths by fifteen and three hundred
and eighty-five thousandths ? "unarea
2324. The product of a multiplication is nine thousand nine hundred
and Beventy.four ten-thousandths and the multiplier is oneTindred a^d
hve thousandths. What is the multiplicand ? ""area and
2325. By what number will you divide fifty.six thousandths to have
one thousand four hundi-ed thousandths as quotient ?
2326 The dividend is two hundred thousandtlis and the quotieut two
hundredths ; wliat is the divisor ? 4"o"eui two
BILLS.
103
4
■4- 0.72
4
-J- 0.80..
4 -
^ 4.007-2
^ 7.9
4 -
^ 2.819
4 -
^ 9.007
i- 8.05
i- 9.05
i- 7.95
f- 16.5
H
1- 23.51
-J
9.1
-J
<- 12.079
~
- 47.805
.
- 27.56
-5
- 79.27
_:
- 99.99
-i
- 12.812
_^
9.009
— fi
- 29.05
-r
• 17.005
-1.
- 340.5
-j-
154.4
-i.
111.11
-5-
201.1
-7-
107.6
235.07
-»-
717.004
-1-
641.07
i C
ontained in
gh
ty-five and
01
le and four
lUI
nber »
dr
edths from
hn
36 hundred
in
s hundred
hi]
ndred and
m
s to ha>e
1«
Dtieut two
2327. By what number will yoii divide two hundredths to have a
quotient of two hundred-thousandths ?
2328. What is the quotient of 564 and 48 hundredths by 36 f
2329. The product of two fractions is 9, one of the factors is 1 and 8
tenths ; find the other.
niLi^.
134. A Bill is a memorandum of articles sold to a person
with their prices.
Models or Bills.
Mr. Paul R. Dillon,
Quebec, January 6, 1893.
Bouffht of S. P. Lf-.amy.
5 lbs. Coffee k | .86
12 «• Lard 14
4 •« Ham 12
8 " Salt Beef .10
12 " Butter 22
6 •• Cheese .16
15 " Maple Sugar .08
Seed Payt,
S. P. Leahy.
II
80
$9 56
104
BILM.
Messrs. Collins tc Co.,
Levis, March 6, 1893.
Bought of Stki'hrn Buos.
6 prs Men's shoes, buff. -i $1.80
6 " Lady's «• 1.2o
* " Boy's " 80
8 " Children's Laced shoos 90
6 •• Men's shoes, calf 3,50
3 '• Lady's " , buff 1.50
£ecd Fayt,
Stephen Bros.
per J. Healy,
Mr. L. T. Moors,
Montreal, January 4, 1893.
Bought of J. C. Hart,
7yds. Ribbon t j gl
10 " English Tweed 2.26
10 *• Merino << j yg
8 " Ked Flannel
6 " Flanders Linen
4 " Grey Cotton .
Total
.30
.45
.08
12 bush.
16
8
20
86
45
24
bILLB.
lot
Mr. F. rERUY,
. Halifax, July 7, 1893.
EoMght o? Kdwaiid Fbaseii,
_ 6 doz. Hhubarb at $ .30
3 buucheB Radish " .40
8 •• Asparagus " .20
2 bushels Spinage " .75
4 pints Strawberries " .25
6 Cucumbers •• .05
2 bunches Carrots •« .12
2 " Turnips «« .10
Tola:
Mr. A. Pattoit,
Quebec, October 2, 1893.
Bougrht of Joseph McDonald,
12 bush. Oats at | .45
16
8
20
35
45
24
Barky No. 1 " .68
" No. 2 " .65
Peas.... " .85
Potatoes " .48
Spring Wheat " 1.09
Autumn « " 1.07
Eecd Fayt,
Joseph McDokald.
Per D. Kbabnst.
100.
BILLS.
Mr. h. C. MoiMiiMsoN,
Montreal, Mny lo, 1803.
To D. R. Barrow,
Oi:.
Aj.iil
Miiy
For M. KiU, Ijf yds. Broadcloth.. . . /© 94.60
1| yds. Lining /© .35
Cut and furnisliing
6|yd8. Vei-vins, Mantle Cloth fQ) 5.10
2iyd8. Blk. Velvet, for furnishing
and collar ® 5.20
Buttons and cut
CO
40
Mr. J. A. Drayton,
Three Rivers, Sept<'uib»'r 6, 1893.
To Arthur Kelly.
Dk
Mnivli
.\|>ii)
iM;iv
20|21b8. Ginger atf .15
60 « Whiting •• .09
3bbl8. Salt •• 1.18
4J do2. Eggs «« .20
5 lbs. Butter «• .13
3 bottles Blue Ink •« ,36
4 gal. Kerosene oil •< 1.12^
12 lbs. Soap «• .08i
5 " Valentia Graps «• .09
25 lbs Prunes •« .11
64" Cheese «« ,18
...
BILLS AND AfCOrNTS.
107
Jlr. 0. SwEBT,
Quebec. December 5, 1898.
To T. 0. MonRisoN, Dn.
IH6»
Jan.
F.b.
Jan.
March
To 45 lbs. Coffee at $ 40
" 18 yds. Broadcloth •• 3.50
" 30 " Meiino «« .75
Cb.
20 By 20 bush Oats at $ .45
c
T
Reed Payt.
T. G. MoRuisKON.
I
I BILLS AND ACCOUNTS.
2380. Montreal. Feb., 2nd, 1893, Mr. John Hogan bought of Mr
Jos. Levin, viz : 7 lbs. Chocolate at 25 cts. ; 15 lbs. Caudles at 22 cts •
12 lbs. White Sugiir at 15 cts.; 18 lbs. Flour at 24 cts. What is the
amonut of the bill ?A
"^5^1. My. John Kearney of Quebec sold to H. Perrault, Feb 6th •
18 yds. Lace at $2.45 ; 5 pairs Kid Gloves at 45 cts. ; 12 Ladies Fans at
70 cts.; 2 Lace Curtoins at 55 eta.; 4 doi. Lamb Skins at 25 cts i«r
pair ; 12 Needle Cases at 24 cts. What> the amount of his i.urchase (^
2382. Feb. 24th, A. Orsali bought oi^. Kearney ; 2 doz. Colored
Shirts at 17.80 ; 3 doz. Handkerchiefs at |4.40 ; IJ doz. Neok-tiesat
•3.40 ; i doz. Shirt buttons at 12* cts. apiece ; 12 yds. Uose ribbon at
16 cts.; lOJ yds. Cotton at 18 cts. Find the amount of tUe bill,
108
8ILL8 AND ACCOUNTS.
I
It'
2333. J. Sweeney of Chicago sold J. McGee, Jan. 6th, 1893, vii : 37
yds. Sheeting at 26 cts;; 43 yds. Merino nt 82 ot;.; Feb. 6th: 75 yds.
Holland Linen at 45 cts.; 209 yds. Calico at 14 cts.; 330 yds. Wrapping
Linen at 16 cts. What is the footing of the bill ?
2334. Miiy 15th, 1893, C. Hart sold to E. Cadieux : 8 " Lessons in
English", Elementary Course, Pupil's E.lition at 25 cts.; 2 "Lessons in
English," Elementary Course, Teacher's Edition at 75 cts.; 6 •• Lessons in
English," Intermediate Course, Pupil's Edition at 40 cts.; 2 "Lessons
in English," Intermediate Course, Teacher's Edition at fl.OO ; 4
"Ijcssons in English," Sup«'rior Course, Pupil's E'lition at 60 cts.; 1
"Lessons in English, "Suprior Course, Teacher's Edition at $1.76. Find
the amount of the purchase ?
2335. March 18th, 1893, Mr. F. Irwin bought of T. Love : 4 yds.
Silk at f3.60 ; 4i yds. Kibbon at 56 cts.; 6f yds. Serge at 72 cts ; l.\
yds. Cassimere at $2.20 ; IJ yds. Blue Cloth ut §3.40 ; 8 pair Slippers
at 36 cts.; 2i yds. Linen at 68 cts.; If doz. Shirt Collars at 92 cts.
What is the amount due ?
2336. March 20th 1893, Mr. T. Doran bought of Brown Bros : 52
lbs. Muple Sugar at 7i cts.; 4 bbls. Flour (extra) at $7.80 ; 9i lbs
Cheese at 16 cts.; 15 lbs Currants at 8 cts.; 7 lbs. Black Pepper nt
42 cts.; 20 lbs Butter at 24 cts.; IJ bush. Peas at 70 cts.; 3 bush.
Beans at $1.10 ; 14i lbs Ham at 16 ; What is the amount of the bill ?
2337. Mrs. Jas. Shea bought of Messrs Duggitn Bros, on May 21 : 1 paii
Black Socks at $1.07. July 2ud, 2 pair Hunting Shoes at $2.90. Sept.
10th, 2 pair Gaiters at $1.80 ; 1 pair English Laced Slioes at $1.30.
What is the amount of the bill ?
2338. Mr. T. O'Connor sold M. Fanning as follows ; March 9th,
1893, 15 pair Hunting Shoes at $3.75 ; 8 pair Woolen Socks at 86 cts.
April 17th, 12 pair Gaiters at $2 72. March 26th, M. Fanning gave in
payment: 12 bbls. Apples at $3.15; April 25th, $10.50 cash. How
much does he still owe ?
2339. C. Hart sold W. O'Brien as follows : May 3rd 1893, 15 lbs.
White Sugar at 14 cts.; 7 lbs. of Butter at 18 cts.; 4 gals. Petroleum
oil at 45 cts.; 7i lbs. Coffee at 32 cts.; 12 lbs. Rice at 7i cts.; 9 lbs.
Tea at 48 cts.; 6 bbls. Apples at $1.80 ; 20 gals. Syrup at 72 cts.; 1 bag
Salt at 37 cts. ; 15 lbs. Prunes at 8 cts. What is the amount of this
transaction ?
2340. J. C. Kearney of Pt St. Charles soM W. C. Rogera, June 4th
1893 : 20 lbs. Coflfte at 24 cts.; 50 lbs. Brown Sugar at 7 cts.; 75 lbs.
Starch at 13 cts.; 12 gals. Syrup at 65 ots.; 90 lbs. Butter cakes at 9
cts.; 54 lbs. Sweet Biscuits at 11 cts. What is the footing of ihe bill ?
fttLI.8 AND ACCOUNTS.
109
1893, viz : 37
6th: 75y,U.
fila. Wrapping
1 " Lessons in
2 " Lessons in
6 " Lessons in
2 •• Lessons
at $1.00 ; 4
I at 60 cts.; 1
it 81.76. Finil
Love : 4 yds.
at 72 cts ; ].\
> pair Slippers
lars at 92 cts.
wn Bros : 52
.80 ; 9i lbs
ack Pepper nt
cts.; 3 bush,
of the bill ?
[ay 21 : 1 paii
$2.90. Sept.
loes at f 1.30.
March 9tli,
ks at 86 cts.
iniug gave in
I cash. How
1893. 15 lbs.
3. Petroleum
'i cts. ; 9 lbs.
'2 cts.; 1 bag
sunt of this
frs, June 4th
cts.; 75 lbs.
er cakes at 9
5 of rlie bill ?
2341. S. Carslcy sold F. Irwin, July lUh, 1893: 5 yds, of Black
Cloth at 13.50 ; 1 Satin Waistcoat at |5.50 ; 3 yds. Gray Linen at 19
cts.; 10 yds. Gray Fringe at 68 cts.; 3 pes. Ribbon at 31 cts. ; 3 yds.
nik. CnHsimore at $2.25 ; 7i yds. Alpaca at 55 cts.; 16 yds. Lining at
lojcts.; 4 skcius Silk at 54 cts. ; 4 yds. Wadding at 6 fts.; 9 yds.
White Flannel at 90 cts.; 2 Cravats at f 1.1 2i ; 4^ yds. Green Fasten-
ing at 58 cts.; 6 Collar Shirts at 15^ eta. What is the amount of the
fn voice t
2342. March 10th, 1893, A. Howard sold C. Cunningham : 18 lbs.
Tobacco at 32 cts. ; 25 lbs. Powdered Tobacco at 40 cts. ; 72 lbs. Tobaci-o
in leaves at 18 cts.; 54 lbs. White Sugar at 12 cts.; 20 lbs. Soup at
14 cts.; 45 gals. Molasses at 37 cts. April 8th, ho received in payment
$3.00. What amount remains due I
2343. June 5th, P. McKenna bought of Hart k Tuckwell of Mont-
real : 32 bis. Apples at $'.^.95; 56 cases Oranges at |2.25 ; 16 cases
I.rf>mons at $1.80 ; 40 boxes Raisins at $2.75 ; 20 boxes Figs at $1.04).
What is the amonnt of the bill ?
2344. May, 20th, 1893, W. Rogers of Ottawa sold J. J. McGee : 40
lbs. of Sugar at 7 cts.; 15 lbs. Coffee at 36 cts.; 76 bush. Potatoes at 45
cts.; 12^ gals. Syrup at 40 cts.; 95 lbs. Sugar Biscuits at 8 cts. What
was the amount of the sale ?
2345. On Feb. 4th, 1893. Mr. G. Harris bought of A. L. Fortier :
17 yds. Broadcloth at $5.25 ; Feb. 15th, 29 yds Cassimere at $1 . 62 ;
March 18th, 60 yds. Linen at 17 cts.; March 14th, 49 yds. Canvas at
27 cts.; the 15th, 18 yds. Blue Cloth at $3.19 ; July 17th, 27 yds.
Grey Cloth at $2.75 ; Sept. 3rd, 75 yds. Red Flannel at 61 cts. Mr.
Hnnis gave on account : Feb. 28th, 1893, Cash $83 ; July 25th. 14 bis.
of Flour at $7.20. Having settled on Sept. 4th, what was the balance
due ?
2346. January 10th 1894, A. Richards sold to S. V. Poston : 174^ lbs.
Quinquina at 60 cts.; 321^ Gum lacque at $1.45 ; 607^ lbs. Rhubarb at
$2 90 ; 720 lbs. Gum Arabic at 25 cts.; 509^ lbs. Sassafras at 15jt cts.
What is the amount Oi the sale t
2347. April 15th, 1893, Mr. H. Farrel bought of Oi-sali O'Hara : 8
spools White Thread at 7 cts.; 6i yds. Merino at $1.08 ; 7^ yds.
Prints at 15 cts.; Cloth and Lining for coat $7.60 ; IJ yds. Cassimere
for pants at $3.12 ; Lining for imnts 37 cts.; 18^ yds. Irish Linen at
52 eta.; 3 yds. Green Ribbon at 35 gts.; what was the ainoant of tha
purchase ?
2348. Sold by D. Raymond to M. A. Scott. August 28th, 1893 ; 12
Jbs. Brazilian Colfeu at 37i cts.; 9 lbs. Oreeu Tea at 66 cts.; 2 boxes
llO
BItL« AND ACOOUlfTI.
rii'volate 70 Ibi. at 22 cU.; 2 W'*"* Grapeg at |3.26 ; 26J Ibf . Porto
Utan fwnonadti at 7 ctt.; 34J lbs. i Herat 19 ct».; Onioua 82 ot«.; 4
yda. BUflk Cloth at $2.76. ; 9i yds. Belgium Linen at 27 ct».; 6 pair Kid
Olcves at 87 eta.; 1} doi. White Handkerchiefs at $2.16 ; what amount
does A. Scott owe !
2349. On May 17th 1893, J. Hardy k Co sold to Mr. P. X. Burns,
the following : 2} doz. Common Glasses at 40 cts. ; 1^ doz. Blue Plates at
76cts.; 3 gals. Honey at 90 cts.; i gal. Molasses at 46 cts.; 3i gnls.
Linseed Oil at fl .26 ; 16 lbs. Cheese at 18 cts. ; 4 lbs. Salmon at 12 cts. ;
i doz. Bottles Olive oil at 66 cts. each ; 2 lbs. Pepper at 45 cts ; 12 lbs.
Fresh Butter at 26 cts.; 74 lbs Pork Chops at 10 cts.; find the amount
of this sale ?
2360. bold by L. Gingras to Madam H. Smith, Juue 20th 1893 :
6 lb». Coffee at 32 cU.; 7 lbs. Sugar at 8 cts.; Pepi>er 16 cU.; 12J
lbs. Maple Sugar at 10 cts.; i lb. Tea at 64cto.; IJ gals Syrup at
70 cU.; 4 bush. Dry Apple* at f2.12 ; 1^ doz. Small Plates at 48 cts.;
H lbs. Bice at 6 cts. ; 6 lbs. Black Tea at 56 cts. ; 8 Tablets Perfumed
Soap at 8 cts. ; 20 lbs. Mackerel at 9} cts. ; 6 lbs. Candy at 22^ cts. ;
find the amount of the sale ?
2351. May 9th 1893, T. Lynch k Co. sold to J. Conlon : 14 yds.
Heavy Cloth at $3.60; 18 yds. Satin at fl.l2i ; 24 yds. Merino at
f 1.90 ; 48 yds. Cassimere ot $1.87i ; «* yds. Colored Flannel at 76 cts.
Find the amount of the bill ?
2352. June 10th 1893, J. 0. Kearney bought of J. Sweeney the
following articles : 7 J lbs. Green Tea at 85 cts. ; 14^ lbs. Black Tea at
46 cts.; lOf lbs. Pepper at 64 cts.; 21 lbs. Common Tea at |1. 07 ; 19
lbs. Superior Tea at f 1.60 ; ]8i lbs. Soo-Choo Tea at 96 cts. What is
fbeamonnt of the bill ?
2353. W. O'Brien owes M. R. Sullivan for merchandise : July 16th
1893, 8 gross Shirt Buttons at 86 cts.; July 17th 1893, 16 d'^/ Woolen
Stockings at |3.l8i ; July 17 1893, 3 doz. Shirt Front* Ht 6r.i5 ,
August 2nd, 1893, 12J yds. Ribbon at 27 cts.; 30 pair Glove »t O'-.aln ,
4 doz. Napkins at $2.85 ; 22J yds. Ticking at 46 cts. Find the
amount I
2364. R. O'Neil sold to J. Sweeney, July 11th 1893 : 478 gals.
Alt«'aat92ct8.; 308i gals. Old Rum at |1.85 ; 610| gaU. Holland
Oint ti 12; August 6th, 207j gals. Rum at |1.80 ; 119i gals.
Coji'-w. -.i-i; .•*-,». 22nd= 401 gals. SootohQin at f 1.05. Received
inpay»e:,, (V*. ^th, 30 bbls. Salmon atf8.75 ; Nov. 6th, Checque
onM-^n: Vi- 3«,Ak for|70 ; 'f^^. gist, C^hf600, Whst amount remaini
4a« \o Jl, Q'is M I
BILU AND ACCOrSTI.
Ill
5| Ibi. Porto
us 82 ct«. ; 4
I.; 6 pair Kid
ihtkt amount
f. X. Burns,
lue Plates at
8.; Signls.
m at 12ct8.;
Ota ; 12 lbs.
the amount
20th 1893 :
15cts.: 12i
kls Syrup at
s at 48 cts. ;
a Perfumed
at 22^ cts.;
>a : 14 yds.
. Merino at
3l at 75 cts.
2355. June 18th 1803, C. WiUon bought of P. Dowi s : IJ lb.
Red Radish at 75 cts.; 14 oz. Pepper at 5 cts.; 5 oz. Cucumbers at 9
cts.; 8| oz. Lettuce at 12 cts.; 19 oz. Onions at 10 cts,; 6 oz. Asparagus
at fl cts. ; 8 oi. Carrots at 6J. What is the amount of the bill I
2356. Roes k Co.. of Montreal sold to E. McMillan, Quebec :
March Jii'l, 1893, n)pr. Men s Calf Boots at $3.75 ; 28 pr. Boots,
Chihlrtu's at 8fl cts.; March 15tli, 40 pr. Slippers at 85 cts,; April 3rd
M(u'sSiipp«i • at fl.16 ; April 3rd, 120 pr. Ladies Laced Bouts ot ?1. 25.
H<' ,:oeivcd in payment : Nov. 27th, Cash f280 ; April 15th, 110 cases
L> uiuns at $3.20. What amount remains due to Hoss & Co.
2357. July 4th, 1893, R. Powei of Quebec sold to C. Jones : 23 yds.
Silk at 95 cts.; 15 yds. Ribbon ot 45 cts.; 12 yds. Muslin at 18 cts.;
July 10th, 4 yds. Blue Cloth at |3.60 ; 3 yds. Bik. Cloth at f4.50 ; 9
yds. Satin at 11.25 : 1 Cravat |1. 30 ; Aug. 15th, 5 pair Calf Boots at
18.50; 3 doz. Sleeves at $2.40; 1 doz. Buttons 50 cts. On this,
imymeut was made as follows : July 20th, 8 bbls. Apples at $3.20 ; 15
bush. Potatoes at 22 cts.; Aug. 20tb, Cash $7.80. When the account
was settled, what balance was due t
2358. L. O'E/me of Pt. St Charles sold toO. Taylor : 50 lbs. Maple
Sugar at 7 cts. ; 75 lbs. White Sugar at 13 tts. ; 20 lbs. Coffee at 24 cts. ;
IS gals. Syrup at 66 cts. ; «0 lbs. Sweet Biscuits at 9 cts. ; 64 lbs.
Bttttai Biwjults at 11 ots. What is the amount of 0. Taylor's bill I
weeney the
lack Tea at
t$1.07 ; 19
I. What is
: July 16th
lo/ Woolen
a ttb .r»f. ''5 ,
it ^i.al A.
Find the
: 473 gals.
B. Holland
119i gals.
Received
1, Cheoqua
int renuini
112
MI8CKLLANE0US PBOOLEUa.
MISCELLANEOUS PROBLEMS.
2359. A fruit merchant sold 4000 apples during a week ; at the rate
of 10 appk-s for 5 cts ; find the amount of the receipts ?
23C0. Henry gave § of 33 oranges to his sister ; how many had he
roniniiiing ?
2301. A merchant sold 4910 yds of cotton, what did he gain, al the
late of $2.06 on every 100 yds.
2302. We received cases of merchandise each weighing 852 lbs
inchuling the boxes ; what is the net weight of the 6 cases of merchan-
di.se knowing that each box weighs 70 lbs ?
2303. Reduce 10| units to an improper fraction.
2304. When 740 eggs cost $7.40, how many dozen can be purchased
with S2.28 ?
2305. If to pay 3 loaves weighing 4 lbs each, at the rate of 3 cts. a
l>ound, you ^ve a baker a 25 cent-piece and an other of 60 cts. ; how
much change will you receive ?
2366. A wire 18 yards long is to be employed to make points, each
point is 9 lines long ; how many dozen points can be made ?
2307. A man having 50 sheep, sells J of them and then buys 32
otliers ; hoAv many has he now ?
2368. 1 bought 10 dozen hats at $2.76 each. 1 gave in payment 40
yards of cloth at $2.50 a yard. How much do I still owe ?
2369. A crockery dealer buys 3600 plates for $140, transportation costs,
$3.00 and commission $1.20 ; what will be his profit if he seUa them at
the rate of 100 for $5.10?
2370. How many units are contained in the fraction ijf* I
2371. Thirteen barrels of wine cost $636, $190 were paid for duty and
§54 for transportation. How much should I sell it a pint to gain $146 on
llie whole, knowing that a barrel contains 30 gallons?
2372. A person bought 16 dozen pencils at 9 cts. a dozen ; what is
his gain if he sells them at one cent apiece ?
2373. I bought certain goods for $152. If I had sold them $8.00 more
I would have gained $12. How much did I sell them for ?
2374. Reduce to the same denominator J, ^and ^.
237.'». Seven heii-s are to share in a donation of $8689 ; two of them
give iheif part to 24 oi-phans. How much will each orphan receive ?
2376. A Father was 48 years old when his son was bom, and 62 years
old at the birth of his daughter ; what will be the age of the father and
daughter when the sou is 16 years old ?
MIROELLAKROrS PnOBLKMS.
118
; at the rate
aauy had he
gain, at the
ling 852 lbs
) of merchau-
be purchased
ate of 3 cts. a
) cts. ; how
points, each
?
lieu buys 32
payment 40
rtation costs,
sells them at
I
for duty and
i^in$146ou
m ; what is
18.00 more
vo of them
ceive ?
nd 62 years
> father and
8377. A woikmau gained $30.25 in 75 days. How much would he
have received, had he worked 15 days less ?
2378. James gave $70 for a watch, and ^ of this sum for a chain ; and
he sold the two for $90. How much did he lose ?
2379. When 10 shirts are bought for $3.50; how much should each
shirt be sold to gain 90 cts. on the whole ?
2380. The sum of two numbers is 1439 and their difference 318. What
are the two numbers t
2381. Two men working together during 30 days gained $72 ; one of
them gains, $1.25 a day ; how much does the other gain ?
2382. Nellie had $360 ; she spends ^ for a pouey, J for a watch and
i for a sleigh. How much has she left ?
2383. If I buy 3 oranges for 5 cts. ; how many could I purchase for
$1.90?
2384. A gentleman boards in a hotel for 80 cts. a day ; how many
weeks did he remain knowing that he paid $44.80 ?
2385. 1 bought 3546 oranges at 2 cts. apiece ; how much will I gain
if 1 sell them at 30 cents a dozen ?
2386. A retail dealer bought 8 dozen of hats at $1.90 ; and givts in
payment 46 yards of velvet at $2.15. How much more does he owe ?
2387. Two pieces of linen cost $71.28. I sell 15 yards for $21.00 and
by so.doiug gain 32 cents per yard. How many yards are there in the
two pieces ?
2388. What is the simplest expression of }| ?
2389. The apartments of a family are composed of 4 like pieces ; one of
which is divided into two cabinets for the children ; the rent is $160,
a year what should be paid for 3 mouths ?
2390. What is the price of an orange knowing that 486 dozen cost
$147.80 1
2891. A workman puts 18 cents aside each day; what shall be his
savings at the end of 12 years, 3 of which contain 366 days and the
others 365 ?
2392. A bag of wheat weighing 200 lbs costs $4.50. How much should
I f cU it a lb. to gain 6 cts. on a pound ?
2393. Reduce to the same denominator f ^ and }f ?
2394. A man spends 10 minutes in smoking a pipe ; find how many
hours will he spend in a year, knowing that he smokes 3 times a day 7
2395. In a family, they eat 2 loaves of bread of 4 lbs each at 6 cts for
two lbs, what is the expense for bread at the end of a week of 7 days I
2396. A farmer while bringing eggs to the markets breaks 35, gives 3
114
UlNOELtAKEOUB FBOBLEUS.
11^
to the poop, and sells 7 dozen on the way and arrives with 476 ; how
many had he when he started ?
2397. A farmer starts out with 480 eggs ; he breaks 27 and sells 6
dozen on the way ; how many had he when he arrived at the market ?
2398. Two persons start (he same day ; one from Quebec and the otliii
from Three Rivers ; one travels 6 miles and the other 9 miles a day.
The distance between these two cities is 90 miles. In how many days
will they meet and how many miles will each have traveled ?
2399. A fruit dealer sets out with 600 oranges, he throws 42 bad ones
away and when he arrived at market he had 456. How many did he sell
on the way ? .
2400. A little boy picked | of a bushel of strawberries and sells half ol
them ; how many gallons has he left ?
2401. A clerk who gains $45 p«r month, was paid $315 ; how many
mouths remain to finish the year ?
2402. What is the salary of a clerk per year knowing that he received
$450 for 9 mouths ?
2403. Coude died 108 years before Florian ; Fenelon 29 years aftti
Conde, Bossuet 11 years before Fenelon and Florian died in 1:94. Find
the year of the death of each of these men.
2404. A baker wants $115 more to buy 70 bbls flour at $6.30 ; how
much money has he T
2406. A hatter bought 16 hats which be sells for $42 and gains 40
cents on each hat ; how much did a hat cost him ?
2406. A person bought a house for $10367.20, repairs amounted to
$637.96. For how much did he sell it knowing that he gained $392.10.
2407. From a sum of $1746, 14 sergeants took $52 each. What
portion of the remainder shall each soldier receive knowing that there
are 450 soldiers ?
2408. I wish to divide $544 between 15 persons ; if the first 7 receive
$24 each ; how much shall each of the remaining 8 receive ?
2409. What shall be the price of 10 dozen of penknives when 6 cost
$4.50?
2410. What will be the cost of 7 barrels of apples, if 2i barrels cost $9 ?
2411. How much money had John, knowing that after his parents had
given him ^10, he gave to 12 beggars 25 cts. each and had $21.50
remaiiiiug?
2412. Charles bought a piece of cloth at $2.40 a yard. In selling it
for $3, h I mnkes a gain of $30. What was the length of the piece ?
2413. Au individual has an annual revenue of $2630. lu 12 years
MISCeLlANEOVA FRODLEMS.
115
ith 476; how
i 27 and sells Ci
t the market ?
c and the othii
9 miles a day.
•w many days
id ?
ft's 42 bad ones
lany did he sell
ud sells half ol
5 ; how many
liat he received
29 years after
Q 1794. Find
S6.30 ; ho^v
and gains 40
amounted to
ined 9392. IG.
each. What
ig that there
first 7 receive
?
when 6 cost
)arrel8 cost $9 ?
lis parents had
1 had $21. 5U
In selling it
he piece ?
lu 12 years
he puts aside $8460. What were his daily expenses allowing 365
days for a year ?
2414. What is the cost of some goods knowing that they were sold for
$1600, and that if they had been sold for $175 more, the gain would
have bei!n $575 ?
2415. I bought 45 pieces of cloth of equal length, at $2 a yard. In
reselling them at $2.40 I gain $900. What is the length of each piece ?
2416. WImt sum docs Louis possess knowing that if I gave him
$14.50 he could pay a debt of $75.50 and would have $12.75 remaining]
2417. H. Harrington says that if his salary were augmented by $28.80,
lie could siKJiid $1.30 each day. Wliat is his revenue '<
2418. A furniture dealer receives 60 cases and pays $1846 for the lot.
.^' cost $34 each ; 20 cost $18 each. What is the price paid for the
rciuainder ?
2419. 50 dozen of pencils cost $6 ; how many will $5 buy ?
2420. A person bought 4 baskets of pears each of 75 dozen at 9 cents
a dozen ; if they are sold 14 cents a dozen, how much will be gained ?
2421 . A hundied bricks cost $5 ; what must be paid for 3 carts which
which contain 1380 each ?
2422. NVhat will a drummer get for selling 6 casks of wine of 85 gals,
each, at the rate of 80 cents for every 10 gallons sold ?
2423. If 100 needles cost 30 cents ; how many can be had for $2.40 I
2424. A fruit dealer bought 5400 lemons on condition that he would
receive 112 for every hundred. How many should he receive ?
2425. A traveller walks during 12 days at the rate of 16 miles a day,
if he wishes to retui'u iu 8 days, how mauy miles will he have to
travel per day ?
2426. A man travels during 32 days at the rate of 20 miles per day,
he wishes to recommence his voyage and take 8 days longer. At what
rate will he have to travel per day ?
2427. A cask was made up of 52 gals, of wine at $1.20 and 8 gals, of
water. What is the price of a gallon of the mixture '
2428. What is the price of a butt of wine containing 55 gallons,
knowing that it is a mixture of 37i gals, at 75 cents and 17i gals, at
60 ceuts ?
2429. What is the price of a butt of wine of 60 gallons, knowing
that it contains 37i gals, of wine at $0.50 and 22i gals, at $1.10 ?
2430. A merchant bought 654J yds. of cloth lor $915.99 ; 957 yds.
of Linen for $190.51 ; 456i yds. of Calico for $9.00 and 145Jyd8. of
Kibbou for $116.36. How many yards did he buy and how much did h«
pay?
116
MISCELLANEOUS PROBLEMS.
w
2431. In a church four collections were made ; the first netted |37.00-
the second $9.00 more than the first ; the tliird $52 and the fourth as much
as the first and second together. How much money was gathered in the
4 collections ?
2432. A merchant bought 16 plates at 6i cts.; 24 dishes at 11 cts •
64 glasses at 4i cts. ; 36 decanters at 1 7 cts. ; he sells the plates at 7i cts ■
the dishes at 12i cts.; the glasses at 7i cts., and the decanters at 25 cts.'
what will he gain on each article ? '
2433. In a family the father receive $1.25 per day, the mother 65
cents ; if the expenses are $1.40 per day ; how much will be saved in a
month of 30 days of which 26 are working days ?
2434. What is the amount of the following bill : 17 yds. Fine Serge at
75 cts. ; 18 yds. of Drugget at 15 cts. ; 15 yds. Scarlet Stuff at $4.50 ; 16i
Menno at $4.72 ; 25| yds. Print at 36 cts ; 17 yds. Gray Stuffat$3.70 ?
2435. A work comprises 12 sheets: it each sheet cost $35 for com-
position and $2i for press-work ; what will 8000 copies cost ?
2436. Four persons divide $16999.50 between them, what will each
receive if the first gets $1157 more than the second ; and the second
$1249 more than the third, and the fourth $325 more than the third ?
2437. A shoemaker finishes 16 pair of shoes for $42 ; he sold half of
them at $2.80 a pair. How should he sell the balance to gain $5.20
on all ?
2438. A merchant buys nuts at 16 cts. a hundred and retails them at
10 for 2 cts. What will he gain daily, if he sells $14 worth ?
2439. A detachment of 15 soldiers received $14.50 for 2 days pay.
Another detachment received $20.80 for 13 days. How many men in the
last company ?
2440. A man set out on a journey and traveled at the rate of 20 miies
for 9 day.s, he returned at the rate of 12 miles a day. How long did he
take to return ?
2441. I owe $556.75 : I gave in payment 123 yds. Merino at $1 66 •
111 yds. Calico at 42 cts.; $184.15 Cash and the remainder in Linen at
• cts. a yard. How many yards of linen did I give ?
2442. May 12th, 1893, I bought of J. Kearny : 18 Ploughs at $11 ;
23 Saws at $3.50 ; 90 Spades at 86 cts. ; May 30th 1893, 86 Shovels at
50 cts.; 46 cwt. Iron at $12 ; June 7th 1898, 17 Hammers at 62 cts •
12^ Mill Saws at $12.12. June 7th, I paid on account $140 ; July 2nd
$775. What balance do I still owe ?
2443. A bookseller buys 20 reams of paper at $1.70 ; 3 dozen books
at 16 cts. each; 60 gross pens at 17 cts. ; 6 registers at 47
cts.
netted $37.00;
burth as much
ithercd in the
lies at 1 1 cts. ;
ites at 7i cts. ;
ers at 25 cts. ;
;he mother 65
>e saved in a
Fine Serge at
«$4.50; 16}
tuff at $3. 70?
?35 for com-
t
liat will each
id the second
he third ?
e sold half of
) gain $5.20
tails them at
I
2 days pay.
r men iu the
3 of 20 miles
long did he
>o at $1.66 ;
in Linen at
ghsat$ll ;
3 Shovels at
8 at 62 cts. ;
J July 2nd
ozcu books
47 cts. : 5
MISCELLANEOUS PROBLEMS.
117
dozen pencils at 1 J cts., and 28 dozen penknives at $3.20 a dozen.
What change should he receive on $200 ?
2444. 137 joists were sold, 43 were paid $731 ; each of the others
were sold for $5.50 euch less than the first lot. What was the price of one
of the second lot ?
2445. In a shop there are 40 workmen, 15 are paid $1.30 per day, 18
$1.05 and the otherj $1.60 ; what gain will the contractor make if he
receives $17660 and pays $468 for rent, the workmen being employed
for 297 days ?
2446. James bought 987 yards linen at 63 cts.; 15 pieces each of
93§ yards at 45 cts. ; 7 pieces each of 101 yards at 39 cts. ; he gave on
account 17 pieces of cloth each 24J yards at $1.95 ; 15 pieces calico 94|
yirdseach at 17 cts. ; the balance was paid cash, what amount was given T
2447. A contractor purchased 20 loads each of 3400 bricks at $5.10 a
thousand, he paid 30 cts. a thousand for transportation and 10 cts. for
loading. What did he spend ?
2448. A horse dealer sold horses for $44834.40 ; he lost $4.74 on each
horse sold, his total loss was $1478.88. How much did each horse cost t
2449. June 30, 1893, C. M. Hart, sold W. Rogers, 473 gals Alcohol at
95 cts. ; 308 gals Old Rhum at $1.90 ; 610 gals Holland Gin at $1.05 ;
Aug. 5, 207 gals Rum at $1.75 ; 119 gals Cognac at $2.10 ; Sept. 22,
401 gals Scotch Whisky at $1.15. Mr. Rogers has paid as follows ; Oct.
4, 30 brls Salmon at $8.75 ; Nov. 6, Cash $520 ; Nov. 22, a drait on
London at 30 days for balance. What was the amount of the draft.
2450. I had at my disposal $1139 to do a certain piece of work ; every
day the receipts were $79.60 and the expenses $33. How many days did
the money last t
2451. A speculation that was commenced with $8000 capital lasted
478 hours, the receipts amounted to $380 every day. What were the
daily expenses ?
2452. From a sum of $76366.75, $813.25 were given to the poor, each
of 43 persons received $247.25 ; the remainder was divided among a
certain number of persons each receiving $168.55. How many persons
were there 1
2453. Reduce to the same denominator the following fractious f, },
f. rr-
2454. I owe $4867 to Thomas : I pay him at one time $3475, afterwards
I give him $950, and I sell him 10 cords of wood for $44 ; if he deducts
$1795 ; how much do I still owe him ?
2466. I mix 647 dozen of oraugcs at 15 cents with 355 dozen at 23
lis
MlSCEI.LANEOl S l"nOllI,F.M8,
cents ; at what price per dozen should I sell them so as to gain S-*! 70
on the whole ? ■ e. v- .
2456. The daily receipts of a factorj' are $522, the expenses during
174 days were $7308 ; find the daily gain ?
c^lt^L ^" ?"'"^ ^* '"'''' °^ ''*"' '""'^ containing 57f gallons, 1 lost
51 02. 50 on the cost price of $1881. 20. At what price per gallon did 1
2458 John sold 217 riding-coats for $1844.50 ; on each coat he spent
§4 J7 for cloth ; 95 cents for lining and $2.08 for cutting and make up.
" liut did he gain on each coat ?
2450. In a family the father earns $1.50 a day, Alex earns 90 cts ,
Henry 50 cts. and Peter 25 cts. How much do the four earn in 17
months, working 25 days each month ?
2460. A clerk's income amounts to $2041.75, his daily expenses are
«4.25; how much will he have saved if he works 3 years, of 365 d.vs
each ? ./ . J
2461 If a clerk received $2041.75 as salaiy for 7 months; what
sliouhl lie receive for a year ?
2462. A mechanic receives $45 a month as salary, suppose he dmws
*40o ; now much remains due on his salary for one year.
2463. If 96 eggs cost 90 cts. to a merchant who retails them at 8 for
10 cts. ; what would he gain on 2 bis each containing 480 ?
2464. Peter bought one dozen penknives for $5.40, if he sells them at
00 cts. apiece, what gain will he make on 8 penknives ?
2465. What is the amount of a bill for 27 yards Silk at $3. 75. 75 yards
Cloth at $2. 45 and 29 yards Velvet at $1.75?
2466. What will be the cost of 58 lbs. of Beef, if 2 lbs. cost 32 cts. ?
2467. A hoj-sedealer bought 18 horses for which he paid $50 each 28
at $68, 15 at §40. and 22 at $35 ; he sells 24 at $68, 21 at $70, 18 at
$41.20 and the remainder at $39. What is his gain ?
2468. A boy wears yearly, 3 pair of pants at $1.11, 2 coats at $3.30. 2
vests at 50 cents, 2 pair of shoes at $1.20, 1 hat at $1.42 and 3 pair
stockings at 25 ; if his father earns $1.60 per day and his mother $1 50 •
IT'V""^? '"" ''"^ ''""' *° ''°'^ '" ^'^y '^' '^^P^"^^^ of their son ?
^40J. ihe Uiflerence between two numbers is 504, the smaller is 9207
what^would remain if from the greater you subtract 748 ? '
2470. I sold 180 barrels of oil at $43.60 a barrel and made $1782 net
S:nn ; what was the price per barrel ?
«iL^"<;.'^'r '"'r o''' '"^'"'''' ^^^^- ^^' '^^' ^''' g*^"" «t °°e time
$1346,35 then $2346.75 ; what remains to be i>aidknowing that the
Ufbtof the second is $5464.80 ? e "
MISCELLAKEOrs mODLKMa.
119
I gain 821.70
lenses during
gallons, 1 lost
gallon did I
coat he spent
nd make up.
irns 90 cts.,
r earn in 17
Expenses are
of 365 d;iys
>nths ; what
le he draws
lemat 8 for
sells them at
75, 75 yards
it 32 cts.?
each, 28
870, 18 at
at $3.30, 2
Jnd 3 pair
;her $1.50;
r their son ?
ler is 9207,
$1782 net
t one time
g that the
2472. A father of a family takes 7 hours for rest, 10 hour* for work
and 2 hours for his meals ; what time does he employ for each of these
occupations during a week of 6 days ?
2473. A man-of-war having made a seizure, the captain received
$18740.25 ; 11 officers each $9643.75 ; 15 sub-officers each $5649.05 and
240 men each $943.75 ; what was the amount of the seizure ?
2474. A clerk whose yearly salary is $840, received $700 ; how many
month's salary did he lose ?
2475. 1 bought 340 volumes for $204, I paid $150 on account ; how
many volun»es remain to be paid ?
2476. A wheel turn? 24 times a minute, and each turn the carriage
advances 5| yds.; what space would it cover in 2 hours 25 minutes ?
2477. HI had sold goods for $2537.60, 1 would have gained $840 ;
for how much did I sell them knowing that I gained $715 ?
2478. I gained $543.25 on goods which 1 sold ; if 1 had gained
$631.40 I would have sold them $4927-35; for how much were the
goods sold T
2479. If I had $924 more, I could pay $12432 and I would have $643
left ; how much have 1 ?
2480. Owen having a certain sum of money borrows $590 ; he pays a
debt of $847.75 and receives $545.85 which were due to him ; he finds
on his return home that he has $946.86, after spending $12.45. What
sum had he at first ?
2481. What is the cost of a house, knowing that it it had been boughtfor
$1875 less, by selling it for $87977 the buyer would have gained $6476 1
2482. A farmer mixed 120 bushels of wheat at $1.25 with 83 bushels
at $1.18 and 74 bushels at $1.05. He sold the wheat at $1.21 a bushel ;
how much did he gain ?
2483. A bookseller buys 756 volumes at 43 cts. a volume ; as he
received 13 books for 12, he gets 819 which he sells at 47 cts. a volume ;
what is his gain ?
2484. One of my friends borrows $450.75 from me, another$879.25 ; I
paid $14825 and I have $248 loft. How much had I before lending any?
2485. Wolfred lends $875.25 ; and he lacks $346.75 to pay two debts
one of $1425.85 and one of $978.75. How much had he before lending
any ?
2486. A lot of goods were bought for $8460 ; how much most it be
sold so a<3 to gain i of the cost price plus $174.45 ?
2487. A lot of goods were bought for $760.40 ; if they had been sold
for $46.70 more I would have gained half the cost price. How much
were the goods sold for ?
120
MISCKLtANKOUS PROBLEMS.
2488. If a merchant in selling goods for $1240 gains i of the cost price
plus f 40.80, how much did he pay for them ?
2489. The 1st of four persons has $1607 ; the 2nd $181 less th^ui tlie
first ; the third has $76 more than the second ; the fourth $206.70 less
than the first. What is each one's share ?
2490. Three partners share in a certain sum ; the 1st takes $450.60,
the 2nd takes the double of the first minus $46.70, the 3rd takes k of the
first and ^ of the second plus $64.75 ; what is the sum tiivided ?
2491. Two men are to share $945.75 so that the part of the second be
double that of the first ; what are the two parts ?
2492. A wood-dealer buys 546 cords of wood, half at $2.75 a cord and
the rest at $3.03. How much did he disburse if he paid 12i cts. per
cord for cutting it T
2493. On adding $194.40 to a certain sum it becomes three times it-
self. What is the sum ?
2494. On adding $146.80 to a certain sum, it wants $24.20 to be
trii>led. What is the sum ?
2195. A lot of goods were bought for $1240.80 ; how much must I sell
them to gain ^ of the cost price ?
2496. After taking $496.45 from a certain sum ; $845.75 more should
be taken in order to have one-third of the sum ; what is this sum ?
2497. I have $345.75 ; how much should I borrow to pay two debts,
one of $879.85 and the other $1245.95, and buy 12 yards of cloth at
^4.871 a yard ?
2498. I bought goods for $946.20 and by selling them for $43 moro
than I did I would have gained | of the cost price. How much did 1
sell them for f
2499. Three persons spent a certain sum : the first spent $784.30, the
second $241.00 more than the first, and the third $301.70 more than the
second. What were the amounts spent by the last two T
2500. A wine merchant bought 12 casks at $87 each. He sells 4 for
$380, how much must he receive for the others so as to realize a profit of
$156 on the whole ?
2501. A merchant pays $3 for every 100 plates he buys, he bought
1640 ; now how much must he sell each plate to gain $9.20 on the whole,
knowing that 40 were broken during the trip and that other expenses
amounted to $2.40 ?
2502. What will 1 pay for 34 barrels of wine of 55 gallons each, which
cost $78 a barrel, knowing that the duty on wine per pint is 6 cts. and
transportation, 76 cts. per b&rr«l ?
MHCRLLANEOtrS rKOBLSlM.
121
r the cost price
less th:ui the
$206.70 less
akes $450.60,
takes i of the
ideH ?
he second be
75 a cord and
[ 12^ cts. per
tree times it-
124.20 to be
sh must I sell
more should
B sum ?
two debts,
is of cloth at
for $43 more
much did I
$784.30, the
ore than the
) sells 4 for
:e a profit ot
s, he bought
•n the whole,
her expenses
each, which
is 5 cts. and
2508. A tap which gives 14 pints in 1 minute, fills a basin in 2 hours.
How many gallons can the basin hold ?
2504. A basin can hold 2980 gallons ; how long will it take to fill it,
the tap running 12 pints a minute ? .
2505. Two taps which run 12 and 16 pints respectively can fill a
basin in 3 hours 15m.; how many gallons can the basin hold ?
2506. A basin can hold 5688 g^illons and can be tilled in 3 hours 57
minutes, by two taps one of which gives Id gallons a minute ; how
many gallons must the other give ?
2507. A bookseller pays $3.50 for a certain book ; how much will he
sell a dozen so as to gain 70 cts. on each book ; knowing that he gives 13
books for 12 H
2508. A bookseller pays $14.50 a dozen for 852 books ; but he reci'ives
13 for 12. What is his gain, if he sells each volume $1.65 i
2509. A merchant bought 50 doz. of locks at 91 cts. each, and got 13
for every 12 ; in aiTanging them he lost 2. What will he gain if he
sells the others at $1.10 each I
2510. A merchant received a box contairing 50 turkeys which should
be sold at 90 cts. each. He gave five to his friends. What should he sell
the others so as to lose nothing ?
2511. A man bought 48 dozen of glasses at 14 cts. apioce and he
received 13 for a dozen. He sold them at 20 cts. apiece. What was hid
gain?
2512. A man bought 12 volumes at $200. He received 13 for 12. What
did each volume cost him T
2513. A milkman brought to the city 18 gals, of milk which he
desired to sell at 20 cts. a gallon. But an accident caused the loss of 3
gals., what should he sell the remainder for so as to lose nothing ?
2514. What is the length of a piece of cloth that cost $175.50,
knowing that I sold 25 yards for $87.50 and gained 50 cents a yard ?
2515. 1 bought 60 pieces of cloth of equal length at $2.60 a yard and
sold them at $3. 10 with a gain of $2100. What is the length of each piece ?
2516. A merchant bought 80 yards of cloth for $240 : what is his gain
on 50 yards which he sells at $3.10 a yard ?
2517. I bought 16 apples for 14 cts. and sold them for 20 cts. :
what will be my gain on 400 apples T
2518. A man buys 16 apples for 14 cts. and sells them for 20 cts. :
what will be his gain on a sale of $18 ?
2519. A watch gained 20 hours during 60 days : how many minutes
did it gaip. hourly ?
122
MTBCELLANEOC* BROBLZMS.
2620, During the last 86 hours, a watch gained 2 minutes erery 8
hours ; what o'clock is it when the hands point to 26 minutes to 6 ?
2621. From 4 o'clock in the morniug, a watch gains 2 minutes every 3
hours, what i.s the time when the hands mark 7 p. m. !
2522. A watch gains 3 minutes every 4 hours, what will it have gained
tt the end of a week ?
2523. A watch lost during the last 33 hours at the rate of 2 minutes
every 3 hours, what hour will the clock mark when it is 8 minutes past
3 o'clock.
2524. A clock was started at 6 p. m. and lost 3 minutes every 2 hours,
what hour will it mark at 10 a.m. next day ?
2525. A person promises to give 90 cents to the poor every time he
gains $12.25 ; what should he give when he gains |47 ?
2526. A merchant gives fl.75 in alms for every $17.75 he gains ; what
sum did he gain when he gave $38.50 in alms ?
2527. Every time a man gains $13.75, he gives a certain sum to the
poor ; find this sum knowing that when he gave $7 to the poor he had
1185.60 remaining?
2628. Each time a boys saves $6.75 his father gives hiit> «1.25 ; if the
boy saves $81, what will he have after his father adds his um (
2529. For every $75 a boy gains, his father pays him $1.50; what
sum did the boy gain when, after his father's gift, he had $99 ?
2530. Each time a young man earns $6.25, his father gives him rt
certain sum, what was this sum, if when the young man earns $93. 76 his
father gives him $1.26 ?
2531. § of a sum of money is $96, what is the sum.
2532. A man spends § of his money, then i and after 4, what has he
remaining on $600 ?
2533. John has half as much as Joseph, who has j of $96, What was
John's money ?
2534. A ship cost $7500. Peter's share is i, John's is | of Peter and
Joseph's the balance ; what does each own.
2535. J of 56 is the § of *rhat number ?
2536. f of $900 is the J of J of John's fortune, what has he ?
2537. One fraction is | and the product if, what isthe other fraction ?
2638. Tobias spends i of the day in study, | in recreation, | in sleep
and the rest in business ; how long does he give to business J
'Ne|5?rD
ites erery 8
:eH to 5 ?
nutes every 3
t have gained
of 2 minutes
ninutes past
very 2 hours,
ury time he
gains ; what
i sum to the
poor he had
1.25 ; if the
m?
M.50 ; what
9 ?
gives him a
18 $93. 75 his
rhat has he
, yifh&t was
if Peter and
e?
ler fraction ?
I i in sleep
CONTENTS.
Addition 6
Addition of Fraction^ 70
Addition of Decimals '.I5
Apothecaries' Weight ^4
Avoirdupoids Weight Si
Bills and Accounts ... I J7
Circular Measure i^8
Common Fractions 04
Cubic Measure ^^
Currency S2
Decimal Fractions 88
Denominate numbers 82
Division 36
Diviacn of Fractious 74
Division of Decimals 101
Dry Measure S7
English Money S3
Exercises in Numeratiuu 4
Fractions C4
Liquid Measure 86
Measure of Length S5
Measure of Time 87
Mental Arithmetic 52
Mental Exercises in Fractious. . 75
Miscellaneous Problems Ill
Models of Bills 103
Multiplication 25
Multiplication of Fractions... 73
Multiplication of Decimals. . . 9i>
Notation 9
Notation of Decimals 91
Numeration 1
Numeration of Decimals 89
Oral Exercises in Numeration. 6
Oral Exercises in Decimals. . . 93
Practical Problems in Addition. 18
Practical *' Subtraction... 21
Practical " Multiplication. 81
Practical " Division 47i
Practical " Fractions TJ
Preliminary Definitions 1
Problems in Mental Aritbmetio. 65
Reduction of Fractions 67
Reduction of Decimals 94
Review Problems 32
Review of 4 Simple Rulcii ... . 47
Roman Figures 4
Solid Measure 86
Subtraction 17
Subtraction of Fractious 71
Subtraction of Decimals 97
Square measure , « » . ■ 85
Troy weight 83
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