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J
FIRST
CANADIAN ARITHMETIC,
INTENDED FOR TUK
PIILHARY DEPAKTHE^T OP COMMN SCHOOLS.
BY ,. . ^' -
:i
H. L. WHITCOMB.
►-•-<
v/ ,'
-^'^,
■■*♦ I
PRINTED roll THE AUTHOR BY JOHN LOVELL,
AND FOR SALE BY ALL B00KSELLEB8.
J860. . 1
M,':3
Entered according to the Act of the Provincial Parliament in
the year one thousand eight hundred and sixty-six, by
H. L. Whitoomb, in the office of the Registrar of the Pro*
viuce of Canada.
The
the foil
PREFACE.
'arliament in
sixty-six, by
r of the Pro-
The distinctivo character of this little work will appear from
I the following:
Instead of a short introduction to all the rules of arithmetic,
leading principles only are introduced, and those are thoroughly
elucidated both in theory and practice, while all vulumiuous
explanations are avoided. -
Mental exercises are combined with the written exercises
throughout, and thus applied to tlie illustration of the same
principles.
The important department of the simple rules is arranged in
lessons according to the pages, a table forming the head of
each lesson, and more copiously illustrated by examples than
in any other arithmetic known to the author.
Analysis takes the place of proportion, it being really what
the latter long pretended to, a key to most of the processes of
arithmetic.
How much soever of reliance is to bo placed on the teacher
in giving life and interest to the recitation, books prepared on
the model he pursues will best assist him in thefe respects, and
will tend to produce uniformity in methods of teaching. No
written system of numbers can by any means supersede the
use of numerous oral exercises, both mental and written, and
illustrations on the blackboard.
For the use of the inexperienced teacher notes are interspersed
throughout the book, and the autliur would respecttully oll'er
the following
SU««ESTI<)NH TO TKACIIE15S.
The mental exercises form the heads of lessons to be prepared
by the pupils, but which should be extended and diversiHed by
the teachers till the principle they embody is fully compre-
hended. No one principle can be passed superiicially without
loss to the luture arithmetician.
In order to form habits of correctness and self-reliance the
pupils should be instructed to prove their vfork ; and for this
purpose the answers to many of the exercises are not' given.
And if the teacher keep by him a book with the answers tilled
out in it, and accustom the pupils to number on their slates tlie
exercises they work out, he can see at a glance, or by occasion-
ally calling for their answers, whether they are working cor-
rectly.
Recitations in written arithmetic should generally be con-
ducted by the use of the blackboard. A usual method is
for the class to go up together, and work ont the exercises
appointed by the teacher in the order of their numbers, and
afterwards in succession to give the demonstration, the most
expert taking the precedence, liy giving these demonstrations
and the solutions of mental exercises in a clear and distinct tone,
keeping before the mind the subject, and not words or rules,
the pupils will acquire not only clear ideas of the principles of
numDers, but also the power of expressing their i4caB, and
g natural and graceful elocution,
CONTENTS.
PAGB
Definitions and Notation 5
Addition 6
Subtraction 30
Multiplication 45
Division 61
General principles^. 74
Miscellaneous exercises in preceding rules 81
Bills of Parcels 83
Analysis 84
Tables of weights and measures 91
Reduction of compound numbers 100
Addition " « . 108
Subtraction " " Ill
Multiplication " " 113
Division " " 115
Analysis " " 119
Miscellaneous exercises 121
•
Answers to exercises 124
1. Aritj
2. A nui
3. A un
4. Anal
5. A sii
one denon
6. Nota
7. Num(
pressed,
figures or
8. Thee
their posi
second te
being equ
9. Thr
following
Ob
P
O
at
&
9
n
7 9
s
4,
18 17 16
The 81
lions, O
Note
nection
ARITHMETIC.
PAGB
5
6
-. 30
. 45
. 61
. 74
. 81
. 83
. 84
. 91
100
108
111
113
115
119
121
124
1. Arithmetic is the science of numbers.
2. A number consists of one or more units.
3. A unit is a single thing of any kind, as 1 book.
4. An abstract number is of no denomination, as 2, 4, 9.
6. A single number is an abstract number, or of but
one denomination, as 3, 6 shillings.
6. Notation is the expression of numbers by characters .
7. Numeration ie the reading of numbers thus ex-
pressed. The characters used in notation are the ten
figures or digits, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.
8. These figures have different values according to
their position, the right hand figure being units, the
second tens, the third hundreds ; each order on the left
being equal to ten of the order next it on the right.
9. Three orders make one period, according to tlie
following,
NUMERATION TABLE.
P
o
at
OB
n
Q
t3
a
s
« 5 "S « j2
K H hJ n E^ p
i
^ w -2
w .« ^5
n H D
•mm
n H P
79 4, 36 7. 83 6, 847
18 17 16 15 14 18 12 11 10 9 8 7,
iH I
W H P
3 6 8
6 6 4,
a
n
9
8
J2
a
ED
a
1
2
6
1 Orders.
The succeedine periods are QuintilUons, Sextillions, Septil*
lions, Octillions, Nonillious, Decillions.
Note.— Notation and numeration should be taught in con-
nection with the simple rules.
6
ARITHMETIC.
10. The four fundamental rules of arithmetic are!
Addition, Subtraction, Multiplication, and Division.
A D D I T I X .
11. Addition is the process of finding the sum of two
or more numbers.
The numbers to be added are called addends, and the
result of the addition, the sum.
12. The sign +, signifies addition. Thus 5+2
denotes that 2 is to be added to 5. The sign = denotes
equality ; 5 + 2 = 7 is read 5 plr.s 2 equal 7.
MFiNTAL EXERCISES.
1. Count 100.
2. How many windows in the school room ?
3. How many panes of glass in 1 window ? in 2
windows?
4. How many boys are in the cla8s ? How many
girls? How many boys and girls?
1
2
3
4
• 1.
2. J|
how
3.
and 3
TABLE.
1 + 1 = 2
2 + 1 = 3
3+1 = 4
4+1 = 5
B + 1 — 6
6+1 = 7
7+1 = 8
8+1 = 9
9 + 1 =
10 + 1 =
11+1 =
12 4- 1 =
10
11
12
13
# X
WRITTEN EXERCISES.
in ad
addc
(I) (2) (3)
(4) (5)
(6) (7)
(8)
Th
bytl
1232 1324 3210
3232 1234 5424
1024 2132
1653 1436
2451 3210
1445 4206
3210
4628
1 Th
1 H®
1 seen
ADDITION.
ritliraetic are
Division.
TABLE.
- sum of two
nds, and the
liiia 5 -f 2
1 = (lenotea
7.
Ij
I =
10
I =
11
. ^:
12
—
13
(8)
10
3210
>6
4628
1 + 2
2 4-2
3 4-2
4 + 2
= 3
= 4
= 5
= 6
6 +
« +
7 +
8 +
= 7
= 8
= 9
= 10
9 + 2
10 + 2
11 + 2
12 + 2
11
12
13
14
• 1. Add two successively to 50 ; thus, 2, 4, 0, 8, 10, &c.
2. John had 3 apples, and his sister gave him 2 more ;
how many had he then?
3. A man gave 1 cent to Harry, 2 cents to Emma,
and 3 cents to Kate ; how many did he give to all ?
(9)
24113
34123
(10)
22222
58764
(H)
34212
12634
(12)
24321
41264
(13)
23214
63412
(14)
14321
83414
(18)
32142
64253
(15)
14213
10142
(16)
31248
83701
(17)
12314
42344
(19)
21021
76235
(20)
32100
61964
* These exercises with the tables are intended to give rapidity
Id adding. Tlie pupil shun! 1 be practised in them till able to
add each figure successively to 100 without the least, hesitation.
The written exercises will be distinguished iVom the mental
by their numbers which are continuea from page to page.
The mental exercises are intended rather as the heads of a
lessou to be prepared by the pupil than a guide to the teacher.
He should modify and enlarge them as circumstauoes shall
seem to dictate.
6
ADDITION.
•
M
42S
a
345
25
•o
<
34
Sum.
827
Proof. 827
18. The addition of siuple numbers is called simple
addition.
14. To add siiuplu numbers, *
Rule with example : Find the sum of 423, 345, 'iC)
and 34.
We write tlie addends units under units,
tens under tens, hundreds under hundreds,
&c. Then, commencing at the units we
add (without naming the figures) thus 4,
9 — 14 — 17 units equal to 1 ten and 7 units ;
set down the 7 units under the column
added and carry the 1 ten to the next
column. Add the remaining columns in the same
manner, setting down the units and carrying the tens ;
because 10 of each order is equal to 1 of the next order
on the left.
NoTB.— The pupilfl should onrly be made familiar with the
names of the onderti, their increaHe lowards the left, and
decrease towards the right in a tenfold ratio, and with tht^
eflbct of removing a flguro in either dUrootion.
15. Proof 1. Commence at the top and add the
columns downwards. If the two results are alike the
work is supposed to be correct.
Ah this process reverses the order of the figures, any mistake
made in the lirst operation is likely to be detected in the second.
Proof 2. Cut off the first addend ; add the others, and
to their sura, add the first addend, The result should
be the same as the first sum.
(33
714
714
(3
\V
12
14
(21)
32414
18365
(22)
14320
42834
(23)
31034
18264
(24)
63214
63296
ADDITION.
9
•ailed simple f l. Add 2 gucceggively to 100.
2. Add 2*8 to lOO commencing with 1.
8. How many are 7 -f 2 + 2 + 2 + 2 ?
^23, 345, 25 f 4- Kitty paid 2 cents for cakes, and 3 cents for
andy, Ijow much did slie pay for both? 2 -f- 3 = how
"nder „nlts, »"'"^' '^
»r hundreds,
»e units we
1*08) thus 4,
tnd 7 units ;
he column
o the next
the same
g the tens ;
next order
»»• with the
le Jett, and
^d with th«
I add the
5 alike the
"y mistake
the second.
hers, and
t should
24)
1214
296
(26)^
(26)
(27)
(28)
21632
32142
10233
40204
•22032
64764
34123
14523
(29)
(30)
(31)
(32)
32404
21042
31610
32147
03721
61459
4&62R
92864
(33)
(34)
(35)
(30)
71468
32187
69789
32168
71464
32187
60789
78679
(37)
(38)
(39)
(40)
11021
32114
21102
31213
12324
12342
14212
21042
14213
13214
13121
33425
(41)
(42)
(43)
(44)
23241
40021
32102
44221
41234
11234
12324
22334
12351
42321
21423
44300
10
ADDITION.
1
TABLE.
1 + 3 = 4
2 + 3 = 5
3 + 3 = 6
4 + 3 = 7
5+3=8
6+3=9
7+ 3= 10
8 + 3 = 11
9 + 3 = 12
10 + 3 = 13
11 + 3 = 14
12 + 3 = 15
3.
Ad
4.
Ad
5.
Ad
6.
Ai
DW
mai
1. How many are 8+3?6+3? 12 + 374 + 3'
9 + 3?
2. Harry paid 5 cents for a top, and 3 cents for al
cord ; how many cents did he expend ?
2]
31
Al
h a'
(45)
(46)
(47)
(48) 1
22133
21421
10032
33232 ■
23022
32130
12431
23123 1
32134
21142
43213
13321 1 1
(49)
(50)
(51)
(52) 1
31023
31021
10213
31023 1
32103
43210
31043
31323 ■
62313
33634
21031
41433 I
(53)
(54)
(55)
(56) 1
13210
32341
34343
10431 f
13426
33123
43432
34234 1
13436
43243
34343
18476 1 •
Note.— The pujiils should be taught to add without naming I
the figures ; thua, in 41st example instead of saying 4 and 2 mal(e I
6and3malce9,(merely toucliiug the figures wita his pencil) name
the sum thus, 4—6—9.
ADDITION.
11
+ 3 =
12
+ 3 =
l;^
+ 3 =
14
+ 3 =
15
13. Add 3's to 50 ; to 100.
'4. Add 3's to 50; commencing with 2, 1.
5. Add 3*8 to 100 ; commencing with 1,— — 2.
6. A man gave 3 peaches to each of his four children,
>w many peaches did he give to all?
+ 3? 4 + 31
3 cents for
(48)
33232
23123
13321
(52)
31023
31323
41433
(56)
10431
34234
18476
thout naminff
? 4 and 2 make
3 pencil) nam*
(57)
(58)
(59)
(60)
21023
23323
21324
21343
31203
33333
41233
33333
32313
34313 .
43343
31033
45300
50261
12510
41504
(61)
(62)
(63)
(64)
13432
22212
21032
312102
42324
24343
34341
231230
23213
30234
32432
321433
36340
46341
64204
330975
(65)
(66)
(67)
(68)
10210
21034
43213
23433
06123
34123
23433
36133
14332
32433
64333
43633
6354
34234
86343
12367
(69)
(70)
(71)
(72)
21010
32610
52433
23333
42632
02321
62004
32433
23436
14333
23031
23044
89796
76389
97889
87682
12
ADDITION.
•
TABLE.
1 + 4 = 5
2 + 4 = 6
3 + 4=7
4+4 = 8
5 + 4=9
6 + 4= 10
7 + 4=11
8 + 4= 12
9 + 4 = 13
10 + 4 = 14
11 + 4= 15
12 + 4= 16
1. What is a unit? a simple number?
2. What does addition teach ?
3. 7 + 4+4 + 4 + 4 = how many ?
(•73)
(74)
(75)
(76)
24341
32102
20343
13102
43241
12341
20343
41234
43221
43214 *
20343
32146
14432
41234
28746
33240
(77)
(78)
(79)
(80)
16214
10410
31030
14342
32432
44236
43444
54342
43462
34340
41234
23463
(81)
(82)
(83)
(84)
10321
25043
21034
42103
46321
24342
86426
26436
21423
14324
36243
14442
60372
56344
(86)
16883
16628
(85)
(87)
(88)
34431
14334
3244
23441
10444
14344
1024
44140
32544
43434
4034
23444
14324
34334
3543
44845
ADDITION.
13
abers to be added called ?
tit of the addition called ?
to 100.
-commencing with 2, 1, 3.
Hattie paid 5 cents for pens, 4 cents for paper,
Id 2 cents for pencils ; what did she pay for all ?
What are the
What is the vf>.-
Add 4's to 50 ;-
Add 4's to 100 ;-
(89)
21043
12342
43244
43423
(90)
13240
34344
43143
43144
(91)
32104
34343
34344
62343
(92)
32210.
4362
1621
4432
(93)
72103
12144
10123
21072
(94)
14213
44342
34521
42341
(95)
14121
21021
23126
10436
(96)
10321
10321
4632
2601
(97)
11241
43262
12303
46384
(98)
32104
43624
40123
32106
(99)
10321
46302
61236
10206
(100)
34321
44304
24342
43414
(102)
3244
4324
3323
4345
(104)
3214
4345
4324
4345
14
ADDITION.
9 4- 5 = 14
10 -f 5 = 15
11 4- 5 = 16
12 + 5= 17
TABLE.
14-5 = 6 54-5 = 10
24-5 = 7 64-5 = 11
34-5 = 8 74-5= 12
44-5 = 9 84-5 = 13
1 . What does addition teach ?
2. What are the given terms of addition?
3. What is the required term ?
4. How are the addends written to be added ?
5. Why do you carry for ten ?
(105)
Find the sum of 5542455 and 863494.
(106)
How many are 2268340 4- 45687098 ?
(107)
How many are 170 4- 360 4- 28 4- 312?
(108)
Find the sum of 154 4- 3265 4" 54.
(109)
(110)
(HI)
(112)
43256
32141
41230
16032
13246
14345
32440
14334
13^45
54354
32144
36755
43214
45544
54610
10054
32143
55324
54081
11246
(113)
(114)
(115)
(116)
326012
14321
63245
5250
143241
45144
41234
5434
325543
35434
43244
5355
432434
14341
54234
5434
121434
43214
55435
5355
- 5 =
- 6 =
- 6 =
14
15
16
17
n?
dded?
494.
098?
■f 312?
i.
(112)
16032
14334
36755
10054
11246
(116)
5250
5434
5355
5434
5355
TABLE.
1 + 6=7
2 H- 6= 8
3-1-6=9
4 -f 6= 10
5-1- 6= 11
6 -1- 6 = 12
7 4- 6 = 13
8 -f 6 = 14
9-1-8 = 15
10-1-6 = 16
11-1-6 = 17
12-1-6= 18
15
A man bought 2 sheep at 6 dollars a head, and a
at 20 dollars ; what did the whole cost ?
John Mills bought a waggon for 20 dollars, he
re 6 dollars to have it repaired, and 5 dollars for
|nting ; what did the waggon cost in all 7
(117)
17 -f 36 -h 75 = how many?
! (118)
gentleman planted on his property 478 oaks, 784
beeches, 64027 firs, 690 apple trees, 160 pear trees,
md 300 other trees ; how many trees did he plant?
(119)
(120)
(121)
(122)
63543
36466
31023
33264
25644
26533
14624
46354
30556
26520
32635
46366
66546
36426
74335
21046
64848
36426
76216
(125)
36781
(123)
(124)
(126)
61002
32475
21006
712106
43263
42364
32056
146305
14326
46364
30556
165346
23216
46734
70256
616564
12789
16734
19866
364656
16
ADDITION.
1. Adcl6'stoY2 ; commencing with 3, 1, 1
2. How many are 19 + 6+64-6-1-64-64-6^^
3. How many are 16 + 6 = 6 + 16 ?
4. Emma is 7 years old, Kate is 2 years older, ani
Colin is 2 years older than Kate ; what is his age, an|
the sum of their ages ?
(127)
Find the value of 2632 + 365 + 4300 + 66321.
(128)
739 + 32 + 46 + 3654 + 30 + 66 = how many ?
(129)
Harry King had 19 geese, 45 turkeys, 150 hens, an|
25 ducks, what is the number of his poultry ?
(130)
145 + twice 145 = how many?
(131)
24356
43562
34566
43562
34566
43562
(132)
26463
23654
26463
43654
66463
63654
(133)
54663
64356
56436
46644
12665
10665
(134)
31021
46063
35466
46563
45466
36563
(135)
36210
63463
34646
63463
34646
63463
(136)
16036
15465
46546
45436
45646
53346
(137)
31064
63545
63466
63566
56345
10066
(138)
36102
46104
66506
46506
4564
536
<^ + 6 4- 6 ?|
jars older, ad
|is bis age, ani
I6632I.
many ?
50 hens, anj
ultry ?
ADDITION.
TABLB.
•
14-7^8
2 4-7=9
3 4- 7 = 10
4 4- 7= U
54- 7= 12
6 4- 7 = 13
7 4. 7 = 14
8 4- 7 = 15
94- 7= 16
104-7 = 17
114-7= 18
12 4- ■? = 19
17
[1. If I pay 60 dollars for a horse, and twice as much
a waggon-; what is the cost of both?
12. 6-1-74-74-74-74-7 = how many?
(139)
Ichard gave 1 7 marbles to each of his 4 brothers ; how
[many did he give to all ?
(140)
man has three farms, one containing 600 acres
[another 243 acres, and another 176 acres ; how many
I acres in the three farms?
(134)
(141)
(142)
(143)
(144)
31021
72463
37104
32576
21043
46063
21463
46707
43747
72664
35466
72767
47663
34576
10550
46563
01264
36746
32747
32660
45466
72106
77637
63576
47660
36563
32147
26717
36747
74068
(138)
(145)
(146)
(147)
(148)
36102
32136
36775
32603
72107
46104
42367
77456
72362
64736
66506
63676
36775
76324
86378
46506
37653
77466
47634
73647
4564
64673
36775
76047
37436
636
46876
77456
56754
63476
9
18
ADDITION.
p.
1. Add Tb to 10 ; commencing with 3.
2. In 1 week there are 1 days ; how many days
there in 3 weeks ?
3. James has twice as many marbles as John, aij
John has 6 ; how many have they both ?
(149)
A box contains 215 grammars, 327 reading books, ^
arithmetics, and 79 geographies; how many boo^
are there in the box?
(160)
A man bought 7 horses at 75 dollars each ; how mui
did he pay for the whole ?
(151)
A man left 2766 dollars to each of his four ohildres
what amount did he leave them 7
(152)
There are four numbers, the first 12776, the secou|
3769, the third 17847, and the fourth 128 more thaj
the first ; what is the sum of the numbers ?
(153)
6789 + 5832 + 4671 + 8907 = how many ?
(154)
(155)
(156)
(157)
762736
675476
763675
706345
716213
126714
712132
706345
216132
361236
237647
706346
177641
210473
167367
706345
146732
173472
234072
706345
412761
623162
147766
706346
123712
413214
417617
706345
ADDITION.
19
a.
lanjr days
as John, a^
TABLE.
1 + 8=9 64-8 = 13 94-8 = It
24-8 = 10 6+8 = U 10 + 8= 18
3 + 8=11 7 + 8 = 16 11 + 8 = 19
4+8 = 12 8+8=16 12 + 8 = 20
|ng books 4^1- ^ ^^^ borrowed $8 at one timej and 3 times as
many boolj"^^ ** another time ; how much did he borrow in all ?
j2. 8 + 3 times itself = how much?
•h ; how muc
'our ohildrej
B, the Beconl
28 more tha^
irs?
(157)
706345
706345
706346
706345
706345
706345
706345
(158)
irry King distributed a number of nuts among four of
I his companions, giving to each 27 nuts, and kept 27
I himself ; how many nuts had he at first 7
(159)
82328
41686
88278
46876
88318
43726
83268
(160)
32107
14706
43807
47806
87387
47686
14787
(161)
32438
14767
34873
48747
16873
21687
38078
(162)
10710
18763
268
732
168
7687
3687
(163)
(164)
(165)
(166)
34681
71634
87645
67146
37600
34216
87645
36478
87630
88274
87645
374074
46784
48648
87645
736488
43867
18027
87645
874688
36847
18776
87645
836488
66728
18767
87645
884674
77i84
38168
87845
798716
20
ADDITION.
I :
It
1. Add S's to 80 ; — commencing with 4, 2, 6.
2. A boy bought a fish hook for 4 cents, a line foi
cents, a pole for 8 cents, and had 8 cents remainin
how many cents had he at first?
(167)
A farmer owned 11 horses, 57 cows, 210 sheep, and
pigs ; what is the number of his live stock? ^'i
(168)
A man paid $86 for a horse, twice as much for a carriH^
and $79 for a harness ; what did the whole cost ?
(169)
(170)
(171)
(172)
72683
71063
36872
91076
1G776
14862
63789
36871
10376
16873
37867
. 6877
62438
34836
68476
6877
37268
67836
62378
6877
36726
67878
87368
9867
71683
36878
86786
1837
62738
84878
76878
837
7608
7896
7698
1890
9698
9986
9898
(175)
6258
(173)
(174)
(176)
46732
12788
46767
8767
71072
37168
18324
8710
45378
8674
14768
7710
45387
2687
76873
8768
62736
7867
68736
18768
87368
2687
86748
78768
16877
7786
73687
78768
87268
1687
61786
96877
74407
8678
63876
42877
6879
6879
6899
8909
7689
1298
1887
1869
2 + 9
3-1-9
4 +
»f the an
ADDITION.
21
4, 2, 6.
fnts, a line for
Hits remaininl
|0 sheep, andj
Istock ?
h for a carrias
whole cost ?
(172)
91076
36871
6877
6877
6877
9867
1837
837
1890
6258
(176)
■ 8767
8710
7710
^ 8768
18768
78768
78768
96877
42877
8909
1869
TABLE.
1 4- 9 = 10 5 + 9= 14
2 + 9=11 6-1-9= 15
3-1-9=12 74-9= 16
4-1-9=13 84-9=17
9 4-9
10 4. 9
114-9
12 + 9
18
19
20
21
Bought 3 cows at $20 a head, 2 calves for $7, and
leep at $9 a head ; what did the whole cost?
94-3 times 9 = how many ?
Eddie is now 2 years old ; in what year will he be
lears old ?
(177)
gentleman left to each of his three daughters $1900,
^o each of his two younger sons $2500, and to bis
eldest son $4000 , how much did he leave. to all ?
(178)
[man sold 3 loads of hay, the first weighing 1670 lbs.,
[the second 890 lbs., the third 1720 lbs. ; what was
hhe amount sold ?
(179)
7S879 + 9 times itself = how many ?
(180)
369878
463786
167362
686746
276386
147368
483769
19867
14789
68796
86378
(181)
867964
789687
710974
270867
168734
687368
178697
896879
876897
786786
368789
(182)
878996
819796
109368
8697
7687
7867
6873
786
689
798
689
(183)
108796
108796
108796
8796
8796
8796
8796
8796
8796
8796
8796
22
ADDITION.
1. Add 9'8 to 100; commencing with 11.
2. What is tho cost of 9 pairs of shoes at $2 a paij
3. Find by addition the number of peas in 6 poii
each containing 9 peas.
4. How many are 19 + 9-|-9-|-9-|-9+9 4-9 +
(184)
Bought a farm for $2368, and sold it again so as to gn
$400 ; what did I sell the farm for ?
(186)
Find the sum of 48763 + 86270 + 4687 + 578 4 4r
+ 18709+ 70471.
(186)
Find the sum of 46C37 + 54263 + 4^986 + 5060 + 8l
+ 641 + 98076 + 7362 + 689 + 1907.
(187)
Add together 587, 9658, 67, 431, 28670, 100000, 63O0,|
851, 8796, and 389476 + 7198 + 87968978. .
(188) s ^:*>^
Find tho value of $8635 + $2194 + $7421 + $93
+ $5063 + $135 + $2196 + $89 + $1225 + $16.
* (189)
Borrowed from A. $735, from B. $634, and from C. as
much as from the other two, how much did I borrow
in all 7
(190)
A man distributed money am< i » li'S rhildren as follows ; |
$700 to '^pch of his three :1au,';'i'e , and 1 :.t8 son a
sum equal to that of all ij ;ntjtera ; how much did he
give to all?
ADDITION.
23
With II.
^068 at $2 a pni]
f peas in 6 pod
gf^ln 80 AS to
ga.
10
10
10
10
10
10
10
10
11
12
13
14
15
16
17
18
TAILR.
9-f 10 =
10 4- 11 =
11 -f 11 =
12+11 —
11 +
11 +
11 +
11 +
1
2
3
4
lU
21
22
23
12
13
14
15
11+5
11 + e
11-1-7
M + 8
11+9
11 + 10
11 + 11
11 + 12
16
17
18
19
20
22
23
^ + B78-f
40
'6 + C060 + gj
7.
^ 100000, 63O0 1
58978. ■
•', ,ifr
>,■'. •■■
$7421 + $93
1225 + $16.
id from C. as
did I borrow
3n as follow?
* "^ "<s son a
much did he
'5*: Crunt lO's to 100; — commencing with 5.
i'ount U's to 100; — commencing with 1.
10 + 3 times itself = what number?
(191)
iRti sold 800 bushels of wheat for $275, 175 bushels
^f oats for $89, 260 bushels of corn for $198, and 75
bushels of barley for $50 ; how many bushels of grait.
lid he sell, and how much did he receive for the
rhole?
(192)
Id four hogs which weighed on an average four
lundred and seventy-nine pounds each ; what did
the whole weigh 7
(193)
|nd the amount of 52G7942B6 + 679362080 + 17736
^+ 368428 + 9570572 + 72576168 + 973826476
+ 596284083 + 987654321.
(194)
Jind the value of 34763460 + 56871936 + 12345678
+ 93648752 + 7494675 + 985421 + 67891 + 72936428
+ 29368 + 1096 + 7898 + 179089 + 7198703
+ 6879 + 69876+ 7690.
24
ADDITION.
TABLE.
f; '
T1
1 + 12
2 + 12
3 + 12
4+12
13
14
15
16
5 + 12
6+12
7 + 12
8+12
17
18
19
20
9+12
1C+ 12
11 + 12
12+ 12
21
22
23
24
1. Add 12's to 100; — commencing with 6.
2. What is the cost of 12 articles at 1 penny eachl
3. 50 + 35 + 15 = how many? (Here add the ted
and units separately thus, 60 — 80 — 85 — 95 — 100, tl|
sum). .vii ■il': ;' •', n'- ...; r ^^r <■>' -''»[ -■.
4. How many are 70 + 80 + 9? 35 + 61? —
20 + 48 + 32? 79+ 79?
■h
(195)
id the
Find the value of 82893 + 45 + 817526 + 456 + 4268:
+ 7676 + 96734 + 124735869 + 3749286.
-. : . . . (196) . ^ . ' •
Find the value of 9482 + 39867 + 29479 + 4892;
+ 9276 + 850 + 5273 + 98 + 7000 + 80072 + 19 1
+ 8467. .•
(197)
Find the value of 978 + 749 + 4764 + 8967 + 94622
+ 45237 + 77592 + 59286 + 89294 + 3789 + 2936
+ 5700 + 619 + 378 + 9168 + 79 + 6899.
(198)
The fore quarters of an ox weigh 108 pounds each, the
hind quarters 124 pounds each, the hide 76 pounds,
and the tallow 60 pounds ; what is the weight of the
whole ox?
:-; ^^^- <199) ' -
A man paid 95 dollars for a horse, the same sum for a
harness, and for a carriage as miich as for both;
what did the whole cost ? :> c , ,; *
1014
Sif
I a
m
ADDITION.
25
,^+12 = 21
^+^2 = 22
|2+12 = 24
Nh 6. ,.
. The number of one order that mukes one of the
higher, is called a ratio.
'^hen the same ratio applies to all the orders it is
led a common ratio. Thus, 10 is the common ratio
pimple numbers. . i ->> r > •" ,;.
■•he system of numbers of which ten is the common
Pennjr each^lilBo is called the decimal system.
;re add the tec,
f— 95-100, i^
-36 + 617 ]
+ 456 + 4268
286. -- ;
^4^9 -f- 4892:
80072 + IS
9967+94623
3^89 + 2936
'899.
^^ each, the
» ^6 pounds,
eight of the
sfore leaving addition, the pupil should be able to add
^mns of figures without any nesitation, and give the order
period of the sum of each column.
''": " (200) ' • ''"'
id the value of 6379 + 6947 + 8476 + 8476 + 4736.
OPERATION. — We write the numbers units under units,
|379 tens under tens, &c., (because units of diflFerent
orders can not be added together, e. g. 6 units
nnd 5 tens would neither be 1 ] units nor 1 1 tens);
commencing at the right hand, 6 — 12 — 18 — 25
— 34 units = 3 tens and 4 units; set down the
4 units under the units, and carry the 3 tens to
^e column of tens ; 3 — 6 — 13 — 20 — 24 — 31 tens = 3
mdreds and 1 ten, set down the 1 ten and carry the 3
mdreds to their proper column ; 3 — 10 — 14—18 — 27 —
hundreds = 3 thousand and no hundreds ; set down
and carry 3 thousand to the thousands' column ; 3,
f, 15, 23, 29, 35 thousand =: 3 tens of thousands and
thousand, both of which we set down ; the sura is
j^hirty-five thousand and fourteen.
'M%
sum for a
for both ;
(201)
'ind the value of 36850 + 4347b + 18964 + 62840
+ 71 500 4- 68400 4- 1 760 + 716^^0 -f 376809 + 16890
+ 7689 + 3796 + 19736 -f 468 + 1678 + .3800
-f 76890 + 768.
26
t
ADDITION.
. . 3- How many units of 1/ "."'' P'"''"'' ?
higher 7 ^ """'» of o-e order make one of the „ J
T'-«arefo„rn™hors:rL.l« „ I
"Ofe than the first- ,h7,u.r^' ""^socond, li
'-"-"i; the fourt ;,tn h ' T ""^ •'"'° 'J
"dded together; whl^Lr? "V'"' *'^' "■"» "■«
.wfi»t.8thesumofthefournumber,
^'"^thevalneoflaJ^'i,,,;,,,
+ 92503 + 684, ^ +_f''2" + 3834 + w,
+ 7934 + 2C8 + 6?^ + 39487'" ^ '' + "'^'
Find the sum of ^^"^^ ' i
--J eight, and ^.^0^ """ '■■"■='^' "^ """'-o.'
The population of Ou.J^*^^ - •' ' '"""' ^
f-«00, Montreal , too" ot?'""' "'^"-Rivers
1^.884, Toronto 44 425 H»!w'"' '"■''*' Kingston
'/'=«' ; What is ihe L^rjT" ''''^»<'' «■"» I-ondon
eight cities 7 'Kgi-egate population of these
Knd the sum of tenths ^'^T
'"ousand and se.e 'trS T"'' "■""<'- --"tr
h-nOred thousand, tt'entf;* "' """"'"' '"^^'^en
fi;e, thirty thousand, fiftr mm """^ *'"' "'enty.
thousand and ten, e'fn^ "'T;"" '""'"^' "'enty
and six. • 'e'^enteen bill.ons, fo„r minions
SW"
notation ?
iod?
^eoneofthenej
^ensonebnndred
'00 i-njts = hoi
the second, il
^ore than tlil
' fi^st and ml
e four numbers I
3834 ^. 9275;!
34935 4- 267i
ADDITION OP THE DECIMAL CTTRRENCY. 27
The decimal currency diflfers from simple numbers
^ving two denominations, viz. dollars and cents,
las the same common ratio, and may be taught in
[ection with simple numbers.
add dollars and cents,
JLE. — Write the numbers with the decimal points
le same vertical column, and add as in simple
jers, observing to place the decimal point in the
j directly beneath those above.
$2.25 -I- $3. 5C = how much?
30 cts. + 40 cts, -f 19 cts. + 99 cts. + 18 cts.
cts. := how much ?
A lady paid for a mantle $12.00, a dress $10.50,
It $2.50, gaiters $3.00, gloves $1.50 ; what was the-
»unt of her bill?
^y, one million
Three Rivers
^4, Kingston!
> and London
'^'on of these
(1)
$72.37
t8.99
47.36
79.90
46.37
25.80
87.68
99.77
19.78
88.73
68.47
90.70
(2)
$128.97
54.73
165.94
75638
418.99
718.55
867.66
479.90
89.78
66.89
977.90
689.00
(3)
$287.91
416.38
478.45
732.61
419.80
968.78
368.90
87.66
76.88
19.72
9.87
.01
(4)
$184.72
37.94
76.48
73.92
16.78
98.76
17.98
54.77
167.90
716.87
748.76
870.99
(5)
pnd the amount of $76.30 + $768 + $8649 + $783.83
4- $987.40 + $8767.94 + $3849.39 -f $9878.44
+ $876.80 4- $799.36 + $376.88.
28 ADDITION OP THE DECIMAL CURRENCY.
ADDI'
11
m
ii
1. How does the decimal currency resemble sira|
numbers ?
2. How does it differ from simple numbers ?
3. What is the common ratio of simple numbers a|
dollars and cents ?
4. Why must the addends be written with units
the same order under each other ?
5. How are dollars and cents added ?
6. 70 cts. -f 35 cts. 4- 42 cts. + 5 cts. + 85 c^
+ 95 cts. + 10 dollars = how much?*
(6)
Find the sum of $58.75, $11.27, $71.43, $91, $41.8P
$77.58, $0.64, $30.72, $95.60. $189.12, $198.15.
O)
A man sold 350 bushels of wheat for $490, 720 busliei
of oats for $129-50, 75 bushels of beans for $93.7;
130 bushels of peas for $95.50, 50 bushels of barle |
for $42.75 ; how many bushels of grains did he sel
and how much did he receive for the whole ?
(8)
A man left $1250 to each of his three daughters, to hi
son, a sum equal to two of his daughters ; how muci
did he leave them ?
• ■' (9)
A merchant's cash sales in one week amounted one
day with another to $231.16 per day; what was tlic
week's receipts ?
(10)
A farmer paid $75.41 for a horse, $54.04 for a yoke
of oxen, $21.00 a piece for two cows, $7.41 each for
three sheep, and $10.21 for three pigs ; what did they
all amount to ?
1
'M
CURRENCY,
fesemble aim
ibers ? ^
fe numbers «
with
units
ADDITION OF THE DECIMAL CURRENCY. 29
A lady paid 50 cents for cambric, 35 cents for
)n, and 16 cents for thread ; what did she pay for all ?
17 + 25 = how many? 45 + 75? 84
^ 32? 72 + 32 + 14?
REVIEW. ,
cts. -f- 85
^91, $41.8.^
$198.15.
>0, 720 bnslieil
ns for $93,7;
3hel3 of barle
ns did he sel
hole ?
% What is arithmetic? 1.
f. What is a number ? 2.
|. What is a unit? 3.
What is an abstract number?
iber? 4. 5. , ,
What is Notation ? — Numeration ?
a
simple
6.
'ghters, to hi
^ ') how muci
nounted one
^hat Was the
for a yoke
41 each for
lat did thej
What are the characters used in expressing num-
? 7.
How does the position of a figure affect its value ? 8.
, In what ratio do the orders in crease and diminish? 8.
. What is the effect of removing a figure one place
he right or left ?
^0. What are the orders of each period ? 9. - *.»
^1. Name the first six periods; backwards.
^2. What are the four fundamental rules of arith-
itic? 10.
ip3. What is addition? simple addition ? 11. 13.
ii^4. What are the numbers to be added, and the result
Hthe addition called? . -.
15. How are the addends written to be added ? — Why ?
16. Why do you carry for ten? 8.
17. How do you prove addition? 15.
18. How do dollars and cents resemble simple
imbers? 17.
19. What is the Decimal system of numbers ? 16.
20. How are dollars and cents added? 17.
30
SUBTRACTION.
To 81^
fill I
V - ■
h "
SUBTRACTION.
BATIOII
Example 1. — James bad 2 marbles and be gave
John; bow many bad be left? I from 2 leaves
many? Ul|. 2091
2. Emma had 4 roses and she gave 1 to Jane, a^^'
to Julia; how many bad she left? .|
3. Charles bad 5 cents, and be paid 2 cents for a i
bow many cents had he left?
Solution. — He had the diflFerence between 5 cents !(<|
2 cents ; 2 cents from 5 cents leave 3 cents. There!
be bad 3 cents left.
NoTK.— The teacher should illustrate by means of visible
jects the process of taking one number from another.
18. The process of finding the difference between t a»bi0ve it,
numbers is called subtraction. bQ^^^^^^^
The greater number is called the minuend^ the 1( ^thftn ^^®
the subtrahend^ and the number found the difference of the n
remainder. to the ^
\fi carr;
gilbtrali
of tbei
19. The sign — , called minusj denotes subtractiot
thus, 8 — 3 = 5, denotes that 3 is to be subtracted froi
8, and is read 8 minus 3 equal 5.
1. Count from 50 backwards to 1 from 100.
2. Take two successively from 50 : thus, 50, 48, 46, &c
.21.
||esu
3 — 2
4—2
5 — 2
6 — 2
1
2
3
4
1
8
9
10
TABLE.
-2 = 5
-2 = 6
-2 = 7
-2 = 8
11
12
13
14
2
2
2
2
9
10
11
12
BUBTRACTION.
81
and he gay,
r 2 leaves
^ to Jane.
cents for a t''^*
'een 5 cents
To subtract simple numbers,
lAMPLE. — Find the difference between 2091 and 147.
taATioN. — Commencing at the right hand, we cannot
„-_- take 7 units from 1 unit, we borrow from
147
1944
CS?i,°J,««* „,
ce between
9 lens 1 = 10 units, 10 + 1 = 11, 7 from
11 leave 4, which we set down beneath
the figures subtracted ; then 4+1 (the I
wed) from 9 leave 4 ; 1 from we cannot ; borrow
2, 1 = 10 of that order, 1 from 10 leaves 9 ; 1
led) from 2 leaves 1.
lULE. — Write the subtrahend under the minuend so
units of the same order may stand under each other,
in addition. Commence at the right hand, and
Sttlitract each figure of the subtrahend from the one
''''^nd, the ]e^^
3 difference *
ve it, setting down the reraftinder under the figure
tracted. If any figure of the subtrahend be greater
the corresponding figure of the minuend, borrow 1
Cthe next higher order of the minuend, add it as 10
*the upper figure and subtract as before, observing
carry the 1 C'orrowed to the next figure of the
^tracted froi liiS)trahend ; (which is thus subtracted from the figure
^the minuend from which it was taken).
subtract
lor
>m 100.
^' 48, 46, &c
m
rf21. Proof, — Add the difftrence to the subtrahend ;
le sum should be equal to the minuend.
: 9
; 10
11
12
(1)
726384
312162
(2)
371680
240120
(3)
328768
121232
(4)
468926
125612
rr
32
SUBTRACTION.
1
^Hr
1. Count 2's to 100 and backwards ;•
—comment]
■
with 1.
n
I
2. A class in
arithmetic
contained
12 girls anfl
■4_3 =
boys ; how many
• more gifls
than boys
in the class 1
KZ3 =
3. Charles had 10 marbles and he
gave 2 to C(J
and 2 to Frank ;
how many
had he left? ]
:; >~''"-^ •
. .vs, !
BCount 1
(5)
(6)
0)
- (8) I
B^^B^^^ ^
Min. 376210
143214
132103
310890 1
Ka ball
Sub. 221032
37824
24322
102629 J
Wn'^
Dif. 155178
(10)
646723
(11)
183264
i
- (1?)
632 J69
Suowm
Proof. 376210
1 (29)
. - ". ■:„-
222222
22222
1*;2836
|128914
(14)
(15)
(16)
J|61232
(13)
w "
3210362
3462046
102144
142110
.wKL (33)
1123141
1217822
23124
101232
ftp
; 1 '
' ' (17) -
(18)
(19)
' (20)
7105198
7149902
316913
321896
2123126
432129
186412
161833
^2843
(21)
(22)
(23)
(24)
i (*^"
6131021
102132
100211
63210
4714214
14321
20423
14341
(25)
(26)
(27)
(28)
1 ("1
2921023
321021
102110
448200
''^m ATQ^
2311224
41234
12312
12325
•commcDji
1 2 girls anJ
In the class
frtve 2 to C(|
(8)
310890
102629
(1?)
632^69
l':2836
(16)
142110
101232
(20)
321896
161833
(24)
63210
14341
(28)
U8200
12325
— 3
— 3
— 3
[7—3
1
2
3
A
BUBtRAOTION.
TABLB.
8—3 = 6
9 — 3 = 6
10 — 3 = 7
11 — 3 = 8
33
12
13
14
15
3
3
3
3
9
10
12
/ount threes to 100 and backwards.
icslie bought a whistle for 3 cents, and exchanged
[a ball which he sold for 6 cents ; how much did
jin?
|How many are 8 — 3 ?
? 15 — 3?
7 — 3? 12 — 3? 6 — 3?
(29)
28914
61232
(41)
T310376
193436
(45)
[479326
1176243
(30)
219786
191623
(34)
406372
133323
(38)
639686
364663
(42)
187265
123923
(46)
109371
81933
(31)
468907
208663
(35)
210321
112323
(39)
290398
87288
(43)
910714
616283
(47)
519231
153823
(32)
910261
123486
(36)
672104
436343
(40)
310769
245433
(44)
194567
163246
(48)
410213
144126
84
•
SUBTRACTION.
«
TABLI.
^
5 — 4=1
9 — 4 = 5
13 — 4= 9
6 — 4 = 2
10 — 4 = 6
14 — 4 = 10
7 — 4 = 3
11—4—7
15 — 4 — 11
8 — 4 = 4
12 — 4 = 8
16 — 4 = 12
1. What does subtraction teach ?
2. Emma is 9 years old and Charles 12, what is the
difference in their ages ?
3. Count 4*3 to 50 and backwards ; to 100. •
4. 27 — 4 — 4 — 4 — 4 — 4 — 4 = how many ?
m
W
(49)
114126
32142
(50)
721043 •
164212
(61)
371021
112634
-(B2)
471021
101234
(53)
612149
144324
(54)
710982
144341
102103
41424
(56)
310214
. 13^34
(57).
371021
123414
(58)
347191-
116234
(59)
372104
141423
(60)
321072
21441
(61)
241327
42341
(62)
362192
142341
(63)
707268
42642
(64)
102134
42345
(65)
768278
654245
(66)
360792
146540
(67)
807368
436434
' (68)
8910726
4163451
L
'
StTBTRACTION.
TABLE.
6 — 5=1
7 — 5 = 2
8 — 5 = 3
9 — 5 = 4
10 — 5 = 6
11 — 5 = G
i2 — 5 = 7
13 — 5 = 8
14—5= 9
15 — 5 = 10
IG — 5 = 11
17— 5 = 12
M
1. What ig subtraction ?
2. In example 59, which is the subtrahend ?
minuend ?—— difference ?
3. Count 5's to 100 and backwards; commencing
with 3.
L
(69)
673678
147634
(70)
368791
143645
(71)
768709
745637
(t2)
710876
555564
(73)
371072
157346
(74)
632637
555414
(75)
916809
601236
^6)
309072
134465
(77)
671073
365586
(78)
680736
836458
(79) '
607368
46345 '
(80)
621073
146704
(81)
687369
645326
(82) ^
710767
136452
(83)
102632
■ 45361
(84)
7102109
126354
« (85)
132104
43645
(86)
687001
' 166524
(87) .
367204
3645G
(88)
109456
64364
i
ii
•
SttBTEAOTiON.
TABLI.
7 — 6 = 1
8 — 6=2
9 — 6 = 3
10 — 6 = 4
i: — 6 = 5
12 — 6 = 6
13 — 6 = 7
14 — 6 = 8
15 — 6= 9
16 — 6 = 10
17 — 6 = 11
18 — = 12
1. Count 6'fl to 72 and backwards.
2. 37 — 6 — 6 — 6 — 6 — 6 = how many ?
3. Charles had 9 cents, and he paid 4 cents for paper,
and 5 cents for a slate ; how much had he left 7
(89)
710423 .
66455
(90)
360210
156456
(91)
402916
132465
(92)
410072
140201
(93)
302641
103265
(94)
703260
86346
(95)
106200
61203
(96)
403621
117654
' (97)
1321072
1421326
(98) "
329073
42674
(99)
182032
40274
(100)
706327
23764
(101)
107210
62774
(102)
810710
107670
(103)
43f672
56C74
(104)
100200
90290
(105)
7210'2
101296
(106)
360721
70864
(107)
360721
101764 •
(108)
320101
120102
-^
8UDTEACTI0N.
TARLI.
8 — 7=1
12 — 7 =.5
16 — 7 = 9
9 — 7=2
13 — 7 = 6
17 — 7 = 10
10— 7 = 3
14— 7= 7
18 — 7= 11
11 — 7= 4
15 — 7 = 8
19 — 7 = 12
37
er.
1. What is Bubtraotion?
2. What is the minuend? — subtrahend? — difference?
3. Count sevens to 70 and backwards.
4. 60 — 7— 7 — 7 — 7 — 7 — 7 — 7 = how many?
'^"' (109)
Find the difference between 1890 and 809.
..
4-
(110)
From 1690021,
take 190166.
•
(111)
(112)
(113)
(114)
730726
709261
710736
109256
416724
12634
• 76376
54674
(115)
(116)
(117)
(118)
327107
3210213
3010321
103210
147648
487648
777778
18881
(119)
(120)
(121)
(222)
3721021
100001
301809
371021
761764
10002
18877
9887
(123)
(124)
(125)
(126)
3121032
3121881
310214
146000
147718
861788
136784
86908
38
SUBTRACTION.
9
10
11
12
8
8
8
8
1
2
3
4
13
14
15
16
TABLE.
— 8 =
— 8 =
— 8 =
— 8
5
6
1
8
It
18
19
20
8
8
8
8
9
10
11
12
1. How do you prove subtraction ?
2. What number added to the subtrahend will give
the minuend ?
3. What number added to 16 will make 24 ?
Solution. — The diflference between two numbers
added to the less will give the greater ; 24 — 16 = 8;
therefore 8 added to 16 will make 24.
4. What number added to 8 will give 16 ? 18 ? 20?
30? 40? 100? . ^ * -■
5. Count S's to 72 and backwards. f
(127)
A man had 215 sheep, and sold 57 of them ; how many
had he left ?
(128)
Find the value of 76897 — 687 — 6937.
(129)
i-^W *,?.;/.
What number added to 1673012 will make 371020243 ?
(130)
Find the value of 7638 + 376 — 172 -^400 + 7321
— 372 — 18.
(131)
A merchant had 2068 yards of cloth ; he sold on Monday
129 yards, on Tuesday 97 yards, on Wednesday 308
yards, on Thursday 92 yards, on Friday 78 yards,
on Saturday 120 yards ; how many yards had he
remaining?
r_ ■"<
^-
10 — 9 = 1
11 — 9 = 2
12 — 9 =3
13 — 9 = 4
SUBTRACTION.
TABLB.
14 — 9 = 5
15 — 9 = 6
16 — 9= 7
17 — 9 = 8
39
18 — 9 = 9
19 — 9 = 10
20 — 9 = 11
21 — 9 = 12
1. Count 9'8 to 100, and backwards.
2. 58 — 9—9 — 9 — 9 — 9 ;— how many ?
3. Emma is 9 years old ; ia what year was she bora?
^r (132)
* , From 70080093000 take 1630032004.
• - ' . •
How much does 784000 exceed, twice 193049?
m' M ■-'!':•:
(134)
From 1 billion, take 1 million,
(135)
.,.. . From twice 7063879, take 806767 — 7600.
(136)
A house and lot are yalued at $1850 ; the house is worth
$960 ; what is the value of the lot?
(137)
4 loads of oats weighed together 6673 pounds ; the two
first loads weighed 1190 pounds each, the third 2350
pounds ; what did the fourth load weigh ?
(138)
(139)
(140)
(141)
167261
872109
9021631
1247683
— 17264
— 4763
612786
— 186176
— 46324
— 2164
— 417268
472168
— 71062
— 1472
— 7689
— 3614
— 147
— 16821
— 7167
18710
1"
40
«
SUBTBAOTION.
_ ■■ ' '■ • . •
f
*
TABLE.
■ .
11 — 10 = 1
19—10= 9
16 — 11 — 5
12 — 10 = 2
20 — 10 = 10
17 — 11 = 6
13 — 10 = 3
21 — 10 = 11
18 — 11 = 7
1 14 — 10 = 4
22 — 10= 12
19 — 11 = 8
•15—10 = 5
12 — 11= 1
20 — 11 = 9
— ' '
16—10 — 6
13—11= 2
21 — 11 = 10
17— 10 = 7
14— 11 = 3
22 — 11 = U
18 — 10 = 8
15— 11 = 4
23 — 11 = 12
1. A man bought a horse foe $100, and 3 cows at $20
a head ; how much more did the horse cost than the cows?
2. How many are 75 — 22 — 30 — 9 7
3. Count lO's and ll's to 100 and backwards ;——>
commencing with 5.
(142)
If 1708 be minuend and 968 the subtrahend, what is the
difference 7
(143)
If the difference between two numbers be 740, and the
subtrahend 968, what is the minuend 7
(144) ^
A merchant was owing $5000; he paid at different
times the sums of $350, $970^ and $2008 ; how much
is yet owing ?
(145)
A man sold a farm for $2000, which was $910 more
than he paid for ib < how much did he pay for it ?
(146)
A man paid $85 for a horse, $150 for a harness, and
for carriage as much as for horse and harness lacking
$25 ; he then sold the whole for $415, did he lose Of
gain bjr tiie bftrgaioj aud how m^cl^ ^ . .»^i,-
-?-
12(
nu
Th
Th
If
If
W
r--^
--'►-
*^ -"*'»-«•
r t
13
14
15
16
12
12
12
12
1
2
3
4
SUBTRA' TIOW.
i
TABLE.
17— 12 = 5
21 —
12 = 9
18 — 12 = 6
22 —
12 — 10
19— 12 = 7
23 —
12 = 11
20— 12 = 8
24 —
12= 12
41
1. Count 12's to 100 and backwards.
2. The sum of two numbers is 300, the less number is
120, what is the greater number ?
3. The sum of two numbers is 300, and the greater
number 180, what is the less number ?
(147)
The sum of two numbers is 19768^ and the greater
number 12769 ; what is the less number ?
(148)
The less of two numbers is 6999, and their sum 19768 ;
what is the greater number ?
(149)
If 879687 be subtrahend, and 4687 the difference, what
is the minuend ?
(150)
If 884374 be minuend, and 4687 the difference, what is
the subtrahend ?
(151)
What number together with these three, viz. 125, 34,
and 970, will make 1800?
^ (152)
A xa&n sold 3 beeves at $35 each, pork to the amount
of $125, and flour for $84. He received in pay, salt
at $15, sugar at $21, tea at $19, cloth to the amount
of $80, and the balance in cash ; how much cash di(|
]xe receive ?
42
SUBTRACTION.
1. The minuend — the subtrahend = what?
2. The subtrahend -f- the diflference = what?
3. 800 is the subtrahend, and 200 the difference ;
what is the minuend?
4. loco is the minuend, and 200 the difference; what
is the subtrahend ?
5. 1000 is the minuend, and 800 the subtrahend ;
what is the diflference ?
(153) •
How long since America was discovered in 1492 ? '^
(154)
Sir Isaac Newton was born in the year 1642 ; hOw long
is it since?
(155) '•
Mont Blanc, the highest mountain in Europe, is 15680
feet above the level of the ocean, and Chimborazo in
America is 21000 feet; what is the difference in the
height of these two mountains? , . , , ,
(156) ^^:r-- ■ ^:-
The area of the earth's surface is about 200 millions
square miles ; of this nearly 60 millions are land, how
much is water?
(157)
The subtrahend is 1090, the difference 1690; what is
the minuend?
(158) ■' ^--A^-^--' •■^■— i ^...t;.-'
British America contains about 2,525,994 square miles,
of which Upper Canada contains 180,000, Lower
Canada 210,000, New Brunswick 27,710, Nova Scotia
19,650, Prince Edward Island 2,134, Newfoundland
57,000, British Columbia 213,500, Vancouver Island
16,000 square miles, and the Hudson Bay Territory
the remainder ; what is its arejv? ^. v^*,.,- .-,,1
-
'»•
e;
. . i ^
SUBTRACTION OP THE DECIMAL CURRENCY. 43
22. Rule. — Write the numbers with the decimal points
under each other, and subtract as in simple numbers.
Place the point in the answer directly beneath those
above.
1. A man bought a horse for $75, and sold him again
for $89.50 ; what did he gain by the transaction?
2. A lady purchased a parasol at $2, a pair of
gloves at $1.20 ; she paid a $5 bill ; how much change
did she receive back?
3. $5 — 5 cents = how much? - '•
Opbhation.— $5.00
.05
m «.Vts;;;
'jv.: !-«'
~^' $4.95 difference.
(1)
Find the value of $167.01 — $68.09.
What sum added to $15.09 will make $20?
- ■ ■ •■ ■ (3) . -■^■•/■":^-'"^
How much does $8767.08 exceed $6298.20 ? '
(4)
Find the value of $17894.37 — $123.71 — $298.67
— ^143.71 —$31.98.
(5)
Find the value of $3142.67 — $2.67 + $4171 — $0.66.
(6)
A man borrowed $767, and paid at different times
$125.25, and $356.80 ; how much does he yet owe?
(7)
A man sold a load of grain for $40 ; he took in pay
a plough at $14.90, 3 hoes at 60 cents each, 4 rakes
at 22 cents, a pitchfork at $1.19, and a spade at 95
cents; how much was yet coming to him?
■*
44 SUBTRACTION OP THE DECIMAL CURRENCY.
1. How arc dollars and cents subtracted?
2. John bought a sled for 75 cents, and gave 24 cents
to have it repaired; he then sold it for $1, how much
did be make by the bargain ?
3. William Mills bought a colt at $25, and sold it
a year after for twice what it cost him, lacking $6;
what did he make by the bargain, allowing $10 for his
keeping?
(8)
A man sold a farm for $769Y, which was $1761.50
more than h'd paid for it ; what did he give for the farm?
(9)
A merchant has $2760 in the bank, $16773 in stock,
$17694 due him, and owes $7693.50; what is he
worth?
(10)
A young lady went a shopping taking with her a $20
bill. She purchased a dress at $8.16, a muff at $3.19,
a bonnet at $3.08, a pair of gloves at $1.12, a pair of
shoes for $1.90, and a fan at 19 cents; how much
money did she bring home ?
' REVIEW OF SUBTRACTION.
1. Wh&t ia subtraction? 18. - .:.
2. What are the given terms of cubtraction?
3. What is the term to be found?
4. What is the minuend ? — subtrahend ?
5. What is the difference or remainder? J
6. The minuend — the subtrahend = what?
7. The subtrahend + the difference i= what?
8. The minuend — the difference = what?
9. The sum of two numbers — the greater = what?
10. The sum of two numbers — the less = what?
11. How is subtraction proved? 21.
12. How are dollars and ceAts subtracted? 22,
MULTiPLICATIOHr.
■-'»' > f -;.. Ji,v:
MULTIPLICATION.
»^
V - -A
*
23. ExAMPLR. — Harry paid 1 cent for an apple ; what
will two apples cost at the same rate 7 2 times 1 cent
are how many cents ?
2. What will 4 pencils cost at 1 cent each? •* ^
3. What cost 2 yards of cloth at $3 a yard?
4. If 1 orange cost 5 cents, what will 3 oranges cost?
Solution. — If 1 orange cost 5 o^nts, 3 oranges will
cost 3 times 5 cents ; 3 times 6 cents are 15 cents.
Therefore three oranges will cost 15 cents.
In this example, 5 cents is added together three
times; 5 cts. + 5 cts. + 5 cts. = 15 cts. Hence,
24. Multiplication is a short method of performing
addition. Or,
Multiplication is the process of taking one number as
many times as there are units in another.
The number to be multiplied is called the multiplicandj
the numbei' we multiply by is called the multiplier, and
the result of the multiplication, the product.
25. In multiplication the multiplicand is added as
many times as there are units in the multiplier.
1. Count 2 successively to 100 ;•
with 1.
•commencing
2 times 1 are 2
2 " 2 " 4
2 " 3 " 6
2 " 4 " 8
TABLE.
2 times 5 are 10
2 " 6 " 12
2 " 7 " 14
2 " 8 " 16
2 tir'^s 9 are 18
2 " 10 " 20
2 « 11 " 22
2 " 12 " 24
46 MtTLTTt>LICATiON. , *
26. To multiply by a number not exceeding" 12,
ExAMPLE.—Multiply 6098 by 2.
Operation. — 2 times 8 are 16, set down the 6 unit^
Multiplicand 6098 ^"^ ^^'""^^ *^^ ^ ^^"> *' ^" ^^^^^'°" 5
Multiplier 2 twice 9 are 18 and 1 carried are 19,
set down 9 and carry 1 ; twice
Product 12196 is nothing, set down the 1 carried ;
twice 6 are 12, which set down in full.
Rdlk. — Write the multiplier beneath the multiplicand,
and commencing at the right hand multiply each figure
of the multiplicand by the multiplier, setting down the
units, and carrying the tens, as in addition.
27. The sign X, denotes multiplication, V X 2 = 14,
is read 7 multiplied by 2 equal 14.
*
3
fo
]
th(
m
(1)
12132
2
(2)
21022
2
(3)
62102
2
(4)
43202
. 2
(5)
31032
2
(6)
62148
2
36504
2
(8)
71079
2
TABLE.
3 times 1
3 " 2
3 " 3
3 " 4
3
6
9
12
3 times 5
3 " 6
3 " 7
3 " 8
15
18
21
24
3X9
3 X 10
3 X 11
3 X 12
27
30
33
36
i;.
(••
MtTLTi:tLICAT10i^.
47
1. What i? the cost of 3 books at 6 cents each?
■ Solution.^ — Tf 1 book cost 6 cents, 2 books will cost
3 times 6 cents; 3 times 6 cents are 18 cents. There-
fore, 3 books will cost 18 ceiits.
Note.— The solution of Himilar questious Rhould be given till
the pupil is periiectly familiar with the principle involved.
2. What will 3 yards of cloth cost at 11 cts. a yard ?
3. Add threes to 100.; commencing with 5 ; 7.
4. How many are 3 x 10? 10 X 3; 30 = how
many 3's? how many lO's?
(9)
•786133
3
(10)
768736
3
(11)
610079
3
(12)
196789
3
W . . A
(13)
760763
3
(14)
160736
3
(15)
.760973
3
(16)
928760
3
(17)
689764
3
(18)
690077
3
(19)
80768
3
(20)
148902
3
I
(21) (22) (23) (24)
103274 642009 104725 873256
3 2 3 2
4 times 1 are 4
4 " 2 " 8
4 " 3 " 12
4 " 4 "16
TABLE.
4 times 5 are 20
4 " 6 " 24
4 " 7 " 28
4 ^' 8 " 32
4X9
4 X 10
4 X 11
4 X 12
36
40
44
48
48
MULTIPLICATION.
28. To prove multiplication, cast the nines from the
multiplicand, and from the multiplier ; multiply the two
remainders together and cast the nines from their product.
Lastly, cast out the nines of the product, and the two
last remainders, if the work is correct, will be equal.
Example.— Multiply 48124 by 3.
Commencing at the right of the multiplicand
4 and 2 are 6 and 1 are 7 and 2 (fiom 8) are 9,
which cast away. 6 and 3 (from 4) make 9
and 1 left, which write at the left of the sign.
3 being less than 9 is written at the right
then 3 times 1 = 3, which we write above the
sign. Of the product 2 and 7 are 9 ; 3 and 4
and 2 (from 4) are 9; leaving 3 which is
written below the sign, and being equal to the last
reuiainder, the work is supposed to be correct.
48124
3
144372
(25)
730260
4
(29)
376843
4
(33)
763871
4
(26)
212340
4
(30)
168736
4
(34)
600873
(27)
167216
4
(31)
716091
4
(35)
807076
4
(28)
721093
4
(32)
768916
4
(36)
281600
4
1.
2.
in e
3.
he y
4.
5.
6,
5 times 1
5 *• 2
5 " 3
6 « 4
5
10
15
20
TAfiLB.
6 times 5
5 " 6
5 " 7
5 " J8
25
30
35
40
9X5
10 X 5
11 X 5
12 X 5
45
50
55
60
6 ti
6
6
6
MULTIPLICATION*
49
1. What does multiplication teach?
2. Point out the multiplicand, multiplier, and product
in ex. 37.
3. If a man can walk 4 miles an hour, how far can
he walk in 6 hours?
4. Add 4*8 to 100 ;—— commencing with 2, 1, 3.
5. Add 5'g to 100 ; commencing with 3, 2.
6. 4 times 8 = how many? How many 4*8? S's?
V rf
(37)
206721
4
(38)
637210
4
(39)
110723
4
(40)
823465
4
(41)
673789
5
(42)
365076
5
(43)
767908
5
(44)
736554
6
(45)
671099
5
; (46)
710877
6
(47)
807836
5
(48)
896708
5
(49)
760734
5
(50)
671076
5
(51)
897687
5
(62)
946589
5
(53)
136276
6
(54)
760736
4
(55)
807326
6
(56)
910731
6
TABLE.
45
50
55
60
6 times 1—6
6 times 5 = 30
ex 9 = 54
6 " 2 = 12
6 " 6 — 36
6 X 10 = 60
6 " 3 = 18
6 " 7 = 42
6 X 11 = 66
6 " 4 = 24
6 " 8 = 48
6 X 12 = 72
50
MtLTlPLlOATlON*
1. A man ]
for a cow ; w
paid $6 for a sheep, and 4 times as much
hat did ho pay for both?
1.
duct
2. Add 6'8
to 100 and
baclt wards ;—
— commencing
2.
with 3.
poun
3. 6X8 + 6X5 = how many ?
1
whal
29. rerform
before addition
multiplication
or tubtraotion
or division indicated by signs 1
3.
4.
(67)
710736
6
(58)
873684
6
(59)
766439
6
(60)
871078
6
5.
(61)
876934
5
(62)
897681
4
(03)
807638
6
(64)
87096
6
77. (
78. i
79. :
80. (
,;';/,
/:=-i-
(65)
236489
6
(66)
973672
6
(67)
367268
6
(68)
876791
6
(69)
786321
5
(70)
190260
4
(Tl)
716921
6
(72)
3171091
5
(T3)
710687
3
(74)
369217
6
(•75)
369214
6
(76)
791896
e
TABLE.
7 times 1=7 7 times 5 = 35 7 X 9 = 63
7 " 2 = 14 7 " 6 = 42 7 X 10 = 70
7 " 3 = 21 7 " 7 = 49 7X11 = 77
7 " 4 = 28 7 " 8 = 56 7 X 12 = 84
(I
as much
nmencing
(1 by signH
(60)
^71078
6
(64)
87096
6
(68)
876791
6
(72)
171091
5
(76)
791896
9
MtJLTIPLIOATION*
u
1. What ia the multiplicand ? multiplier ? pro-
duct? -*
2. Emma bought 6 pounds of soap at 7 cents a
pound, and 6 pounds of starch at 10 cents a pound ]
what did she pay for all ?
3. 7 -}- 6 times itself = how many 1
4. 7X6+7X6 = how many ?
5. Add 7*8 to 100 ; commencing With 4,*— i,
— 6, 3.
77. 6873768 X 7.
78. 87600976 X 7.
79. 32109671 X 7.
80. 69678981 X 7.
81. 67199676 X 7.
82. 6980779 X 7.
Find the value of,
83. 37102 X 6 X 6 X 2.
84. 71986 X 7 X 6 X 6.
86. 89106 X X 6 X 7.
86. 8103 X2X3X4X6.
87. 189 X 4 X 5 X 6 X 7.
88. 89 X 7 + 180 X 7.
89. What cost 128 barrels of flour at $7 a barrel ?
90. How many yards of cloth in 6 pieces containing
67 yards each, and 7 pieces each containing 64
yards ?
:91. A house has 8 windows in front each containing 6
panes of glass, and 6 windows in the back con-
taining 12 panes e«ch ; how many panes of glass
docs the house contain?
TiiBLB.
9
10
11
12
63
70
77
84
8 times 1=8
8 times 5 = 40
8 X 9 ^ 72
8 " 2 — 16
8 " 6 = 48
8 X 10 = 80
8 "3 — 24
8 " 7 = 66
8 X 11 =88
8 " 4 = 32
8 " 8 = 64
8 X 12 = 96
52
MULTIPLICATION.
30. The multiplicand and multiplier are called the
factors (i.e. producers) of the product.
1. 8 and 4 are the factors of what number ?
2. 2, 3, and 5, are the factors of what number ?
3. What are the factors of 24, 56, and 40 ?
4. Add 8's to 100 ; commencing with 5, 2,
1.
that :
So]
man
3 me:
I work
2.
92. 809263T X 8.
93. 7254368 X 8.
94. Y462344 X 8.
95. 7169779 X 8.
Find the value of,
96. 91026 X 2 X 6 X 8.
97. 987 X 3 X 4 X 5 X 8.
98. 98 X 7 X 8 + 389.
99. 8X8 + 6X8+7X8.
100. Sold 769 bushels of flaxseed at $4 a bushel, and
received in pay 300 barrels of flour at $8 a barrel,
and the balance in cash ; how much cash did I
receive ?
101. What cost 350 barrels of herrings at $5 a barrel ?
102. A man bought 150 acres of land at $5 an acre and
sold it again at $8 an acre ; how much did he
gain by his bargain ? "^'^ ** ^ "
103. 17638 + 8 times itself = how many ?
104. 20, 8, and 7, are the factors of what number?
105. A farmer sold 5 cows at $24 a head, 7 young cattle
at $16 each, 45 sheep at $3 a head, and 10 pigs
at $2 each ; what did the whole amount to ?
106.
107.
108.
109.
110.
116.
I 117.
118.
9 times 1=9
9 " 2 = 18
TABLD.
9 times 5 = 45
9 " 6 = 54
X
9 X
9 =
10 —
81
90
9
9
"3 =
(( A —
27
4 = 36
9
9
7 = 63
8 = 72
9 X 11 = 99
9 X 12 = 108
1
10 ti
10
10
10
10
10
10
10
e called the
3r?
mber?
?
ith 5, 2,
X C X 8.
: 4 X 5 X 8.
8 + 389.
X84-7X8.
k bushel, and
|8 a barrel,
ch cash did I
$5 a barrel ?
I an acre and
much did he
f ''^: .
umber ?
young cattle
, and 10 pigs
ount to ?
MULTIPLICATION.
X 9
X 10
X 11
X 12
81
90
99
108
53
1. How long will 1 man take to do a piece of work
that 3 men can perform in 9 days ?
Solution. — If 3 men take 9 days to do the work, 1
man will take 3 times 9 days = 27 days. Therefore, if
3 men take 9 days, 1 man will t::ke 27 days to do the
work.
2. Add 9's to 100; commencing with 2,— 5,
106. 6897684 X 9.
107. 38726347 X 9.
108. 38769984 X 9.
109. 71689768 X 9.
110. 76987684 X 9.
Find the value of,
111. 76 X 9 X 7 X 8.
112. 80 X 8 + 178 X 9.
113. 787s X 9 — 768.
114. 91768 — 9 X 87.
115. 1716 X 7 X 8 X 9.
316. How long will a quantity of hay suflBce 1 horse,
that 9 horses would eat in 29 days?
117. If a man earn $3 a day, how much will he earn in
a year ?
118. If a man drink 3 glasses of spirits a day, how much
will he drink in a year ; how many cents would
it cost at 5 cents a glass?
10 times 1
10 " 2
10
10
10
10
10
10
a
3
4
5
6
7
10
20
30
40
50
60
70
TABLB.
10 times 9
8 = 80
10
10
10
11
11
11
11
10
11
12
1
2
3
90
100
110
120
11
22
33
11
11
11
11
11
11
11
5 =
6 =
8 =
9 =
10= 110
11 = 121
55
66
77
88
99
4= 44 11 X 12 = 133
h! I
54
MULTIPLIOATION.
81. To multiply by 10, 100, 1000, ftc, annex as many
ciphers to the multiplicand as the multiplier contains
ciphers. Thus, 3 X 100 = 300.
1. What cost 100 yards of cloth at $3 a yard?
2. At $5 a barrel, what cost 1000 barrels of flour?
3. 1000 X 10 = how many ? 10 X 1000 ? 100 x 100 ?
4. Gount lO's and ll's to 100 and backwards;
commencing with 5.
119. 9, 10, 19, and 100, are the factors of what number ?
120. If 68 men can do a piece of work in 11 days, how
long will it take 1 man to do the same ?
121. What sum must be distributed among 100 men, to
give each one $590?
122. How many pins will a boy point in 9 weeks, if he
work 8 hours a day, and point 10,000 pins in an
hour?
123. In 1 year are 365 days ; how many days in 10
years ?
124. 716937 X H + 8763809 X U — 39864 X H
:= how many ?
125. In 1 pound are 20 shillings, and in 1 dollar, 5 shil-
lings ; how many shillings are there in 746
~ pounds, and 600 dollars ?
126. A gentleman's yearly income is $1000, and his
expenses $3 a day; how does he stand at the
ilV end of the year ? t ■ -
.3»X^
TABLE.
12 times 1 = 12
12 times 5 = 60
12 X 9= 108
12 " 2 = 24
12 " 6 = 72
12 X 10= 120
12 " 3 = 36
12 " 7 = 84
12 X 11 = 132
12 " 4 = 48
12 " 8 = 96
12 X 12 = 144
1
I
f
MULTIPLICATION.
55
lez as many
er contains
ard?
of flour ?
100 X 100?
wards ; -
at number ?
I days, how |
le?
100 men, to
^eeks, if he
) pins in an |]
days in 10
9864 X 11
liar, 5 shil-
)re in 746
0, and his
md at the
9
10
11
12;
32. A composite number is oso that is the product of
two or more factors. Thus, 21 is a composite number,
being the product of 3 and 1.
33. A prime number is one that is not the product of
two factors ; as 3, 5.
34. To multiply by a composite number,
RuLB. — Multiply successively by the factors. The
last product is the answer. Ciphers at the right hand
of the multiplier or multiplicand may be omitted and
annexed to the product.
1. What are the factors of 8, 20, 24, 36, and 200 ?
2. Add 12'g to 144;— —commencing at 6.
3. What is the value of 45 ac. of land at $128 per acre ?
Operation. The pupil should name
1128 price of 1 acre, only the figures of the
_____ product in multiplying.
?;40 " 5 acres. Thus,' in the example,
9 multiplying by 5 we say,
"- — 40 — 14 — 6 at the same
$5760
" 45 acres.
, units and carrying the tens.
time setting down the
Find the value of.
1. 720 X 11 X 10 X 100.
2. 678 X 12 X 11 X 12.
3. 768 X 24 X 33.
4. 378549 X 27.
5. 357928 X 35.
6. 707584 X 22.
7. 580726 X 44.
8. 428571 X 540.
9. 405719 X 960.
10. 64839 X 1200.
11. 6974 X 144 -f 28.
12. 4567 X 132 + 129.
13. 6, 11, 18, and 24 are the factors of what number?
14. If 250 acres of land worth $25 per acre be exchanged
for 300 acres valued at $24 per acre, what is
; gained by the transaction? •- - -
56
MULTIPLICATION.
1. What is a composite number 7 '
2. What is a prime number ?
3. What are all the composite numbers below 100 V—
the prime nunibers ?
4. How do you multiply by a composite number?
5. What cost 4 do^en chairs at $3 a piece ?
35. To multiply by a number exceeding 12 that is not
a composite number,
Bulk. — Write the multiplier under the multiplicand
and multiply the multiplicand by each figure of the
multiplier separately, taking care to place the first
figure of each parti.J product directly beneath the figure
multiplied by ; then add the products.
ExAMPLE.—Multiply 3*71 by 47. j*
3ll
47
.2597
1484
Here 4 = 4 tens ; 1 unit X 4
tens = 4 t<^ns; hence we set
the 4 in the «ens' place. In the
Proof, same way units multiplied by
— — hundreds would give hundreds,
17437 Prodn<;t. ^^jts ^y thousands would give
thousands, &c. Hence, we set down the first figure of
each partial product directly beneath the figure we
multiply by.
Find the value of.
1. 47963852 X 23.
2. 25836974 X 45.
3. 59826473 X 67.
4. 52007498 X 405.
6. 7964280 X 337.
6. 607 X 356 -f- 349.
7. 498857 X 4967.
8. 390867 X 50989.
9. 862479 X 537089.
10. 378600 X 75000.
11. 687900 X 87400 + 90.
12. 93000 X 97000 + 79.
MULTIPLICATION.
57
low 100 ?—
umber?
?
that is not
altiplicand
ure of the
* the first
1 the figure
1 unit X 4
ce we set
56. In the
tiplied by
hundreds,
ould give
figure of
figure we
7.
89.
089.
30.
)0 + 90.
) + 79.
1. What is the weight of 25 bushels of wheat, 60
pounds being allowed to a bushel ?
2. What is the cost 01*45 barrels of pork, at $18 a brl. ?
3. What cost 1000 barrels of flour at $7 a barrel ?
4. 40, 20, and 100, are the factors of what number?
6. How many are 7x5 + 7x6+7x8 ?
9 X 4 + 9X5 + 9 X 6? 7 X8 + 6x8 + 6x9^
112 X 11 — 11 X 1J2?
13. How many are six hundred and forty one chousand
four hundred and forty times four hundred and
ninety seven thousand three hundred and sixteen ?
14. Two trains leave Toronto at the same time, going
in opposite directions, one at ibe rate of 25 miles
'!'' an hour, and the other at 37 miles an hour ; how
far apart will they be at the end of 2 / hours ?
15. What time will one man require to dig a trench,
that 37 men can dig in 9 days?
16. 36, 78, 99, and 1000, are the factors of what number ?
17. What sum must be distributed among 25 men and 19
boys, to give each man twice a boy's share, and
each boy $15 ?
18. What is the number of the strokes of the hammer
of t clock in a day ? year ?
19. Plow many seeds were produced by a bean which had
14 stems, each stem, 19 pods, and each pod, 6 beans?
20. How much does one thousand thousand exceed fifty
times twenty thousand ?
21. A man left to his son $19536, and lO each of his six
daughters $9768 ; how much did he leave them ?
22. How many bushels of oats will fill 500 of each of
three kinds of bags, which contain respectively
3 bushels, 3 bushels, and 4 bushels ?
58 MULTIPLICATION OF THE DECIMAL OUBRENCY.
86. To multiply dollars and cents.
Rule. — Multiply as in simple numbers, and point off
the two right hand figures for c^ts.
Example. — What cost 5 yards of cloth at $1.75 a yard ?
Operation.
$1.75
5
$8.75
If 1 yard cost $1.75
5 yards would cost
5 limes $1.75 = $8.75.
1. A lady purchased 6 yards of satin at $2.50 a
yard, 4 yards of muslin at 75 cents a yard, and a pair
of gloves at $ 1 . 10 ; what is the amount of her purchase ?
2. A man bought 4 rakes at 25 cents a piece, 3 pitch-
forks at $1.50 each, 5 hoes at 70 cents each, and a
grin istokie at $2.50 ; what did he pay for the whole ?
3. What cost 2 dozen brooms at 20 cents each?
Find the value of,
.■:?'
1. $9609.30 X 72.
2. $874.03 X 611.
3. $172.01 X 1000.
4. $497 X 2600 + $0.01.
5. $0.06 X 15950. '
6. $1.89 X 279 + $1.44.
7. $9.46 X 103260 + $2.40.
8. $15.07 + $41.07 X 700.
9. What is the cost of 95 ploughs at $15.25 each, and
78 harrows at $9 each ?
10. At 12 cents a pound, what must be paid for three
boxes of sugar each containing 125 pounds ?
11. Bought 11 yards of French merino at $1.05 a yard,
« 14 yards of cambric at 12 cts. a yard, 25 yards
% ' of cotton at 15 cts., 1 dozen setD of cufiFs and
. collars at 15 cts. per set, a hat at $2.30, and
gaiters for $3.25 ; What did the whole cost ?
IRENCY,
MULTIPLICATION OP THE DECIMAL CURRENCY. 59
point off
a yard ?
)st $1.75
Id cost
t= $8.75.
$2.50 a
id a pair
irchase ?
, 3 pitch-
, and a
^hole ?
:h? ..
$1.44.
■f$2.40.
1 X 700.
ich, and
or tliree
ds?
a yard,
5 yards
iffs and
JO, and
iSt?
1. How do you multiply dollars and cents?
2. What cost 100 nails at 1 cent each ? — at 3 cents ?
3. What cost 300 oranges at 7 cents a piece ?
Solution. — 100 oranges at 1 ct. = 100 ct. = $1. ^
100 " " 7 cts. = 700 ct3. = $7.
;' w-^- 300 " " 7 cts. = 3 times $7= $21.
87. To r .ultiply by 10, 100, 1000, &c., remove the decimal point
as ir < ly places to the right as the multiplier oontaina ciphers,
annfA.ing ciphers if necessary. The decimal point is under*
stood when not expressed at the right ot dollars.
4. What cost 400 shad at 5 cents a piece ?
5. What cost a barrel of pork (200 lbs.), at 8 cts. a
pound? , , ,^,; .-'■"■'..-v „...,., /. ";: ./X--^:.
12. What is the difference in the value of two pieces of
cloth, the first containing 57 yards at $3.85 a
yard, the second, 47 v- -ds at $4.75 per yard ?
13. What cost 1000 barrels oi apples at $2.35 a barrel?
14. What cost 1000 bricks at 2 cents each ?
15. At 5 cents a pound, what would 15 barrels of beef
amount to ?
16. A man bought a horse at $97.50, and to p. for
him gave 6 tons of hay at $9.25 per ton, and the
balance in wheat at $1 a bushel ; how many
bushels of wheat must he give ?
17. A lumber merchant bought 95 thousand feet of
white pine at 10 cts. a foot, IIS thousand feet of
red pine at 22 cts., 16897 feet of oak at 32 cts.
and 69768 feet of elm for $1567 ; if he sell the
whole v.>n an average of 25 cents per foot, what
will be his net gain ?
60 MULTIPLICATION OF THE DECIMAL CURRENCY.
1. How do you multiply by 10, 100, Ac. ?
2. What will 8 barrels of beef amount to at 9 cents
per pound ?
3. Wliat cost 20 barrels of pork at 2 cents a pound,
and 15 hundredweight of cheese at 11 cents a pound?
18. What will the wages of 16 men amount to in a
year, at $1.25 a day to each men I
19. A man killed an ox which he sold as follows ; the
hind quarters weighing 129 pounds each at 6
cents a pounds ; the fore quarters 125 pounds
each at 5 cents a pound, and the hide and tallow
weighing 163 pounds at 1 cents per pound ; what
did the whole amount to ?
REVIEW OP MULTIPLICATION. :
1. What is multiplication ? 24. "'
2. What are the multiplicand, multiplier, and pro-
duct ?
3. How many times do you repeat a number by
m'ultiplying it ? 25.
4. How is multiplication proved ? 28.
5. What is a composite number ? 32. "^
6. What are the factors of a number ? 30.
7. What are all the composite numbers below 100 ?
the prime numbers ?
8. How do you multiply by a composite number ? 34.
9. How do you multiply by 10, 100, &c. ? 31. 37.
' 10. How do you multiply by a number exceeding 12,
that is not a composite number? 35.
11. Why do you place the first figure of each partial
product directly beneath the figure multiplied by?
:^2. How do vou multiply dollars and cents? 36.
DIVISION.
61
DIVISION.
38. division teaches us to find how often one number
is contained in another.
The number to be divided is called the dividend, the
number we divide by is called the divisor, and the
number that shows how often the divisor is contained
in the dividend is called the quotient. If anything
remains after dividing it is called the remainder.
Example 1. How uany pens at 1 cent, can you buy
for 2 cents ?
2. How many penc'^s at 2 cts. can you buy for 6 cts. ?
Solution. — For 6 cents, I shall have as many pencils
at 2 cents, as the number of times I can take 2 cent^
from 6 cents, which is 3 times. Therefore for 6 cents I
shall have 3 pencila.
3. If a man can earn $2 a day, how long will it take
him to earn $8 ?
Solution. — At $2 a day, it will take him as many
days to earn $8, as the number of times %2 is contained
in $8 ; $2 in $8, 4 times. Therefore at $2 a day, he must
work 4 days to earn $8.
The following tables should be learnt thoroughly, and the
relation they sustain to the others clearly explained.
■";■,, ■'-'(''..-
, TABLE.
2 in 2 =: 1
2 in 10 = 5
2 in 18 = 9
2 "4—2
2 " 12 = 6
2 " 20 = 10
2 "6—3
2 " 14 = 7
2 " 22 = 11
2 " 8 = 4
2 " 16 z= 8
2 a 24= 12
62
DIVISION*
30. Example 1. Divide 8G754 by 2.
2J8076G Having written the divisor on the loft of
~" the dividend we commence at the highest
order to divide. 2 is contained 4 times in 8 ;
set down the 4 under 8 ; 2 in 6, 3 times ; 2 in 7, 3
times and 1 over ; 1 = 10 of next lower order, added to
5 make 16 ; 2 in 15, 7 times and 1 over; 1 = 10, -f 6
= 16 ; 2 in 16, 8 times.
Rule. — Begin at the left hand and divide each figure
of the dividend by the divisor, setting down the quotient
figure directly beneath the figure divided. If there bo
a remainder join it as so many tens to the next figure
of the dividend, and divide as before.
40. Proof. — Multiply the quotient by the divisor
adding in the remainder if any ; the product should be
the same as the dividend.
41. The sign -f- denotes division. 8 -r 2 = 4 is read
8 divided by 2 oqual 4.
Division is also denoted by a horizontal line separat-
ing the terms ; as | = 4.
2. Divide 736827 by 2. t
Divisor 2 ) 736027 Dividend.
1. 2)86021848
Quotient 368013 — 1 rem.
2. 2)40267342
}-)h
736027 I
'roof.
TABLE.
3 in 15 = 5
3 " 18 = 6
3 " 21 = 7
3 " 24 = 8
3. 2)9462
3 in 3=1
3 " 6 = 2
3 " 9 = 3
8 " 1-2 = 4
3 in 27= 9
3 " 30 = 10
3 " 33 = 11
3 " 36 = 12
i
xnel
mvisioN.
63
Jn the left of
t the highest
4 times in 8 •
s ; 2 in 7, 3
der, added to
^ = 10, + 6
each figore
the quotient
If there bo
' next figure
the divisor
t should be
= 4 is read
ae separat-
) 86021848
1. At $2 a bushel, how many bushels of wheat can
we buy for $10?
2. Charles distributed 21 apples among a number of
this companions, giving each one 3 apples ; how many
f boys were there ?
t 3. HowmanythreesinlO? 36? 24? 9? 27? 21? 18?
g| 4. Count threes to 100 and backwards; com-
lencing with 8, 4.
(4) (5) (0)
[2)699318621 2^687073638 * 2)l87368768
(7) (8)
2)132675672 2)710703360
(10) (11)
3)821607362 3)814674368
(13) ' (14)
3)876873684 3)l7l073687
(9)
2)876836822
(12)
3)973687368
(15)
3)871025546
(16)
3)189074687
(17)
3)187209671
(18)
3)72099878
TABLE.
4 in 4=1
4 in 20 := 5
4 in 36 — 9
4 " 8 — 2
4 '< 24 = 6
4 " 40 — 10
4 " 12 = 3
4 " 28 = 7
4 " 44= 11
4 " 16 = 4
4 " 32 =8
4 " 48 = 12
I
64
DIVISION.
1. What does diyision teach ?
2. Which are the dividend, divisor, and quotient, in
the 19th exercise ?
3. Seven times 4 = how many? how many 4*8?
7's?
4. 40 = how many 4's? lO'a?
6. Count 4's to 100 and backwards ; commencing
with 3, 1, 2.
6. How many coats each containing 4 yards, can be
made from 18 yards of cloth? What remnant is left?
(19)
4)897689124
(22)
4)8321096725
(25)
3)7137689142
(28)
4)68732854
(31)
4)9175387690
5 in 5, 1 (once)
5 " 10, 2 times
5 " 15, 3 "
5 " 20, 4 «
(20)
4)8710768734
(23)
4)932768737
(26)
4)127143685
(29)
3)671321099
(32)
4)7435491073
TABLE.
5 in 26, 5 times
5 « 30, 6 "
5 " 35, 7 "
5 " 40, 8 "
(21)
4)6710216325
(24)
4)832710237 ^ 5
(27)
4)83210973
(30)
4)3871073211
(33)
4^)6531269057 |
5 in 45, 9 times
5 « 50. 10 "
5 " 55', 11 "
5 " 60, 12 "
DIVISION,
66
quotient, ia
ly many 4*8?
■commencing
rards, can be
ant it} left ?
(21)
)671021G325
(24)
1)832710237
(27)
4)83210973
>• (30)
4)3871073211
(33) ■
4)6531269057
1. If5burrels offish cost $20, what is that per barrel ?
Solution. — If 5 barrels cost $20, 1 barrel will cost
5 times less or 1 fifth of $20 ; 1 fifth of $20 = $4 ;
much therefore 1 barrel would cost $4.
2. Emma paid 45 cents for 5 Second readers ; how
is that for each book ?
3. 13 times 5 = how many? how many 12'8?
5 '8?
4. Count 5'8 to 100 and backwards; commencing
[with 3, 1, 4.
(34)
5)876930024
(37)
5)710736809
(40)
'5)l87l02G32
(43)
5)912691438
(46)
5)567100263
(35)
5)312072691
(38)
5)483607268
(41)
5)710736891
(44)
3)144671832
(47)
3)417168973
TABLE.
(?>)
6)871687068
(39)
4)312007303
(42)
4)402073689
(45)
6)371689073
(48)
6)891683732
in 45, 9 times
" 50. 10 "
'' 55', 11 "
" 60, 12 "
6 in 6—1
6 in 30 — 5
54 -^- 6 = 9
6 " 12 — 2
6 " 36 = 6
60 -^ 6 = 10
6 " 18 = 3
6 " 42 — 7
66-^6 = 11
" 24 — 4
6 " 48 — 8
72 -^ 6 = 12
*•■':'■.;
66
DIVISION.
1. What does division teach ?
2. What are the given terms of division ?
3. What is the required term ?
4. Count 6's to 100 and backwards; commenciDg
with 4, 2, 11, 9.
V^ ^*w^
(49) (54) (59)
'721073689 -f 6 1 673268 T40 -f- 6 107326889-^4
(50) (55) (60)
610726478 — 6 1710932674-^5 109768769 -j- 6
(51) (56)
847687367 -r 6 4007326871 -r 5
(61)
1473G8766 -^ 6
(52) (57)
8109265543 -f 6 8107268718 -i- 5
(53)
732609368 -f 6
(58)
710736879 -i- 6
(62)
447891870 -^ 6
(63) ^
876807681 -^ 3
C4. A man paid $1974 for 6 village lots ; what is the
cost of each lot ?
65. If 1000 acres of land be divided equally among six;
persons ; what is each share ?
«rty»
TABLE.
6 in 6=1
6 in 30 = 5
54 -f- 6 = 9
6 " 12 = 2
6 ♦' 36 = 6
60 -^ 6 = 10
6 " 18 = 3
6 « 42 = 7
66-^6= 11
6 " ^4 i_ 4
6 « 48 = 8
72-^6 = 12
DIVISION.
67
ng
r4
re
v-3
the
six
1. If 3 books cost $13 what cost 1 book ?
Solution. — If 3 books cost $13, 1 book will cost 3 times
less or 1 third of $13 ; 1 third of $13 =■ $4, and $1 over
which must be divided into 3 equal parts ; $1 -~ 3
= $^ (39). I book will cost $4 + J of a dollar = $4^,
Note.— I is read 1 third; f, two thirds; |, three fifths, &c.
These nttmbera being parts of a unit are called fractions.
2. How much is } of 20 ? of 75?
3. 7 X 12 = how many times 7? 12? 6?
4. Count 7's to 100 and backwards ; commencing
with 3, 5, 9, 4.
66. 9107368732 -7- T-
67. 10721036871 -r T.
68. $9870073847 -J- 7.
69. $8167367284 -^ 7.
70. Harry King divided 108 marbles equally among 4
of his companions ; how many did each receive?
71. A man paid $127 for 7 cows; what is the price of
1 cow at that rate ?
72. How many 5 bushel bags can be filled from a bin
containing 3870 bushels of oats ?
73. j of 6789768 dollars = how much ?
74. ^^ ^s-i- = how many ?
75. A man had 81 sheep, and sold 1 third of them;
how many had he left? T ^ ^^
76. How many coats each containing 4 yards, can be
made from 2 pieces of cloth, each containing 47
yards?
TABLE. , : : '-1
8 in 8=1
8 in 40 — 5
72 -i- 8 = 9
8 " 16 = 2
8 " 48 — 6
80 ~ 8 = 10
8 " 24 = 3
8 " 56 — 7
88-i-8 = 11
8 " 32 = 4
8 " 64 = 8
96 H- 8 = 12
es
DIVISION.
Division is the reverse of multiplication. Division
diminishes a number as many times as multiplication
increases it ; hence,
42. Multiplying and dividing any quantity by the
same number does not change it.
12 X 8
1. How much is 8 X 10 -7- 10? ?
8 '
2. 68Y X 8 = how many times 8 ?
3. How do you prove division ? Why ? 41.
4. Reckon 8's to 100 and backwards ; commencing
with 5, 2, 6, 4.
(n)
8)8t2637246
08)
8)38t632645
(t9)
8)8Tl64T68t
(80)
8)683268716
> (81)
8)137168732
(82)
7)193729687
(83)
8)839837988
(84)
8)507302938
(85)
8)68976878
(86)
6)176873678
(87)
8)47694369
(88)
8)987387689
8768 67325 •
89. X 8 ^ X 7 = how much?
8 7
90. If 1958 tree? be planted in 8 rows, how many trees
will there be in each row? ., > , 1
^*
TABLE.
9 in 9 = 1 (once) 9 in 45 =1 5 times
9 " 18 = 2 times 9 " 54 = 6 "
9 " 27 = 3 " 9 " 63 = 7 "
9 " 36 = 4 " 9 " 72 = 8 "
81 -^9 = 9
90 -r- 9 = 10
99-7-9 = 11
108 -7-9 = 12
i
i ■
DIVISION.
69
911
on
he
?8
5Y8
69
689
rees
rC^v
9
10
11
12
1. If 6 cows sell for $126, and 3 pigs for $21 ; how
many pigs are equal in value to one cow ?
2. A man invested $360 in flour, paying $9 a barrel ;
if he sell at $11, how much will he gain on the trans-
action?
3. If 63 be the dividend, and 9 the divisor; what is
the quotient?
4. Reckon 9'3 to 100 and backwards ; commencing
with 3, 6, 1, 7, 5, 8.
Find the value of,
91. 7207389 -^ 9.
92. 8173610354 -f- 9.
93. 71548954736-^9.
94. 38907687314 — 9.
2107689768987
95. .
9
96. 3876847 —7-7-9.
97. 8716878 4- 9 -r 8.
98. 8716876 -r 6 -r 8.
99. 71096789799-7-9.
1476871819
100. 7689.
9
101. It is required to put 216 Iiats into 8 boxes; how
many hats will there be in each box ?
102. $28970, is the dividend, and 8 the divisor; what
is the quotient?
103. How many sheep at $5 a head, can be bought with
the avails of 25 cords of wood, sold at the rate
of $3 a cord ? ^
TABLE.
^11 = 1
11-f 99= 9
12 H
'- 60= 5
- 22 = 2
11 -J- 110 = 10
12 H
^ 72= 6
-33 = 3
11-M21 = 11
12 H
^ 84= 7
r 44 — 4
11 -J- 132 = 12
12-:
- 96= 8
r55 = 5
12 -i- 12= 1
12-;
1- 108 = 9
r66_6
12 -^ 24= 2
12-
'r 120 = 10
f-77 = 7
12 -^ 36 = 3
12-:
'r 132 = 11
f-88 = 8
12 -f- 48= 4
12 H
- 144 = 12
70
DIVISION.
ill'
I'M.
M
m
IS;
If
1 1 1
1. How many oranges at 5 cents, and lemons at 6
cents ; and of each an equal number, can be bought for
33 cents?
2. How many cows at $12, must be exchanged for
120 sheep at $5 each ?
3. Reckon ll's and 12's to 100 and backwards ;
commencing witL 8. 9, 8, 1, 2,
5, 10.
Find the value of,
104. 1170'7368V2
105. 4710736891
106. 7109736891
107. 8107356432
108. 8710736878
•^ 11.
T" !!•
T- 11'
r* ll-
r- 11'
109. 9107687681 -^ 12.
110. 71321076871 -^ 12.
111. 81473687368^ 12.
112. 91210736871 -r 12.
113. 1072163872 -r 12.
tii-n
117.
114. A teacher's salary is $300 per annum ; how much
may he spend monthly, and save $100 in one year ?
115. Divide 100 cents among Emma, Kate, and Colin, so
that Colin may have twice as much as his sisters ?
116. How many canisters each holding 12 pounds, can
be filled from 1584 pounds of tea ? , ,
7689 X 12 7689
Find the amount of X H.
12 11
118. How many bags holding respectively 2 bushels,
and 3 bushels, and of each kind an equal number,
can be filled from a bin containing 5876 bushels ?
119. 12 times one thousand is how many times 12 ?
6710978897896 ;/ , i, ...-.
120. ■■ =z how many? " ,
12
121. A gentleman possessing an estate of $68000, be"
queathed 1 fourth to his wife and the remainder
to his four children : what was the share of each ?
N »?'<'
h-^
DIVISION.
71
6
or
br
43. To divide by a compoaite number exceeding 12.
Rule. — Divide successively by the factors. To obtain
the true remainder, multiply the last remainder by the
first divisor, adding in the first remainder if any.
To divide by 10, 100, &c., cutoff as many figures from
the right of the dividend as the divisor contains ciphers.
Thus, 198 -r- 10 = 19.8, (19 times and 8 over).
1. If 2 dozen chairs cost $72, what is the price of
1 chair ?
Solution.— 1 chair = $72 -f- 12 ~ 2 = $3.
2. Divide 5771 by 45.
Operation. — 5
I 1
Quotient.
5771
1154 — 1
128 — 2
9
1154 X 5
45 = 5 X 9.
2x5+1 = true rem.
128H. Ans.
Proof. 5771
7920000
1.
2.
11 X 10 X 100
1073952 -r 12
Find the value of,
5. 12527480 + 35.
6. 19966848 + 22.
7. 25551944 + 44.
8. 231428340 + 540.
9. 389490240 + 960.
10. 77806800 + 1200.
11. 1004284 + 144.
12. 602973 + 132.
11 X 12
3. 608256 + 24 + 33.
4. 10220823 + 27.
13. 28512 = how many times 66 X 18 ?
14. Bought 250 acres of land for $6250, and excbjingod
it for 300 acres valued at $7200 ; what is the
■ difference in the cost of 1 acre of each kind?
*» ' "t)'*^'*
72
i/IVISION.
1|:
I J'
1. How do you divide by a composite number?
2. How much is 720 -'- 10 ? 100 ?
Ji!
i' I
BM
i t
44. To divide by a number exceeding 12, that is not
a composite number.
Rule. — Find how oft<' •. the divisor is contained. In V'Mi
least number of figures at the left of the divideiiil that.
will contain it, and place the niimbtr in the qi u'icnt,
at the right of the dividend. Ma]ti[>ly the divisfr by
quotient figure, subtract ilie product from the figures
divided, and to the remaini]()r anno: be next figure of
the dividend ; divide thid number as before, and eon-
titvue the operation till the whole of the diviuend is
When thory are cipliOrs at tlip right of the divisor cut them
off, uldo as »-.'>viy figures at the right of the dividend, which muht
be annexed i (ho vf'nuiinder 43. 49.
Example.— 05 vido G6040 by 31.
3l)660'.l9(2K-iG}^ quot.
i>3
31
40
91
93
Here 66 is the least num-
ber of figures that will
contain the divisor; 31 is
66049 Proof.
contained in 66, 2 times ; 2
times 31 = 62 ; 62 from 66,
leave 4. Annexing to 4 we
leave 40 the next number
to be divided ; 31 in 40
goes 1 time, once 31 sub-
tracted from 40 leaves 9 ; to
this we bring down the next
figure of the dividend, and divide as before. — 31 is con-
tained in 66049, 2130^^] times.
19
Find the value of,
1.
2.
3.
4.
5.
1103168596 -r 23.
1162663830 -7-45.
4008373691 -^ 67.
21063036690-^405.
3082176360 -f- 387.
6. 216441 -f- 607.
7. 2467902719 -^ 4967.
8. 19929917463-^50989.
9. 463227983631 -f 537089.
10. 28395000000-^-75000.
11. 60122460900-^87400.
12. 8924000079 -f 97000.
uA-f^' —
IMVISIOK.
ii
V«- ,'™'
1. What three factors will produce 240?
2. The product of two or more factors divided by one
factor gives what ?
3. What number multiplied by 50 will give 1000?
4. What number divided by 20 will give 50?
5. If 864 be dividend, and 72 quotient j what is the
divisor? - ■'/ "■
13
.^^
14
15
16
What number multiplied by 497316 will give
318998375040?
Two trains leave Toronto at the same time, going
in opposite directions, one at the rate of 25 miles
an hour, and the other at 37 miles an hour; in
what time will they be 1426 miles apart?
In what time should 37 men dig a trench that one
man can dig in 333 days?
What factor together with these three, viz. 36, 78,
and 1000, will produce 277992000?
17. Divide $1035 among 25 men and 19 boys, and give
each man twicp a boy's share.
18. The strokes of th . hammer of a clock are 5b340 in
a year ; how many is that per day ?
19. 1596 beans were produced by a bean which had 4
stems, and each stem 19 pods ; how many beans
each pod?
20. One million is how many times one thousand?
21. A man's eflFects amounted to $78144; of this, his
son was to have ^, and the remainder was to be
divided equally among his six daughters ; what
was each one's share?
22. How many bags containing respectively 2, 3, and 4
bushels, and an equal number of each, can be filled
from a bin containing 4500 bushels of oats ?
d
74 GENERAL PRINCIPLES AND APPLICATIONS.
45. The product of two factors, divided by one factor,
gives the other ; 108(9 X 12) -M2 = 9 ; and 108 -r9= 12.
Note.— Tho dividend corresponds to tlie product, tlie divisor
and quotient are its factors.
46. The product of any number of factors, divided by
one or more of the factors, gives the product of the
remaining factors. Thus, 3X4X 5-r3-^5=:4.
47. Multiriying the dividend, or dividing the divisor,
multiplies ^ne quotient.
40 X 2 40
Thus, ^^- = 10, while or = 20 (or twice 10).
^ 4 4-^2 r
48. Dividing th3 dividend, or multiplying the divisor,
divides the quotient.
28 -r 2 28
Thus, ^7^ = 4, and or = but 2.
7 7X2 ^,,. ,, .
49. Multiplying or dividing both dividend and divisor
by the same number, does not affect the value of the
12 X 2 12^4
quotient. Thus, ^4^. — ■ = = 3.
4X2
4-4-4 ^^j',^
1. 3 X 4 X 5 -7-3 -^ 4 = how many? 45.
2. 900 is the product of three factors, two of which
are 4, and 25 ; what is the third factor?
3. 270 is the product, and 90 the multiplicand ; what
is the multiplier ?
4. What is V multiplied by 6? > . [
5. How much is %^ X 3 ? \l X 6 ? 46.
6. How much is Y "r 3 ? ^ -7- 4 ? 47. ,
GENERAL PRINCIPLES AND APPLICATIONS. 75
1. Give examples of Art. 44 and 45.
2. Give examples of Art. 46, 47, and 48.
I. Find the value of 4 x 6 X 20 divided by 10 x 5 X 4.
Operation. — Here the operation may be shortened
4 X 6 X 20 by cancelling any factor common
to the dividend and divisor ; for
this only divides both dividend
and divisor by the same number,
which does not change the value
of the quotient (48.) 4 cancels
4 and 4, and 10 cancels 10, and
6X2
=\2 — 2)^ Ans. reduces 20 to 2, leaving
= i«^ = 2?. 5
10 X 5 X 4
2
^ X 6 X ^IS)
iq X 5
6X2
X 4
60. When multiplication and division occur in the same ques-
tion, the terms should be first connected by signs and cancelled ;
to facilitate which the following ahould be borne in mind :
Any even number is divisible by 2. If the two last figures di-
vide by 4, the whole will divide by 4. If the three last figures
divide by 8, the whole will divide by 8. A number ending in
0, is divisible by 10 and 2.
.... J .
Find the value of, ^ \
2. 40 X 12 X 8^(5 X 8\
3. 87 X 9 X 8 -r 8 -j- 7.
70 X 6 X 4 X 18
^' 9X3X4 •
5.
6.
12 X 50 X 72
9 X 24 X 25"
88 X 20 -i- 36 X 100
4000 '
7. If 15 be multipled by 7, 27, and 40, and the product
divided by 54 multiplied by 40, 10, and 2 ; what
will be the result?
8. How many pounds of butter at 15 cents, will be
required to pay for 60 pounds of sugar, at 9 cents
per pound ?
9. A man exchanged 28 boxes of soap, each containing
24 pounds, at 9 cents a pound, for 126 barrels
of ashes each containing 3 bushels ; what was
allowed a bushel for the ashes ?
t6 GENERAL PRINCIPLES AND APPLICA1*I0N8.
51. When the multiplicand or multiplier contains a
fraction :
ExAMi'LE 1. What cost Al yards of cloth at 25 cents
a yard ?
Operation.— 4 yards at 25 cents will cost 4 timts 25
cents = 100 cents =$1. ? of a
yard will cost 3 of 25 cents. But
§ denotes 2 -J- .3, hence, to multi-
ply by §, we must multiply by 2,
and divide the product by 3 ;
25 cts. X 2
=: 1G3 cents, which
25 cts.
4
100
165
$1,165
25 cts.
2
'50 •
16?
added to 100 cents = 1165 cents = $1,165. Ans.
Note.— The flffnre below the line, which corresponds to tlie
divisor, is callea the denominator; and the figure above the line,
whicli corresponds to the dividend, is called tlie numerator.
Rule. — To multiply the fraction, multiply the numera-
tor, and divide I'le product by the denominator ; multiply
the whole number separately,and add the products.
52. Proof. — The best method of proving multipli-
cation is by division.
2. What cost 2i yards of cloth .at 20 cents a yard?
.- 3. Multiply 6 by 4i, i, G}.
: 4. What cost 8 sheep at $5^ a head?
1. What cost 35 books at $25 each ?
2. What will 1224f bushels of oats weigh at 34 pounds
to the bushel ?
3. How much is ? of 143 bushels of corn?
4 In 254 dress patterns, each containing lOJ yards;
how many yards?
5. What cost 15.? yards at $2.50 a yard? '
6. If a man travel 2-^ij miles in an hour, how far will
he travel in 3 days at 12 hours a day ?
)N8.
itains a
J5 cents
time a 25
§ of a
ts. But
o multi-
)ly by 2,
by 3;
I, which
n3.
lis to the
the line,
ator.
nuroera-
^ultiply
Ct3.
in u Hi pi i-
yard ?
i pounds ^
\ yards;
far will
86
t8
8
CJENERAL PRINCIl'LES AND APPLICATIONB. 77
53. When the divisor or dividend ontains a fraction :
ExvMPLB 1. Divide 12 by 4,J|.
OPERATION.—We first multiply both divisor and
4i 72 dividend bv the denominator of the
_^ ^ fraction, which does not change the
13) 216 (l6H^T^^°^^®^^ (48)» ^n order to get rid of the
\ W fraction, and then divide as in whoh*
numbers. 3 times J = § = 1 (46 and
50) ; 3 times 4 are 12, iind I carried are
13 ; 3 times 12 are 216 ; then 216 -J- 13
= 16-i'*j^. Ans.
Rule. — Multiply both divisor and dividend by the
denominator of the fraction, and divide as in whole
numbers.
2. If 2| yards cost 45 cents, what is that per yard?
3. Divide 3 by U ; by 2i.
4. 4g bushels of buckwheat weigh 180 pounds ; what
is the weight of 1 bushel ?
5. If the ploughing of 3 acres of land cost $7^ ; how
is that per acre ?
1. If 35 books cost $93J, what is the price of 1 book?
2. 1224f bushels of oats weigh 41620f pounds ; what
is the weight of 1 bushel?
3. How much is 61^ -f- ? ?
4. In 2667 yards of silk how many dress patterns of lOJ
yards each ?
5. 15| yards of cloth cost $39 ; what is it per yard?
6. At $17 a ton how many tons of hay can be bout^hr,
for $164^? ' .♦ v^:.,.- V V
7. If a man travel 11} miles in 3 days, travelling 1?
hours a day, how much is that per hour?
78 DIVISION OF THE DECIMAL CURRENCY.
64. To divide dollars and cents by a simple numbci* :
Rule. — Divide as in simple numbers, and point off
the two right hand figures fur cents. The quotient is
of the same denomination as the dividend. '
55. To divide by dollars and cents :
Rule. — Reduce both terms to cents by taking away
the decimal points, and divide as in simple numbers.
The quotient will be a simple number.
Taking away the decimal point multiplies by 100, tho number
of cents in 1 dollar; and since both terms are ir.v.Itiplied by the
same nnmber the quotient is not changed. 48>
Example 1. Divide $3 into 4 equal parts.
4N$3.00
i $3 = 3 X 100 c. = 300 c. ; 300 c. -r-4 =75c.
$0.75
2. How many cents in $5 ? $2 ? $10 ? $9?
3. How many pens at 3 cents, can you buy for $1 ?
' Find the value of, '
1. $6918G9.G0 -~ 72.
2. $534032.33-7-611.
3. $172010 -r 1000.
4. 1292200.01 -r 2600.
5. $9574- $0.06; -r$0.15.
6. $528.75 -^ $1.89.
7. $976842 -J- $9.46.
8. $28764.07 -J- $41.07.
9. A man paid $1448.75 for 95 ploughs, and $702 for
78 harrows ; what is the price of 1 plough, and
1 harrow? - <
10. Paid $45 for three boxes of sugar, each containing
125 pounds; what is the price per pound? ■
11. A lady purchased 11 yards of French merino for
$11.55, 14 yards of cambric for $1.48, 25 yards
of cotton at 15 cents a yard, a hat at $2.30, a
■' - pair of gaiters at $3.25, and a number of sets
of cuflFs and collars dt 15 cents per set, which
amounted in all to $25.53 ; I demand the number
of sets of «. iflfs and collars ?
DIVISION OF THE DECIMAL CUREENCY. 79
^
66. To divide by 10, 100, &c., romore the decimal
points 1, 2-, &c. places to the left.
1. How do you divide dollars and cents by a simple
number? Of what name is the quotient?
2. How do you divide by dollars and cents?
3. What is the price of 1 pencil, at $1 per hundred?
4. At $11 per hundred weight, what is the price of 1
pound of clieeso? . , , ...
Solution. —
1 lb. at $1 per cwt., would cost ^^^ of $1 = 1 cent.
1 lb. at$ll per cwt., " " 11 times I ct.= 11 cts.
5. At $2 per hundred, what would 15 herrings cost?
12. Bought 57 yards of cloth for $219.45, and 47 yards
for $223.25 : what is the difference iu the price
of 1 yard of each?
13. Paid $2350 for 1000 barrels of apples ; what is the
price per barrel ?
14. How many bricks at 2 cents, will amount to $20 ?
15. 15 barrels of beef cost $150 ; what is the price per
pound?
16. A man sold a horse at $97.50, and took in pay 42
. bushels of wheat at $1 a bushel, and 6 tons of
hay ; what was the hay valued at per ton?
17. A lumber merchant purchased 95 thousand feet of
white pine, which amounted to $9500; 113
thousand feet of red pine for $24860 ; 16897 feet
of oak for $5407.04 ; 69768 feet of elm for $1567 :
what is the cost of each kind per foot, and at
what average price should it be sold, to gain
$32332.21 on the whole ?
18. The wages of 16 men amounted to $6260 in 1 year ;
what is the price of 1 day's work? '** '' "
80 DIVISION OF THE DECIMAL CURRENCY.
— quotient?
not exceed-
1. $T per hundred is how much per unit? , «pt
2. Whatistbepriceof 1 poundofpork, at$9abarrel?
19. A man sold an ox as follows : the hind quarter at
6 cents a pound, which amounted to $15.48 ; the
fore quarters at 5 cents, which amounted to
$12.50 ; the hide and tallow at 7 cents, amounted
to $11.41 ; what was the weight of the ox?
REVIEW OF DIVISION.
1. What does division teach ? 38.
2. What are the given terms of division? the
required term ?
3. What is the dividend? divisor?—
4. How do you divide by a number
ingl2? 38.
5. He *v do you prove division ? Why? 40. 42. 52.
6. How do you divide by a composite number? 43.
I. How do you divide by 10, 100, &c.? 43. 66.
8. How is long division performed ? 44.
9. Describe the relation division bears to multiplica-
tion. 42.
10. What is the eflfect of multipl^'ing and<K dividing a
quantity by the same number ? 42.
II. The product of two or more factors divided by
one factor ' ves what? 45. 46.
12. What is the effect of multiplying the dividend, or
dividing the divisor? 47.
13. What is the eflfect of dividing the dividend, or
multiplying the divisor ? 48.
14. What is the eflfect of multiplying or dividing both
dividend and divisor by the same number? 49.
15. How do you multiply by a fraction? 51.
16. How do you divide by a fraction? 53.
17. How do you divide, dollars and cents, by a simple
number ? Of what name is the quotient ? 54.
18. How do jou proceed when both divisor and
dividend consist of dollars and cents ? Of what name
is the quotient ? 55.
7. Ti
9.
17
1 10.
Th
11.
A
12.
H(
r.
MISCELLANEOUS EX. IN PRECEDINQ RULES. 81
)arrel ?
rter at
:8; the
ited to
lounted
X?
the
)tient?
exceed-
42. 52.
•? 43.
66.
Itiplica-
viding a
rided by
[dend, or
Ldend, or
ling both
9.
1.
r a simple
risor and
hat name
1. What will the wages of 7 men amount to in 3
weeks, at $2 a day ?
2. What number is that from which if 250 be taken,
the remainder will be 500 ? ^ -
3. Upper and Lower Canada were united in 1841 ;
how long is it since ? , ^
1. How many pounds of pork at G cents, can be bought
for $375?
2. What number added to 9994, will make 100900 ?
3. If a man spend $1.17 a day, how much will he spend
in a year ?
4. How many times can 1000 be taken from one million ?
5. The United States contains 2,936,1 IG square miles;
the British North American Provinces, 2,878,361
square miles ; what is the diflference in the areas
of these two countries ?
6. A gentleman's estate came to X25000, and he left
£2000 to each of his three daughters, £4000 to
each of his two younger sons, and the rest to his
eldest son ; what was his portion? . ,
7. From 27 yards of cloth were cut 8 coats, each con-
taining 21 yards ; how much cloth remained ?
762 X 380 68 X 30 X 8.
8. Find the value of 1-
190 15 X 16 X 4.
9. 17 times 3400 is how many times 68 ?
10. There are 32 quarts in one bushel ; how many quarts
must I dip from a bin of grain to make 1 i bushels ?
11. A man spends $310.25 in a year, and saves $180 ;
what is his daily expense ?
12. How many tons of coal at $6, will be required to
pay for 70 barrels of flour at $6.35 a barrel ?
V
82 MISCELLANEOUS EX. IN PRECEDINQ RULES.
1. A.'s age multiplied by 2, or B.'s divided by 2,
equals 30 years ; what are their ages ?
2. 60 is divisor, 1 the remaiader, and 40 the quotient;
■what is the dividend?
3. What number divided *y 1500, and multiplied
by 1000, will make 1000?
13. How much is (200 + 300 —
-j- 500 — 50 X 15?
14. Find the value of
3760 730X4
1600 X 796 H 1
80 8
100) X 400 -r 100
700
280-4-720 —
35
15. Nicholas Copernicus was born at Thorn, Prussia, in
1473, and died in 1543 ; how old was he at his
death?
16. 978 is the sum of two numbers ; 897 is one number,
what is the other ?
17. If 90007 be minuend, and 908 the diflference, what
will be the subtrahend? ' ' "'
18. The product of two factors is 4891095, and 369 is
■y-''^'^ one factor ; what is the other factor ?
19. If the divisQr be 69874, and the quotient 896385;
what is the dividend ?
20. 28395000000 is the dividend, and 75000 the divisor ;
what is the quotient? ^ ,v
21 . Bought 35 barrels of pork at $10.75 a barrel : if the
whole is retailed at 9 cents per pound, what is
gained by the transaction ?
22. Bought 12 dozen pairs of scissors for $36 ; if I sell
them out at 37 cents per pair, what do I gain
per pair and on the whole ?
Miss
12 .T
^ds
m
(<
25^
it
51
ii
25
(<
6 pal
d by 2,
Liotient ;
iltiplied
~r 100
ussia, m
le at his
[lumber,
:e, what
id 369 is
896385;
divisor ;
I: if the
what is
if I sell
) I gaiu
BILLS OP PARCELS.
Toronto, April 13tb, 1866.
Mr. JOHN McDonald,
Bought op MURRAY & CO.,
7 yds. Broad Cloth, /® $4.50
10 " Shalloon, fa) $0.90 ,„t j:
12 " Serge, ^$0.75
25 " Cassimere, /5) $1.09
20 '' Cotton, ^$0.20 -,. .
Thread, fd) $0.25
Buttons, /© $0.25
$••••■
Clinton, January 3rd, 1866.
Miss KATE DANVERS, ... -
Bought of B. O'REILLY,
12 yds. Fine lace, fd) $3.50
13i " Satin, fa) $2.15
25g " Damask, ^$1.90
51 '' Cambric, ^$0.19
25 " Cotton, rS) $0.20
6 pairs Kid Gloves, ^$1.35
$
Montreal, August Ist, 1865.
Mr. H. GRANT,
Bought of J. LABELT.E,
92 lbs. of Tea, fco $0.90
85 " Coffee, ^^ $0.30
80 " Soap, rtT) $0.05
450 <' Sugar, /&) $0.12i
125i " Currants, (f?^ qDO.lO
119i " Raisins, ^(3? $0.20
$
Received payment,
' ' " J. LABELLE.
84
ANALYSIS.
I I
57. Analysis is the solution of problema on general
principles, unaided by specific rules.
By analysis a question is resolved into its parts, and
each part considered separately ; thus rendering each
step of the solution plain and intelligible.
The following general principles should be observed :
58. When the price of 1 unit of any quantity is
given, to find the price of that quantity ; multiply the
price of 1 unit by the quantity.
59. When a quantity and its price are given, to find
the price of 1 unit of that quantity ; divide the price by
the quantity.
60. The price of a quantity and the price of a unit of
that quantity being given, to find the quantity ; divide
the price of the quantity by the price of unity.
1. If 1 barrel of flour cast $6, what will 25 barrels
cost?
Solution. — If 1 barrel cost $6, 25 barrels will cost 25
times $6 = $150. 58.
2. If 25 barrels of flour cast $150, what will 1 barrel
cost ?
Solution. — If 25 barrels cost $150, 1 barrel will cost
^Vof$l50 = $6. 59.
3. At $6 a barrel, how many barrels of flour can be
purchased for $150?
Solution. — Since 1 barrel cost $6, for $150 we can
get as many barrels as $6 is contained times in $150 ;
$150 4-$6 = 25 ; therefore for $150 we can purchase
25 barrels. 60.
4. If 50 sheep cost $125 what is the price of 1 sheep ?
5. At 15 cents each, what will 1000 cedar rails cost ?
6. How many rails at 15 cents, will amount to $150 ?
U'. '
ANALYSIS.
I general
tarts, and
ing each
)bserved :
lantity is
Itiply the
in, to find
s price by
a unit of
T ', divide
5 barrels
II cost 25
1 1 barrel
will cost
ir can be
we can
in $150 ;
purchase
1 sheep ?
lils cost ?
to $150?
1. If 3 pounds of coffee cost 24 cents, what will 5
poundL cost?
Solution. — First find the price of 1 pound ; if 3
pounds cost 24 cents, 1 pound will cost one third of 24
cents = 8 cents.
If 1 pound cost 8 cents, 5 pounds will cost 5 times 8
cents = 40 cents.
2. A merchant sold 5 yards of cloth for $15 j what
will 7 yards of cloth cost at the same rate ?
3. 5 oranges cost 25 cents; how much is that per
dozen ?
4. If 8 barrels of flour cost $76, what will be the cost
of 326 barrels?
Solution. — If 8 barrels cost $76,
1 barrel will cost i of $76 = V^P
325 barrels will cost 325 times $V =
19
$X^ X 325
(cancelled by 4) = $3087.50
61. Write down first the term tliat is of the same name as the
answer, and compare the other terms with it to make the state-
ment. Connect the terms by signs and cancel, before multi-
plying, &c. 49-
1. What cost 5 oranges at 60 cents a dozen?
2. If 4 yds. of cloth cost $25.50, what will 24 yds. cost ?
3. If 24 yds. of cloth cost $153, what will 4 yds. cost?
4. What will 51 cords of wood amount to, at $10 for 3
cords? ,
5. If 8 sheep cost $32, what -ill 5 sheep cost?
6. If 7 pounds of wool cost .ip2.10, how much will 29
pounds cost?
7. What cost 8 chairs, at $25.60 a dozen?
8. If 42 acres of land cost $252, what will 182 ac. cost ?
86
ANALYSIS.
1,. If $3 pay for G yards of linen, how many yards
will $7 pay for? . . .. ,. ,
Solution.— If $3 pay for 6 yards, $1 will pay for i
of 6 yards = 2 yards. If $1 pay for 2 yards $7 will
pay for 7 limes 2 yards. =: 14 yards.
2. If$7payfor 14 yards how many yds. will $3 pay for?
3. If 3 yards cost $2 how much can be bought for $8 ?
9. If $4 pay for 5 days' works how many days' works
will $20 pay for ?
10. If 40 bushels of oats cost $8, how many bushels can
be obtained for $125?
11. If $125 pay for 625 buphels of oats, how many
bushels will $8 pay for ?
12. What cost 625 bushels of oats at $8 f'>r40 bushels?
13. What cost 40 bushels, at $125 for 625 bushels ?
14. If 5 hogs cost $32.50, how many will $201.50 buy ?
15. If 15 pounds of wool make 13 yards of cloth, how
many yards will 240 pounds make ?
16. If 18 bags of salt cost $l7.20,what will 171 bags cost ?
17. Paid $45 for 18 pairs of boots ; how many pairs
can be obtained for $187.50 ?
18. If 4 cows make 26J pounds of butter a week, how
much should be expected from 25 cows in the
same time?
19. If 385 yards of linen cost $252, how much will 110
yards cost ?
20. How many pounds of wool will make 208 yards of
cloth, at 15 pounds to 13 yards ?
21. If three yards of broad cloth cost $13.20, what will
24^ yards cost?
22. If 90 yards of shalloon cost $72, how many yards
can be bought for $390 ?
31.
32.
atttti
M
ANALYSIS.
87
lany yards
pay for J
ds $1 will
$3 pay for?
ght for $8 ?
lays' works
)ushels can
how many
:0 bushels?
ishels ?
)1.50buy?
cloth, how
bags cost ?
nany pairs
week, how
)ws in the
chwill 110
'8 yards of
, what will
any yards
i
1. What cfM a barrel of beef at 7 cents a pound?
SoLUTioM. — 100 lbs. at 1 cent = 100 cents = $1.
100 lbs. at 7 cents = 7 times $1 = $7.
200 lbs. at 7 cents = 2 times $7 = $14.
2. What cost 5 cwt. of cheese at 10 cents a pound?
3. At 5 cents a pound, what cost 3 barrels of beef?
4. What cost 4 pounds of beef at $7 per cwt.?
Solution. — 1 lb. at $1 per cwt, = j,',V of $1 = 1 cent.
1 lb. at $7 per cwt, = 7 times 1 cent = 7 cents.
4 lbs. at $7 " " =4 times 7 cents = 28 cents.
5. What cost 1 pound at ^i per cwt.?
6. At $6 per cwt., what cost 2 pounds? 5 pounds?
23. What would 15 brls. of beef amount to at C cts.per lb?
24. What cost 65 cwt of cheese at lOJ cts. per pound?
25. At $15 a barrel, what will 32 lbs, of pork cost?
26. What cost 375 bricks at $8 per thousand ?
Solution. — If 1000 cost $8, 1 brick will cost tx,Vit of
$8 $8
$8 = , and 375 bricks will cost 375 times
1000
$8 X .375
1000
= $3.
1.000
27. At $252 a thousand, what cost 7896 cedar rails?
28, What cost 897G9 feet of boards at $25 a thousand ?
29, What will 125 barrels of fish cost at 2^ cts, per lb.?
30. 24i yards of cloth cost $107.80; what is the price
of 3 yards ?
31, What cost 15 brooms at $20 per hundred?
32. How many hoes will amount to $45.50, at $8.40 per
dozen?
33. What cost 17 thousand bricks at 10 bricks for 3 cts?
34, Paid $262.20 for 276 gallons of molasses; what
quantity can I purchase for $452.50?
88
ANALYSIS.
1. How long would 3 men be employed at a piece of
work that 4 men can accomplish in 10 days?
Solution. — If 4 men take 10 day^!, 1 man would
require 4 times 10 days = 40 days to do the work.
If 1 man take 40 days, 3 men would do the work in
i of 40 days = */' = 13i days.
2. If 2 men can do a piece of work in T days ; in what
time would 5 men do the same ?
3. If T) men can mow a piece of land in 8 days, in how
many days should 10 men mow it?.
35. How long should 18 horses feed on a quantity of
oats, that would last 6 horses 21 days.
3G. If 7 men build a house in 24 days, in what time
should 18 men build it?
37. If Ann can spin 20 bkeins of yarn In 4 days, in
what time can she spin ;{5 skeins?
38. If li cwt. of sugar coal .f9.90, what will 25 pounds
cost?
39. How many yards of cloth, 3 quarters wide, will
line 27 yards that is 5 quarters wide?
40. If 5 coats be equal in value to 9 cloaks, how many
coats will be equal in value to 25 cloaks?
41. If 2000 men have provisions for 6 months, how
many men would the same quantity serve 8
months ?
42. If 275 reams of paper cost $330, how much can be
bought for $1188?
43. If 56 pounds of tea cost $34, what will 7 boxes
each 2| cwt. cost?
44. What cost 8973 shingles, at $8 per thousand?
45. If 7 men can build a wall in 20 days, how many
men should build it in 7 days ?
1.
of wo^
SoM
|$2.15
J them
in$2l|
2. II
ifor 20[
3. l|
,i
i
|4G. H
reqmr
47. Hi
48. Pi
49. W
50. If
51. H
52. V
V 53. I
54. I
55. ^
I 56. :
M
ANALYSIS.
at a piece of
I?
man would
e work,
the work in
ys ; in what
ays, in how
quantity of
I.
wliat time
4 days, in
25 pounds
wide, will
how many
b?
aths, how
T serve 8
ch can be
I 7 boxes
1. Bought 100 sheep at $2.15 each ; how many pounds
of wool at 30 cents will pay for them?
Solution. — 100 sheep at $2.15, will cost TOO times
$2.15 r= $215 ; it will take as many pounds U> pay for
them as 30 cents, the price of 1 pound, is contained times
$215
in $211
= "riGj pounds.
$0.30
2. How many pounds of teaat 40 cents, must be given
for 20 pounds of butter at 12 cents per pound?
3. How many pounds of butter at 15 cents will be
required to pay for 3 cows at $25 a head?
40. How many acres of land at $6.60 should be given
in exchange for 630 acres at $3? *
4*7. How many barrels of flour at $4.90, are equivalent in
value to 1000 bushels ofwheat at $1.09 per bushel?
48. Paid $49.60 for 32 yards of silk ; what quantity can
be purchased for $223.20?
What is a man's wages for 146 days, at the rate of
$148.80 per annum?
If 2 horses be equal in value to 5 cows, how many
cows must be given for 20 horses ?
51. If 2 springs of a dog be equal to 3 springs of a hare,
how many of the dog's springs equal 150 springs
of the hare ?
52. What is the assessment on $767.25, at 2 cts. in the $ ?
53. If 4 casks of raisins each \\ cwt. cost $92, what
quantity can be obtained for $2.30 ? '
54. If 75 cwt. be carried 20 miles for $2.50, how far
should 325 cwt. be carried for the same money?
55. What will 46 pieces of cloth, each containing 57
yards, cost at $4 for 3 yards ?
56. 14 packs of wool each 420 pounds cost $896, what
is that per hundred weight ?
49
50
l:i
90
ANALYSIS.
1,1 i
1. Kittj's age multiplied by 12, or Colin's by f), will
malre 144; what is the difTercnce in their nges?
2. W, t number added to 5 times itself will make '24?
3. A woman sold 3 dozen egg3 at 1 touts a dozen,
and 10 pounds of butter at 15 cents a pound. She
took in pay G yards of print at 20 cents a yard, and
the balance in sugar at 12 cents a i)onnd; how many
pounds of sugar did she receive ?
57. If 7 men consume 1 2 pounds of bread a day, how much
bread will serve a garrison of 350 men a year?
58. How many feet of sawed lumber, at $15 a hundred,
would be equivalent to 62368 foot of timber, at
$70 A thousand ?
50. If 28 reapers finish a harvest in 36 days, how many
reapers will do it in 9 days?
60. If $100 gain $6 in 1 year, how much should $030
gain in 2 years?
How many books at 85 cents, can I buy with the
avails of 1 cords of wood, sold at the rate of $11
f -r 3 cords?
A )i;an sold 15 hundred weight of cheese at 11
cents a pound. He received in pay $60 in cash,
17 yards of cloth at $3.27 a yard, 52 yards of
cotton at 18 cents, a hat at $2.10, and the
balance in tea at 75 cents a pound ; how much
tea did he receive ?
63. If a man earn $2.50 a day, and spend $4 a week,
how many acres of land at $1.75 can he purchase
with the earnings of a year, (313 days) ?
64. A grocer bought 7 hundred weight of beef at 7 cents a
pound, and paid for it in tea at 95 cents, sugar at 13
cents, coir«e at 32 cents, giving of each an equal
quantity ; how many pounds did he dispose of in all ?
61
62
02.
but on(
03.
nomiii
Tabl
NOTK
roiiiifct
with H(
The
cent p
Tlie
weigh
*1. (
2. (
COMPOUND NUMBERS.
91
02. Simple Numbers are those that express things of
but one kind or denomination, as 2 shillings, also 4, G, 8.
63. Compound Numbers express more than one de-
nomination, as 1 pound 5 shillings.
Tables of Money, Weights, and Measures.
NoTK.- I'lio tablps nnd mciitiil exorcises hIiouUI 1)o tnnRht In
cniiiiectioii with n'duction; tlie first HerioH uf mental exercises*
A\ifli Keductiuii DoHCendinp:, (67.) and the eecond sorios t witli
Kodiu tlon Ascending. (68.)
CANADIAN DECIMAL MONF-^V
100 cents (ct.) make 1 dollar, ' *^
The CM ns are a 5 cent piece, a 10 ci nd a20
cent piece of silver, and a one cent pit )nze.
Tlie cent piece is one inch in diameter, and 100 cents
weigh one pound Avoirdupois.
UNITED STATES OR FEDERAL MONET.
10 mills (m) make 1 cent marked ct.
10 cents " I dime
10 dimes " 1 dollar
10 dollars " 1 eagle
*1. Give an example of a simple number.
2. Give an example of a compound number.
3. Repeat the table of Canadian decimal money.
4. Repeat the table of Federal money.
(1
d.
i(
$
((
E.
5.
In 3 dollars and 25 cents, how many cents?
Solution.— 1 $ = 100 c. ; 3 $ = 3 times 100 c. = 300 c.
300 c. + 25 c. = 325 c.
6 How do you multiply by 100 ? 1000?
7. How many cents in $7? $7.90? $19.50?
8, In $8 and 2 dimes, how many dimes, cents, and
mills?
fl. In 325 cents, how many dollars?
2. Reduce 600 cts., 725 cts., and 1508 cts., to dollars.
3. In 8000 mills, how many dollars?
>
r
^V ■*•"
^^.
'/
IMAGE EVALUATION
TEST TARGET (MT-3)
1.0
I.I
^ lii 122
us. 12.0
lU
lU
lit
I
11.25
U 11.6
Hiotographic
Sciences
Corporalion
23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716)872-4503
'^^
^z,^
^^>
■i
6^
'
92
WEIGHTS AND MEASURES.
OLD CANADIAN CURRENCY.
make 1 penny marked d.
s.
(I
II
4 farthings
12 pence " 1 shilling
5 shillings " 1 dollar
20 shillings or $4 " 1 pound
1 farthing is written | of a penny.
2 " " i
3 " « J
1. Repeat the table.
2. Repeat the table backwards, thus :
1 pound = 20 shillings.
1 shilling = 12 pence.
1 penny = 4 farthings.
3. In 3 shillings, how many pence ?
Solution. — 1 shilling =: 12 pence ;
3 shillings = 3 times 12 pence = 36 pence.
4. How many pence in 5s., 9s., 4s. 6d., 7s. 9d., 15s.?
5. In 1 shilling how many farthings ? In 2 shillings ?
6. How many shillings in £2, £4, £6, 2s. ?
1. How many shillings in 36 pence ?
Solution. — It takes 12 pence to make 1 shilling; in
36 pence there will be as many shillings as 12d. is con-
tained times in 36d. ; 36d^ 12d= 3. Therefore, 36 pence
= 3 shillings.
2. How many shillings in 24d., 36d-., 70d., 40d., 44d.,
'72d.j 80d., 96d.?
3. How many pounds in 40s., 70s., 60s., 45s., 90s., 48s.,
70s., 240d., 960 farthings.
ENGLISH OB STERLING MONEY. '
4 farthings make 1 penny, marked d.
12 pence " 1 shilling " s.
20 shillings " 1 pound " £
The sovereign represents the pound sterling; 1 guinea is 21
shillings ; and 1 crown, 6 shillings.
1. Repeat the table. 2. In 5 crowns, how many penc6?
WEIGHTS AND MEASURES.
93
AVOIRDUPOIS WEIGHT.
This weight is used for all ordinary purposes of weighing.
16 drams (dr.) make 1 ounce marked oz.
16 ounces " 1 pound " lb.
25 pounds " 1 quarter " qr.
100 pounds or 4 qr. " 1 hundred weight, cwt.
20 cwt. or 2000 lbs. " 1 ton " T.
28 lbs. to the quarter, or 112 lbs. to the hundred weight, was
formerly allowed.
1. In 4 pounds, how many ounces?
2. How many ounces in 3 lbs.?
3. In 7 cwt., how many pounds?
4. In 4 tons, 16 cwt., how many pounds ?
6 lbs. 2 oz.?
1. In 48 ounces, how many pounds ?
2. lu 310 lbs., how many hundred weights? *
3. In 4800 lbs., how many tons?
. ^ TROY WEIGHT.
24 grains (gr.) make 1 pennyweight marked dwt.
20 penny weights " 1 ounce " oz.
12 ounces " 1 pound " lb.
Troy weight is used in weighing the precious metals,
also in scientific investigations.
1. In 3 lbs. 2 oz,, how many ounces?
2. In 1 ounce, how many grains? -^
3. How many pounds in 50 ounces?
4. How many ounces in 65 penny weighty?
APOTHECARIES WEIGHT.
Apothecaries mix their medicines ly this weight, but
they buy and sell by Avoirdupois weight ?
20 grains (gr.) make 1 scruple marked scr.
3 scruples " 1 dram " dr.
8 drams " 1 ounce " oz.
12 ounces "1 pound " lb,
94
WEIGHTS AND MEASURES.
DRY MEASURE.
2 pints make 1 quart marked qt.
4 quarts " 1 gallon *' gal.
2 gallons" 1 peck " pk.
4 pecks " 1 bushel " bu.
36 bushels" 1 chaldron " ch.
Grain is often sold by weight, allowing for a bushel,
60 lbs. of wheat, peas, Timothy or red clover seed,
56 lbs. of rye or Indian corn, 50 lbs. of beans, 48 lbs.
of barley, 40 lbs. of buckwheat and 34 lbs. of oats.
1. In 1 peck, how many quarts? pints?
2. In 1 bushel, how many quarts? .
3. Reduce 8 bus. 2 pks. to gallons.
1. How many gallons in 40 pints ? , ^ ;
2. In 40 quarts, how many pecks? , . ;
3. In 32 quarts, how many bushels?
-ri LIQUID MEASURE.
4 gills (gi.) make 1 pint
2 pints
4 quarts
31i gallons
2 bar. or 63 gal.
2 hogshead
2 pipes
36 gallons
54 gallons
1. In 4 gallons, how many pints?
2. In 1 barrel, how many quarts?
> 3. In 1 pipe and 1 barrel, how many barrels?
1. In 48 pints, how many gallons?
2. How many hogsheads in 189 gallons?
3. In 9 barrels, how many pipes ? "* '
marked pt.
" 1 quart "
qt.
" 1 gallon "
gal.
" 1 barrel "
bar.
" 1 hogshead "
hhd
" 1 pipe "
pi.
1 ton "
tn.
1 barrel of beer.
" 1 hogshead of beer.
WEIGHTS AND MEASURES.
95
OLOTH MEASURE.
2$ inches (in.) make 1 nail
4 nails " 1 quarter "
4 quarters " 1 yard "
3 quarters " 1 Flemish ell. "
5 quarters " 1 English ell. "
6 quarters " 1 French ell.
marked n.
qr.
yd.
Fl. e.
E.e.
" Fr. e.
In 3 yards, how many quarters ?
In 1 yard, how many nails and inches?
3. In 4 E. e., how many quarters?
1.
1
1. In 20 quarters, how many yards?
2. In 36 inches, how many yards?
3. In 2 yards, how many Fl. ells.?
LINEAR MEASURE.
Linear or Long measure is used in measuring lines.
12 lines (1.) --'
12 inches
3 feet
5 J yards r-
40 rods '
8 furlong's or 320 rds.
3 miles
69^- miles (nearly)
make 1
((
inch, marked in.
1 foot, " ft.
1 yard, " yd.
1 rod, pole, or perch, " rd. p.
1 furlong, " fur.
1 mile, " m.
1 league, " lea'
(t
((
t*^5 ■-
-J-
1 degree, " deg. or
4 inches make 1 hand, (used in measuring horses).
18 inches " 1 cubit.
1 pace. *'
1 fathom.
1 cable length.
1. For what is Linear measure used?
How many inches in 2 ft. ?-^ Y ft. 3 in. ?
In 4 yards, how many inches ?
In 1 mile, how many yards and feet ?
180 inches = how many yards ?
3 feet
6 feet
120 fathoms
2.
3.
4.
1.
96
WEIGHTS AND MEASURES.
09
I I
I I
30 i square yards
40 square perches
4 roods or 160 sq. per. "
640 acres
<<
((
sq.
pr
((
r.
((
a.
11
sq.
m
i.
It is
di-
SQUARE OR LAND MEASURE.
1 yd. =3 ft. lu square measure both length and
' breadth are considered. A square yard
is a yard long and a yard wide, or 3 feet
long and 3 feet wide, equal to 3 rows of 3
square feet each. A square foot consists
of 12 rows of 12 square inches each, i.e. 12
times 12 = 144 square inches. Hence :
Length multiplied by the breadth gives the square
contents, or area of any surface.
144 square inches make 1 square foot, marked sq. ft.
9 square feet " 1 square yard, " sq. yd.
1 square perch
1 rood,
1 acre,
1 square mile.
In measuring land Gunter's chain is used,
vided into 100 links : -,
7^^,T inches make 1 link. *
100 links or 4 rds. " 1 chain.
,^ - 80 chains " 1 mile.
u- „ 10000 square links " 1 sq. chain. >/
10 square chains " 1 acre.
1. What dimensions are considered in square measure ?
2. What is a square foot ?
. 3. How are the square contents of a surface found 7
4. How many sq. ft. in a board 5 ft. long and 2 ft. wide ?
5. What are the square contents or area of a court
10 rods long and 4 rods wide ?
6. What is the area of a room 25 ft. long and 20 ft. wide?
1 What is the length of a room that is 12 feet sq. ?
"2. What is the length of a board that contains 20
square feet and is 2 feel wide ?
3. What is the width of a room that contains 120
square feet and is 12 feet long ?
CUBIC OR SOLID MEASURE.
w
8 feet
.a
CO
la cubic measure, length,
breadth, and thickness, are
considered. A cubic yard
is 3 feet long, 3 feet wide,
and 3 feet thick, and is
equal to 3 X 3 X 3 = 27
cubic feet. Hence,
The solid contents of
any body is found by
multiplying together the
length, breadth, and thick-
ness. •
re measure ?
1 20 ft. wide?
7228 cubic inches (cub. in.) 1
= 12 X 12 X 12,thati8l2 '
inches in length, 12 in [
width, and 12 in thickness, J
27 cubic feet =3 X 3 X 3 feet
40 cubic feet of round timber or
50 cubic feet of hewn timber
make 1 cubic foot, cu. ft.
<(
((
1 cubic yard, cu. yd.
1 ton.
ton.
A cord of wood is a pile 4 feet high, 4 feet wide, and 8 feet
long, = 4 X 4 X 8 = 128 eolid fieet. 1 toot in length of such a
pile in called a cord loot; hence 8 cord feet make 1 cord.
1. State the difference between linear, square, and
cubic measure.
2. What do you mean by a cubic yard ?
3. How are the solid contents of a body found ?
4. What are the solid contents of a block, 3 feet
high, 2 feet wide, and 4 feet long ?
5. How many solid yards in a wall, 3 feet high, 3
feet wide, and 100 yards long?
In 5 cubic yards, how many cubic feet? ^^
ontains 120
1. In 54 cubic feet, how many cubic yards ?
[2. What is the width of a block, that contains 24 solid
feet and is 3 feet high, and 4 feet long? " ,
G
98
CIRCULAR MEASURE.
Circular or Anj^lar tnoasuro is used in astronoTnical calcula*
tions for reckoning latitude and luugituUc. measuring angles,
&c.
60 seconds (") mnke 1 minute, marked '.
60 minutes " 1 degree, " °.
60 degrees " 1 sign, " s.
12 signs or 360 degrees " 1 circle, " c.
Every circle is divided into 860 degrees, hence the length of
a degree depends on the size of the circle.
i
TIME ME
ASURB.
make 1 minute,
marked mln.
«
1 hour,
" h.
i(
1 day,
« d.
<(
1 week,
" wk,
<(
1 lunar montb, " mo.
, V %'.
It
1 year,
II
60 seconds (sec.)
60 minutes
24 hours
7 days
4 weeks
13 lunar months,
12 calendar months,
52 weeks, or
365i days.
The months are January, February, March, April,
May, June, July, August, September, October, Novem-
ber, and December. ' • ' •• '
The number of days in each month may be remembered from
the following lines ;—
30 days hath September,
April, June, and November;
H ¥■■■
February hath 28 alone,
All the rest have thirty-one ;
Except in leap year, at which time,
February's days are twenty-nine.
1. In 1 day, how many minutes ? x-
2. In 20 weeks and 3 day^, how many days?
, 3. In 1 lunar month, how many days? minutes?
1. In 56 days, how many weeks and lunar months?
2. In 600 hours, how many days? *
3. In 9t weeks, how many Junar months ? . , .
WBianTS AND HBASUBSS.
99
lical calcula-
^uring angles,
the length of
lembered from
THK ROMAN NOTATION,
So called because it was used by the ancient Romans,
employs seven capital letters, viz. :
One, five, ten, fifty, hundred, five hundred, thousand.
I V X L C D . M
All other numbers are expressed by repeating or combining
these. I, X, C, and M, only, can be repeated, and these but
three times.
I...
II...
TIL.
IV..
V...
.VI..
VII.
VIII
IX.,
X...
XI.
XII.
XIII
XIV
1
2
3
4
5
6
7
8
9
.10
11
12
13
,14
XV....
XVI 16
XVII 17
TABLE.
. 15 OC
XVIII . . .
XIX
XX
a2\.2\w ...
XL
L
LX
LXX • . • .
LXAX . . •
xc
c
18
19
20
30
40
50
60
70
80
90
100
ceo
CD
D
DC...
DCC
DCCC
CM
M
MM
MMM
MDCCCLXVI..
MXIV
200
300
400
600
600
700
^00
900
1000
2000
3000
1866
1014
MXIV 1014000
When a character precedes one of higher value it is
to be subtracted ; as IV, four ; in all other combina-
tions the sum of the characters is der < <;^d; as VI, six,
A dash over a character multiplies it by 1000 as
V^ five thousand. Read XXIX ; L V ; XXXIX; CI 5
CCCXI; XCIX; MMCLI ; MOX ; CIX.
PAPER AND BOOKS.
A sheet folded into two leaves is called a folio, into 4 leaves a
quarto, into 8 leaves an octavo, into 16 leaves a 16 mo, into 18
leaves an 18 mo, &c.
hr"
_ .,. ._*,. — .
100
WEIGHTS AND MEASURHs.
PAPKR AND BOOKS.
24 sheets of paper makel quire.
20 quires " " 1 ream.
2 reams " " 1 bundle.
bundles or 10 reams " 1 bale.
V
MISCELLANEOUS TABLE.
12 units
make I dozen.
12doz.
,
1 gross.
1 2 gross
1 great gross.
20 units
1 score. * «
14 pounds
1 stone. ' ' .
56 lbs. of butter
1 firkin. ' :*;
100 lbs.
:? i '
1 quintal. ' '
200 lbs. of pork or
beef
1 barrel.
196 lbs. of flour
1 barrel. ^
REDUCTION. •
64. Reduction is the process of changing numbers
from one denomination to another, without changing
their value.
65. Reducing numbers from a higher to a lower
denomination, as pounds to shillings, is called Reduc-
tion Descending. .... ,.
66. The changing of numbers from a lower to a
higher denomination, as pence to shillings, is called
Reduction Ascending.
, J.|< ;-»
''.'.J
67. REDUCTION DESCENDING.
ExAMPLB!. — Reduce JE13 lOs. to pence.
13 10 £1 = 20s., XIS = 13 limes 203.
2> =z 260s.; 260s. + 10s. = 270s.
n^ Is. =± 12d. ; 270s. = 270 times 12d.
12 = 3240 pence.
3240 pence.
REDUCTION DESCENDING. 101
1. In $500 how many cents 7
2. In $7 how many mills?
3. Reduce i;i to pence ; to farthings.
To perform reduction descending,
RuLV.— Multiply the highest given denomination by
that number of the next lower that is contained in one
of its units, adding in the given number, if any of the
lower denomination ; reduce the result to the next lower
denomination in the same manner, and continue the
operation till the quantity is reduced to the required
denomination.
Proof. — By division.
»«£1J
3.
4.
').
6.
* 1. Reduce to cents $703 ; $72.70 ; $1000. )
2. Reduce 7E. $2 7 dimes, 9 cts. 2m. to mills.. V.-jil
Reduce $25, $91, $.02| to cents and mills. }f
Reduce £700 to shillings.
In £1080, how many pence ?
In £19 3s. 5d., how many pence ?
7. Reduce l7s. lOJd. to farthings.
8. Reduce £1760 198. Gd. to farthings.
9. In 1 guinea, how many half pence ?
10. In 17 lbs. 2 oz,, how many ounces and drams ?
11. In 25 cwt., how many pounds ?
12. Reduce l7l cwt. 3 lbs. to pounds and ounces.
13. Reduce 15 tons 17 cwt. 1 qr. 22 lbs. to drams.
14. Reduce lb lbs. 6 oz. 12 dwts. 13 gr. to grains.
15. In 760 lbs. of silver, how many half ounces ?
16. Reduce 2 lbs. 2 oz. to scruples. ,,, y. ,;-'
17. Reduce 117 lbs. 8 oz. 2 dr. 12 gr. to grains. {
18. How many quarts and pints in 1 bushel ? 4
19. Reduce 17 bus. I pk. 1 pt. to pints, , .„ ; :
f' ^ arr
U
1*1,
102
REDUCTION DESCENDINQ.
1. la 1 hbd., how many quarts?
2. In 10 jds. 2 qr., how many quarters ?
3. How many sq. feet in a floor 20 feet long and 15
feet wide ?
20. What is the weight of 65 bushels 5 pounds of wheat,
and 50 bushels of oats ? ...
21. Reduce 3 hhd. 1 bar. 19 gal. 2 q. to pints.
22. How many quart bottles may be filled from I ton
of wine ?
23. In 350 pipes how many pints? •:".;.
24. Reduce 975 yards to quarters and nails. '
25. Reduce 17 yds. 3 qr. 3 na. U inches to inches.
26. Reduce 31 Fl. e. 3 na. to inches.
27. In 1 mile how many yards? feet? ■
28. Reduce 5187 yds. 1 ft. to feet and inches.
29. Reduce 17 lea. 1 m. 2fur. 7rds. 1 ft. 6 in. to inches.
30. In 1 sq. mile, how many sq. feet ?
31. Reduce 2 r. 16 sq. per. 19 yds. 8 ft. 121 in. to sq.
inches.
32. Reduce 27 sq. m. 2 sq. yds., to sq. inches.
33. How many sq. are perches in a piece of land 200
rods long and 80 rods wide ?
34. Reduce 3 cub. yds. 6 cub. ft. 222 cub. in. to cub. in.
35. In 12^ cords of wood, how many solid feet?
36. How many solid feet in a crib of timber 20 feet long,
8 feet wide, and 10 feet high ? ' " ' '•
37. Reduce 1 lun. mo. 20 seconds, to seconds.
38. How many days from June 2nd to March 22nd ?
39. How many days from Dec. 3rd to Feb. 29lh ?
40. Reduce 9s. 13^ 25' to seconds.
41. Express in the Arabic or common Notation, LIY,
XLI, CV, MDVjDOOCIX, MMVI, MDMCCXCVJII,
REDUCTION ASCENDINO.
103
08. Example. — Reduce 3240 pence to pounds.
12'3240d. We reduce the pence to shillings by divid-
ing by 12, because every 12 pence makes 1
- _^ shilling; 3240d. = 270s. Wo reduce the
X'13 10s. shillings to pounds by dividing by 20,
because 20 shillings makf I pound, aAd
ubtuiu X'13 lOs. the number of pounds ia 3240 pence.
RuLB. — Divide by that numbbr of the given denomin-
atiou thnt make 1 of the next higher denomination, und
so on till the number is reduced to the required deno-
minatiuu.
The remainders urc of the same name as their divi-
dends, ' 1
121 in. to sq.
1. IIow many dollars in 1000 cents?
2. Reduce 15000 mills to dollars?
3. Reduce 000 farthings to pouada.
4. How many shillings in 67d.? 98d.?-
«-.87d. ? 44d. ? 29d. ?
■78d.?
1. Reduce to dollars, 70300 cts., 7270 cts. and 100000 cs.
2. Reduce 72792 m. to cts., dimes, dollars, and eagles.
3. How many dollars in 250O0 m., 91000 m., and 25 m. ?
4. In 14000 shillings, how many pounds?
5. In 259200 pence, how many pounds ?
6. Reduce 4G01 pence to pounds.
7. Reduce 858 farthings to pence, shillings, &c.
8. Reduce 1G9053G farthings to pounds.
9. Reduce 504 halfpence to guineas.
jlO. In 4384 drams, how many pounds ?
ill. In 2500 lbs., how many hundred weights? '
[j3. Reduce 273648 ounces to hundred weights.
104
REDUCTION ASCENDING.
1. What is Reduction?
2. What is Reduction Descending? Ascending?
3. How would you reduce pounds to farthings?
farthings to pounds ? — tons to ounces ? — ounces to tons ?
13. Reduce 8127232 drams to oz., lbs , etc. '"'"
14. Reduce 89581 grains to pounds.
15. Reduce 18240 half ounces to pounds. i
16. Reduce 624 scruples to pounds.
IT. Reduce 677892 grains to pounds.
18. In 64 pints, how many bushels ? ■ '
19. In 1105 pints, how many bushels?
20. Of 5605 pounds of grain, 50 bushels are oats, the
remainder is wheat ; how many bushels of wheat
are there ?
21. Reduce 1920 pints to hogsheads.
22. In 1008 quarts of wine, now many tons?
23. Reduce 352800 pints to pipes.
24. Reduce 3900 quarters to yards.
25. In 647 inches, how many yards? ' '
20. Reduce 843| inches to Fl. ells.
Reduce 5280 feet to miles.
Reduce 186744 inches to yards. -. . .- ^
29. Reduce 3311964 inches to leagues.
30. Reduce 27878400 sq. ft. to sq. miles.
31. Reduce 3789481 sq. in. to sq. ft., yds., etc.
32. Reduce 108391221792 sq. in. to sq. miles. '.
33. A piece of land contains 16000 fn. perches, and is
200 rods long; what is its brenilth?
34. Reduce 150558 cub. in. to cub. ft., cub. yd., etc.
35. In 1600 cub. feet, how many cords. of wood?
36. What is the length of a crib of timber that is 10 ft,
high, 8 ft. wide, and contains 1600 solid ft, ?
27.
28.
REDUCTION ASCENDING.
105
1. In 1280 cubic feet, how many cords of wood?
2. In 1670 seconds, how many hours?
3. What is the length of a room that is 25 feet wide,
and contains 1000 sq. feet?
c.
3.
hes, and is
^d., etc.
>od?
at is 10 ft.
id ft. ?
31. Reduce 2480420 seconds to lun. months.
38. A note is drawn on the 2nd of June, payable in 293
days ; when will it be due ?
39. When will a note become due, dated December 3rdi
and drawn at 84 days ?
40. Reduce 1020300 seconds to signs.
41. Express in Roman numerals 54, 41, 105, 1505, 809,
11006, 16298.
69. To reduce^ old Canadian money, (pounds, shil-
lings, and pence) to the new or Decimal currency.
Example. — Reduce £3, 16s. 6id. to dollars and cents.
Solution.— £1 = $4; £3 = 3 times $4 = $12.
p , Is. = 20c. ; 16s. = 16 times 20c. = 320c.
i. 3. a. '
6| 6d. ,-wV ' = loc.
5 i d. = 2 far. = 2 times -j^c. = jf = . 00'^.
3
4
3.
16
20
I 2
12 320 1§ = ^
3.20
10
$15.30
6*
6
$15.30& Aus.
Rule. — Take four times the pounds
as shillings ; 20 times the shillings as
cents ; reckon 6 pence, 10 cents ; 3
pence, 5 cents; ]| pence, 2 J cents.
The remaining pence and farthings, reduce to farthings ;
then to cents by multiplying them by -j\ of a cent, the
value of 1 farthing.
For, 3d. = 12 fiir. = 5 cts., hence 1 far. = -^^^ of 5 pts,
~~ '\ li ct. ,
■■MMiinnri
106
REDUCTION.
i- (
1. Reduce £5, 5s. to dollars and cents.
2. How many cents in Is. 6d.?— 13s.?— Ojd.?— 'T^d.?
Reduce to dollars and cents,
1. £ 1 10s. 6d.
2. £11 Is. 9d.
3. jEIO Is. Oid.
4. i:i5 15s. 9id.
5. je23 Us. 4Jd.
6. £11 17s. 7id.
7. £ 33 13s. 113d.
8. jei90 17s. lOJd.
9. £295 168. 8id.
10. £180 OS. lid.
11. £190 Os. 6d.
12. £720 193. U^d.
70. To reduce the Decimal Currency to pounds
shillings, and pence.
Example. — Reduce $25.87 to pounds, &c.
Operation.— $25 -r $% the number of dollars in 1
4)$25 87
6.
5 . 20) 187
T. 1
5)21
£6 9s.4^d. Ans. 4^-
pound, = £6 and $1 rem.
$1 or 100 cts. + 87 cts. = 187
cts. ; 187 -r- 20 cts. the number
of cents in 1 shilling, = 9s. and
7 cts. over.
1 ct. = ^d., 7 cts. =: 7 times gd.
3X7
= = 4td- Then add the
5
results which equal £6 93. 4^d.
Rule. — Take I of the dollars as pounds, 1/0 of the cents
as shillings, and i of the remaining cents as pence (since
5 cents = 3d. 1 cent = J- of 3d. = ^d.) 10 cents may
be reckoned 6d.; 5 cents, 3d. ; 2^ cts IJd.
Reduce to pounds, shillings, &c., $1, $40, 40 cts.,
80 cts., 15 cts., 5 cts., 2 cts.
Reduce to old Canadian money,
1. $ 6.10.
2. $68.35.
3. $40.21.
4. $38.37.
5. $47.16.
6. $71.52.
7. $126.09.
8. $377.18.
9. $460.13.
10. $ 71.15.
11. $190.91.
12. $876.99,
REDUCTION.
107
i J-.
1. Rfvvice 7 m, 6 fur. 14 rd. 3 yds. 2 ft. 1 in. to lines.
2. In £lj 193. ll$d., bow manj dollars and cents?
3. In 33395236 cub. in., how many tons of bewn
timber ?
4. In 100800 cub. feet, how many cords of wood?
5. In X50, how many three-pences ?
6. Reduce JCISO, 10s. to four-pcnces.
7. In 20 half-guineas, how many 7 shilling pieces ?
8. Reduce Jt'l, 19s. lOJd. to cents.
9. How many cents will 27 lbs. 8 oz. of metal make?
10. In 70 E. ells, how many yards ?
11. In 7 Fr. ells 1 qr., how many yards? •
12. How many Fl. ells in 170 yds. 2 qrs. ?
13. How many quart ^bottles may be filled from 4
hogsheads of wine? : -y* :/ v -^^v %ii \W>i« : -
14. How many powders of 3 grains each may be
made from 1 i pounds of quinine ?
15. In 16810 bushels of wheat, how many pounds?
L In 5832372 lines, how many miles? >-■•:,
2. Reduce $31.90fjj to pounds, &c.
3. Reduce 586 tons hewn timber, 25 ft. 1636 in. to
4. Reduce 787 cords 64 cyb. ft. to cub. ft. [cab. in
5. In 4000 three-pences, how many pounds ?
6. In 903 four-pences, how many pounds ?
7. How many half-guineas in 30 seven-shilling pieces
8. Reduce $7.97^ to the old Canadian currency.
9. What is the weight of $27.50 in cents?
10. In 87 yds; 2 qrs., how many E. ells ?
11. In 10 yds. 3 qrs., how many Fr. ells ?
12. How many yards in 227 Fl. ells 1 qr. ? ' *'- ■ '
13. 1008 quarts = hovf many hogsheads? ^ * *
14. 2880 powders of 3 grs. each = how many pounds ?
15. 1008600 pounds == how many bushels of wheat?
^^
. « ■(
..M*!mi«;gMM
ir-^
108
COMPOUND ADDITION.
Hi!
£
s.
d.
7
17
9
14
6i
8
8
9J
3
4
45
n
7
3i
£36 12 Oi sum.
71> Compound Addition is the addition of numbers
of more than one denomination.
' Example. — Findtheamount of £7, l7s., £9, 14s. 6Jd.,
£8, 8s. 93d., £3, 4s. 4|d., and £7, 7s. 3id. ' • -
Having written the addends with
units of the same denomination
under each other, we commence to
add at the lowest denomination. —
1 — 4 — 7 — 9 farthings =, divided
by 4 the number of farthings in 1
penny, to 2 pence, and 1 farthing,
£36 12 Oi proof, or 2id. ; set down the id., and
carry the 2 pence to the pence
column. 2 — 5 — 9 — 18 — 24 pence =, divided by ] 2, the
number of pence in one shilling, to 2 shillings; set
down 0, there being nothing over, and carry 2 shillings.
2—9—13—21—25—32—42—52 shillings, = £2, 12s.;
set down 12s., and carry the £2 to the column of
pounds, which add as in simple numbers.
Compound addition differs from simple addition in
the orders not increasing and diminishing in a uniform
tenfold ratio. The sam*? principle applies to all opera-
tions on compound numbers.*
Rule. — Write the addends so that units of the same
denomination may stand in the same vertical column.
Add first the lowest denomination, reduce the sum to
the next higher denomination, set down the remainder
if any under the column added, and carry the units of
the next order to their proper column. Proceed thus
through all the denominations to the last, which add as
in simple numbers.
Proof. — As in simple numbers, -.- , ,
\'
COMPOUND ADDITION.
109
1 of numbers
1. Peter paid 3 shillings for a fifth book, 2s. 6d. for
a grammar, and 6 pence for a slate ; what did the whole
C08t?
2. 13s. 6d. + Is. 3d. -f 9d. = how much?
3. What is the amount of 1 yd. 4* 3 yds. 2 ft.
-f-4yds. 2 ft. 1 in.?
I of the same
ical column.
! the sum to
le remainder
the units of
Proceed thus
which add as
(0
(2)
(3)
£ s. d.
£ s. d.
£ s. d.
18 17 6^
n
58 11
18 19 11
15 03
6 10 m
19 12 lOi
1 10 Hi
46 15 lOi
13 14 U
16 16 6i .
68 19 HI
19 15 3i
85 14 10|
93 8 7i
17 19 Al
60 17 9i
56 16 111
(4).
(5)
(6)
£ s. d.
£ s. d.
£ s. d.
9 7 6i
98 17 72
254 14 Hi
*10 19 lOi
87 16 lOJ
715 18 lOi
11 18 9^
76 19 Ul
916 15 5|
12 17 lU
65 16 9J
175 10 7i
13 16 8^
48 18 10^
89 13 4i
14 15 lOi
73 13 7i
(8)
7 19 7i
•
(7)
(9)
£ s. d.
£ 8. d.
£ 8. d.
328 14 7i
476 16 6i
816 17 8J
800 17 5i
567 18 8i
389 10|
407 12 8i
678 19 111
31 17 11
670 18 lOi
789 17 lOi
346 18 6i
598 10^
890 15 4i
407 13 8|
742 8 Hi
910 13 31
748 11 11
967 17 Ul
678 8 111
567 14 4|
864 18 lU
497 7 5^
687 15 lOi
r^T"
lid
COMPOUND ADDITION.
1 . What is a simple number ?- — a compound number ?
2. What is compound addition ?
3. How does compound differ from simple addition ? |
4. Hoiv do you add compound numbers ?
5. How much is 7 tons -f 3 tons 16 cwt. + 15 cwt.?|
(10)
(11)
(12)
t.
cwt. lb.
oz.
pks. gal. qt.
yd. ft. in.
13
13 80
4
3 13
17 2 11
90
17 45
3
'6 1 2
20 2 10
16
14 19
14
3 3
8 1 8
16
17 10
10-
v\ 2 1
2 7
39
9 90
12
/ 19 1 2
13. A man sold on Monday, 456 yds. 3 qr. 2 na. ; on I
Tuesday, 386 yds. 3 qr. 3 na. ; Wednesday, 648
i yds. 2 qr. 2 na. ; Thursday, 139 yds. 3 qr. 1 na. ;1
' ' I Friday, 758 yds. and Saturday, 827 yds. ?J qr ;
how much did he sell in the week ?
14. A farm consisted of lire fields ; the first measured I
, 24 a. 3 r. 37 per.; the 2nd, 18 a. 2 r. 19 per.lO yds.;
. the 3rd, 27 a. 1 r. 12 per. 9 y|^s. ; the 4th, 15 a.l
3 r. 32 per.; the 5th, 21 a. 2 r. 25 per. 20 yds.;
how many acres were in the field ?
15. Add together, 1 c. 7 c. ft. 12 cub. ft., 14 c. 2 c. ft.
; 13 cub. ft., 75 c. 7 c. ft. 9 cub. ft. 90 c. 10 cub.
' ft. and 78 c. 6 c. ft. 11 cub. ft.
16. What is the amount of 40 wks. 3 d. 1 h. 5 m. + 16
wks. 6 d. 4 m. + 27 wks. 5 d. 2 h. ? =<;
17. What is the amount of 2 a. 75 p. 248 sq. ft. 72 sq.
» in. 4- 3 a. 120 sq. ft. 3 r. ; 177 sq. ft. 85 sq. in.
' + 15 a. 17 per. 84 sq. ft. 80 sq. in. ?
COMPOUND SUBTRACTION.
Ill
pound nnmber?
72. Example. — Ellen purchased a hat at 189. She
gave a £5 note in payment ; what change must she
receive ?
Solution. — She will have the diflference between £5
and 188. ; from £5 borrow £1 = 20s. ; ISa. from 208.
leave 2s. She will receive £4, 2s. in change. •
2. 3 yds. 2 qrs. — li yds = what?
3. From £10 18s. 2Jd. take 18s. 3id.
Operation. — Jd. — \d. (2 far. — 1 far.) = id. ; we
£ s.
10 IH
18
d.
2i
H
9 19 Hi Ana.
10 18 2i Proof.
cannot take 3d. from 2d., borrow from
18s., Is. = I2d.; 12d. + 2d. — 3d.
= lid. ; 18s. + Is. (the one bor-
rowed) from 18s. we cannot ; borrow
from £10, £1, = 20s., 20s. + 18s.
— 19s. = 19s. ; £10 — £1 =: £9.
RuLK.— "Write the subtrahend under the minuend with
units of the same denominations under each other. Subtract
each denomination of the subtrahend from the one above
it, commencing at tho lowfist denomination. If any deno-
niintition of he subtrahend be greater than the correspond-
iug nuinbpr of tho minuend, borrow 1 unit of the next higher
denomination, reduce it to the lower denomination, add it to
that, and subtract as before ; call the number from which j'ou
borrowed less 1, or the one borrowed may bo included in the
next figure of the subtrahend and thus subtracted from the
upper.
rnoOF.— As in simple numbers.
(1)
■ 'u': .
^. m^ Y'--
. . r (3)
■ -1
£ s.
d.
£ s. d.
£ 8.
d.
10 12
6i
900 1 lOJ
.. > i
3
19
4i
98 12 95
03
(4)
' V ' -^^
'•'" (5) "
£ s.
d.
£ 8. d.
£ 8.
d.
296 3
8i
314 10 4^
715 14
172 12
n
275 14 5J
620 15
6J
r--
■ i
112
COMPOUND SUBTRACTION.
1. £1 — id. =:howmuch? ' ■ '
2. Bought a hat at 10s., gloves at 5s. 6(1., paid a
pound note ; how much change is due?
3. How do you subtract compound numbers?
0) ■• (8) ' (9)
cwt. qr. lb. m. fur. rd. yd. y. d.
17
8
3
3
20
24
7
7
2
38
3
4
17
24
29
h.
12
19
10. From 29 lbs. 10 oz. 2 drs. 1 scr., take 9 lbs. 10 oz. 7 drs.
11. From 16 yds. 2 ft. 10 in., take 6 yds. 2 ft. 11 in.
12. 1 acre — 1 perch = how much?
13. From 18 c. yds. 20 c. ft. 183 c. in., take 1000 c. in.
14. From 19J yards of cloth, cut a coat pattern of 2
yds. 2 qrs. 2 na. ; how much is left?
15. The circumference of the globe — 45° = how much ?
16. A man sold 50 gallons from a tun of wine ; how
! • much was left? ■; ' ■ ' > '
17. A young man had in the saving's bank £750, lOs. He
drew at diflferent times the sums of £8, 18s. 8Jd.,
• ;. £19 13s. 2Jd., and £27, 6s. 35d. ; how much had
he remaining ?
18. Lent 1000 guineas, and received back £680, 153.;
how much is still due ?
19. 1000 yds. — [250 yds. 3 qrs. -f- 78 yds. + 100 yds.
1 qr. — 950 yds. 3 qrs.] = how much?
Note.— The numbers within the brackets must be considered
as but one quantity.
20. How much does 3 pks. 1 gal. 3 qts. larck of 1 bushel?
What sum subtracted from 1 sovereign, will leave
3 crowns, 3 shillings and 3 pence ?
From 25 cords of wood was sold 13 c. 4 c. ft., and
9 c. 6 c. ft. ; what quantity of wood is left ?
21.
22.
COMPOUND MULlPIPLlfeATION. 113
3s. = 27s. which added to 23. 3d.
. )
73. Example. — What is the cost of 9 books at 3s. 3d.
each?
Solution. — 9 books at 3s. 3d. a piece will cost 9 times
8. d. 3s.3d. ; 3d. X 9 = 27d. = 28.3d.9time8
3 3
XT-^I Ans. = 29«- 3d. = i^l, 93. 3d.
2. What cost 15 sheep at ill, 6s. each?
3. What is the weight of 3 pigs, each weighing 1
cwt. 50 lbs ?
4. What is the value of 12 articles at Id. each ? — -
at 2d. ? at 9d. ? at 7d. ?
5. What is the price of 24 articles at 4d. each ?
Solution.— 12 articles at Id. = 12d. = Is. ; 12
articles at 4d. = 4s. ; 24 will cost 2 times 4s. = 8s.
6. At 5d. a yard what would be the cost of 36 yards ?
of 48 yards ? of 60 yards ? of 1 20 yards ?
of 1200 yards ?
Rule.— Multiply all the denominations of the multiplicand
separately, commencing at the lowest by the multiplier; reduce
oach product to the next higher denomination, and carry as in
addition.
When the multiplier exceeds 12, and is a composite number,
multiply by the factors of the multiplier.
Find the value of,
£14 63.
£ 9 8s.
£74 18s.
£18
1
2
3
4
5. £17
6. £ 4
7. £
8. £70
9. £19 13s.
10. £12 138.
11. £35 Os.
12. £23 15s.
7Jd. X 7.
4id. X 8.
lUd. X 9.
Os. Hid. X 10.
8s. 0|d. X 5.
7id. X 6.
4id. X 12.
Os. Hid. X 11.
7td. X 4.
OJd. X 21.
6s.
9s.
7id. X 22.
0,|d. X 24.
13. £13 17s. Ija. X 35.
14. £ 9 8s. lOJd. X 27.
15. £13 lis. Bid. X 42.
16. £ 17s. Hid. X 56.
17. £ 1 15s. 5id. X 77.
18. £ 4 58. 3id. X 840.
19. £ 8 7s. 7id. X 1080
20. 7 cwt. 2 qrs. 18 -bs. X 9.
21. 151bs. 13oz.8drs. X H.
22. 271 gal. 3 pt. X 22.
23. 8 a. 2 r. 14 sq. per. X 8.
24. 5d. 17 h. 37 nd. X 121.
H
:!!|
114
COMPOUND MITLTIPLICATION.
1. What cost 20 yards at Is. a yard?— at 38. ?
at 9b.? at 198.? What cost 40 yards at lOs.?
at 10b. ?
25. Find the value of 144 dozen eggs at T^d. per dozen.
26. " " 99 tin pans at Is. 2Sd. each.
74. When the multiplier exceeds 12 and is not a
composite number,
Rule. — Resolve the multiplier into any convenient
parts, as units, tens, &c., multiply by these several
parts, and add together the products.
1. What cost 663 yards at 15s. 7d. per yard? , -
Operation.— 663 = 500+604-3 = 10x10x5+10X6+3.
£0 15 7X3,
10 '. ; f'
7 15 10 X 6
10
77 18
RuLB 2. — Multiply by
the nearest composite
number, and add to, or '|
subtract from the pro-
duct, so many times the
multiplicand as the as^
389 11 8 price of 500 yds. sumed composite number
is less or greater than
the given multiplier.
4
5
46 15
2 6
9
60 "
3 <«
438 13
5
563 "
- i'l'A-'^
.■■-tiSv
' ■-■'
Find th
2. £16
3. £ 6
18s.
lis.
4Jd.
3 d.
X 52.
X 66.
4. £ 10s. lljd. X 360.
5. £ 7 188. Oid. X 59.
6. £37 128. 3^d. X 79.
7. £27 143. 5id. X 103.
8. £ 7 138. 7Jd. X 348.
9. £1 5s. OJd. X 7081.
10. £6 78. 8id. X 9008.
11. 850cwt. lelbs. X999.»
12. 60 rds. 4 ft. X 354.
13. 5 dwt. 9 grs. X 436.
14. 6d. 17 h. 44 m. X 137.
15. $178.90 X 100000.
* Multiply by 1000 aud subtract once the multiplicand.
COMPOUND DIVISION.
115
nd is not a
convenient
hese several
76. ExAMFLB. — If 3 books cost 2 shillings, what ia
tbe price of 1 book ?
Solution. — If 3 books cost 2s., I book will cost ) of
2s., 2s. = 24a. ; J of 24a. = sa. Therefore 1 book will
cost 8d.
2. What cost 1 pair of scissors at £l 4s. per do?.. ?
3. If 4 acres of lana cost £75 7s., what is the price
1)6 1* acre ?
Solution. — 1 acre would cost i of £75 78. i of X75
£ s. d. = £18 and £3 = 60a. remaining ;
4)75 7 60 4- 7s. = 67s.; i of 67s. = 16s.
and 38. = 36d. over ; i of 36d. = 9d.
1 acre would cost £18 16s. 9d.
Ans. 18 16 9
Rule. — Divide the highest denomination as in simple
numbers, reduce the remainder to the next lower deno-
mination, adding in the given number of that deno-
mination if any ; divide again and proceed in the same
manner to the lowest denomination. The quotient is of
the same denomination as the dividend.
When the divisor is a composite number, divide suc-
cessively by its factors.
Proof. — As in simple numbers.
Find the value of.
1. £100
2. £ 75
68.
6s.
3. £674 lOs.
4.
£180
9s.
5.
£ 87
Os.
6.
£ 25
19s.
7.
£ 5
12s.
8.
£770
10s.
9.
£ 78
143.
10.
£265
14s.
4id.-^7
10d-r8.
7id.-J-9.
9id.-f-10.
35d.^5.
9d.4-6.
3d. — 12.
Ojd.-T-U.
7d. -7- 4.
3^d.-^21
11. £770 13s.
12. £570 Is.
13. £484 19s.
14. £255
15. £570
16. £ 50
17. £136
18. £3581
3Jd.-J-22.
6d.-r24.
4jd.-J-35.
2id.-r27.
3d.-f42.
6s. lOd. -^56.
88. 8id.-^77.
2s. 6d. -J-840.
Os.
Is.
19. £9050 128. 6d.-^1080.
20. 69 cwt. 12 lbs. -T- 9.
Ah
■ ■■ f
J
'its-i; '
m
g '( ^
116
COMPOtND DIVWIO!^.
1. Paid X7, 108. for 15 books; what cost I book?
2. What cost 1 article at Is. a dozou?— — at 3s.?
21. l741bs.4oz.4dr8.-hll. I U3. 68 a. 2 r. 32 p. -{-8.
22. 5970 gal. 1 qt -h 22. | 24. CDSd. 19h. 37in. — 121
25. What cost 1 doz. eggs at jC4, 79. for 144 doz. ?
2G. 99 tin pans cost £6, Is. 8Jd. ; what is the price of
1 pan ?
76. When the divisor exceeds 12, and is not a com-
posite number: ,^ ^
Rule. — Divide by long division as follow^* :
1. Divide £4561, 15s. 9id. by 87.
£ s. d. £ 8. d.
87)4561 15 9(62 8 8 quotient.
436
211
174
37
20
8 X 11 — 1 =87
419 9 IX 11
4G14 2 8 + 21d. rem.
— 52 8 8
4561 15 9 proof.
755
696
69
12
717
69 '»
21
We divide the pounds by 87, and obtain
£52, and £37 remaining, which we reduce
to shillings, adding in the 15s., and again
divide by 87; we reduce the remainder
to the nex' lov.or denomination, and
divide ageii., anr' ; roceed ' - the same
way to the end.
2. £879 15 6-^52.
3. £426 11 3-T-65.
4. £197 6 -r 360.
5. £ 466 3 25 H- 59.
6. £2971 12 8i h- 79.
7. £2855 7 OJ -H 103.
iDMPOUND DIVISION.
117
1. How do vou divMe a compound number by an
abstract number? '^f what nfime is the quotient?
2. If 1 doz. <(('»8 cost 1" , what is that per ogg ?
Solution. — If 1 doz. cost Is. 1 egg = Va of la. = Id.
3. What is the price of a broom at 63. a dozen?
4. If 5 doz. oranges cost 15s., what is that per orange ?
lot a corn-
Find the value of,
8. £2673 Is. 6d. -f- 348.
9. X'8866 08. id. -f- 7081.
10. £5710 9s. -7-908,
11. £849309cwt. 84lb.-i-999
12. 2l325rd. lITft. 6iii.-7-354
13. ll7oz.3d\vt. 12gr.-7-436
14. 786 d. 5h. 28 m. -J- 137.
15. $17890000 -r- 100000.
77. To divide by a compound number.
RuLB. — Reduce both divisor and dividt nd to the
lowest denomination contained in either an 1 divide as
in simple numbers. The quotient will be a 1 abstract
number.
1. How many books at 3id. can be bought for Is. Id. ?
Solution. — As many books as 3id. is contain' d times
3id.)ls. Id. (4 books.
4 ^12 ^
13
12
4
62
in Is. Id.; Is. = 12d., 4- Id-
= 13d. ; 13d. X 4 = V2 far-
things. 3ld. = 13 farthings.
52 farthings -— IJ farthings
= 4 books. Ans.
1. How many times can 1 far. be taken from £1 ?
2. Divide £18 15s. by 8g. 4d,
f WMi ' J~ m:7M n »utmmi. -m!m^'-
118
!!( i
COMPOUND DIVISION.
1. Divide £16, IDs. 3Jd. by Is. G^d.
2. £87, 6s. 8d. = how many times £1, Ys. 3Jd. ?
3. How often will a cart wheel, 10 ft. 6 in. in circum-
ference, turn in 1 mile?
4. A lot of land containing 8 acres is 80 rods long ;
what is its width ?
5. How many parcels of 3^ lbs. can be made of 2 cwt. ?
6. 37i yards of cloth will make how many coats,
each requiring 4 yds. 2 qrs. 3 na. ?
REVIEW OP COMPOUND NUMBERS.
1. What is the difference between simple and com-
pound numbers ? 62. 63.
2. How do the denominations of compound numbers
differ from the orders of simple numbers? 71.
3. What is reduction descending, and how is it per-
formed? 65. 67.
4. What is reduction ascending, and how perform-
ed? 66. 68.
5. How do you add compound numbers, and of what
denomination is the sum? 71. .
6. How do you subtract compound numbers ? 72.
7. How do you multiply compound numbers ? 73.
8. How do you multiply by a composite number ? 73.
9. How do you multiply by a number exceeding 12,
that is not composite? 74.
10. How do you divide a denominate number by an
abstract number ? Of what denomination is the quo-
tient? 75.
11. How do you divide by a composite number?
by a number exceeding 12 that is not composite? 75.
12. How do you divide a denominate number by a de-
nominate number ? Of what name is the quotient ? 76.
ANALYSIS IN COMPOUND NtJMBEAS. 119
1. If 5 yards of cloth cost XI, 10s.; what will 15
yards cost?
Solution. — If 5 yds. cost £1, 10s., 1 yd. will cost ^ of
£1, 10s.
£1, 10s. = -, and 15 yds. will cost 15 times as
5 3 . . , ,...,,.
much = £1, lOs. X 1S{
— £4, lOs. \
5 ••■'.-:■./■■."; ■■• .',":'' ' .
2. If 9 yds. of cloth cost £2, 28., what will 6 yds. cost?
3. If 2s. 6d. will pay for 3 yards of cotton, how much
can be bought for 10s. ?
Solution. — If Is. 8d. = 20d. pay for 3 yds., Id. will
pay for -sq- of 3 yds. = ip^ yds., and 10s. = 120d., will
6
- -- - ■'■f -■ ■ 3yds. X 1^^ '■• ' "■■■■' ^■
pay for 120 titaes /„ = =18 yds. Ans.
4. How much tea may be bought for £1 4s., when 2
pounds cost 6 shillings ?
78. When a term of both dividend and divisor is of different
denominations, they must be reduced to the lovrest denomina-
tion contained in either. (In comparing the terms to make the
statement, the inferior denominations may be disregarded.)
1. If 6 yards of cloth cost £4, 10s., what will 30 yards
cost? .- .
2. If 30 yards cost £22, 10s., what will 6 yards cost?
3. If I pay £4, 10s. for 6 yards of cloth, how many
yards can I buy for £22, 10s.
4. If 30 yds. cost £22, lOs., how many yards will*I get
for £4, 10s.?
5. If 148 acres of land cost £119, 10s., what will 111
acres cost?
0. If 36 tons of logwood cost £310, Is. 3d., what will
4 tons cost?
p
I
m
SE
120 ANALYSIS IN COMPOUND NUMBERS.
1. If 2 oz. of tea cost Is., what will 1 lb. 2 oz. cost?
2. What is the cost 5 lbs. of beef, at XI 10s. per. cwt. ?
I. If £89, 12s. 6d. be paid for 111 acres of land, how
many acres can be bought for £119, 10s ?
8. What is the cost of 3 cwt. 25 lbs. of sugar at $6,50
per cwt. ?
9. If 36 a. 3 r. of land are rented for $168, what should
be the rent of 21 a. 3 r. 20 per. ?
10. How mucb cloth can be bought for £2 8s. at the
rate of 50 cts. for li yds. ?
II. If 7i lbs. of sugar cost 6s. IJd., what will I3 cwt.
• cost? .X ... ,-J ^ V.:.,'-,;',, ._ At
12. If 4 casks of vinegar contain 63 gal. 8 qrt., what
will be the contents of 37 casks ?
13. What is a man's wages for 146 days at the rate of
£37 4s. Id. per annum ?
14. Paid £9 for 6 cwt. 96 lbs. of flour, what quantity
can be bought for £5 18 ?
15. How many yards of cloth at 15s. are equivalent in
value to 24 reams of paper at I7s. 6d. per ream?
16. If 3 quarters of a yard of cloth ^ost 1 guinea, what
will three pieces each 25i yds. cost?
17. If a man feed to his stock in 7 months 41 bu. 3 pk.
4 qt. 1 pt. of grain, how much is required ibr 7
years? -
18. How much cheese at £4 13s. 4d. per cwt. can be
bought for £25 ?
19. How many yards of carpeting 1 yard. wide will
cover a floor 25 ft. long 21 ft. wide ?
20. There is a certain pile of wood 120 ft. long, 6 ft.
high, and 4 feet wide, what is its value at $2.50
ler cord?
MISCELLANEOUS EXERCISES.
121
1. Divide 6 pence between Hal and Hattie, and give
Hal 1 farthing more than Hattie.
2. What number is that from which if STS bo taken
the remainder will be 187?
3. Printing was invented in 1440; how long is it
since?
I. The sum of two numbers is 1876, their difference
nothing ; what are the two numbers ?
72 X 96 X 70 70 X 90
2. Find the value of ' -f •
48 X 21 X 9 100
3. Find the sum in dollars and cents of one crown, 1
pound, 1 guinea, 1 shilling, and 1 penny?
4. What is the value of 35 barrels of soap, each 254
pounds, at 4Jd. per pound ?
5. How many bushels of wheat at $1.50, must be given
for 15 yards of cloth worth 2s. 3d. per yard?
6. A jeweller sold jewels to the value of £1200, for
which he received in part 876 French pistoles, at
16s. 6d. each ; what sum remains unpaid?
7. If I buy books at 12^ cents, and sell them at 15 cents,
how much will I gain by the sale of 10000 ?
8. Bought 3 boxes of shoes each containing 52 pairs,
for £33, 3s., if the whole are sold at $1.25 per
pair, what is gained by the transaction ?
9. A. has 24 cows worth 108s. a head, and B. has 7
horses worth £23 each ; if they interchange their
droves, how much will make good the difference ?
10. A man's yearly income is £500, and his daily
expenses £1, 3s. 6jd. ; what does he save?
I I . A man earns £l, 13s. a week, and his daily expenses
aye 3s. 10|d., what does he lay up in a year?
122
MISCELLANEOUS EXERCISES.
1. At 4 cts. per pound, what will 100 barrels of pork
amount to? . .
2. How many yards of cloth at $2 must be given for
for 3 cwt. of cheese at 12i cts. per pound ?
3. How many barrels of flour at £1, lOs. will amount
to £30?
12. What is the value of 166^ gallons of vinegar at
3s. 9 iid. per gallon? ^
13. If 809i acres of land cost £1955, 13s. 9d., what
is the price per acre ?
14. How many yards of cloth at $3.50 can I have for
13 cwt. 56lbs. of wool worth 2s. 4d. per pound?
15. From 7 cheeses each weighing 1 cwt. 61 lbs., how
many allowances for seamen may be cut each
weighing 5 oz. Y drs. ?
16. What is the value of 179 bogheads of tobacco, each
weighing 13 cwt. at £2, 7s. Id. per cwt.?
17. Divide $100 between A. and B. giving A. 99 cents
more than B.
18. The less of two numbers is 460, their difference 365,
what is their sum and product ?
19. 1870744 is the product of two factors, 2468 is one
factor ; what is the other ?
20. If 283950000 be dividend, and 75000 the quotient,
what will be the divisor?
21. What number divided by 10 mills will give 1879?
22. Two persons take a train at Montreal at the same
time, and travel westward, one at the rate of 18
miles an hour, and the other at 25 miles ; hoV
far apart will they be at the end of 12 hours ?
23. What is the value of 3 tons, 7 cwt. 60 lbs. 8 oz.
Qf metal in cent pieces ?
MISCELLANEOUS EXERCISES.
123
vinegar at
1. What coat 12 articles at Id. each ? at 2d.?
6d.? Is. 3d.?
2. At 4 pence each, what is the cost of 24 articles?
of 36 articles ?
3. What is the cost of 5 Second readers at 5d. each,
4 Third readers at Is. 3d., and 6 Fourth readers at
is. 9d.? ' "
24. How many half pence in 6247 crowns ?
25. In 74962 E. ells, how many Fr. ells ?
26. Divide $1875 among three persons giving one exactly
$75.99 more than each of the others.
27. A and B bought a quantity of wine for $340, of
which A paid 3 times as much as B ; how much
did each pay ?
28. If 28 casks contain 227 gal. 4 pt., what will 7 of
them contain ?
29. What is the assessment on $87689.50 at 3 cents in
the dollar ?
30. If 1500 men have provisions for 15 days, how many
men would the same quantity serve 36 days ?
31. M. White bought of Murray & Co., Montreal : 15
tons of iron at £17, 5s. per ton, 70 hoes at 3s. 3d.,
115 rakes at lid., 40 pitchforks at 5s. 2d., 25
shovels at 6s, 3d., 88 spades at 4s. 6d., 50 ploughs
at £3, 10s., 15 horse rakes at £1, 15s., 5 threshing
mills at £40 ; what did the whole amount to?
32. A merchant had £19118 to begin trade with: for 5
years together he cleared £1086 a year ; the
next 4 years he made good £2715, 10s. 6d. a
year; but the following years he lost one year
with another £475, 4s. Gd. a year. Whet was
his fortune at the 12 years' end?
124
ANSWERS TO THE EXERCISES.
90. 73618.
91. 4650.
92. $1675.
105. 66439 trees.
114. 73618.
115. 4660.
116. 239.
139. 68.
140. 918 acres.
149. 1021.
150. $525.
151. $11064.
152. 47296.
153. 26199.
158. 135.
163. 431321.
ADDITION.
«
164. 336510.
165. 701360.
166. 459152.
167. 343.
168. $337.
177. 14700.
178. 4280.
179. 768790.
184. 2768.
185. 278538.
186. 258611.
187. 88521007.
188. $27067.
189. $2738.
190. $4200.
191. 1300 bu.
$612 cost.
192. 1916 lbs.
193. 3846453109.
194. 286615495.
195. 129533167.
196. 238810.
197. 411058.
198. 600 lbs.
199. $380.
201. 883994.
202. 2957.
203. 324628.
204. 1011098.
205. 296984.
206. 1718885520.
ADDITION OF THE DECIMAL CURRENCY.
81
1. $98.92
2. $4.91.
3. $2468.
4. $1729(
83. 2226
84. 151K
85. 1871
86. 9723
87. 1587
88. 1883
89. $896
90. 720
91. 120.
96. 873?
97. 473^
98. 587'
1. $805.92.
5. $34013.34.
8. $6250.
64. $32
65. 166
70. 27
71. $1
2. $5414.69.
6. $866.15.
9. $1386.96.
3. $3866.97.
7. 1325 bu.
iO. $17188855203
4. $3065.87.
$851.50.
*
72. 77
.
SUBTRACTION.
73. $9
74. 12
109. 1081.
136. $890.
147. 6999.
75. 54
110. 1499856.
137. 1943 lbs.
148. 12769.
76. 23
127. 158 sheep.
138. 32464.
149. 884374.
89. 7(
128. 69273.
139. 846889.
150. 879687.
■ 90. 2^
129. 369347231.
140. 9202293.
151. 671.
■ 96. 6
130. 14373.
141. 1548771.
152. $179.
■ 97. 1
131. 1244 yds.
142. 740.
153. 374y.tol866
I 98. 1
132. 60450060196
143. 1708.
155. 5320.
1
133. 397902.
144. $1673.
156. 140000000.
■ 2 9(
134. 999000000.
145. $1090.
157. 2780.
■ 3. 8'
135. 13328591.
146. $30 loss.
158. 1800000.
1 4. 2i
Ai^SWEftS TO THi! EXERCISES.
SUBTRACTION OF THE DECIMAL CURRENCY.
125
1 • «]piJoit7a.
2. $4.91.
3. $2468.88.
4. $17296.30.
83. 2226120.
84. 15116850.
85. 18712200.
86. 972360.
87. 158760.
88. 1883.
89. $896.
90. 720 yds.
91. 120.
96. 8738496.
97. 473760.
98. 5877.
5. $7310.34.
6. $284.95.
7. $20.«8.
MULTIPLICATION.
99.
100.
101.
102.
103.
104.
105.
111.
112.
113.
114.
8. $5935.50.
9. $29533,50.
10. $2.30. '
168.
115.
804804. '
$676.
117.
$939.
$1750.
118.
5475 cts.
$450.
119.
171000.
158742.
120.
748 days.
1120.
121.
$59000.
$387.
122.
4320U00 pins
38304.
123.
3650 days.
2242.
124.
16211612.
70116.
125.
17920s.
90985.
126.
$95 in debt.
Division proves Multiplication.
DIVISION.
64. $329.
65. 166^ acres.
70. 27 marbles.
71. $18|.
72. 774 bags.
73. $969966f.
74. 12525«|.
75. 54 sheep. ^
76. 23 coats, 2 yards rem.
89. 76093. . .
90. 244§ trees.
96. 61.537 + .
97. 121067+ .
98. 181601.
99. 7899643311.
100. 166311402.
101. 27 hats.
102. 362128+ .
103. 15 sheep.
114. $16iV
115. 0. 50, E. 25, K. 25.
116. 132 canisters.
117. 0.
118. 11751^ bags of each.
119. 1000.
120. 559248074824-,V
121. $12750.
2. 96.
3. 87.
4. 280.
GENERAL PRIXOIPLES.
5. 8. 8. 36 lbs.
6. 1584. 9. 16 Cts.
7. 7J.
^ !
M
l26
ANSWERS TO THE EXERCISES.
MISCBLLANEOCS EXERCISES IN PRECEDING RULEH.
1. 6250 lbs.
2. 90906.
3. $*27-05.
4. 1000 times.
5. 57755 sq. in.
6. £11000.
7. 9 yards.
8. 1541.
9. 850.
10. 40 qt.
11. 85 cts.
12. 62-/V tons.
14. 1273989.
16. 70 yards.
16. 81.
17. 89099. '
18. 13256.
19. 62634005490.
20. 378600.
21. $253.75.
,r^'
22. 12 cents per pair, $17.28 whole gain.
1. $
2. $ i
3. $ ^
4. $ (
6. $ I
6. $ '
7. $ l:
8. $ 7
9. $11
10. $ 7
BILLS.
1. $109.84J.
!■'■ t-! .■■■-
2.
$149.44.
ANALYSIS.
3.
$205.02i
4. 170.
27.
$1989.792.
46.
286/jr acres.
6. $20. '■
28.
$2244.225.
47.
222J§ bu.
6. $870.
29.
$625.
48.
144 yards.
7. $17,065.
30.
$13.20.
49.
$59.52.
8. $1092.
31.
$3.
50.
60 cows.
9. 25 days.
32.
65 hoes.
51.
100.
10. 625 bu.
33.
$51.
52.
$15,345.
14, 31 hogs.
34.
476 + gal.
53.
15 lbs.
15. 208 yards.
35.
7 days.
54.
4i^.f miles.
16. $163.40.
36.
9i days.
55.
$3496.
17. 75 pairs.
37.
7 days.
56.
$15.23^{.
18. 165| lbs.
38.
$1.98.
57.
219000 lbs.
19. $72.
39.
45 yards.
•58.
29105^ ft.
20. 240 lbs.
40.
13^.
59.
1 12 men.
21. $107.80.
41\
1500 men.
60.
$75.60.
22. 495 yards.
42.
990 reams.
61.
30i«.
23. $180.
43.
$1168.75.
62.
503 lbs.
24. $682.50
44.
$71,784
63.
328f acres.
25. $2.40.
45.
20 men.
64.
35 lbs. of each
LBH.
5.
4006490.
00.
L75.
5.02J
At^SWBES TO THE EXERCISES.
,.s OF THE DBCmXL CURUKNCY.
UBDUOTION OF X"''
rt _ A
127
1. $ 6.10.
2. % 68.35.
3 $ 40.20|.
4. % 63.15iV
5 <$ 94.27i.
6. $ n.52i.
7 $ 134.79-,V
8 $ 163.57.
9. $1183. 33i.
10. $ 720.12H-
£ 8.
d.
13. 10 ^ 3
9 11 10^
5. 11 15 9|,
7. 31 10 5?.
8. 94 U 1^^^
9. 112 10 n-
COMPOUND ADDITION.
2i| bu.
4 yards.
,9.52.
I cows.
10.
L5.345.
) lbs.
,% miles.
3496.
15.23^^
19000 lbs.
9105^ ft.
12 men.
575.60.
^^5 \-
'M lbs.
328f acres.
35 lbs. of each
X £ 108 193.
2. £ 165 15s.
o £ 331 3s.
4 X 73 16S.
5* £ 452 3s.
6 £2160 12S.
7* £5381 108.
p.; £5490 189.
9 £3996 103. 1U<1-
2jd.
lOd.
4|d.
9d.
9id.
lOid.
4id.
2d.
10. l77t.l2cwt.46lbs•ll<>^"
ll. 35 pk. 1 g^^- 3 ^^•
12. 48 yd. 1 tt.
13. 3218 yds. -gyds.
14 I08ac. 2r. bper. oj
6 ft. 108 in.
W 1 *. f t 7 cub. It.
15 261 c. 1 c. 1^ ' ^
16*. 85wk. 3h.9m.
17. 20a.97p.9yd.5ft 2lm.
COMPOUND SUBTKACTION
1 £ 18 139. 2id.
o 193. Hi^-
^' « -.* ^ nr 21 lb.
7. 8 cwt. 3qr.^^
14. 16 yd. 3 qr. 2 na.
15. 350 deg.
16. 202 gal.
17 £694 Us. U-^*^*
7-. 8 cwt. 3 qr. 21 It)- g £309 5s.
8 6m. 7ft. 3 r 4yd. 1ft. 61 L^ 82U yds
9- 16^^^^t^3dr iscr. 20. iqvjart.
10 19lbs.ll02-3<ir. i« 21. 19. 9d.
il 9yd.2ft.U^«- 22. lc.6c.ft.
12. 3 r. 39 per. ^^ i„.
128
ANSWEES to THE EXEROtSES.
1. 217.
2. 64.
COMPOUND DIVISION. 77-
3. 502^ times. I 5. 57{.
4. 16 rds. 6. 8.
ANALYSIS IN COMPOUND NUMBERS.
1. X22 lOs.
5. jeSD 12s. 6d.
6. £35 3s. Old. J.
7. 148 acres.
8. $2112.50.
9. $100.
10. 24 yards.
11. £6, 28 6d.
12. 58t) gal. 2 qt. IJ pt.
13. X14 178. 7id. J.
14. 4 cwt. 56 lbs. 4fV 07.'.
15. 28 yards. - -
16. £107 28.
17. 502 ba. 2 pk. 6 q.
18. 5 cwt. 35 lbs. 11^ oz.
19. 58J yards.
20. 25. J •' "^
: .^ • «::,.',< •,^-
MISCELLA^^EOUS EXERCISES.
1. 938 each. .
18. 1285 sura, 379500 prod.
2. ii6i. i :
19. 758.
3. $9.4U.
20. 3786,
4. £166 133. 9d.
21. $18.79.
5. 4J bu.
22. 84.
6. £477 6s.
23. $6760.50.
7. $250. . .^. . .
24. 749640 half pence. *
8. $62.40. '
25. 62468 Fr. E.
9. £4 128. ". :.
26. $675.66 to one and
10. £70 78. 3jd.
$591.67 two, each.
11. £15 Os. 7i.d
27. A. $255, B. $85.
12. £31 9s. lO^d.-l-.
28. 56 gal 7 pt.
13. £ 2 88. 4d+.
29. $2630.685. \; ,'-
14. 180 yd. 3^ qr. , ^
36. 625 men. , [, [/■
15. 3316^^. *:^
31. £714 lis. lOd. ; ; ",
16. £5478 2s. lid: "
32. £33984. Zz. 6d. >. ' ' ■
17. A. $50,495, B. $49,505.
, , r • ' ^ '
4fS;0Z.
6 q.
11 if OZ.
9500 prod.
pence.
one and
I, each.
;#,^''^]
:u
^ %
'tl
••»;V»-
LOd. ■
, 6d.
. J ^
U -'JA?
-■^ JiL ^»i'