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32X
1 2 3
1
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PUB]
Anthorizt
c
THE
PUBLIC SCHOOL ARITHMETIC
AND
MENSURATION^.
Authorised for use in the Public Schools of Ontario hy the
Minister of hVucation.
NEW EDITION.
TORONTO :
CANADA PUBLISHING COMPANY,
(LIMITKD).
)0'0
PS
'^. I
\2nteied lucording to Act of Parliamejit of Canada, in the year 1!M)0. by the
Canada Pubmshino Company (Limited), In tlie Office of the Minister
of Agric'ulture.
PREFACE.
The main purposes which liavo been kept in view by the
authors of this Arithmetic are — (1) to aid a pupil in becoming
aeeiinite and rapid in calcukition; (2) to train him in
independent thinking and in applying his knowledge of
nximbor to the actual business transactions of life; (3) to aid
the teacher in assigning s.pplieations of the various principles
which have been explained. The classification of the problems
has been given with this last aiu) mainly in view.
Explanations of theory and all formal rule? have been
omitted, the authors believing that teachers can best supply
what is necessary in these respects, as the pupils are led to a
clear comprehension of the principles which should be explained
by the teacher before the pupils are required to examine the
problems. It may be here stated that the exercises and
problems are mainly intended to be used as applications of the
theory taught. While no direct explanation of theory has been
given, much lias been suggested by the character of the
problems and by their arrangement.
The definitions have been carefully prepared and stated in
such a way that it is believed the pupil will find little difficulty
in understanding them.
Numerous mechanical and practical exercises on the
fundamental rules for seat work form an important feature of
the book. In many eases the answers to the mechanical tests
have been omitted to enable the teacher to judge of the progress
of his pupils in accuracy and rapidity.
The exercises are a well graded and progressive series,
carefully arranged to develop the reasoning powers of the
pupil, and at the same time to familiarize him with the
important practical applications of the science of number.
The Metric System has been introduced to meet the growing
demands of the time.
CONTENTS.
Facie
I.— Dkf'Nitions, Notation, Numeratkin 7
II.— TnK Simple Kules—
I. AdtUtiou 11
II. Subtntetion 22
III. Multiplication 30
IV. Division 37
V. MiscellaneouH Exercises 43
III. — Compound Numbers 
Tables, Definitions, Etc 50
IV.— Simple Applications op i.ie Previous Rules—
I. Bills and Accounts GO
II. Simple Measurements (53
Carpeting 64
Plactering 06
Wall Paper 67
Board Measure 68
Rectangular Solids 69
III. Sharing 72
IV. Averages 75
V. — Factors, Cancellation, Measure^, and Multiples —
I. Factors 78
II. Cancellation 79
III. Measures... 80
IV. Multiples 82
VI. — Fractions —
I. Definitions, Notation and Numeration 84
II. Reduction of Fractions 85
III. Addition of Fractions 90
IV. Subtraction of Fractions 92
V. Multiplication and Division of Fractions 95
VI. Complex Fractions 101
VII. G. CM. and L. CM. of Fractions 102
VIIl. Denominate Fractious 103
IX. Applications of the Previous Kules 105
Vl C'ONTKNTS.
Vil. — DKf'IMAI.S—
I. DefiiiitioTis, Notation and Nuinovation 115
II. Addition of Dccinmls 117
III. Subtnu'tion of J)t'<'inialM 118
1\'. iMultipliciition of Dfciniuls 121
V. Division of Doeinials 122
VI. Reduction of IhMdniiils 124
VII, Applications of tlic I'lcvioiiH Rules 125
VIII.— Pkuckntaoe  121)
IX. — API'MCATIONS of PF,K('KNTA(iK—
I. Trade Discount 134
II. Profit and Loss Hid
III. Commission 1;{S
IV. Insurance 140
V. Taxes 142
VI. Simple Interest 144
VII. Compound Interest 14G
VIII. Bank Discount 147
IX. Stocks and Dividends 14J>
X. F^quation o£ Piiyincnts ir)2
X. — Pautnership ir)4
XI.— Invom'TIon and Ev<)r,i"ri(»x —
1. Involution loG
II. Square Root 1.'58
III. Cube Root ir.9
XII. — Mensuration IGl
XIII. — The Metric System of Weights and Measures.... 172
XIV. — Miscellaneous P^xercises —
I. Cireulatiuf? Decimals 177
II. Problems Relating to Work Done 180
III. Clock Problems 181
IV. Problems Involving Velocity 182
V. Problems Involving the Sum and Difference of
Two Numbers 183
VI. Review Exercises for Third Class 185
VII. Review Exercises for Fourth Class 187
VIII. Review Exercises for Fifth Class '. 190
XV.— Answers 198
ARITHMETIC.
CHAPTER I.
DEFIINITIOINS. INOTATIOIN. INUMERATIOIN.
A Unit is a single thing or a definite quantity; as
1 lK)f)lv, 1 foot, 1 score, 1 fouroiinee weight, i half
ounce weight.
A INumber is that which is applied to a unit
or to a group of units for the purpose of answering
the question ' ' How many ? " or " How much ? ' '
Arithmetic is the science whi<'h treats of numbers
and the art which uses them in computation.
Numbers are either Concrete or Abstract.
A Concrete INumber is one whi(*h names the kind
of unit used; as 4 tons, 6 horses, 3 dozen eggs, 5
half ounce weights.
An Abstract INumber is one in which the kind of
unit is not named, as 4, 6, 9, 17.
Notation is the expression of numbers by means of
symbols.
Arabic Mctation is the expression of num))ers by
means of figures.
Roman INotation is the expression of num])ers by
means of (certain letters called liomati Numerals.
Numeration is the reading or writing in words of
a number expressed in symbols.
8
1.
2.
3.
4.
6.
6.
7.
8.
9.
10.
(>
If)
i<;
94
2:{
(53
4'J
2H
79
AKITIIMKTIC.
EXERCISE 1.
rords tlic
followinR
: —
T)
9
7
21
12
31
(>!
71
81
9;i
30
47
H({
68
76
:i4
43
45
78
87
91
2;')
52
20
95
59
(59
48
84
04
8
4
i:i
17
18
92
74
49
07
.'{2
54
50
19
24
02
82
90
97
46
100
EXERCISE II.
Write In words the following;: —
1.
500
700
800
200
000
400
2.
830
470
(509
714
800
990
3.
007
700
070
7(50
901
109
4.
847
784
478
748
874
487
5.
205
400
507
705
570
750
6.
4705
5843
91(58
2049 4905
4231
7.
8007
8070
8700
7080 7008
9045
8.
50(58
9008
0202
1508 3746
5780
9.
21.34
1234
1243
4321 4132
8009
10.
9001
1009
9001
9100 9010
9080
EXERCISE III.
•
Write
in words tlie following: —
1.
40870
54089
30070
91111
2.
54089
40058
39007
40100
3.
81095
59100
95101
37098
4.
819075
891492
294710
410101
5.
210010
918005
231040
217000
6.
1470931
3790842
910010
2103001
7.
3091000
4007007
190100
3019047
8.
17091807
93704905
903705
21010101
9.
40097000
30910405
9317900
70000005
10.
2309400100
91491591(591
1013210012
7060700001
EXERCISE IV.
Write in figures: —
1. Fifteen; twentyone; tliirtyfour; seventyeight; eighty 
seven; nineteen; ninetyone.
DEFINITIONS, •.OTATION, NUMERATION.
2. One hundred; one hundred and seven; three hundred and
Hix*«'»'n; four hundred and forty; nine hundred and nine; nine
hundred and nineteen; nine hundred and ninetyone.
3. One thousand; one thousand, four liundred and two; eijcht
thousand and six; eijfht thousand and sixty; two thousand, four
hundred and ninetysix.
4. One thousand and eleven; ten thousand, six liundred and
four; twentynine thousand, four hundrtid and seventy; eighty
thousand, nine hundred and ninety.
rt. Eight hundred and four thousand and sixteen; two
hundred and ninetyone thousand, seven hundred and four.
6. One million, one hundred and one thousand and one; five
million, four thousand and thirty.
7. Nine hundred and fiftyfour million, eight hundred and
six.
8. Seven million, seven hundred and seven thousand, seven
hundred and seven.
0. One hundred and fortysix million, one hundred and
fortyseven thousand and fortyseven.
10. Five hundred and thirtysix million, three hundred and
forty seven thousand, nine hundred and seventy two.
11. Six billion, ninetyfive thousand, one hundred and
fortyeight; seven hundred billion and one.
12. Ninetynine billion, thirtyseven thousand and four.
13. Eight hundred and sixtyfour billion, five hundred and
thirtyeight million, two hundred and seventeen thousand, nine
hundred and fifty three.
14. Forty billion, four million, four hundred thousand, four
hundred and fourteen.
15. Fortynine trillion, fiftyeight thousand, seven hundred
and ninetyeight.
Write in Roman numerals
1.
5
2.
15
3.
25
4.
49
5.
109
6.
240
7.
404
8.
796
0.
875
10.
973
11.
1900
EXERCISE
V.
erals :
6
8
16
18
26
28
45
94
104
105
249
394
444
499
789
777
857
578
9(55
999
1889
1899
9
19
24
98
219
388
589
766
894
987
1849
4
•14
44
99
329
356
594
699
984
944
1904
10
ARITHMETIC.
i£XERCISE VI.
Write in figures: —
1. XV, XC, XCIV, LXIX, XLIV, XCIX, LXXXIX, CX.
2. CXI, CIX, CXLIV, CCXXIX, DIV, CCXLIX, DCCIX.
3. CDIV, DCCXXX, DXL, CDXLIV, DXXIX, DCXXIV.
4. DCCCXXXIII, CDLXXXIV, CCCXXXIII, CDXXXIV.
5. DV, CDXXX, CCXCVII, CCXLIV, CCCXXIII, DLV.
G. MCXI, MD, MXIV, CMXC, CMXCIX, AICCCLIV.
7. MCCXC, MDLV, MCDXLJV, MIX, MCCXXII, ^ICDXC.
8. MMCCXXII, CMXLVII, MCMVI, MCD, MCvIIX, MDLV.
y. MDCCXLIV, MCDXLIX, MDCLXVI, MMIX, MCXIX.
10. MDXCIX, MCM, MCMI, MDCCCXCIX.
EXERCISE VII.
1. Write in Arabic Nrnnerals the smallest number that can
be expressed by two figures ; by three ; by four.
2. Write in Roman Numeruls the largest number that can be
expressed by three figures.
15 . What is the effect of writing a letter of less value before
one oi a larger valuef Give four examples illustrating this,
4. To the left of only what letters can I be placed in Roman
Notation?
"). To the left of only what letters can X be placed in Roman
Notation i
6. Write the significant ngures and express each in Roman
Notation.
7. What letters in Roman Notation are never repeated?
8. Write in words the following sentences: — The earth is
92890000 miles distant from the sun. The lei.gth of the equator
is 'i:{827033 yards. The cheese factories of Ontario produced
13r'>b:?91G pounds of cheese in 1897. The milk used in making
*iiis cheese was 1455937148 pounds. In 1898 the 98 creameries
lii '.''i'" returns to the Bureau of Industries produced 9008992
pounds of butter, valued at 1632234 dollars.
9. What numbers can be expressed by means of the letters
V and X taken separately or in combination?
10, Express "n Arabic Numerals all the numbers of three
figures that can be expressed by means of the letters X and G
taken together or separately.
CHAPTER II.
THE SIMPLE RULES.
I. ADDITIOIN.
Addition is the process of linding a number equal
to two or more numbers of the same kind.
Tlie Addends are the numbers to be added together.
Tlie Sum is the single number which results from
the addition.
The sign of addition is +, called plus, and when
placed between two numbers it shows that these are
to be added.
1.
2.
8.
4.
EXERCISE VIII.
14
41
52
42
33
21
23
12
12
21
32
13
25
15
123
421
241
222
234
321
110
345
333
311
231
242
102
123
132
313
123
410
321
321
134;)
2111
1012
1000
4443
2231
4001
3421
1234
2224
2423
2403
1323
2423
1201
3000
3121
4231
5231
5341
2100
5123
4112
7111
7231
4132
5234
4211
5000
3412
G210
7110
5341
3123
4123
3111
4231
0204
4351
5201
11
12
5.
AUITHMETIC.
71112
52123
71241
71122
82013
41231
41024
32026
20311
41012
51640
62301
41010
42133
50601
41013
70021
52401
54332
41203
6. 2031+1234+3122f 1010+100.
7. 1207+3040+2430+112+2000.
8. 51+3027+2000+1500+1320.
9. 21021+12+32+2700+12000+102+21.
iO. 12201+21+142+23000+2100+2012.
EXERCISE IX.
1. John has 10 cents; Bob has 25 cents; Harry has 14 cents.
How many cents have thev together?
2. A cow cost $21, a pig $14, and a sheep $12. How much
did all cost?
3. A farmer drew five loads of wheat to market. He had 41
bushels in the Ist load, 42 in the 2nd, 40 in the 3rd, 42 in the
4th, and 44 in the 5th. How many bushels were in the five
loads?
4. I walked 21 miles on Monday, 22 on Tuesday, 21 on
Wednesday, and 23 on Thursday. How far did I walk in the
4 days?
5. A train goes 31 miles the Ist hour, 30 the 2nd, 32 the 3rd,
and 31 the 4th. How far has it gone in the 4 hours?
6. The population of four cities is as follows: the first
111203, the second 21.n23, the third 11221, and the fourth.
611222. What is the total population of these four cities?
7. A merchant bou.crht four pieces of cloth. The first was
203 yards long, the eeeoud 321, the third 223, and the fourth
222. How many yards were in the four pieces?
8. An ocean steamship sailed 312 miles on Tuesday, 324
miles on Wednesday, 320 miles on Thursday, and 411 miles or
Friday? How far did it sail on these 4 days?
9. A steamship leaving Montreal for Liverpool had on board
415 cattle, 240 sheep, and 131 horseB. How many head of live
stock were on board?
10. A history consists of 4 volumes. In the first there are
412 pages, in the second 410, in the third 415, and in the fourth,
431. How many pages are there in the entire history?
d on board
ead of live
ADDITION
>
13
EXERCISE
X.
1. 323
233
123
312
311
2323
232
222
132
123
233
3211
333
333
213
323
322
2332
233
310
231
333
113
3123
312
232
2133
321
2323
223
3213
333
23132
2323
2. 3233
32133
3233
3032
3223
2133
21332
32332
2332
3321
3332
3321
33213
32223
3123
3333
2332
2332
23323
23322
3321
2332
21321
3212
32212
3323
23213
32133
12233
3. 31333
23213
32132
23213
21332
31232
23223
32123
22321
31220
32132
21332
32213
32233
31223
33303
32013
21321
33223
32213
20301
10332
32103
33233
13322
32132
21303
12321
23321
13321
32332
21331
33233
4. 34124
41234
24134
41234
41341
21314
31413
32134
24413
44341
24143
44143
24130
24341
34123
24132
34124
21321
24133
43214
41244
41421
34143
40143
40241
43441
32412
34134
21414
21434
30213
14234
22141
21414
34140
24143
T). 13412
41324
41321
51321
32132
51324
4G712
62132
35326
41324
46213
42676
3r)273
41653
45624
41324
24132
25014
24134
25623
52334
50604
3(5213
30629
4r)0o2
32134
41302
60621
41621
46532
3r)213
43253
10343
40132
41321
42624
0. 41324
41324
41321
32562
41324
41321
34120
16213
62162
31416
30143
41032
604(52
40123
42342
20413
62143
40162
30(521
30(523
62103
401(52
40132
32162
41032
43216
66552
41324
40110
41314
41(521
2U32
45625
51602
62162
62132
14
ARITHMETIC.
7.
5232
4013
6217
3017
1472
1213
41321
00213
41002
41321
42321
41021
32134
22343
402()2
S21(i3
41323
41021
413212
413210
413210
4()r)271
017172
312711
3121
4137
5702
3502
5213
4134
37124
34135
25312
40352
70712
34372
8. 81876
41342
21341
41832
41372
41783
413^2
48324
62437
41072
47726
47807
34027
78772
24167
32171
68783
87710
18704
40724
82416
42313
27107
37872
31241
37802
37137
57717
27178
47132
01375
41371
41683
87071
37183
41367
9. 41340
41837
41372
41672
41834
41837
21347
08773
46837
37183
67832
41678
70827
41701
46713
63784
41786
38678
48372
37450
48783
32487
67138
32168
48372
75071
67187
67137
41687
41767
41071
38710
38147
47183
48371
89168
0. 41071
13716
41371
41372
71324
41674
00872
41372
02710
48637
67168
34187
41876
67187
04701
24873
32417
62184
86716
47183
37124
21437
03418
67132
40713
80713
37072
67138
40728
48667
87241
40713
48372
63418
87832
47183
EXERCISE
XI.
1. 370693
732894
507]
126
770655
764845
777777
555123
432733
007755
999999
531234
456789
567643
554488
888888
135789
579040
219872
998877
777777
973124
843757
876464
776654
666606
70383
984329
597777
897987
245678
507890
432173
66466
764896
457896
2. 348037
460375
963]
[72
849652
962847
272405
841681
300725
361728
777888
530034
239724
403;:
48
412381
888999
109871
763256
721003
035403
789789
093036
437891
387356
872545
678678
704543
825432
241653
400223
897987
233038
285678
u03'J
80
294867
387047
428432
310720
5321
70
811230
480578
ADDITION.
15
37124
34135
25312
40352
70712
34372
3897(53
210045
76080(5
(53(5215
253734
251600
575453
807720
403521
687489
324061
530724
623452
487(538
290731
803256
278321
829248
171320
20(>782
461027
589203
248639
730461
576037
213744
764368
305216
436720
823284
217436
592301
364728
246374
478369
287456
93(5478
184369
678456
286397
4. 379623
891371
889977
789
8000000
7542
919198
732894
723
667755
25320
171296
555123
674
44332
57644
1478(57
456013
1674
3355778
908176
182371
579646
19006
986754
73409
929292
843751
1916
71347
3147
292929
984329
■ 986986
981675
67039
777777
432173
97979
19198
5. 3824442
67124332
25927871
3267362
7778889
4563358
31734324
71684655
2152837
4581986
1612119
19524324
69351437
4627792
3599872
5121223
53414325
35927212
3564465
2998767
8232535
57384327
21614892
2152322
9887651
6348442
42624329
74321572
4617777
8776548
3454384
75218671
69987452
3564416
7665434
2563125
83186438
25654232
2152362
6554326
4673995
41986974
71381011
4617727
5443213
6. 6739484
87665163
94358975
95639888
99888777
5263898
57946295
2848
86872569
22586972
9688626
43937568
9184
11191993
57486976
7445853
89264339
45339
32384345
21586972
6899438
2613
987672
95339888
93456975
8123814
9155
93783891
85372569
46556972
4598603
5278
26753984
14891173
25496977
2355792
87667549
66344839
36684845
47556979
1773424
49623
94982172
71739188
21457979
7. 4008811
31412
657118
294044
95299
1854239
30088
182595
199639
8720834
705
150
5520
17228
436292
14872
1500
525
17370
400283
6498119
5363277
497454
41762
2344900
1 055308
3187
57768
482511
12137980
371498
18015
23247
1027
11089359
4040559
4(5976
990019
1088534
3633750
12526543
1278225
2150113
9414575
295984
«^ia..
16
3
ARITIFMETIC.
8
1288153r)
624564
2610287
6214458
131917
2171188
209840
373898
1530581
3400/17
9947r)2:{,
213954
2297433
2142822
28()0765
683069
1957
109897
417
25396S
9243811
2434454
1364034
296259
71894
3086160
3975
477438
4494680
41729
8071370
7088142
585138
31211
535955
7065878
1011492
2043283
4925889
11212616
4346234
21191
559619
137990
4286131
7834359
203572
1627164
2981652
517562
9.
6967056
3196563
1108476
185658
57636799
9487210
365756
375396
1601190
63927094
79766094
49741413
10071301
13121498
19154873
4146290
95921
970738
2130102
25981652
34449379
20819542
10196".71
14487351
7165.3431
39878418
2505034
4481ii70
15367691
62327299
995670
316508
129692
49
29987988
2981850
4970
487233
1066277
7565487^^
8139585
177681
1364378
1619386
61321716
10.
8529883
27932143
93789391
22872769
75700757
3593652
53969235
26745984
75191997
36471241
9658934
49265558
66357839
96484343
75057906
6475424
87647389
94946172
81539885
44346505
3757873
87931693
93787391
12872568
91753002
3363662
53929135
26782644
.35791979
77647300
8829744
49298258
66359199
96284343
76044071
2293413
87651589
94945222
81339885
82872633
7958882
87973397
93787511
12672568
99872517
8175659
75982231
65781737
35891219
86297761
(
EXERCISE XII.

1.
Add togeth
er 763, 4663, 37, 49763,
6178, and 671.
Add together 15, 7896
, 1, 13, 106, 113, 156, 100,
and 2201.
3.
Add togeth
er 100375, 406780, 467300;
), 4112, 2478,
79, !Uid8.
4.
Add together 123405,
2354210, 79431
27, 36547, and 789.
5.
Add together 275L32, .
345007, 4567801, 365, 1896,
and 78G9.
6.
Add togeth
er 70, 189,
3684, 72, 8967, and 798.
7.
Add togeth
er 982, 369
, 764, 8, 89, 75, and 396.
8.
Add togeth
er 7, 89, 8,
7098, 38, 471
, 78, and 1899.
9.
Add together 968, 777
, 78, 408, 700,
9009, and 7
.
10.
Add together 7698, 4,
790, 87, 3694,
78, and 897
•
i.iion
'^H
3400717
28(507<)r)
•jriiujes
71894
41729
r):{r)9r>5
11212616
4286131
5l7r)62
57636799
a
63927094
19ir)4873
25981652
716."i3431
62327299
29987988
7565487'^
61321716
75700757
36471241
75057906
44346505
91753002
77647300
76044071
82872633
99872517
86297761
671.
)0, and 2201.
78, 79, and 8.
■;
and 789.
\
)6, and 7809.
i
1.
i
6.
1899.
li 7.
897.
■
^
ADDITION.
EXERCISE XII.I.
17
1. 7634129+ 7634f830604937+856312+37140+694713284
85'j4695.
2. 9093+846295+37G05f54+57312858+581401+393+4301201.
3. 51316281+7413819+543628+71434717562+8319886.
4. 79+;'*(53+900832+8632+473423+644+1000000.
5. 789632+71+879002+876+970+329449.
6. 92+853+7654+65432+543210+4321098+321976+2109+
1098+182.
7. 6290+704+713+4631+5214+289+3102+41.
8. 483+9000+648+3750+9840+24680+5096.
9. 103421538+120952657+116843889+116491051.
10. 82+92+102+873+824683+2000201+489076.
EXERCISE XIV.
1. B^ind the sum of 27, 36, 45, 52, 8V, 29, 16, and 11.
2. A farmer has five fields of grain. In the first there are
27 acres; in the second, 42 acres; in the third, 97 acres; in the
fourth, 86 acres; and in the fifth, 102 acres. How many acres
are there in the five fields?
3. James has 27 marbles; John has 83; Harry has 116; and
Tom 46. How many have they all?
4. James rode 17 mi]es on Monday, 23 miles on Tuesday,
41 miles on Wednesday, 36 miles on Thursday, 17 miles on
Friday, and 24 miles on Saturday. How far did he ride during
the 6 days?
5. A farm cost $4816, a house $2345, a horse and buggy $158,
and a cow $34. How much did all cost?
6. A drover had 327 sheep, 245 cows, 584 pigs, and 117
horses. How many animals had he in all?
7. In a~i orchard there are 417 apple trees, 176 peach trees,
245 plum trees, and 47 pear trees. How many trees are there
in the orchard ?
8. Add 294, 421, 76, 109, and 217 together, and express the
result in Roman numerals.
9. In 1897 the population of the County of Oxford was as
follows i Townships, 28780; Towns, 15801; Villages, 1810.
What was the total population of the county in 1897?
10. To the sum of 14, 17, 25, and 96, add the sum of 18, 12,
19, and 25.
18
ARITHMETIC.
EXERCISE XV.
1. Tom had 17 mnrbles; ho houj?ht 5 mor«*, and his brother
gave him IS. How many had he then f
2. A man paid $22 for a suit of clothes; *$2 for a hat; $6 for
a pair of boots; and $1") for underwear. What did he pay
for all?
3. John's book has 216 pages; Mary's, 492; and Harry's,
162. How many jtages are there in the three books?
4. A man travelled 247 miles on Monday, 36 miles on Tues
day, and 17 miles on Wednesday. How far did he go in the
three days?
5. Find the sum of 47 cents, 93 cents, 107 cents, 483 cents,
and 270 cents.
6. Add $128, $1275, $468, $17, and $12.
7. A man spent $127 one day, $47 another, and $96 another.
How much did he spend altogether?
8. Edwin had 35 cents: he found 16 cents, and his brother
gave him 47 cents. How much had he then?
9. A man wheeled 37 miles on Monday, 46 on Tuesday, 34
on Wednesday, 52 on Thursday, 28 on Friday, and 11 on
Saturday. Ho v far did he wheel altogether?
10. A man began business with $3795. His gain the first year
was $824; the second, $491; the third, $726; the fourth, $1211;
and the fifth, $809. What is he now worth?
EXERCISE XVI.
1. Find the sum of all the numbers, from 749 to 760,
inclusive.
2. Three men bought a farm. The first paid $2468; the
second, $2032; and the third, as much as the other two. Find
the cost of the farm.
3. Ella picked 378 baskets of berries, and Jane picked 58
more than Ella. How many did both pick?
4. A schoolroom is 32 feet long and 21 feet broad. How
many feet is it round the room?
5. Willie gave John 37 cents and Mary 48 cents. He had
as many cents left as he had given away. How many cents had
he at first?
6. A farmt?r bought a pig for $19, a cow for $39, a sheep for
$13, and a horse for as much as he paid for the pig and the
cow. How much did he pay for all?
7. My brother gave me 32 cents; my father gava me 8 cents
more than my brother, and my mother. gave me as much as
both. How much money did I receive?
ADDITION.
19
8. Helen spent 117 cents for books, 121 cents for ornnjjes,
44 cents for peacheH, l.'Jl cents for sugar, and had 87 cents left.
How much had she nt first?
9. A farmer has lo acres of whwit, 29 acres of barley, 17
a^'res of peas, 19 acres of corn. The rest of the farm is in
pasture, and there are as many acres of pasture as of grain.
How many acres has he altogether?
10. A drover >)ought 27 sheep for $11.'5 from one farmer; from
a second, he bought 35 sheep for $142; and from a hird, 28
sheep (or $1.32. How many sheep did he buy, and how much
did they cost him?
EXERCISE XVII.
1. Find the sum oi $42, $9136, $254, $29, and $530.
2. At the World's Fair a man spent $37 the first week; $46
the second; $84 the third; and $9o the fourth. His other
expenses were $87. How much did he spend during the four
weeks ?
3. In 1897 the population of the County of Essex was 431.54;
of Kent, 44183; of Elgin, 29659; of Norfolk, 29231; of Haldi
mand, 2^263; and of Welland, 30305. What was the total
population of these six counties?
4. In 1896 the debenture debt of Ontario was as follows: Of
township^, $2866904; of towns, $9598063 ; of villages, $1163096;
and of cities, $37471231; of counties, $1848982. What was the
total ^ jbenture debt of Ontario?
5. A drover bouj^ht three flocks of sheep. The first contained
967, the second 133 more than the first, and the third 450 more
than the second. How many sheep did he buy altogether?
6. Sarnia is 62 miles west of London: Ijondon is 115 miles
west of Toronto, and Toronto is 333 miles west of Montreal.
How far is it from Sarnia to Montreal ?
7. T lost $29 by selling ahorse for $71.
horse cost me ?
How much did the
8. For how much must I sell a horse which cost me $91, so
as to gain $29 ?
9. John has 27 cents more than Willie, who has 84 cents.
How much money have both together?
10. The first of three number" is 846, the second is 987, and
the third is as much as the other two. Find the sum of the
three numbers.
20
ARITHMETIC.
EXERCISE XVIII.
H 1 1
l! Il
1. A boat Bails from St. Catharines to Toronto, 45 miles;
from Toronto to Montreal, 93.") miles; and from Montreal east
ward a distance eijiial to that from bt. Catharine*? to Montreal.
Find the total distance sailed.
2. Add 675, one Taillion and nine, four thousand and six,
302, fortj one thousand six hundred and four, 21436, ninety
seven, 84, and ninetyone thousand four hundred and seven.
3. 1 bought wheat for $4')i)i], corn for $2347.1, oats for $8796.
I sold the wheat at a gain of $1404, the corn at a gain of $6525,
and the oats at a gain of $204. How much did I get for allf
4. After selling 1016085 oranges, a merchant had two lots
left, one containing 69756 and the other 85619. How many
oranges had he at first?
5. A man sold a horse for $986, and three cows for $680
each. He lost $125 on the horse and $220 on each cow. How
much did all cost him?
6. How many times does a clock strike in 12 hours?
7. I bought wheat for $7962, corn for $12649, oats for $8763.
I sold the wheat for $780 more than the cost, and the corn and
oats at a gain of $1685 on both. How much did I get for all?
8. A lady paid $380 for a piano, $275 more than that sum for
furniture, and*$2675 for a house, and has still $8375 in the bank.
What sum had she at first?
9. A fai'mer gave to each of his three sons $6580, .and to his
daughter $920 more than to two sons. How much did he give
away altogether?
10. A man gave his wife $10560, his two sons $7325 each, and
his daughter $485 more than a sou's share. How much did he
give away?
EXERCISE XIX.
1. In 1S97 the population of the townships of Ontario was
1113530; of the towns, 312947; of the villages, 1.33560; and of
the cities, 430940. What was the population of Ontario in that
year?
2. In the B'vttle of Waterloo it is said that of the soldiers
engaged 36273 were Briti«)i, 7447 were Hanoverians, 8000 were
Brunswickers, and 21000 were Belgian, whilst there were about
75000 French. How many were there of the four allies, and
how many combatants were there altogether?
3. A father leaves an estate to" his son, daughter and wife.
To his son he leaves 5355 dollars, to the daughter 500 dollars
more than to the son, and to the wife 1500 dollars more than to
the daughter. What was the amount of the estate ?
ADUITIUN.
21
1, 45 miles;
mtreal eiint
trO Montreal.
ind and six,
436, ninety
nd Heven.
,ts for $8790.
ain of $6525,
;et for allf
had two lots
How many
)W8 for $680
li cow. How
lurs?
its for $8763.
the corn and
get for all?
that sum for
) in the bank.
iO, .and to his
did he give
325 each, and
much did he
' Ontario was
]3560 ; and of
ntaric in that
4. John threw a hall 34 yards up the road, and another 43
yards down the roml. How fur must he walk to bring them
both ba<'k agiiin ?
5. The first of four numbers is 4768, the second is 170
more than the first, the third is 90(5 more than the second, and
the fourth is as much as the other three. What is the sum of the
four imnibcrsf
6. Mary bought a book for which she gave 95 cents; Maudo
bought oiH' for which she gave 13 cents more than Mary; aiul
Maude's book cost 23 ci'iits less than Jane's. Find the cost
of .lane's book.
7. Find the number of days in a year — the days of the
respective months being as follows: January 31, February 2H,
March 31, April .30, May 31, June 30, July 31, August 31,
September 30, ()ctol»er 31, November 30, December 31.
8. Adam lived 930 years; Seth, 912; Enos, 905; Cainan,
910; Mahaleel, 895; Jared, 962; Enoch, 365; Methusaleh, 969;
Lamt^ch, 777; Noah, 950; Shem, 600; Arphaxad, 438; Salah,
433; Heber, 464; Peleg, 239; Keu, 239; Serug, 2:10; Nahor,
148; Terah, 205; A>»raham, 175; Isaac, 180; Jacob, 147;
Joseph, 110; Moses, 120; Joshua, 110. What is the sum of all
their ages?
9. Watermills were invented in the year 555 after Christ;
windmills 744 years after watermills; pumps 126 years after
windmills; printing 15 years after pumps; watches 37 years
after printing; the spinningwheel 53 years after watches;
the steamengine 119 years after the spinningwheel; the fire
engine 14 years after the steamengine; the spinningframe 98
years after the fireengine; and the electromagnetic telegraph
71 years after the spinningframe. In what year was the electro
magnetic telegraph invented?
10. A man bequeathed his estate as follows: To each of his
two sons, $12450; to each of his three daughters, $6500; to his
wife, $650 more than to both the sons; and the remainder,
which was $1000 more than ho had left to all his family, he
gave to benevolent institutions. What was the whole amount
of his property?
f the soldiers
ns, 8000 were
re were about
ur allies, and
ter and wife,
er 500 dollars
1 more than to
e?
oo
ARITHMETIC.
II. SUBTRACTIOIN.
Subtraction is tlio process of ftndiiijf ilie differenco
between two iiuinbers of the same kitid.
The IMInuend is the number from whieli tlie other
number is taken.
The Subtrahend is the number whieli is taken
from the minuend.
The Difference or Remainder is the num1)er
found by taking the subtrahend from the minuend.
The sign of Su])traetion is — , called minKs, and
when written between two numbers it shows that the
number after it is taken from the one before it.
EXERCISE XX.
».
4.
i).
59
07
29
47 9()
87
99
23
54
t()
21 32
52
73
786
938
897
984
593
898
245
412
504
421
242
452
674
849
928
547
693
989
52
417
415
231)
451
472
8947
5986
9397
8946
4918
4765
4312
3241
4152
4235
3807
1234
70846
89476
91708
.59487
49387
.39587
50314
13012
40532
23152
29245
21432
6. 35276 40547 48456 57345 73840 904782
21042 31023 22304 31021 21413 130531
45987
21257
47543
31213
48053
32423
49735
13425
54398
51281
50347
12345
98764
12321
38704
32532
74820
50412
45708
42323
01895
()2352
78456
.32012
i(» (lifFcroiKM'
•li tlic Otllt'l*
•h is taken
he number
ninuend.
mhu(s, and
wa that the
re it.
87
J)9
52
73
503
808
212
452
G03
989
451
472
1918
4705
5807
1234
)387
39587
)245
1840
21432
004782
1413
5347
130531
98704
2345
1895
12321
78450
2352
32012
428357
423142
SUBTRACTION.
028954 039847
523412 032123
718047
715415
li
905783
120321
4370<)8
312415
800087
304015
705347
705123
308718
123718
470084
412382
10.
EXERCISE XXI.
1. A niiui had 151 iows. JIu sold 40 of them. How many
hail \w Wat
2. Harriet and VAh'ix tofrctln'r liavo 83 littln fhickons, of
which Harriet owns 43. How many btdonff to Kllenf
3. A man boiijrht n horse for $\27 and sold it for $104. How
much did he losef
4. A hook has 210 pajjes. Tom has read 103 pages. How
many pages has lie yet to read?
5. A merchant having bought 587 gallons of syrup, sold a
pertain quantity and hud 315 gallons left. How many did he
sell?
0. A man paid 275 dollars for a horse and buggy; the horso
cost 125 dollars. What was the price of the })Uggy?
7. In one year a merchant sold 1578 barrels of flour and
1324 barrels cf sugar. How many more barrels of flour did lie
sell than sugarf
8. A drover having 1465 sheep sold 233 of them. How many
had he renniining?
9. A farmer has two farms containing together 875 acres.
Tn one farm there are 442 acres. How many are there in the
other?
• 10. A fanner liouglit a farm for 4f3()00 and sold it for $4200.
How much did he gain?
EXERCISE XXII.
1.
90
40
50
00
70
80
100
35
13
27
31
40
29
75
327
930
574
928
726
850
142
484
381
182
145
160
590
700
40G
732
824
751
143
178
184
185
108
328
3450
3700
4870
5340
5938
9418
1235
2340
2527
2128
2970
5493
u
'"*
ARITHMETIC.
4'J:J8
5129 6248
7206
7462
4915
L'HiC}
as?) 498:5
:{K94
59158
.'5897
427:56
24:582
53829
28596
61705
28483
80727
45384
49376
31949
57146
29418
9.
400300
295246
500000
273827
506207
49185
500200
:J9:5186
400000
285458
402508
84274
700400 800500
398327 496478
600000 700000
365879 486347
604506 703605
89251 78382
300700
12:5456
400000
267410
802507
76832
600500
287684
800000
120076
907608
30709
10. 924:590 705180 527082 816141 423453 700600
4:52412 44:5544 232154 1:55212 141514 123416
1. From
2. From
3. From
4. From
5. From
6. From
7. From
8. From
9. From
10. From
1.
o
3.
4.
5.
6.
7.
8.
9.
10.
EXERCISE XXIII.
924 take 379; from 970 take 182.
1000 take :!78; from 1111 take 999.
2450 take 1097 ; from 6040 take 644.
44444 take 14847 ; from 44444 take 15789.
50505 take 27895; from 55,555 take 48776.
6G6666 take 278954; from 600000 take 123007.
100600 take 99999; from 777777 take 297998.
486413 take 164184; from 418786 take 219186.
600078 take 142368; from 300007 take 108819.
672246 take 487128; from 578472 take 169386.
EXERCISE XXIV.
6005
8002
8003
6005
9004
6003
7035
7023
8021
8064
2:547
2636
2746
2748
2615
2846
2648
2896
;3472
2397
78253569
H412— 3756
9000—1234
7018—6243
87655999
6200—4756
8006—7184
8574—6497
74S2— :5597
8100—6718
9012
7064
7000
7000
8000
8000
9000
9000
6324
6245
3684
2768
2546
3748
5318
3526
3725
2745
2538
3789
:t
■a
SUBTRACTION.
25
7462
5938
49376
31949
4915
3897
57146
29418
300700
123456
600500
287684
400000
267410
800000
120076
802507
76832
907608
30709
423453
141514
700600
123416
EXERCISE XXV.
44.
e 15789.
e 48776.
take 123007.
ako 297998.
take 219186.
take 108819.
take 169386.
9012
7064
7000
7000
8000
8000
9000
9000
6324
6245
3684
2768
2546
3748
5318
3526
3725
2745
2538
3789
is
r
I
1.
.56739— 24316
36751
2S976
431250—153697
2.
68507—47623
90006
29384
920503—476829
3.
47865—12341
71020
.)43(i7
523146—286759
4.
72006—48315
43002
27659
647352—268574
5.
65043 17872
71300
450.35
502304—186475
6.
8100025143
64434
25679
625030—274384
7.
90000—30906
76456
29898
720301—368596
8.
90503—47628
56307
18497
842003—459687
9.
41009—31214
70000
39458
715324—369857
10.
43020—36748
78536
47658
900500—465783
EXERCISE XXVI.
1.
8467321—3478271
700'
rOOO— 2009001
o
3178632—1478371
6789012—700999
3.
9004100—30012
764.89687—999999
4.
100010110—990991
7000000—636363
5.
49716368—42894938
7400002—123807
6.
3714908—2916409
5000005—900009
7.
37080605—2934716"
>
10101011—303033
8.
23456789— 149307()8
27689714—9337778
9.
1000000—11
476.
5879—707070
10.
4000000—199091
5005005—1234567
EXERCISE XXVII.
1. How much must be added to 76 to make 150?
2. Take 713968 from one million.
3. From 9410068 take 3090801.
4. What is the difference between 76104 and 108403?
5. The greater of two numbers is 705, and the difference
between them is 29. Find the smaller number.
6. Find the remainder, after taking 7854 as often as possible
from 57692.
7. What number taken from one million will leave 473916?
8. To what number must 8764 be added to make 11342?
9. 7900000— 467846— 7()4839.
10. From the difference between 287368 and 789560, take
360194.
2G
AUITHMKTIC.
EXERCISE XXVIII.
1. A man l»ad 374 nhcep and sold 28;"). How nianv had he
left?
2. James has I'lT') ; Tom has $'MH. How much more has
James than Tom f
3. If a man receives $3415, and si)end8 $2947, how much lias
he left?
4. If I buy 47964 bushels of wheat and sell 23796 Imshels,
how many bushels are left ?
5. Mr. Jones has $7698 and Mr. Williams $5919. How much
more has Mr. Jones than Mr. "Williams?
6. I bought a farm for $7916 and have paid $5748. How
much do I still owe for the farm?
7. A owed B $378 and paid him $329, and gave him a cow for
the balance. What was the value of the cow?
8. A man started to walk 3400 miles, and has finished 1968
miles. How far has he yet to go?
9. In 1897 the population of Ontario was 1990977; in 1886 it
was 1828495. How much had the population increased during
*;his period?
10. In 1897 there were 940236 milk cows in Ontario; in 1888
there were 781559. How many miik cows had been added to
the cattle of Ontario during this period?
EXERCISE XXIX.
1. A merchant sends $4796 to his agent to buy goods, and
receives $3989 worth. How much does the agent keep?
2. James bought 98 marbles and then sold 59 of them. How
many had he left?
3. In an army of 24907 men, there are 10908 who are over
36 years )f age. How many are younger?
4. I sold a farm for $4713 and gained $897. What did it
cost me ?
5. There are 525600 minutes in a year, and 173964 in the
first four months. How many minutes are there in the rest of
the year?
6. Jane has two books containing 736 pages, and one has
297. How many has the other?
7. A railway cost $63475916, and of that sum $41968959 have
been paid. How much is still owing?
8. A boy starts from Montreal for Vancouver, a distance of
14680000 feet, and travels 8379164 feet. How far has he yet
to go?
SUBTRACTION.
27
9. In 1897 there were 312947 persons in Ontario living in
towns, and 430940 living in cities. How many more persons
lived in cities in Ontario than in towns?
10. In Ontario in 1883 there were 53513032 pounds of cheese
niaimfactured, and in 1897 13736291G pounds. How many more
pounds were manufactured in 1897 than in 1883?
EXERCISE XXX.
1 . A boy paid 52 cents for a geograpliy and 25 cents for an
arithmetic. How much inore did lie pay for the geograpliy tliau
for the arithmetic?
2. A boat had 720 passengers and lauded 438 at a port.
How many remaiued on the boat?
3. A man began bnsiues« with $15264 and lost $3271. How
much had he let'tif
4. A man had $100. He paid $65 for a buggy and the rest
for harness. How much did the harness cost?
5. Sir Isaac Newton died in 1727 at the age of 85. When
was he l>orn?
(5. Gladstone was born in 1809 and died in 1898. To what
age did he live?
7. The Universitv of Camltridge was founded in 915. How
old was it in 1898? '
8. Mount Logan, the highest mountain in Canada, is 19500
feet high. How much higher is it than Mt. Blanc, the highest
mountain in Europe, which is 15812 feet high?
9. At an election there were 2784 good ballots cast. The
successful candidate received 1459 votes. How many votes
were given to the defeated candidate?
10, In 1898 the population of Greater Loiidon was 6291000,
and of Greater New York it was 2321644. How much did the
population of Loudon exceed that of New York?
EXERCISE XXXI.
1. ^11 a school of 489 scholars there are 267 girls. How
mauy more girls tlian boys are in this school?
2. I bought a house for $2127. I paid $365 for repairs, and
then sold it for $2690. How much did I gain?
3. A miller bought 1000 bushels of wheat from one farmer,
and 500 bushels from another. After selling 825 bushels to one
merchant and. 460 to another, how mauy had he left?
28
AUITIIMKTIC.
4. A {^eiitleraan at his death left 12000 dollars to be divided
between his wife, his son and his two daughters. To each of
the daughters he gave 287") dollars, to the son aOOO dollars, and
to his wife the remainder. What was the wife's portion?
5. A man bought a horse for $175 and another for $216. He
sold both for $42;{. How much did he gain?
G. A man is worth $175968. Of this $29347 is in real estate;
$14743 in bank stock; $23928 in railway bonds, and the rest is
in the bank. How much is in the bank?
7. A cattle drover bouglit cattle for $19376. He paid $8949
in cash, gave a cheque on the bank for $3249, and his note fcr
the balance. For liow much was the note drawn?
8. There are 1760 yards in a mile. Find by su])traetion
how many miles there are in 8937 yards, and how many yards
remain.
9. Two persons are 375 miles apart; they travel towards
each other; at the end of one day, one has travelled 93 miles
and the other 57 miles. How far apart are they still?
. 10. At an election 12572 votes are taken, of which the suc
cessful candidate received 7391. By what majority was he
elected?
EXERCISE XXXII.
1. A man deposits in the Ontario Bank 2374 dollars. At
one time he draws out 897 dollars, at another time 543 dollars,
and at a third time 689 dollars. How much still remains in
bank?
2. A man was 21 years old in 1896. In what year will he
be 75 years old?
3. A gentleman dying left 4500 acres of land to his wife, his
son and his daughter. To his wife he gave 1564 acres, to his
son 1449 acres, and to his laughter the remainder. What was
the daughter's portion?
4. A gentleman 83 years old has two sons; the age of the
older son added to his makes 128 years, and the age of the
younger son is equal to the difference between the age of the
father and that of the older son. How old is each of his sons?
5. A man bought three estates; for the first he gave $5260,
for the second he gave $3585, and for the thiid he gave as
much as for the first two together. He afterwards sold tliem all
for $15280. Did he gain or lose, and how mucli^
6. James has 25 marbles; John has 32. The first time they
played John won 7, but the next tinn; James won 13. How
many marbles has each now?
SUBTRACTION.
29
7. On a farm of 112 acres there are 14 acres in wheat, 15
acres in barley, 12 acres in oats, 17 acres in peas, 9 acres in
hoed crop, and the rest in pasture and bush. Ilow many acres
are in [»aHtur(» and bush?
H. How many days are there from June 28th to September
oth, inc'hisive?
9. James and Henry have together 45 marbles; Henry and
John have togetiier 63 marbles; John and William have together
HI marbles; William has 45 marbles. How many marbles has
James?
10. In 1897 the population of Ontario was 1990977; in 1896 it
was 1972286; in 1895 it was 1957390, and in 1894 it was 1936219.
By how much did the population increase during 1894, 1895 and
1896 respectively?
EXERCISE XXXIII.
1. From th(i difference between 17496 and 5378 take the
sum of 4125 and 1247.
2. Simplify 2187+374—1763+9436—1479+8161—3948.
3. The sum of three numbers is 2897. One of these is 794,
another is 497. Find the other.
4. What must be added to 1000000—6093 to give 3746918—
94786?
5. The sum of six numbers is 40917. Five of them are 4876,
9127, 4763, 8294, and 7328. What is the sixth number?
(). What nuTuber added to the sum of 7089, 987, 3469, 58732,
29 and 4:536, will make one million?
7. What numl>er must be taken from the difference ]>etwe» n
3789 and 7968 to leave 1645?
8. What number added to 1271 will give the sum of 40370,
.3684 and 30916?
9. From the sum of all the odd numbers l»etween 436 and
448 take the difference between 39476 and 38979.
10. The subtrahend is the sum of 784, 965, and 1894. The
niinuend is the difference between 7689 and 19785. Find the
remain ier.
11. The sum of four numbers is 45364. The first number is
5215, the second is 457 more than the first, and the third is 128
It'ss tlian the first and second together. Find the fourth
UUnilKM'.
12. The remainder is 7894 after 9462 has been subtracted 7
times from a certain number. Find the uumJ»er.
80
ARITHMETIC.
III. MULTIPLICATION.
l\1ultiplication is the process of finding the sum of
a number called the multiplieand, repeated as many
times as inhere are units in another number called the
multiplier. *
The Mlultiplicand is the number to be multiplied.
The IMultiplier is the number by which the multi
plicand is to be multiplied. It shows how often the
multiplicand is to be repeated as an addend.
The Product is the result of the multiplication.
The multiplier and the multiplicand are called the
Factors of the product.
THE MULTIPUCATIOIN TABLE.
Twice
Three
Four
Five
Six
Seven
times
times
times
times
times
1 is 2
1 is 3
1 is 4
1 is 5
1
is 6
1 is 7
2 . . 4
2 . . 6
2 . . 8
2 . . 10
. . 12
2 . . 14
3 . . 6
3 . . 9
3 . .12
3 . . 15
3
. . 18
3 . . 21
4 . . 8
4 . . 12
4 . . 16
4 . . 20
4
. . 24
4 . . 28
5 . . 10
5 . . 15
5 . .20
5 . . 25
5
. . 30
5 . . 35
6 . . 12
6 . .18
6 . .24
6 . . 30
6
. . 36
6 . . 42
7 . . 14
7 . .21
7 . . 28
7 . . 35
7
. . 42
7 . . 49
8 . . 16
8 . .24
8 . . 32
8 . . 40
8
. . 48
8 . . 56
9 . . 18
9 . . 27
9 . . 36
9 . . 45
9
. . 54
9 . . 63
10 . . 20
10 . .30
10 . .40
10 . . 50
10
. . 60
10 . . 70
11.. 22
11 . . 33
11 . . 44
11 . . .55
11
. . 66
11 .. 77
12 . . 24
12 . . 36
12 . .48
12 . . 60
12
. . 72
12 . . 84
Eight
NMne
Ten
El«>ven
Twelve
times
tiiiies
times
1 is 10
times
times
1 is 8
1 is 9
1 is 11
1 is 12
2 . . \G
2 . . 18
2 . . 20
i) »)>)
2 . . 24
3 . . 24
3 . . 27
3 . . 30
3 . . 33
3 . . 36
4 . . 32
4 . . 36
4 . . 40
4 . . 44
4 . . 48
5 . . 40
5 . . 45
5 . . 50
5 . . 55
5 . . 60
6 . . 48
6 . . 54
6 . , 60
6 . . 66
6 . . 72
7 . . 56
7 . . 63
7 . . 70
7 . . 77
7 . . 84
8 . . 64
8 . . 72
8 . . 80
8 . . 88
8 . . 96
9 . . 72
9 . . 81
9 . . 90
U . . 99
9 . . 108
10 . . 80
10 . . 90
10 . . 100
10 . . 110
10 . . 120
11 . . 88
U . . 99
11 . , no
11 . . 121
11 . . 132
12 . . 96
12 . . 108
12 . . 120
12 . . 132
12 . . 144
MULTIPLICATION.
81
the sum of
3(1 as many
V called the
multiplied.
I the multi
»w often the
id.
plication .
3 called the
Seven
times
6
1
is 7
12
2
. 14
18
3
. 21
24
4
. 28
30
5
. . 35
36
6
. . 42
42
7
. . 49
48
8
. . 56
54
9
. . 63
60
10
. . 70
66
11
. . 77
72
12
. . 84
Twelve
♦ imes
1 is
12
o
24
3 . .
36
4 . .
48
5 . .
60
6 . .
72
7 . .
84
8 . .
96
9 . .
108
10 . .
120
11 . .
132
12 . .
144
1. 3040204
o
11. 5789645
EXERCISE XXXIV.
4302432 423042 340243
5
5
8950()94
5478946
4897649
5
3204302
o
974234
4963241
2
879716
2
9847456
7084567
2
3.
768064
2
578467
708096
2
598746
2
967865
4.
863428
2
768497
2
700608
2
367496
o
784967
2
5. a456454 3454645 4543456 6534356 3545464
3 3 3 3 3
6. 8768475 9647364 8769456 9484965 7899486
3 3 3 3 3
7. 3404134
4
634243
4
4137404
4
978649
4
1678343
4
6783437
4
8. 54:{7489
4
6789013
4
345987
4
4139764
4
9. 230456
5
5432061
5
3475264
5
2536472
5
1234567
5
10. 4597045 9682469 7893086 7080904 7684963
8647649
12. 3741064 34071064 3718643 41890701 4196804
6 6 (i 6 6
82
ARITHMETIC.
EXERCISE XXXV.
1. 4375780
6
0892405
5080700
3(589427
()
784(5952
2. 7890905
()
4709(547
8490790
0894579
887799(5
a. 7450948
7
7045093
7
8450784
7
9009078
7
7084905
7
4. 245078
7
37425(54
7
5420034
7
4253042
7
700(5457
7
5. 4087900 4087054 3090874 4897054 9870543
7 7 7 7 7
6. 3042054 32400(55 4004503 2345035 4352073
8 8 8 8 8
7. 4794086 8887(55(5 9234507 7890543 0700809
8 8 8 8 8
8. 7684907 2503128 1536211 3306525 5010323
8 8 8 8 8
9. 1234505 5043204 2073465 4234507 5704507
9 9 9 9 9
10. 3004789 0478975 8090403 5408795 7864087
9 9 9 9 9
11. 1760689 5311695 3155093 1534091 5135491
9 9 9 9 9
12. 7689745 7000068 9506078 5078943 7684796
10 10 10 10 10
MULTIPLICATION.
33
EXERCISE XXXVI.
1. Multiply n7Sr)417H:{ hy 2, hy li, ».y 4, by f), by G, by 7.
2. Multiply 47H(JO():{U4 by 2, by :{, by 4, l>y '>, by (J, by 7.
;{. Multiply :{7S()41H:t4 by 2, by ;{, liy 4, l)y fi, by <5, by 7.
4. Multiply 4()H:{71«:{4 l»y 2, l>y ;}, by 4, l»y f), by (i, by 7.
'.. Multij.ly HyiSO(»:;47 by 4, by 5, by 0, liy 7, by 8, by !).
«>. Multiply ()()7S9019r) by 4, by f), by G, by 7, by 8, by 1).
7. Multiply H(i7H:{4071) by 5, by (5, by 7, by 8, l»y 9, by 10.
H. Multiply G78:{418»5<) by .^), by 0, by 7, by 8, by !), by 10.
J). Multiply 478:{780()r) by 5, by G, by 7, by 8, l»y 9, by 10.
10. Multij.ly 418:J4784G by 5, by G, by 7, by 8, by 9, by 10.
EXERCISE XXXVII.
What are the factors of 15? of "^1 ? of 28? of 42? of Uf)?
1. Multiply 4879 by the factors of 15, of 28, of 18, of 'A'k
2. Multij.ly 6785 by the factors of 14, of 18, of 25, of 42.
:{. Multiply 708G by the factors of .•{2, of 3'J, of 42, of 49.
4. Multiply 9584 by the factors of 21, of 45, of 49, of 54.
5. Multiply 2539 by the factors of 24, of 25, of 3G, of 63.
6. Multiply 6407 by the factors of 32, of 45, of 54, of 72.
7. Multiply 7685 by the factors of 48, of 50, of 60, of 70.
8. Multiply 9685 by the factors of 70, of 80, of 90, of 100.
9. Multiply 7689 by the factors of 45, of 54, of 63, of 81.
10. Multiply 4875 by the factors of 30, of 40, of 50, of GO.
EXERCISE XXXVIII.
1. Multiply 78546 by 21, by 31, by 41, by 51, by 71.
2. Multiply 68095 by 61, by 71, by 81, by 91, by 19.
3. Multiply 789G7 by 13, by 17, by 19, by 29, by 37.
4. Multiply 64758 by 78, by 87, by 95, by G4, by 59.
5. Multiply 47896 by 234, by 345, by 456, by 579.
G. Multiply 97640 by 567, by 892, by 347, by 638.
7. Multiply 90070 by 325, by 257, by 689, by 976.
8. Multiply 76847 by 306, by 405, by 708, by 704.
9. Multiply 98764 by 4008, by 7006, by 5009, by 9040.
10. Multiply 87009 by 5090, by 7080, by 7096, by 9007.
:h
ARITHMETIC.
EXERCISE XXXIX.
1. A train riiiiH L'~) iiiilis iiii hour. How t':ir tlocs it run in
4H lionrH?
2. Mr. Brown luis I'WIG liorsen. Wluit uro llny worlii at
;{. How many ouncjs are there in :{7U(»8 pounds, it' tlnre are
IG ounces in one jtoundf
4. The earth in its annual journey around tiic sun moves
altout (iKOOO miles an hour. J low far does it mov«f in a day, or
24 hours f
[). Find the cost of 7H1)(5 ytirds of cotton at H cents a yard.
G. In a ^rove there are 9 rows of trees and 7H trees in each
row. How many trees are there in the f^rovef
7. How fai' can a iiorso travel in 'M'ui Incurs at tlic rate of 8
miles' an hour?
8. How many hills of corn are there in a litld containing
42(» rows, and 224 hills in a Towi'
9. What will G5 miles of plunk road cost at 2007 dollars per
mile?
10. How many lemons are there in 24:5 boxes, each box
containing 309 lemons?
EXERCISE XL.
1. A merchant V)ought 1275 barrels of sugar of ,300 pounds
each at 4 cents a pound. Find tlie cost of the sugar.
2. A merchant bought 27 bales of cloth, each bale eontaluing
'}.1 pieces, and each piece containing iiG yards. How many
yards were there in all?
3. How many nails will it take to shoe 74 horses, if there
are 8 nails in each shoe?
4. How far will a train go in 87 days at 30 miles per hour?
(1 day=24 hours).
5. How many inches are there in 475G yards, there being
3 feet in a yard and 12 inches in a foot?
G. A man buys 4795 pounds of tea at 5 cents an ounce/
What did he pay for it? (10 ounces=l pound).
7. Find the cost of 78 bales of cotton, each bale containing
412 yards at 15 cents per yard.
8. Find the value of 68 farms of 120 acres, eacli at $25 per
acre.
9. There are 60 minutes in an hour and 24 hours in a day.
How many minutes are there in 3G5 days?
10. The Montreal Star hasa daily circulation of 146819 copies.
How many papers will be sent out in G weeks of G days each?
MI'I.TIPMCATIOK.
35
in it vm\ in
y \vt)l'tll ut
it' tlu'n< are
SHU mONM'H
ill ii day, or
iits a yiu<l.
vivH in •■acli
lit' I'iitc of H
I coiitainiiif^
7 dollars per
s, each box
' 300 pounds
ar.
e eoiitaraing
How many
I'si's, if there
es Iter hour?
Iliere being
ts an ounce.*
e containing
•h at $2;') per
urs in a day.
46819 copies.
G days each?
EXERCISE XLI.
1. Multiply tho suni of all the odd nuinin'is Itetwoen 'M niid
40 by the sum of all the evei numhers between ;{7 and 47.
2. A drover }>ought 475KJ eiittle at $4') each, and 4iM;{7r) sheep
nt $5 each. How much more did the sheep cost than the cattle;'
;{. A farmer sold 'J."» cords of wood at $'A pirconl aii<l received
in jtaynieiit four $'J0 bills. What change must lu* give liack/
4. Kind the aujoimt of the following bill: —
14 pounds ri(M' nt, 4 cents a pound.
8 yards cotton nt 7 <'ents a yard.
19 spools thread at 4 cents a spool.
73 pounds sugar nt 5 cents n pound.
r». A drovei liough. 124 cows at $.")7 each, and 71) horses nt
$90 ea<'h. How much more did the horses cost than the cows?
(!. The drover sold the cows in last (piestion at a gain of $13
each, and the horses at a loss of $20 each. Did he gain or lose,
and how much?
7. A merchant liought 473G turkeys in London at 75 cents
each, aTui sent them to Montreal at a cost of 5 cents each.
Here he sold them for $4730. How much did he gain on the
transaction?
8. A merchant luid 793 yards of cloth. He sold 120 yards
to one nuin and 304 yards to another. What is the remainder
worth at 8 cents a yard?
9. Two persons start from the same point, and travel in
oj)))osite di ections. One travels 29 miles a day, and the other
32 miles a day. How far apart will they be in 17 days?
10. A drover bought 127 head of cattle at $34 a head, niul 97
head at $47 a head, and sold the whole lot at $40 a head. What
was his entire profit or loss?
EXERCISE XLII.
1. The two factors of a certain nundjer are 428 and 403.
What is the number?
2. The three factors of a certain number are 187, 29, and 43.
What is the number?
3. Find the continued product of 11, 13, 17, 19, and 23.
4. One of the three equal factors of a number is 407. Find
the numl»er.
5. The multiplicand is 40009 and the multiplier is the
number whose ructors a " .">, 7, and 11. Find the product.
86
ARITIIMKTir.
<5. Tho multiplicand is th« UiflTi'n'uco iM'twcMn one million
iumI ono thou8)in(l and one. Th«> nniltiplier in tliu Huui of 407,
70'J, and U(>:i. Find l\u> product.
7. TliH difference between two numl>ers i^^tlle product <)f 4',)7
and .'iOf). The Hirniller of the two nuinbeiH Ih lUOlOO. Multiply
tho lar^^er number l>y .')0()0.
H. The ditTerence between two numbers iH.^)0()7. The >.'r(«ater
number is thu product of 70(1.') and UOOM. Find vh:: smaller
number.
y. How much must be taken from the product of .^>07 and
7i{r> to ^et tho product (tf r>()7 and iVAiif
10. From the Hum of •)r>XH7 antl 7«>XJ>S, take the ditTerence
between 78X87 and 97X8.').
EXERCISE XLIII.
1. Multiply the sum of I'JOG and 7ri7{) by their difference.
12. How nnieh is the product of 579 and 758 greater than the
product of 577 and 758*
;{. Multiply together all the uumbers that end in IJ, 5, 7, or
9, between 12 and 20.
4. Multiply the greatest number that can be expressed by
four figures by the greatest one expressed by three figures.
5. From the product of 9009 and 7007, take the product of
7090 and 7909.
6. If Mr. Brown owns 3 houses, the first worth $2783, the
second 3 times, and the thiil 7 times as much as the first, what
are the 3 houses together worth?
7. A drover bought a drove of 33 oxen, paying as many
dollars for each ox as there were oxen in the drove. He paid
$514.85, and gave his note for the balance. For how much does
he give his note?
8. The area of Ireland is 32535 square miles, and 5096490
acres are cultivated. How nuiny acres are uncultivated, there
being 640 acres in a square mile?
9. A field of oats has 19 rows of stooks ; each row has 37
stooks in it, and there are 12 sheaves in a stook. How many
stooks are in the field? How many sheaves?
10. The sum of 4 numbers is 20000; three of them are 4785,
5769, and 2807. Multiply the sum of the greatest and least by
the sum of the other t"'c.
DIVISION.
37
II g as many
e. He paid
w much does
and 5096490
ivated, there
1 row has 37
How many
em are 4785,
and least by
IV. DIVISION.
Division is t]i<» pnxM'ss ]»y which, \vh«'ii th«' itroduct
mid out' fnrfor an ^iv«'ii, thf ofin r farfor is t'ouiid.
The Dividend, tiic j^ivm pnMlm't, is Mic iimiilHT
to Im' divided.
Tiie Divisor, the pivcMi fjictor, is th«' nutidMM hy
which the <livideiid is to l)e divi(h*d.
The Quotient, the faetor to be found, is tlie result
of Ihe division.
The Remainder is wlmt is over wlien tlie dividend
does not contain the divisor an e.xaet number of times.
Thus, The Dividend is ecjual to the proihict of the
Pirisor and Qnotii nl, increased l»y the RemnimUr.
Tlie sij.ii of Division, written — , shows that the
number )re('edinj^ it is to be divided by the nund)er
foHovviii}^ it.
EXERCISE XLIV.
NoTK. — It is recommended that this exercise ]»e worked by
the Long Division plan.
1.
«>
3.
4.
5.
(i.
7.
H.
9.
'J4— 2
4(58—2
9(53—3
4844
r)8575
(518— (5
749—7
9(588
819—9
10. 4r)(i8— 8
3. 2)428042
2. 2)157996
3. 3)3960(59
4. 4)534768
5. 5)1847(50
402
4722
699—3
568—4
(535—5
3(5(5—6
847—7
H40— 8
918—9
7389—9
96—2
836—2
(587—3
730—4
205—5
4806
5747
928—8
7299
5243—7
EXERCISE XLV.
2)208462 2)242680
2)135794
3)156945
4)784724
5)501035
2)351792
3)40:?716
4)813492
5)741800
2)424820
2)537958
3)804957
4)674508
5)357185
84—2
946^2
87(5^3
624^4
745^5
9(500
9457
728—8
360^9
2709^9
2)462860
2)315970
3)745683
4)562732
5)9276.50
38
AniTIIMRTlO.
«;. (i)»;s47r»(!
7. 7)7\4HV2
H. H) 728128
!». y)'Ji47:M
1(1. 8)810L'48
(!)()rj:}4'j
7)!Mr)707
8)!(14(i4()
!tj8:t4r)(n
u)Do;{(ir)4
())H417r)2
7)r)847(i(i
8)8iM:j»;o
!»)47r):!()2
i>) 748r):5«j
EXERCISE XLVI.
())9;n47(;
7):{214()l
8)7412;i2
!»)<)8478;{
7)i2:{4r)U
(5)700002
7)(i;no4:{
8)i48r.:5(;
;i)r>48:}7!>
7)y:j47(5o
1. Divide
2. Divido
:{. Divido
4. Divide
il. Divide
(5. Divido
7. Divide
8. Divide
<J. Divide
10. Divido
4178():J4
()7();{40()
40(i78()7
G78:5S()7
41(5708()
4078(iO:{
3070(542
3070412
4012(578
3070804
by 2, by ',], by 4, l)y f),
by 2, by 3, by 4, by .^),
]>y 2, by 3, by 4, by .'),
by 2, by 3, by 4, by f),
by 3, by 4, by 5, by (5,
by 3, ])y 4, by 5, by G,
l>y '5, l»y 4, by 5, by G,
}»y 4, by f), by G, by 7,
by 4, i»y 5, by G, by 7,
by 4, by 5, by 6, by 7,
i»y <»,
I'y 7,
by 8.
I'y <i,
I'y 7,
by 8.
i»y <i,
by 7,
by 8.
I'y 0,
by 7,
by 8.
I'y 7,
'•yH,
hy !).
i'y7,
i»y8,
v>y 9.
i>y7,
by 8,
by 9.
I'ys,
by 5),
by 10.
i'y«,
by 9,
by 10.
by 8,
by 9,
by 10.
*^i
EXERCISE XLVII.
1. At $;i ]H'r ynrd, iiow niaiiy y.ards of silk onn be Iton^lit I'oi'
$48? For $84? 'For $132? For $2(M?
2. Divide $968 eciuully iiniong 8 persons.
3. If I buy 12 horses for $900, liow much will one horse cost?
4. If flour costs $8 a barrel, how many barrels can be bought
for $2(532 f
5. A grocer packed 994 pounds of butter in 7 tubs of equal
size. How many pounds did he put into each tub?
6. Seven bales of cotton weighed 3(508 pounds. What was
the average weight per luile?
7. If 5 carloads of iron weigh 7532;) i)ounds, what would be
the avera,ji' weight of one carload?
8. In 1 ioek there are 8 quarts. How many pecks are there
in 4250 quarts?
9. A ship worth $38125 was owned in ecjual shares by 5 men.
Find the share of each.
10. At six dollars a ton, how many tons of coal can be bought
for $2274 ?
DIVISION.
30
EXEKCISE XLVIII.
1. A Hliip sailed across the Atlantic Oceaii, a distance of
'JHHO miles ill days. J low far did it sail each day?
L*. In one mile there are r)280 feet. How many yards are
there in a mile, there bein<^ '.I feet in one yardf
;{. The wages of 8 men for one week were 104 dollars. How
much did each earn per week?
4. How long will a bicycle rider who goes at the rate of U
miles pel' houi take in going 117 miles?
.'). Find the price of a dozen oranges at two for five cents.
(5. A drover bought 11 head of cattle for 352 dollars. What
was the price per head?
7. An excursion train consisted of five passenger cars and
carried 8") persons. What was tlie average number of pas
sengers in a car?
8. If a locomotive runs 289(5 miles in 8 days, what is the
average run per day?
9. The sun is 9;{000000 miles from tlm earth. Light travels
tills distance in about 8 minutes. What is the velocity of light?
10. Four farthings make a penny. How many pence are
there in 22008 farthings?
i
•e bought for
EXERCISE XLIX.
1. Divide 022,14 by 51, by 01, by 71, by 81, by 91.
2. Divide 17253 by 31, by 41, by 71, by 81, by 91.
:j. Divide 127551 by 41, by 51, by 01, by 81, by 101.
4. Divide 105243 Vjy 01, by 71, by 81, by 91, by 301.
5. Divide 594130 by 401, by 801, by 901, by 500, by 704.
0. Divide 471582 by 301, by 501, by 201, by 007, by 809.
7. Divide 095847 by 611, by 721, by 821, by 541, by 441.
8. Divide 437650 by 531, by 651, by 751, by 654, by 885.
9. Divide 904375 by 825, by 925, by 795, by 333, by 555.
10. Divide 704578 by 972, by 492, by 954, by 870, by 385.
EXERCISE L.
1. Divide 987C54 by 912, by 922, by 934, by 975, by 942.
2. Divide 785469 by 845, by 876, by 889, by 892, by 875.
3. Divide 870549 by 777, by 78^^ by 795, by 799, by 789.
4. Divide 987054 by 078, by 089, by 695, by 699, by 697.
40
ARITHMETIC.
r». Dividf 7Sr)9()7 by 508, by nST, by ')[)(]. by HSO, by .lOS.
(). Divide 7»)()(W() by 485, l)y 490, })y 491, by 478, by 497.
7. Divide 87()497 by :507, by :{78, by :W9, by :J99, by ;590.
H. Divide 700000 by 285, by 290, by 278, by 294, by 289.
9. Divide 1000000 by 49, by iW, by 29, by 17, by 19, by :i7.
10. Divide 12:54507 by i:{, by 17, by 18, by 19, by 29, by :{9.
EXERCISE LI.
1.
Divide 17:J255 by the factors of 15;
of 18;
of 21;
of 25.
l>
Divide 87045C by tiie factors of 24;
of 30;
of 30;
of 42.
3.
Divide 954708 by the factors of 45;
of .54 ;
of 50;
of 03.
4.
Divide 743045 by the factors of 25;
of 32;
of 30;
of 40.
5.
Divide 875976 by the factors of 32;
of 35;
of 42;
of 54.
C.
Divide 900007 by the factors of 30;
of 42 ;
of 72;
of 81.
7.
Divide 397486 by the factors of 30 ;
of 40;
of 50;
of 60.
8.
Divide 780978 by the factors of 00 ;
of 70;
of 80;
of 90.
9.
Divide 987641 by the factors of 100;
of 200;
of 300
; of 400
10.
Divide 987685 by the factors of 500 ;
of 600 ;
of 700
of 800
EXERCISE Lll.
1. Divide 470880 by 6 times 12.
2. Divide 337103025 by 861.
3. How often is 77 contained in 37704821?
4. Divide 7364063 by 7 times 7.
5. Divide 888888 by the continued product of 3, 7, 8, and 11.
6. By what number must 129546 be divided that the quotient
may be'27f
7. Divide the continued product of 12, 5, 183, 18 and 70 by
ttie continued product of 3, 14, 9, 5, 20, and 6.
8. The product of two numbers is 2177280; one of them is
the continued product of all the even numbers between 5 and
13. Find the other number.
9. What number besides 7087 will exactly divide 68070635?
10. When a certain number is divided by 478, the remainder
is 205 and the quotient the same as the divisor. Find the
dividend.
EXERCISE Llll.
1. The distance from Montreal to Vancouver is 2948 miles.
How long will it take a man to walk the distance at 22 miles
per day?
.f busl
DIVISION.
41
^
i>y
r.98.
s,
I'y
497.
9,
by
:{9().
4,
by
2S9.
y
19,
by M.
y
29,
by :59.
f 21;
of 2r).
f
:ui;
of 42.
E
r)() ;
of g:{.
f
:u> ;
of 40.
)f 4l>;
of M.
)f
72;
of 81.
)f 50;
of GO.
)f
80;
of 90.
of 300
; of 400
^t 700
; of 800
, 7, 8, and 11.
M
,t the quotient
•1
18 and 70 l)y
1
ne of them in
etween 5 and
g
ie cmiomr^ ?
:'**
the remainder
or. Find the
:S
is 2948 miles.
?e at 22 miles
•1
2. If $.^40^)l is equally divided among 17 men, what sum
will each receive?
;{. A miie contains G.'WfiO inclies. How many steps of 24
inches each will a boy take in walking a mile?
4. How many pounds of 16 ounces each are there in 473G48
ounces?
5. A man paid $ir)i;i4 for cf«ttle at $23 each. How many
head did he i)uy?
0. Tn 42 acres there are 6720 square rods. How many square
rods are there in one acre ?
7. If a steamship sails 1144.5 miles in 35 days, what is the
average speed per day f
8. The area of a country is 8315 square miles, and the
population is 2286625. How many people are there to each
Sipiiire mile?
9. If 2800 sacks of coffee weigh 470400 jjounds, what is the
average weight i)er sack?
10. If 1 man can finish a work in 261 days, how long would
29 men recjuire to do the work?
EXERCISE LIV.
1. There are 320 rods in a mile. How many miles are there
in 572K0 rods?
2. There are 3() inches in a yard. How many yards are
tiiere in 34S9624 Inches?
3. How many miles are tliere in 33440 yards, there being
1760 yards in one mile?
4. There are 48 j)otinds in a bushel of barley. How many
bushels are there in a load of barley of .3072 pounds?
5. A farmer l»rought 30(50 ])Ounds of jmtatoes to market.
How many Itushels had he, there being (50 pounds in each
bushel of potatoes?
6. In a bin of oats there are 8330 i>ounds. How many
l)usliels ar«^ there in the bin, there being 34 pounds in eneh
bushel of oats?
7. ^'liere are 160 acres of land in a nuarter Rection. How many
quarter sections are there in a township containing 23040 acres?
8. A cubic yard contains 27 cubic feet. How many cubic
yards are there in a heap of earth containing 2025 cubic
feet ?
9. There are 196 pounds in a barrel of flour. How many
barrels are there in 40572 poutids of flour?
10. A pile of wood contains 90112 cubic feet. How many cords
p,re there In It, there being 128 cubic feet in one cord of woodf
42
AHITHMKTIC
EXERCISE LV.
1. How many times can 7H })o taken fiom tlio <'ontinued
product of i:{X 7X1012*
2. Find the sum of all the numbers between 90 and ISO that
are exactly divisible by llj.
;i. Divide the sum of 4077, ;59(), and 8745)1, })y the diff<'rence
between (i;{84 and 7492.
4. Find the value of :{()984X 2739(5^761.
5. What is the true remainder when 69472') is divided by the
factors of 10;')?
(). Hew often can you take the sum of the even numbers
between 241 and 253 from forty thousand and fourteen.
7. If 213X84X190X264 be divided })y 30X56X36, what
will the quotient be?
8. When 82965;j is divided by 1022, the remainder is 811.
What is the quotient?
9. Divide 41579 by the factors of 42, and find the true
remainder.
10. The quotient of one number by another is 74; tlie divisor
is 321, and the remainder is 95. Whatjs the dividend?
EXERCISE LVI.
1. The divisor is 77; the quotient is 97; there is no
remainder. Find the dividend.
2. The dividend is 632; the quotient is 27; the remainder
is 11. What is the divisor?
3. The 'divisor and quotient are equal to each other, each
bein<^ 794 and the remainder is the largest possible. Find the
dividend.
4. The divisor is 801 ; the quotient is 403, and the remainder
the largest ]»ossible. Find the dividend.
5. The divisor is the difference between 204 and 2^58; the
quotient is their sum, and the remainder is the largest ]>ossible.
Find the dividend.
6. Find the least numl»er which must be added to 17634 to
make it exactly divisilde by 236.
7. What number besides 364 will exactly divide 89180?
8. Of wiiat number is ;}45 Itotli divisor and (puttient?
9. When 169 is added to the dividend it is exactly divisible
by 7H5, the (piotient being 978. Find the dividend.
10. Find the smallest number which, subti'ucted from 78654,
will make it exactly divisible by 458.
th(
MIS(!KLI.\NKOlS KXKK(MSES.
43
livided by tlio
the reniiiiiHler
'a\ to 17634 to
V. IV1ISCELLAINE0US EXERCISES.
EXERCISE LVII.
1. Tlie i)laypfround is 93 steps lonp and 47 wide. How many
Hteps >\ill a boy take in iio'xu^ around it tliree times?
2. From 479'JO take 3H1219, and to the result add 4901 >
3. Simj.lifv 4K7 + 19(5+ 14732 — 1984 — 4756 + 1734— 1S96 +
4111412—1739648.
4. Find thevahieof 761+276—849+98—121—317+963+438.
5. Multiply 68754 by 6 and by 8, and add the products.
6. Multiply 59846 l>y 1))8 and by 105, and subtract the products.
7. In a mile there are 1760 yards. How many inches are
there in 4 miles? (12 inches=l foot; 3 feet=l yard).
8. Multiply 500302 by 40102.
9. Divide 275264 by 736, and multiply 45697^ by 78, and
sul>traet one result from the other.
10. Find the amount of the following bill:
473 yards cotton at 7c. a yard.
916 pounds tea at 40c. a pound.
19 pounds raisins at lie. a pound.
EXERCISE LVIII.
1. Multiply seventeen thotisand nine hundred .ind forty
three l»y 5079^
2. A ])erson earned $85 a month and spent $2 a day. How
nnich did he save in 1896?
3. A numl)er divided by 243 gives 4713 for quotient and 89
for remainder. Find the number.
4. How manv times is the i)roduct of 75 and 109 contained
in the sum of 2063014, 17005000, 469, 30214707, and 3885?
5. Find a number which multiplied by 369 will give the
same iiroduct as 615X18;{57.
6. Wliiit number multiplied bv 86 will give the same i»roduct
as 163X430.
7. Find the quotient when the i»roduct of 86947 :ind 248 is
divided by 217.
8. A man Itought 52 liors»'s at .t75 each, and 214 jiigs at $\\
each. How mucli more tiiiin +()000 did all cost.'
9. The divisor is 473(5, the (U(»tient 299, and the remainder
the largest number ]>ossible. Whiit is t!ie dividend?
10. A grocer bought 16 cheese each weighing 70 jtounds for
10080 cents, and «old it at 11 cents a pound, How much did he
gain?
44
ARITHMETIC.
EXERCISE LIX.
1. A carpoiiter ♦■iiftaf^es 4 men nc $2 each por day. flow
much will they earn in 7 weeks?
2. JV farmer owes his grocer 2640 cents; he gives in jtayment
147 pounds of butter. What is the butter valued at per lb,
;{. "A drover sold 495 sheep and 27;') laml)s for .fIJiJOO; he
received $y apiece for the lamba. How much did he get for
each sheep f
4. A man bought ducks at 47 cents each and sold them at
100 cents a pair. What did he pay for the ducks which he sold
for 2800 cents?
f). A man bought 5 pounds nails at 4c. a pound; ') gallons of
oil at 1(5 cents per gallon; a stove for $l~) and an ixe for .$2.
How much change will he get out of a $20 bill?
(). A man bouglit a horse for $7') and :hen exchanged it for
[) slieep and $G2. If a sheep is worth $7 Hnd his gain?
7. If I give $78;}0 for 90 head of cattle and sell them at $H)')
ejich. How much is the gain?
8. A farmer sold 97 cattle at $65 each, and with the money
l)ought sheep at $i;j each. How many did he buy?
9. What numl>er divided by 3008 gives 3875 for <iuotient and
1397 for remainder?
10. A man earns $75 a month and spends $50 a month, how
long will it take liim to pay for 60 acres at $40 an acre?
EXERCISE LX.
1. A certain number was divided by the factors of 35; the
qtiotient was 72, the first remainder 2 and the last remainder (i.
What is the number?
2. I bought 28 barrels of sugar, each weighii\g 310 pounds
net, at 1200c. a barrel and sold it at 6c. ajtound. Find the gain?
3. Two i»ieces of cloth of e(ual length cost 5()00c. and 7600('.
respectively; the first piece cost 70 cents a yard, find the price
per yard of the second piece?
4. What is the least number that nmst bo added to 10000000
to make the sum exactly divisible by 653?
5. A number was divided by the factors of 77, the quotient
was 137, the first remainder 9, the second 6. What is the
dividend ?
6. A farmer exchanged 162 Inishels of wheat at 160c. per
bushel for 27 barrels of flour. What was the value of fiour ;^er
barrel ?
'. A grocer bought 126 pounds of tea at 68c. a ])ound. Ho
kept 18 pounds and sold the rest at 80 cents a pound How
much move money did he receive than Ue paid out?
MISCELLANEOUS EXERCISES.
46
8. A frciith'HiMn s]>«'iit durinp: tlu' yonr IHIK} ^\{) n day mid
laid away ^KK) a nioiitli. Wliat was his inconicf
J). Find a nimilM'r s'lcli that it' it U' added L':5 tiiius to :;7<)(ll
ill. siiiii will Ik 4(Hi(K».
Id. The itrodtu't of two imniltcrH is l'J7«);{74 and lialf of one of
tlu'U) is ;J1L"J. What is the other?
i month, how
EXERCISE LXI.
1. If 2 oranfict'*^ ^'^^^ ^' cents, find the oost of 9 oranges.
L*. If 9 pounds of riee cost 36 cents, what will 4 pounds of
rice cost?
;{. If John walk 27 miles in 9 hours, at the same rate how
far will he walk in seven hours*
4. If 12 yards of cloth cost $.'30, find the cost of 17 yards of
the same kind of cloth.
;'). If 17 tons of coal cost $102, find the cost of 25 tons.
0. If $40 laiy 20 yards of cloth, how many yards can be
bought for $00?
7. If ir)0 yards of cloth are required to make 15 dresses,
how many dresses can be made from 210 yards?
8. If 17 men can husk 1088 bushels of corn a day, how many
bushels can 27 men husk in the same time?
9. If a train goes 21G miles in 8 hours, how long will it take
to go 297 miles at the same rate?
10. If 2800 sacks of coffee weigh 470400 pounds, what will be
the weight of U^oO sacks?
d to 10000000
EXERCISE LXII.
1. If 7 men can do a piece of work in 9 days, in how many
days can 3 men do the same work ?
2. Ten men can finish a piece of work in 57 days; how long
will it take 6 men to do it?
3. If 12 men can build a wall in 30 days, how long will it
take 18 men to do it?
4. If a garrison of 150 men have provisions for 45 days, how
long will they last 250 men?
5. How long will it require 20 horses to do the work of 24
horses for 15 days?
(]. If 25 men can do a piece of work in 9 days, how many
men will be required to do it in 15 days?
7. If a drain is dug by 36 men in 100 days, how many men
would be required to dig it in 80 days?
46
AKITHMKTIC.
S. A i»i»*«'«' of work was to h:ivo Ikuti ]>«'i'forin(Ml ])y (!0 men
in 4") days, but a iiuiuh*'!' worn MiHcliar^^fil and so tin* work lasted
50 days. How many were discliarj;ed?
9. A fyarrison of 1200 men had provisions to last 4 months,
but in a battle a number were killed and the i)rovisions lasted
the remainder 5 months. How many were killed If
10. If 25 men can do a pieee of work in li6 days, how many
men will be required to do '.i timen as much work in 12 days?
EXERCISE LXIII.
1 . Divide 36 marbles between two boys so that one may have
4 more than the other.
2. Two boys together liave 50 marl»les and one has ten more
than the other. How many has eachf
'.i. Two loads of wheat toj^ether contain 85 V)ushols and one
has 7 bushels more than the other. How many busliels are
there in eaeh load?
4. Two pieces of cloth tojsjether contain 100 yards; one of
the pieces is 16 yards longer tlum the other. How long is each?
5. There are 94 examples in two exei'cises. There are 6
more in one than in the other. How many are there in each
exercise?
6. The sum of the ages of two boys is 27 years, and one is
3 years older than the other. How old is each?
7. In a game of cricket two boys together made 47 runs.
One made 9 more than the other. How many did each make ?
8. At an election 240 persons voted. There were two
candidates and the successful one beat his opponent by 18 votes.
How many votes did each receive?
9. In two journeys a bicycle rider rode 157 miles. He rode
23 miles farther the second journey than the first. How far did
he go on each journey?
10. Two skaters race for an hour round a circular course.
The sum of the number of circuits made is 387. The winner
beats his opponent by exactly 3 rounds. How often did each
go round the course?
EXERCISE LXIV.
1. A number when divided by 5 gives 3 for remainder, and
when the quotient is divided by 7 the new quotient is 241 and
the remainder is 4. Find the number.
2. The remainder after division is 97; the quotient is 342,
and the divisor is 91+97+342. Find the dividend.
MISCELLANEOUS EXERCISES.
47
ne may have
las tt'n more
:}. A drover houglit I'J7 (attic at .$.")(» each, and 93 more at
$45 each. He lost 1 of tlu* first lot and 'J of the second, and
sold all the r»«Ht at $(5;') euch. Find his f?ain.
4. A train starts from Toronto for C^ucIk'c, HIG miles away,
at 2li miles per hour. At the same time another starts from
(Quebec for Toronto at 21 miles per hour. How far from Toronto
will they meet?
5. A man earns $1180 per year. He spends $348 during the
year. How much does he save per week if 52 weeks make a
year?
G. A newsboy buys 120 papers at 2 cents each and sells them
all at 2 for 8 cents. How much dees he gain?
7. A wagon loaded with coal weighs 2612 pounds. The
wagon alone weighs 1112 pounds. If the load is woith 450
cents, what will be the cost of a ton of 2000 pounds?
8. In a stack of hay there are 23G88 pounds. A buys it at
!j<15 per load of 2632 pounds. How much is the stack worth?
9. Multiply the greatest of the following numbers by the
least, and divide the product by the other number: 324, 510, 108.
10. A merchant was in business 17 years. He gained $2240 a
year during the first G years and $3036 a year afterwards. What
was his whole gain?
otient is 342,
EXERCISE LXV.
1. From the sum of 47916, 842, 4983 and 1714, take 47168;
multiply tho remainder by 184, and divide the result by 46.
2. If 75 bushels of wheat cost 6375e., for how much must 1
sell 63 bushels to gain 252c. on what is sold?
3. A grocer gave 153 barrels of flour at 900e. a barrel for 81
barrels of sugar of 170 pounds each. What did sugar cost per
pound ?
4. The product of three numbers is 7650, and the product
of two of them is 450. What is the other number?
5. A man gave 50 geese and 35 turkeys for 55 bushels of
wheat at 100c. a bushel. If turkeys are worth 90e. each, what
are geese worth?
G. If 65 bushels of wheat cost 8450c., what should 195
bushels cost, when the price has fallen 20c. a bushel?
7. A grocer pays 20864c. for syrup at 128c. per gallon.
Some leaks out, and the rest is sold for 25920c. at 180c. per
gallon. How many gallons leaked out?
8. A drover bought 68 cattle at $47 each. He sold half of
them at $54 each and the rest at $45 each. How much did he
gain?
liBulB
48
ARITHMETIC.
9. A nncrcliiuit l»<>ii^,'lit 4S yards clotli iit 02 cvuU a yanl nnd
81 yiinis iit 7">c. a yanl. Ho s«>M tlio first lot at Sic a yaid
and tlif latt«'r at HiU. a yard. Fiiul his total j^aiii.
Id. If 1!> liorst'H aii*l 'JS cows are worth .tl.M'_':», and 1 I horses
are worth pj'.i'>, lind tin? value of lil cows.
EXERCISE LXVI.
1. How many fjeent pieces are there in ITocfllOcjlOle.
+2()r)e.?
2. How many luilfdollar pieces are there in 1710c. +2940c.
+1 5250.+ 1775c.?
3. How much greater is IS times $1054 tlian 9 times $3307?
4. A person Itonj^ht a inimber of cows at ^'<iS each and as
many liorses at $90 each. He paid $2814 for all. How many
of each did ho btiy?
5. If 120 feet of lumber cost 240c., what will 900 feet cost?
0. If 17 tons of hay cost $204, liow many stacks of liay, each
containing 9 tons, can be bought for $1 1H8?
7. A merchant bought 07 i>ieees of cloth of 94 yards each at
240c. a yard. He sold it all at 288c. a yard. How much did ho
gain?
8. A farmer bought land at $49 per acre and an equal
quantity at $78 per acre. He paid altogether $31750. How
many acres did he buy?
9. If 17 yards of silk cost 5100c.. how many bushels of potatoes
at 55 cents a bushel must be given for 11 yards of silk?
10. If 5 hats cost as much as 9 pairs of gloves, and one pair
of gloves cost 125c., how many hats can be bought for 3825c.?
EXERCISE LXVil.
1. A man bought wheat at 47 cents a bushel and sold it at 50
cents a bushel. He gained 327045c. How many bushels did
he buy?
2. A merchant bought 13 bales of cloth of 27 pieces each,
and each piece contained 34 yards. What is it worth at 17
cents a yard?
3. A moulder has 17385 pounds of metal. Find the least
number of pounds he must buy in order to mould cannon balls
weighing 08 pounds each and use all the metal.
4. A jeweller sold 15 clocks and 22 watches. For the clocks
he got $12 each, and for a watch 7 times as much as for a
clock. How much did he get for all?
5. A man bought 103 barrels flour at $9 a barrel; 15 barrels
were spoiled, and the rest sold at $11 a barrel. Did he gain or
lose, and how much?
MISf'KLLANKors KXKKC'ISKR.
49
I II liorm'rt
fi. Tf 4 Ituslicls (if wlifiit of (!0 ])nini(ls ciMli will iiiiiko 1
hnncl (if ll(»tir, how iniiiiy itoiiiids of wheat will he nMiuiri'd for
1(50 barrels of flour?
7. I borrowed from A OaSfic. ; from B, 40:510.; from (\
101 HHe., and from J), DOHc. 1 paid E u debt of 197580. How
much had I leftf
8. I ])ou{;ht :J24 i)onv.,ls of tea for LU.'JOOc. If I sold it at an
ndvaneo of 15 eeiils a pound, what was my whole gain and my
Belling ]»ri(*e j>er ]»oun(ll'
9. How mueh tea at 46 cents a pound must be given in
cxelmnge for 18 gallons of maple synip at 92 eents a gallon?
10. What number multiplied by 79 will give the same product
as 1279 multiplied by 55.'{?
EXERCISE LXVIII.
1. In a division question the divisor is 8 times nnd tho
quotient is 7 times the remainder. What is the dividend, tke
renuiinder being 1()8?
2. It two steamers leave Quebec for Liverpool at the same
tinie, one going 18 miles and the other 14 miles an hour, how fur
will the first be ahead of the second in 37 hours?
;{. By selling 31 horses for $3100 I lose $155. For what
should I sell 16 horses to gain $597?
4. If 59 articles cost 4307c., for how much must 23 of them
be sold to gain 183c. on those sold?
5. A drover bought 84 horses for $11424. He sold them at
$108 each. Find his gain.
0. Two equal sums were divided, the one among 9 men, the
other among a number of boys. Each man received 300c. and
each boy 18e. How many boys were there?
7. The salary of the President of the Fiiited States is
$.50000 a year. What sura may he expend each year, and yet
save $75584 in 4 years, his term of office?
8. A man bought a farm for $3012. He sold half of it at $50
an acre for $2408. How many acres did he buy and what dM
he give per acre?
9. Two men had an equal interest in a herd of cattle. One
took 72 at $35 apiece and the other took the rest at $42 apiece.
How many cattle were there in the herd?
10. A man travels due north for 7 days at the rate of 37 miles
a day. He then returns on his path at the rate of 29 miles a
d;iy. How far is he from the startingpoint at the end of 12
days' travel?
CHAPTER III.
COMPOUND INtlVIBERS.
I. TABLES, DEFIINITIOINS, AIND REDUCTION.
A Simple quantity is one expressed in terms of a
single unit, as 4 yards, 5 miles, 16 onnees.
A Compound quantity is one expressed in terms
of more tlian one unit, as 4 yards 2 feet.
Reduction is the proifess of (Oianjjing the unit or
denomination of a simpki or eompound quantity
without changing tlie value of the quantity.
Reduction Descending is the i>roeess of ehang
ing a quantity from units of a higher denomination
to those of a lower denomination.
Reduction Ascending is the process of changing
a quantity from units of a lower denomination to
those of a higher denomination.
Canadian Money.
100 pentH (ct.) = l dollar, or $1.
Ten Mills make one cent. The mill is not coined.
EXERCISE LXIX.
Reduce the following to cents: —
1. 7 dollars 25 cents; 4 dollars Scents; 5 dollars and 5 cents.
2. 30 dollars 4 cents; 100 dollars 90 cents; 3000 dollars.
3. $7.0(5; $10.45; $80.07; $100.90; $27.05; $404.04.
4. $100.01; $1000; $101.81; $1000.01; $70007.70.
5. $371.75; $575.49; $6184.72; $378.84; $907.09.
Reduce the following to dollars or to dollars and cents: —
6. 700 cents.
7. 1001 cents.
8. 27010 cents.
9. 97000 cents.
10. 470S41 cents.
3084 cents.
57648 cents.
47006 cents.
2000007 cents.
1010101 cents.
50
44968 cents.
10000 cents.
7400007 cents.
4710071 cents.
20600609 cents.
TAHI.KS, DKKINITIONH, ANI> RKDUCTION. 61
StcrMnfl, or English (Money.
4 farthingH (fiir.) = l penny, or Id.
12 pence =1 shilling, or 1h.
20 shillingH =1 pound, or £1,
21 Hhillings =1 guinea.
A farthing is written Jd. ; two fartliings, M.
EXERCISE LXX.
Hodiire to farthings: —
1. Hd.; 124d.; 375d.; 451d. ; 784d.; 1960d.; 7000d.
Kedn('(« to pence: —
2. OS.; 71s.; lOOs. ; 241s.; 3C9s. ; 2978.; 9000s.
Hcduce to shillings: —
;{. C7; i:i7; €90; £419; £48 178.; £100 12s.
Keduce to farthings: —
4. 58. Gd.; 88. 4d. ; lOs. fid.; 12s. 3 far.; 19s. 9d. ; £10.
T). CO 10s. ; £4 18s. ; £7 8d. ; £5 l.'Js. lOd. ; £50 lOs. 5id.
licduoe to pence: —
<). 30 far. ; 720 far. ; 425 fur. ; 900 far. ; 1000 far. ; 2700 far.
Reduce to shillings: —
7. 80d.; 168d.; 37r«d. ; 1805d. j 17G89d.; SOOOd.
Reduce to pounds: —
8. 80s. 764s. 1879s. 4.567s.
9. 768d. 3689d. 7416d. 87651 d.
10. 3084 far. 7689 far. 45672 far. 78947 far.
Avoirdupois Weight.
16 ounces (oz.) =1 pound, or 1 lb.
100 pounds =1 cental, or hundredweight, or 1 ewt.
20 hundredweight=l ton, or 1 t.
7000 grains (gr. ) =1 pound avoirdupois.
437A grains =1 oz. avoirdupois.
14 lb. =1 stone.
Avoirdupois weight is used for weighing all articles, except
the ]»reeious metals, jewels, and medicines when dispensed.
In Great Britain 2240 lb. make a ton, called the long ton.
sSassfaK:
iiBMi
52
ARITHMETIC.
Troy Weight.
24 fcrains (gr.) =^1 pennyweight, or 1 dwt.
20 penny\veight8= 1 ounce, or 1 oz. Troy.
12 ounces =1 pound, or 1 lb. Troy.
480 grains =1 oz. Troy.
57G0 grninfj =1 pound Troy.
Troy weight is used for weighing the precious metals, gold,
silver, and platinum.
Apothecaries* Weight.
20 grains (gr.) = l scruple, or 1 ^ _
3 scruples =1 drair, or 1 3
8 drams =1 ouncu, orl ^^
12 ounces =1 T>ound, or 1 Bb.
Apothecaries' weight is used in compounding medical
prescriptions.
Long, or Linear Measure.
12 inches (in.) = l foot, or 1 ft.
3 feet =1 yard, or 1 yd.
5 J yards =1 rod, or 1 rd.
320 rods =1 mile, or 1 mi.
mi. =320 rd.=1760 yd. =5280 ft,^80 cfiains.
A huTid, used in measuring horses, 4 in.
A knot, used in navigation, =6086 ft.
A fathom, used in measuring depth at sea, =6 ft.
Gunter's Chain, used in measuring land, = 100 links.
1 chain=4 rd.=22 yd. =66 ft. =792 in.
Square, or Surface Measure.
144 square inches (sq. in.) = l square foot, or 1 sq. ft.
9 square feet =1 square yard, or 1 sq. yd.
30i square yards =1 square rod, or 1 sq. rd.
160 square rods =1 acre, or 1 A.
640 acres =1 square mile, or 1 sq. mi.
10000 square links (sq. 1.) =] square chain, or 1 sq. "h.
10 square chai'.is =1 acre.
^4840 sq. yd.
160 acres =1 quartersection.
TABLES, DEFINITIONS, AND REDUCTIONS.
53
Cubic, or Volume Measure.
1728 cubic inches (on. in.) = l cubic foot, or 1 eu. ft,
27 cubic feet =1 cubic yard, or 1 cu. yd.
128 cubic feet =1 cord, or 1 cd.
Firewood and rough stone are measured by the cord.
A cord is equal to a pile 8 ft. long, 4 ft. wide, and 4 ft. high.
Dry Measure.
2 pints (pt.) = l quart, or 1 qt.
4 quarts =1 gallon, or 1 gal.
2 gallons =1 peck, or 1 pk.
4 pecks =1 bushel, or 1 bu.
In Great Britain gr.iin is sold by the quarter (8 bushels).
Certain articles are sold not by bulk, but by weight. The
following table gives the weight of a bushel of a number of
these: —
Dried Apples, 22 lb.
Oats, 34 lb.
Barley, 48 lb.
Buckwheat, 48 lb.
Timothy See'l, 48 lb.
Flax Seed, 50 lb.
Indian Corn, 56 lb.
Kye, 56 lb.
Fine Salt, 56 lb.
Beans, 60 lb.
Peas, 60 lb.
Clover Seed, 60 lb.
Wheat, 60 lb.
Potatoes, 60 lb.
Turnips, 60 lb.
Onions, 60 lb.
Liquid Measure.
2 pints {pt.) = l quart, or 1 qt.
4 quarts =1 gallon, or 1 gal.
The Imperial gallon contains 277*274 cu. in.
A cubic foot of water weighs 1000 oz. or 62i lb. and contains
Gi gal. Thus a gallon of water weighs 10 lb.
Time Measure.
60 seconds (sec.) = l minute, or 1 min.
60 minutes =1 hour, or 1 hr.
24 hours =1 day, or 1 da.
7 days =1 week, or 1 wk.
,'565 days =1 common year, or 1 yr.
I)(i() days :=1 leap yt;M'.
Tliirty days have Septehil>er.
A]>ril, »luiie and November.
'V\u' other months, cxMcpt Fcltruary, liavc ;J1 days each.
Felti'uai'y has 28 days, except in leaj* year, wheii it has 2iK
Sj«e
54
ARITHMETIC.
The leap years are those whose numbers can be divided
exactly by 4, except in the ease of the even hundreds. These
must be exactly divisible by 400. Thus 1892, 1896 and 1600
were leap years; 1894, 1897 and 1900 were not leap years.
Each day is considered to commence at midnight.
Circular, or Angular Measure.
60 seconds (") = 1 minute, or 1'.
60 minutes =1 degree, or V.
360 degrees =1 circumference, or 1 C.
A degree of the circumference of the earth at the Equator
contains 60 geographical miles, or 69' 16 statute miles.
Miscellaneous Units.
12 units =1 dozen, or 1 doz.
12 dozen — I gross, or 1 gro.
12 gross =:1 great gross. 196 lb.
20 units. =1 score, or 1 sc. 200 lb.
24 sheets=l quire, or 1 qr.
20 quires=l ream, or 1 rm.
= 1 barrel of Hour.
= 1 barrel of pork.
29 lb.
7 t. 1200 ll>.
nso oz.
:J671S4 oz.
128 lb.
7 t. b') oz.
7162 oz.
789641 oz.
29 ft. :} in. 145 It. (i in.
EXERCISE LXXI.
Reduce to ounces Avoirdupois: —
1. 2 lb. 5 lb.
2. 2 t. 3 t. 50 11».
Reduce to pounds Avoirdupois :
3. 36 oz. 480 oz.
Reduce to tons: —
4. 4216 lb. 82161 lb.
Reduce to inches: —
5. 7 ft. 9 ft. 8 ill.
Reduce to yards: —
6. 27 ft. 464 in.
Reduce to square inches: —
7. 8 sq. ft. 17 sq. ft. 100 sq. in.
Reduce to square yards: —
8. 78 sq. ft. 876 sq. ft. 3()89 sq. in.
Reduce to cultic inches: —
9. 3 (Ml. ft. 5 cu. ft. 9 fii. ft. 121 (Ml. ft. 100 (mi. in.
Reduce to cords: —
10. 1768 cu. ft. 5768 cu. ft. 9764 cmi. ft. 96."341 cu. ft.
37'6i") in.
f) sq. yd.
17854 in.
^q. ft.
17(5415 s<. in.
TABLES, DEFINITIONS, AND REDUCTIONS.
55
96 qt. 1 pt.
568 pt.
EXERCISE LXXII.
Reduce to pints j —
1. 4qt. 7 qt.
Reduce to gallons: —
2. 27 qt. 761 qt.
Reduce to bushels: —
3. 4768 lb. wheat.
Reduce to pints: —
4. 3 gal. 5 gal. 1 qt.
Reduce to gallons : —
T). 17 pt. 245 pt.
Reduce to seconds: —
6. 7 mill. 5 sec. 17 hr. 15 min.
Reduce to days: —
7. 120 hr. 71856 min.
Rediue to seconds: —
8. 24' 768' 17"
Reduce to degrees: —
9. 700'
471 qt. 1 pt.
9765 pt.
57896 lb. oats. 76891 lb. rye.
7 gal. 3 qt. 9 gal. 1 qt. 1 pt.
7689 pt. 2010 pt.
5 da. 1 hr. 7 min.
33333 min. 796841 sec.
34° 15' 19"
956'
7689"
S«'lect the leap years out of the following: —
10. 1760 1815 1800 1837
EXERCISE LXXIII.
1856
171° 51"
76451"
1890
Add the following: —
1.
£
s. d.
24
12 6
25
13 9
17
18 10
15
7 8
o
c\v*.
lb. oz.
17
xG 14
18
21 10
18
16 7
i1
9 4.
3.
vd.
ft. in.
15
I 7
23
2 9
35
6
2 11
£
s.
d.
25
16
8
17
13
9
14
17
11
16
10
7
t.
cwt.
lb.
40
16
16
16
18
94
47
15
87
21
9
75
yd.
ft.
in.
3
o
10
4
')
5
5
6
4
2
7
£
s.
d.
123
14
6
137
18
10
246
19
11
301
8
9
t. cwt.
lb.
oz
7 17
15
15
18 14
47
12
19 8
76
10
9 20
87
14
y*i
ft.
in.
17
2
11
14
1
9
12
1
7
13
6
I
56
ARITHMETIC.
4. bu. i»k. qt.
5 1 3
6 I 1
2
3 2
5. gal. qt. \)t.
13 2 1
2 3
15
_ 7 1 _1
Subtract the followint?;
G. £ s. d.
7 9 6
4 5 9
V>ii. ])k. qt. i»t.
6 3 5 1
8 16 1
9 2 5
7 3 4 1
da. hr. mill. see.
15 18 50 49
1 13 59 59
4 23 4
10 11 1 4
f?Hl,
qt.
pt
36
')
1
42
1
1
25
3
28
3
1
10.
t.
ewt.
lb.
27
14
56
16
18
94
1)U.
l.k.
qt
56
1
27
3
1
da.
hr. mill.
sec
5
16
21
18
2
22
12
37
o
/
,'/
48
51
17
17
57
28
£
s.
d.
50
1
30
10
10
yd.
ft.
in.
14
1
4
10
2
11
bn.
]>k.
qt
27
1
1
18
1
3
wk. da. hr. min. sec .
1 2 13 40 30
2 6 10 8 3
5 22 55 45
2 3 4 1 15
ewt. lb. oz
20 45 7"
16 22 13
yd. ft. ill.
54
6 19
gal. qt. pt,
4 10
3 2 1
wk.da. hr. rain. sec.
3 4 23 45 30
1 6 16 30 45
25 36 15
18 45 36
c. yd. eft. c.iii. p. yd. eft. c. in.
48 16 1000 100 760
16 2^ __! 245 4824 1 000
EXERCISE LXXIV.
Multiply the following:
1.
£
s.
d.
£
H.
d.
ewt.
lb.
oz
13
5
10
5
75
15
8
6
15
18
9
9
3.
t. ewt. IV). oz.
7 14 16 7
8
bu. pk. qt. i)t.
4 2 3 1
4. gal. qt. ]>t.
15 2 1
12
yd.
ft.
ill
17
1
11
12
bu.
pk.
qt.
l»t
7
3
7
1
12
dit.
11'. mill.
17
17
17
9
yd.
ft.
in.
87
9
11
gal
qt.
pt.
4
3
1
7
da. lir.
mill.
sec ,
5 19
41
52
8
TABLES, DEFINITIONS, AXD REDUCTIONS.
57
qt.
pt.
2
1
1
\
3
3
1
min.sec.
40
30
8
3
5a
45
1
15
t. lb.
oz
45
7
; 22
13
I. ft.
in.
i
3 1
9
il. qt
. pt.
4 1
3 2
1
.
D '
ft
:5 36
15
S 45
30
•.ft.
0. in
760
24
1000
lb.
o/,.
18
9
9
. ft.
ill.
Ml
9
n
ll. qt.
pt.
3
1
7
. mill
Hce
1 41
52
8
5.
17' 41' 57"
t
84" L>7' 28"
5
f. yd. eft.
7 24
e.in,
245
11
J
Divitl
t tlu' followiiif^: —
0.
£ s. d.
4)81 17 8
& 8. d.
7)36 7 5
cwt. lb.
6)47 15
oz.
4
r
t. cwt. lb. oz.
8)20 5 16 8
yd. ft. in.
6)75 2 6
yd. ft.
1;)83 2
in.
3
8.
bu.pk. qt. pt.
7)34 2 5 1
bu.pk. gal. qt.
9)73 1 1 1
gal. qt.
5)78
pt.
1
y.
gal. qt. pt.
7)30 2 1
hr. min.st'.
9)1479 57 36
diX. hr. mill
3)563 17 47
. sec.
51
10.
4)77° 2' 48"
7)876° 5' 48"
e.yd. eft.
9)178 14
c.in.
81
EXERCISE LXXV.
Divide the following: —
1. £30 6s. 8d. by £2 6s. 8d. ; £8 18s. by 5s. 6fd.
2. 3 t. 16 cwt. by 19 lb. ; 1 t. 16 cwt. 83 lb. 12 oz. by 105
lb. 4 oz.
3. 44 yd, 2 ft. 9 in. by 33 in. ; 7 yd. by 6 in.
4. 78 A. 71 sq. rd. by 1 xV. 3 sq. rd. ; 100 sq. yd. by 1 sq. ft.
36 sq. in.
5. 327 eu. ft. 1094 eu. in. by 1 cu. ft. 14 cu. in. ; 74 cords
by 148 eu. ft.
6. 87 bu. by 1 qt. 1 pt. ; 29 bu. 1 pk. 1 qt. 1 pt. by 5 pt.
7. 33 gal. 3 qt. by 1 qt. 1 pt. ; 30 gal. 2 qt. 1 pt. by 7 pt.
8. 12 hr. 48 min. by 16 sec. ; 8 da. 3 hr. by 1 hr. 15, miu.
9. 2° 42' 30" by 2' 5"; 7,C. by 1° 30'.
10. 35 rm. by 15 sheets; 75 rm. 15 qr. by 5 qr.
EXERCISE LXXVI.
1. Wliat is the height of a horse that stands 14 hands high?
2. How many pints of molasses are there in a hogshead
containing 63 gallons?
3. Find the number of hours in January.
4. How many parcels, each weighing 15 lb. 4 oz., can be
made from 1 ton, and what weight will be remaining?
m
m
%
58
ARITHMETIC.
f). If nil onnoo of i>iiro pnld is worth C3 17s. lO^d., find thr
value of 11 l»ar of pur** f^ohl wjifjclilii};; 2 ll». G o/,.
(}. What IS the value of K2 marks, when a mark is worth
138. 4i\.1
7. A rect.aiffular box is 4 ft. 4 in. long, 1 ft. 10 in. wide and
17 in. deep, outside measurement. Find the lengtli of a string
that will go round it — (1) lengthwise, (2) crosswise.
8. The angles of a triangle contains 180^. One angle is
42° 36' 45", another is 29° 42' 37". Find the third angle.
9. If the posts in a telegraph line are 45 yards apart, how
many are there in 9 miles?
10. If the wool from a sheep each year weighs 7 lb. 8 oz.,
find the value of the wool from a flock of 300 sheep at $19.()0
per cwt.
EXERCISE LXXVII.
1. A merchant bought tobacco at $55 a cwt., and sold* it at
4 cents an ounce. How much did he gain on 3 cwt.?
2. How many telegraph poles are there in 1(5 mi. 80 rd. of
line, the poles being 4 rd. apart?
3. Find the cost of a pile of wood containing 3328 c. ft. at
$4 per cord.
4. A farm is 50 chains long and 20 chains wide. How many
yards long are the boundary fences?
5. Find the value of 17 sq. miles 85 ae. of land at $15 per
acre.
6. Find the number of minutes from 17 minutes to ten in
the forenoon till 25 minutes past three in the afternoon.
7. A grocer bought a cheese weighing 45 lb. 6 oz. He sold
2 lb. 4 oz. to one woman, 1 lb. 8 oz. to a second, and 3 lb.
12 oz. to a third. How much of the cheese remains unsold?
8. A cubic foot of water weighs 62 lb. 8 oz. How many
tons of water are there in a tank containing 480 c. ft.?
9. A gallon of water weighs 10 lb. How many gallons art*
there in the tank in question 8?
10. Find the cost of grading a railroad 57 miles long at $5.50
per yard.
EXERCISE LXXVIII.
1. How many tons of provisions are required to feed 480
men for 60 days, if each man receives 3 lb. 2 oz. each day?
2. How many silver spoons, each weighing 2 oz. 8 dwt., can
be made from a bar of silver weighing 12 lbs. ?
3. How often can 2 ft. 3 in. be subtracted from 81 yards?
TABLES, DEFINITIONS, AND REDUCTIONS.
5U
4. If Mar> takes 'J miii. 20 see. to reiul a l)af,'o ol" a book,
how many such pa^^es ean sh« read in I{r> minutes?
T). If a bicycle rider jroes 2 miles 'Ait rods every (i min., how
far will lie go in '2 hours?
(). A merchant bouf?ht 7H0 yards of doth at J)s. lid. a yard,
iind retailed it at 12s. Id. a yard. Find his total gain.
7. If it costs 12s. Gd. more to build a fence ^5 yards long
thiin one IJO yards long, find the cost of building 75 yards of
such fence.
8. A man bought 3G72 lb. of oats at 27 cents a bushel and
3136 lb. of rye at 4G cents a bushel. How much had he to pay?
9. Seventyfive bushels of wheat at 68 cents a bushel will
buy how numy yards of cloth at 85 cents per yard?
10. A merchant bought 71) reams of foolscap, for which he
paid $237. How nnich did he pay for a quire?
EXERCISE LXXIX.
1. A merchant sold to one man 19 gal. 3 qt. 1 pt. of
molasses; to another he sold 27 gal. 2 qt. 1 pt., and had 48 gal.
1 i)t. left. How much had he at first?
2. Out of a cask having 27 gal. 1 pt. of vinegar, 14 gal.
2 qt. were sold. How much remained in the cask?
3. A farmer sold six loads of wheat which grew on one field,
as follows:— The first weighed 47 bu. 36 lb., the second 48 bu.
15 \h., the third 47 bu. 35 lb., the fourth 47 bu. 55 lb., the
fifth 48 bu. 19 lb., and the sixth 38 bu. 56 lb. How much
wheat grew on this field?
4. There are 12 acres in the field referred to in the last
example. Find the yield per acre.
5. A clock which gains 45 seconds every 8 hours is set right
at noon on Monday. When it is 8 o'clock in the evening of
Wednesday what time will the clock show?
6. Find the weight of two dozen sterling silver spoons, each
one weighing 2 oz. 4 dwt.
7. If 2 lb. of gold are coined into 89 guineas, find the value
of i)ure gold per ounce.
8. 7000 grains make a pound Avoirdupois, and 5760 grains
a i)ound Troy. How many pounds Avoirdupois are of the same
weight as 350 lb. Troy?
9. Find the cost of feeding 120 horses for 20 weeks when
hay is $8 a ton and oats 30 cents a bushel, if a horse eats 20 lb.
of hay and 10 quarts of oats a day?
10. A wagon with 128 packages weighs 2 t. 60 lb. If the
wagon weighs 1 t. 140 lb., find the average weight of a package.
CHAPTER IV,
SIMPLE APPLICATIONS OF THE PREVIOUS RtLES.
I. BILLS AND ACCOUNTS.
A Debtor, in business transactions, is a pureliasor,
or a person wlio receives money, goods, or servi(^es ,
from another.
A Creditor is a seller, or a person who parts with
money, goods, or servi(*es to another.
A Bill is a detailed statement of goods sold or of
services rendered, and of payments, if any, made. It
should show the place and time of each transaction,
the buyer and seller, the quantity, price and cost
of each article, and any payments received.
Mrs. F. S. Brown.
Form of a receipted Bill.
Toronto, Jan. 12, 1900.
Bought of Hii.r. & Weir.
»ee.
26
( <
27
28
u
( (
12 yd. Calico, @ 16 ct. . . .
2 Silk Scarfs, @ $1.35 . . . .
30 yd. Linen Crash, @ 21 ct. .
4 pair Kid Gloves, @ $1.50 . .
Ik doz. spools Cotton, 60 ct.
1 piece Ticking, 42 yd., @ 37 ct.
Received Payment,
1
92
70
6
30
6
00
90
15
54
$33
Henry F. Wat^^rbury,
for KtLL & Weir.
60
36
BILLS AND ACCOUNTS.
61
i
RULES.
Li'chaser,
servi(^es
arts with
old or of
aacle. It
usaction ,
and cost
12, 1900.
1
92
70
6
30
6
00
90
15
54
$:j3
36
EXERCISE LXXX.
Make out Bills for the following, supplying names of places
and dates where necessary: —
1. Mrs. James Brown bought of John Marsh: — pair shoes
(li) .$3.25, 8 yd. silk @ $2.40, 3 pair gloves @ $1.25 and 9 collars
(a) 25 ct.
2. Mrs. John Green sold Charles Jenkins: — 75 bu. apples (ff>j
S5 ct., 5 tons hay @ $10.85, 50 bu. potatoes @ 60 ct. and 50
cabbages @ 10 ct.
3. John Smith sold Peter Brown: — 25 horses @ $115, 143
cows @ $27, 24 oxen @, $45 and 175 sheep @ $5.50.
4. J.ames Sparrow bought of Messrs. Jones & Son: — 52 lb.
butter @ 18 ct., 16 yd. silk @ $1.45, 23 pair boots @ $2.40, 19
lamps @i $2.35 and 28 lb. sugar @ 6 ct.
5. Mrs. R. Philp bought of the R. Simpson Company: — 6
l»ureaus @ $8.75, 3 easy chairs @ $15.25, 12 dining chairs @
$4.(50, 15 mattresses @ $4.50, 2 tables @ $18.75 and 4 mirrors
@ $9.75.
6. Samuel Purdy sold Mrs. T. Jones: — 125 lb. sugar @ 8 ct.,
17 bbl. flour @ $7.75, 48 lb. lard at 11 ct., and 48 lb. meat
13 ct.
7. Mrs. T. Rorer bought of Messrs. Jones & Co.: — 4 yd.
cloth @ $1.25, 12 pair stockings @ 38 ct., 6 pair kid gloves @
$1.15 and 27 yd. ribbon Qt} 5 ct.
8. Simon Brown sold Mrs. T. Smith:— 21 lb. butter @ 22
ct., 12 lb. cheese © 16 ct., 114 doz. eggs @ 15 ct., 23 qt. milk
@ 6 ct., 27 bu. potatoes at 45 ct. and 32 bu. carrots @ 40 ct.
9. Mrs. Blake bought of the T. Eaton Company: — 2 lb.
candy @ 15 ct., 5 books @ 25 ct., 3 slates @ 12 ct., 2 quires
l>aj)cr @ 10 et., 1 box pens @ 35 ct., and 1 box slate pencils
@> 10 ct.
10. The R. Simpson Co. sold Mrs. P. Scott: — 25 lb. sugar @
7 ct., 32 lb. tea at 45 ct., 84 11). coifee @ 35 ct., 62 lb. raisins
(<i/ 9 ct., 39 lb. currants @ 8 et. and 47 lb. biscuits @ 10 ct.
EXERCISE LXXXI.
Make out bills for the following, supplying names of places
and dates where necessary: —
1. .Tames Smith bought of Edward Jones: — 75 cords hard
wood @ $4.50, 10 tons coal @ $6.50 and 15 cords pine @ $2.50.
He ]»aid cash $150.
2. Peter Douglas sold James Rogers: — 10 lb. sugar @ 5 ct.,
(5 lb. tea @ 35 ct., 8 lb. colTee @ 25 ct., 5 lb. rice at 7 ct., and
9 lb. cheese @ 16 ct. He took in exchange 4 bags potatoes at
90 cts. and the balance in cash. Make out a receipted bill.
IR.
■1
m
ARITHMETIC.
3. William Taylor bought from John McMurtry:— 10 lb.
sugar @ 8 ct., 6 lb. tea @ 45 ct., 1 set dishes @ $10. .50, 1.') lb
soap @
another.
15 ct. He paid $5 iu cash at one time and $1 at
Make out tin* bill.
4. Thexton Bros, bought from RoV>ert Smith:— 25 tons hay
® $7.r)0, 66 bu. rye Qi^, 40 ct., 104 bu. barley (n), iV.i ct. and 9H
bu. wheat @ 72 ct. They give iu exchange 5 bids, flour Oi}
$7.25, and 75 lb. oatmeal @ 3 ct. and the balance in cash.
Make out a receipted bill.
5. Smith & Weir bought from Thomas Scott:— 1140 lb.
wheat @ 84 ct. per bu., 1802 lb. oats @ 45 ct. per bu., 540 bu.
peas© ^0 ct. and 1200 !b. barley @ 48 ct. per bu. On Oct. 17,
1899, he received $100 in cash and the balance on Oct. 28.
Make out a receipted bill.
6. Mrs. Brady bought from Smith & Jones:— 7 doz. eggs @/
18 ct., 19 lb. soap @ 11 ct., 10 lb. butter at 22 ct., 13 lb. cheese
@ 17 ct. and 20 lb. rice @ 4 ct. She gave in exchange 5 geese
weighing 54 lb. @ 6 ct. and the balance in cash. Make out a
receipted bill.
7. Mrs. R. Porter bought from Jones & Co., Belleville: —
27 yd. flannel Qi} 80 ct., 32 yd. calico @ 9 ct., 6 pair gloves at
90 ct. and 16 yd. muslin (a) 12 ct. She paid $10 cash. Make
out her bill.
8. John Smith bought of Hill & Groves, London: — 16 yd.
silk (a>, $1.15, 72 yd. ticking @ 14 ct., 42 yd. shirting @ 15 ct.,
12 yd. flannel @ 40 ct. and 24 yd. print @» 13 ct. He paid
cash. Make out a receipted bill.
9. Thomas Taylor bought of Lewis & Sons, May 5: — 5 doz.
coat hooks @ 35 ct., 7 door knobs @ 20 ct., 25 lb. nails @ 4
ct., June 1st, 5 door locks © 75 ct., 12 doz. screws at 7 ct., 3
sets fireirons @ $3.15. Thomas Taylor sold Lewis & Sons,
June 10, 1 pair boots @ $3.50, 1 pair rubbers @ 75 ct. The
balance was paid June 20. Make out a receipted bill.
10. Henry Philps sold to Aaron Brown: — 75 yd. Bri.ssels
carpet @i 96 ct., 1 piece cotton, 31 yd., @/ 11 ct., 1 box hooks
and eyes @ $1.75, 1 piano cover @ $5.50, 1 table cover @
$3.25. Brown worked 10 days @ $1.40 per day for Philps and
paid the balance in cash. Make out a receipted bill.
11. June 14, 1899, Samuel Farwell bought the following
items of H. J. Thompson & Co. : 9 lb. of paint at 12 ct. a
pound; 10 rolls of paper at 20 ct. a roll; 28 rolls at 8 ct. a roll;
44 rolls at 10 ct. a roll; 4 rolls at 25 ct. a roll; 34 yards of
border at 6 ct. a yard; .58 yards at 2 ct. a yard; 60 yards at 1
ct. a yard. July 7, 1899, Mr. Farwell returned 3 rolls of paper
at 8 ct. a roll, 5 rolls at 10 ct. a roll, and 5 yards of border at 6
ct. a yard. Make out Mr. Farwell's ivccount.
SIMPLE MEASUREMENTS.
G3
II. SIMPLE IV1EASUREIVIEINTS.
A Rectangle is a flat surface bounded by four
straight lines and having its four angles equal to one
nnother.
A Square is a rectangle contained by equal sides.
A Rectangular Solid is a space enclosed by six
rectangular surfaces.
EXERCISE LXXXII.
Draw the followinj^ rectangles and find their perimeter: —
1. 2 in. by ii in., 4 in. by 3 in., 5 in. by 6 in., 4 in. by 4 in.
2. Tlu3 ceiling of a rectangular room is 16 ft. by 12 ft. Find
its perimeter.
3. A rectangular lot is 50 yd. long and 40 yd. wide. Find
the cost of fencing it at 25 ct. per yard.
4. How many boards 12 ft. long are there in a fence round a
rectangular lot 60 yd. long and 40 yd. wide, the fence being 5
boards high.
5. The posts in a fence round a rectangular lot 60 ft. by 144
ft. are 6 ft. apart. Find the cost of digging the post holes at
5 ct. each.
6. How much will it cost to fence a farm 200 rods long and
80 rods wide at $1.25 per rod?
7. How much will it cost to fence both sides of a road for 1
mile with wire which weighs 1 lb. per rod and costs 8 ct. per
lb., the fence being 5 wires high?
8. A square cattle ranch is 2 miles long, how many yards of
fencing will enclose it?
D. How much will it cost to enclose a mile square with wire
fencing at $4.50 per chain?
10. A rectangular room is three times as long as it is wide.
Its perimeter is 320 feet. Find its length and width.
EXERCISE LXXXIII.
1. Find the area of each of the following rectangles: —
34 ft. by 36 ft.
32 ft. by 38 ft.
72 yd.
by 78 yd.
2. Find the number
of acres in each
of the
following
rectangular fields: —
36 rd. by 40 rd.
25 rd. by 64 rd.
75 rd.
by 32 rd.
70 rd. by 96 rd.
48 rd. by 50 rd.
38 rd.
by 80 rd.
3. How many square feet are there in a board 18 ft. long
and 12 in. wide?
64
ARITHMETIC.
4. How many sciimre yards are thfro in :i rt'ctaii>?ular floor
33 ft. by l»l ft.f
5. A Bqiiare garden is 48 yd. long. How many Kqiiaro yards
doeH it contain f
6. A close board fence 6 ft. liigh and 100 yd. long is to bo
painted. How numy square yards are tliere in the fence?
7. How numy square inches are there iu the surface of a
brick 8 in. long, 4 in, wide, and 2 in. deep?
8. How many square foet are there in the walls of a rectan
gular room I'J ft. high, 28 ft. long and 1(5 ft. wide?
9. A rectangular i)]ot 00 ft. by 130 ft. has a path roiind the
outside 5 ft. wide. Find the number of square feet iu the
path.
10. How many square feet are there in a board 18 ft. long
and 13 in. wide at one end, 19 in. wide at the other.
EXERCISE LXXXIV.
1. A rectangular floor contains 48(5 s(i. ft. It is 27 ft. long;
find its width.
2. A rectangular surface contains (i48 sf. yd. If it is 108
ft. long, find its width.
3. A rectangular field containing 1(5 acres is G4 rods long.
IIow wide is it?
4. A rectangular field containing 18 acres is 80 rods long.
Find the cost of fencing it at $1.25 per rod.
5. A rectangular lot contains 1(500 sq. yd. Its length being
240 ft., find the cost of fencing it at 25 ct. per foot.
6. How many boards 12 ft. long would be required to enclose
a rectangular lot containing 9600 sq. yd. with a straight fence 5
boards high, the lot being 240 ft. wide,
7. The walls of a room contain 96 sq. yd. The room is 12
ft. high. Find its perimeter.
8. A bought a farm containing 220 acres. If it is 176 rods
wide, what will it cost to fence it iu at $1.25 per rod?
9. To paint a close board fence 6 ft. high at 15 ct. per sq.
yd. costs $36. Find the length of the fence.
10. At $25 an acre a farm costs $2000. This farm is 200 rd.
long. • Find the cost of fencing it at $1.25 per rod.
CARPETIINCi.
In computing how nnicli carpet is needed for a room
there are two modes of procedure — (1) the mathema
Heal, where the quantity equal to the floor space is
SIMPLE MEA8URKMKNTS.
C5
found, and (2) tlio p)'((r(iral or (wbifnu'i/, whcro the
iimiilMT of strips of cjirix't r('«i.ir('d is first found,
imd, an allowance beinj^ made for nuitchint? tln^
pattern as well as turning? iind<'r ait the side when
necessary, the ([uantity reciuired is then computed.
EXERCISE LXXXV.
1. Find what length of ciupt't 30 iti. wide is required for a
H'ctanK'iln''' room 24 ft. by 15 ft.
12. A r«'('tan{,'ular floor ^(5 ft. by 25 ft. is to bo covered with
oilcloth GO in. wide. How many yards will be rc(niiredf
;{. How many yards of carpet 27 )u. wide will cover a
rectangular room 18 ft. by 12 ft.
4. A rectangular room is 27 ft. by 17 ft. 6 in. How many
yanls of cari)et 27 in. wide will cover it?
5. There is a square room 42 ft. long to be covered with
carpet 1 yard wide. How many yards are required?
G. Find the cost of carpeting a rectangular room 24 ft. by 18
It. with carpet 27 in. wide at 90 ct. per yard.
7. A rectangular room 15 ft. by 12 ft. is covered with carpet
:») in. wide which costs 65 ct. per yard. Find the cost.
8. Find the cost of carpeting a rectangular room 36 ft. by 20
ft. with carpet a yard wide at $1.25 per yard.
9. Find the cost of carpeting a rectangular room 12 f1 . by ^S
ft. with carpet 27 in. wide at 75 ct. a yard.
10. Find the cost of carpeting a stairway of 24 steps, each
step being 11 in. wide and rising 7 in., with carpet at $1.05 per
yard.
EXERCISE LXXXVI.
1. How many strips of carpet 36 in. wide are required to
cover a rectangular room 27 ft. by 18 ft. — (1) if the strips run
lengthwise, (2) if they run crosswise?
2. How many strips of carpet 27 in. wide are needed to
cover a rectangular room 18 ft. wide, if the strips run
lengthwise?
3. How many strips of carpeting 30 in. wide are needed for
a square room 40 ft. long?
4. How many strips of oilcloth GO in. wide are required to
cover a room 40 ft. wide, the strips running lengthwise of the
room?
"). A rectangular room, 22 ft, 6 in. wide, is covered with
carpet 27 in. wide. How many strips are there?
* •.I
'cm
66
ARITHMETIC.
6. How many yards of carpet 30 in, wide will be required
for a rectangular rooru 27 ft. V)y 20 ft., the strips running
lengthwise of the room ?
7. How many yards of carpet 36 in. wide are needed for a
rectangular room 24 ft, by 18 ft., the strips running lengthwise
of the room?
8. Find the cost of carpeting a rectangular room 24 ft. l>y
21 ft., witli carpet a yard wide at $1.05 per yard, the strips
running lengthwise of the room.
9. Find the cost of carpeting a rectangular room 27 ft. by
20 ft., with carpet 27 in. wide at $1.10 per yard, the strips
running crosswise of the room.
10. Find the cost of carpeting a rectangular room 30 ft. l>y
22 ft., with carpet 30 in. wide at $1.25 per yard, the strips
running crosswise of the room.
PLASTERING.
Ill reckoning tlie area to be plastered in a room,
there are two methods of procednre— (1) the mafhema
tiraJ, wliere the exact number of square yards is found
l)y finding the total area within the boundary line of
the work, and from thi leducting the area of all the
openings; and (2) the irbitrarij or practical method.
In this case the total i.i'ea within the boundary lines
of the work is found. From this area, half the are?i
of the doors and windows is subtracted. The nearest
whc^ d number of square yards in the remainder is the
area for which the plasterer is to be paid.
EXERCISE LXXXVil.
1. How many square yards of plastering are there in the .
ceiling of a rectangular room 30 ft. by 24 ft. ?
2. How many squar(^ yards of plastering are there in tlie
walls of a rectangular spfce 38 ft. long, 25 ft. wide and 12 ft.
high ?
3. How many square yards of plastering are there in the
walls and ceiling of a rectangular rocm 30 ft. by 24 ft. and
12 ft. high?
4. Find the cost of plastering the ceiling of a rectanguhw
room 24 ft. by 18 ft. at 19 ct. per square yard.
5. Find the cost of plastering a surface equal to the walls
and ceiling ot a rectangular room 27 ft. by 18 ft. and 12 ft.
high at 23 ct. per square yard.
^^
SIMPLE MEASUREMENTS.
67
6. A rectjuij?ul!ir room 27 ft. by 18 ft. and 10 ft. high has 3
doors, each 7 ft. by 4 ft.; '.i windows, eaeli (5 ft. by 3 ft., and
1 window G ft. by 4 ft. Find the area to \m plastered on the
walls only — (1) mathematically, (12) practically.
7. Find the cost of pljiHterin<j: the walls only of a rectangular
room 30 ft. by 'J4 ft. and 112 ft. high, there being 3 doors, each
8 ft. by 5 ft.; 3 windows, each 7 ft. by 4 ft., and 1 window
() ft. by f) ft., at 20 ct. ])er sq. yd. — (1) mathematically, (2)
piaetically.
8. At 25 ct. per sq. y^.., And the cost of plastering tlie walla
of a rectangular room 25 ft. by 20 ft. and 10 ft. high, there
being 2 doors 7 ft. by 5 ft., 3 windows (5 ft. V)y 3 ft., and 1
window 5 ft. by 4 ft. — (1) mathematically, (2) practically.
9. At 25 ct. per sq. yd., find the cost of plastering the walls
and ceiling of a rectangular room 24 ft. by 21 ft. and 12 ft.
liigh, there being 3 doors 8 ft. by 4 ft. and 3 windows 7 ft. by
4 ft. — (1) mathematically, (2) practically.
10. At 27 ct. per sq. yd., find the cost of plastering the
ceiling and walls of a hall 3G ft. by 27 ft. and 14 ft. high,
there being 2 doors 9 ft. by 8 ft. and 9 windows 7 ft. by 4 ft. —
(1) mathematically, (2) practically.
M
WALL PAPER.
Ill Canada and in the United States, wall paper is
usually made into rolls 8 yd. long: <>i' donl)le rolls
IG yd. long and 18 in. wide. In Great Britain the
usual width is 21 iu.
EXERCISE LXXXVin.
1. How many yards of pape. '''' in. wide will paper the
ceiling of the room in example 1, last exercise?
2. How many yards of paper 21 in. wide are required to
pai)er the walls of the room in example 2, last exercise?
3. How many yards of paper 18 in. wide will paper the walls
iiiid ceiling of the room in example 3, last exercise?
4. How many yards of paper 18 in. wide will pap^u the
ceiling of the room in example 4, last exercise?
5. How many yards of paper 18 in. wide will paper the
walls and ceiling of the room in example 5, last exercise?
6. How many yards of paper 36 in. wide will paper the
walls of the room iu example 6, last exercise?
7. The room in example 7, last exercise, is papered with
piiper 18 iu. wide. How much is "required for the walls and
ceiling?
<'A
B\
!?;• .1
asm
68
ARITHMETIC.
8. The walls of the room in example 8, last exercise, are
papered with paper 21 in. wide. How nmch is needed?
9. Find the cost of covering the plaster of the room in
example 9, last exercise, with paper 18 in. wide at 15 ct. ]>er
roll of 8 yards.
10. Find the cost of papering the walls and ceiling of the
hall in examjjle U), last exercise, with paper 18 in. wide at
25 ct. per roll of 8 ^ards.
BOARD MEASURE.
Boards one inch or less in thickness are sokl by tlie
square foot.
Thus, a board 18 ft. long, 1 ft. wide and 1 in. or
less thick contains 18 ft., board measure.
Boards more than an inch thicik are sold by the
number of feet, board measure, to which they are
equivalent.
Thus, a plank 18 ft. long, 1 ft. wide and 3 in.
thick contains 54 ft., board measure.
EXERCISE LXXXIX.
1. Find the number of board feet in the following :
(a) A board 12 ft. long, 9 in. wide and 1 in. thick.
(b) A board 18 ft. long, 16 in. wide and 1 in. thick.
(c) A board 16 ft. long, 18 in. wide and 1 in. thick.
{(i) A board 16 ft. long, 9 in. wide and 2 in. thick,
(e) A board 16 ft. long, 10 in. wide and 3 in. thick.
(/) A board 18 ft. long, 16 in. wide and i in. thick.
(g) A board 16 ft. long, 9 in. wide and i in. thick.
2. How many feet of lumber are there in a close board fence
5 ft. high, 660 ft. long, the boards being 1 in. thick?
3. How many feet of lumber are there in 100 pieces 14 ft.
long, 6 in. wide and 6 in. thick?
4. How much lumber is required to put a 12 in. board
around a rectangular field 220 yd. by 150 yd.?
5. How many ft. of lumber are there in a sidewalk 160 yd.
long, 8 ft. wide, the ])lanks being 2 in. thick?
6. How many feet, board measure, are there in 8 planks,
4 in. thick, 18 ft. long and 16 in. wide?
7. How much lumber is there in 220 yards of fencing, con
sisting of 5 sixinch boards?
SIMPLE MEASUREMENTS.
69
'W
8. A pile of lumber consists of 250 boards, each 16 ft. long,
10 in. wide and 3 in. thick. How many board feet are there f
9. Find the cost of 500 planks, 10 ft. lont?, 12 in. wide and
3 in. thick, at $20 per thousand, board measure.
■ 10. What is the value of a pile of inch lumber consisting of
2000 boards 15 ft. long and 12 in. wide at $18 per thousand?
RECTANGULAR SOLIDS.
EXERCISE XC.
1. How many e. ft. of air are there in a rectangular room
18 ft. by 16 ft. and 10 ft. high?
2. How many c. ft. of timber are there in a rectangular
stick 35 ft. long, 3 ft. wide and 2 ft. deep?
3. How many cubic yards of stone are there in a rectangular
pile 15 ft. long, 12 ft. wide and 9 ft. high?
4. How many cubic yards of earth are taken from a cellar
30 ft. long, 21 ft. wide and 9 ft. eep?
5. White pine weighs 24 lb. per cubic foot. What is the
weight of a rectangular stick of such timber 28 ft. long, 3 ft.
wide and 2 ft. thick?
6. What will the digging of a cellar 18 ft. long, 15 ft. wide
and 9 ft. deep cost at 45 et. per cubic yard?
7. A gravel pit 60 ft. wide and 360 ft. long is excavated to
the uniform depth of 17 ft. How many cubic yards of gravel
are removed?
8. How many cubic yards of stone and mortar are in the
fourrdation of a barn 60 ft. long and 36 ft. wide, the wall being
2 ft. thick and 8 ft. high?
9. How many cubic feet of masonry are there in the founda
tion of a house 40 ft. long and 30 ft. wide, the vtaii being 9 ft.
high and 2 ft. thick?
10. Find the cost of 24 rectangular blocks of stone, each 9 ft.
by 6 ft. by 5 ft., at $5.75 per cubic yard.
EXERCISE XCI.
1. How many cords of wood are there in a pile 24 ft. long,
16 ft. wide, 10 ft. high?
2. Find the number of cords of wood in a pile 48 ft. loirg,
14 ft. high and 12 ft. wide.
3. Find the number of cords in a pile of wood 120 ft. long,
4 ft. wide and 8 ft. high.
4. How much should be paid for a pile of 4foot wood,
128 ft. long and 7 ft. high, at $3 per cord?
•'m
till
■n>s
■"Tlfgl
70
ARITHMETIC.
.". Find the value of l(i pileis of w^oil, each 24 ft. long,
4 tv. wide, 8 ft. high, at $2.25 per cord.
G. Find the cost of a pile of wood 112 ft. long, 5 ft. wide
and 8 ft. high, at $2.15 per cord.
7. There are GO cords of wood in u pile 8 ft. wide and 12 ft.
high. How long is the pile?
8. There are ;{5 cords of wood in a pile 14 ft. high and 64
ft. long. How wide is the pile ?
9. Tiie cost of a pile of wood at $3 per cord is $;{60. It is
240 ft. long and 8 ft. wide. How high is tiie pile?
10. At $2.25 per cord a pile of wood is worth $2;{G.25. It is
5 ft. wide and 12 ft. high. How long is the pile?
EXERCISE yxil.
1. There are 70 e. yd. of earth taken from a cellar 18 ft.
long and 15 ft. wide. How deep is the cellar?
2. A rectangular room 30 ft. by 25 ft. contains 8250 c. ft. of
air. How high is the room?
3. In a pile of wood there are 6 cords. The i)ile is 4 ft.
wide and 8 ft. high. How long is it?
4. A stick of square timber contains 180 c. ft. It is 30 ft.
long and 2 ft. wide. How thick is it?
5. A brick wall 2 ft. thick and 40 ft. high contains 89G0
c. ft. How long is the wall?
6. A l)rick contains 64 c. in. How many bricks are there in
a rectangular pile 12 ft. long, 8 ft. wide .and 7 ft. high'
7. There are 3072 c. ft. of masonry in a stone wall 8 ft. high
and 2 ft. tliiek. How long is the wall?
8. If the wall in example 7 is the stone foundation of a barn
60 ft. long, how wide is the barn?
9. A rectangular box 48 in. long and 30 in. deep, inside
measurement, contains 25 e. ft. How wide is the box?
10. A rectangular cutting 360 yd. long and 25 ft. wide has
17000 c. yd. of earth taken out of it. What is the average
depth of the cutting?
EXERCISE XCIII.
1. Twofoot wood is piled 6 feet high. How long must the
pile be to contain 3 cords?
2. How much will it cost to have a tin roof put on a stable,
each slope of which measures 25 ft. by 14 ft. at $5.75 per 100
sq. ft.?
n
SIMPLE MEASUREMENTS.
71
3. From a lot 40 rods square IGO sq. rods wtMe sold. Wlint
is the value of the remainder at $120 per acre?
4. A cubic foot of black spruce weif^hs 2K lb. Find the
wcifjfht of 10 planks of this wood, each 16 ft. long, 1 ft. wide
and o in. thick.
f). A ton of hard coal occui)ies 4L* c. ft. How many tons of
hard coal will a bin 1(5 ft. long, 12 ft. wide and 7 ft. deep holdt
0. How many tons of water will a tank 1<) ft. long, 12 ft.
wide and 8 ft. deep hold? (1 c. ft, weighs 1000 oz.)
7* A street (»()0 ft. long and 24 ft. wide lias to be filled in to
the depth of li ft. How many cubic yards of earth wil' be
required?
8. Find the cost of laying a tile drain a mile long at 15 ct.
per foot.
9. What will it cost to enclose a mile square with wire
fencing at $4.50 per chain?
10. What will it cost to shingle a barn, the roof of which is
80 ft. long and the slope on each side 30 ft. at $1.50 por 100 sq.
ft.?
EXERCISE XCIV.
1. How much will it cost to ])aint a close board fence G ft.
high around a rectangular lot 36 yd. by 32 yd. at 12 ct. per sq.
yd.?
2. What length of road 66 ft. wide will contain one acre?
3. How many rectangular sods each 20 in. by 9 in. will be
required to sod a rectangular lawn 60 ft. by 75 ft.?
4. What must be the depth of a wagon box 10 ft. long and 4
ft. wide that the contents may be 120 c. ft.?
5. A rectangular box is 6 ft. 8 in. long, 4 ft. 6 in. wide and
3 ft. deep, inside measurement. Find the cubic content of the
box.
6. A bicycle wheel is 10 ft. 1 in. around the tire, and turns
17280 times in a journey from A to B. How far is A from B?
7. What length of board 16 in. wide will contain 20 sq. ft.?
8. What length of board 15 in. wide will contain 11 sq. ft.
;{G sq. in.?
9. How many square yards of oilcloth will be required to
cover a rectangular room 20 iiu, 3 in. long and 16 ft. wide?
10. A rectangular box 11 ft. 3 in. long and 5 ft. 4 in. wide
contains 300 cu. ft. How deep is the box?
Ill
m
72
ARITHMETIC.
III. SHARIING.
EXERCISE XCV.
1. Divulo !f40 bt'twoiMi two )»oys so that one may have $6
more thau tlie otlier.
2. James and Thomas have 41) yd. of cloth, and James has
11 yd. more tlian Thomas. How many has each?
',i. Divide 84 marbles between James and Robert, giving
Robert 12 more than James.
4. Divide $99 between two boys, giving one $1.50 more than
the other.
'). Divide $50000 between A and B, giving B $4000 hiSs than
A.
0. A hovso and bnggy are wortli $375, and the liorse is worth
$55 more than the bnggy. Find the value of each.
7. A man earned $790 in two years. In the first year he
earned $54 more thau the 2nd, find the amount earned each
year.
8. Two trains start at the same time from Montreal and
Harnia, a distance of 508 miles. When they meet one has gone
M miles less than the other. How far has each gone?
9. 750 votes were polled for two candidates. The elected
one had a majority of 34. How many votes had each?
10. A house and lot together cost $5750. The house cost
$3250 more than the lot. Find the cost of each.
EXERCISE XCVI.
1. A yacht and its fittings cost $0400. The yacht cost
$3840 more thau the fittings. Find the cost of each.
2. A farmer raised 4375 bu. of wheat in two years. In the
second year he had 247 bu. more thau iu the first. How many
bu. had he in each year?
3. A merchant bought $4908 worth of hardware and groceries.
The groceries cost $484 less thau the hardware. Find the cost
ot the hardware.
4. The perimeter of a rectangular field is 1200 yd. and the
length is 119 yd. greater thau the width. Find the length and
width of the field.
5. Three times the sum of two numbers is 1830, and one is 18
more than the other. Find the numbers.
0. Four times the sum of two inimbers is 3984, and one is 72
less than the other. Find the numbers.
SHARING.
78
<! t
7. Two men topfether chopped 52 cords of wood. One
chopped 3 cords 50 c. ft. more chan the other. How much did
each cho])?
H. Two adjacent fields together contain 20 acres. The larger
contains 90 sq. rods more than the other. Find the area of each
lieUl.
9. Two men are ten miles apart. They walk straight
towards each other, and when they meet one has gone 90 rods
less than the other. How far has he walked?
10. Two loads of hay together weigh 3 t. 8 cwt., and one
weighs 12 cwt. more than the other. Find the weight of each.
EXERCISE XCVII.
1. Divide 120 marbles between two boys giving one three
times as many as the other.
2. Two books together contain 762 pages, and one has twice
as nniny pages as the other. How many p'tges are in each?
[i. Two pieces of cloth together contain 115 yards, and one
piece is 4 times as long as the other. How long is each?
4. Two houses are together worth $12250. One is worth 4
times as much as the other. Find the value of each.
5. Two men have together $243. One has $18 more than
twice as much as the other. How much has each?
(). Two lots are together worth $607. One is worth $27 more
than thrice tiie other. Find the value of each.
7. Two farms are together worth $139.50. One is worth $150
more than three times the other. Find the value of each.
8. Find the length and breadth of a field whose perimeter is
240 rods and the length three times the breadth.
9. A and B together own 120 acres, A having 24 acres more
than B. A sells his part at $84 an acre and B sells his for the
same amount of money. What does B get per acre?
10. At an election 4977 votes were polled. The successful
taTulidate received 17 votes more than three times as many as
liis oi>ponent. How many votes did each receive?
EXERCISE XCVIil.
1. Divide $84 between two men, giving the first $3 as often
as the second gets $4.
2. A mixture of 210 bu. of oats and peas is made up as
follows: — For every 2 bu. oats there are 5 bu. i)eas. How
many bushels are there of each?
3. A roll of bills contains $153. It is made up of an equal
number of $5 bills and $4 bills. How many are there of each ?
^'!ii
74
ARITRMETIC.
4. Divide $19500 between two men so that when the first
f^ets $2 the second may get $3.
5. Two books together contain 605 pages. B^or every five
pages in the first bool< there are six pages in the second. How
many pages are there in each book?
6. Divide $120 among three men so that when the first gets
$1 the second may get $2 and the third $'l.
7. Divide 150 marbles among t' ~ boys so that when t'le
1st gets 2 marbles the 2nd may get . :.d I . 3rd 5.
8. A sum of money, $2.40 is made n of Ir ct. pieces, t( n
ct. pieces and twentyfive ct. pieces and the ^.XAie number 3f
each. How many are there of each?
9. Divide $1120 among A, B, and C, so that A may have 3
times as much as B, and C may have as much as A and B
together.
10. Three houses are together worth $16410. The first is
worth twice as much as the other two together and the second
is worth $570 more than the third. Find the value of each.
EXERCISE XCIX.
1. A man sold three sheep for $31. For the second he
received $2 more than for the first, and for the tliird $3 more
than for the second. How much did he receive for each?
2. Three men weigh 456 lb. The 1st weighs 18 lb. more
than the 2nd and the 2nd 18 lb. more than the 3rd. Find the
weight of each.
3. Three pieces of cloth contain 444 yd. The 1st has 25 yd.
more than the 2nd but 19 yd. less than the 3rd. Find the
length of each piece.
4. Three loads of hay weigh 6400 lb. The 1st weighs 200
lb. more than the 2nd and the 2nd 400 lb. more than the 3rd.
Find the weight of the 1st.
5. Three pigs weigh 402 lb. The 1st weighs 27 lb. nfbre
than the 2nd but 48 lb. less than the 3rd. How much does
each weigh?
6. In three days A rode 125 miles upon his bicycle. The 1st
day he went as far as on the other two days all but 5 mi.
The 2nd day he rode 15 mi. less than the 3rd day. How far did
he go each day?
7. The perimeter of a triangular field is 249 rd. The 1st
side is 36 rods longer than the 2nd but 42 rd. shorter than the
3rd. How long is each side?
8. In three books there are 108G pages. The 3rd has 74
more than the 2nd and 196 more than the 1st. How many
pages are there in each book?
AVERAGES.
75
9. In three years a man saved $1593. In each year he saved
$81 more than in the preceding one. How much did he save
each year?
10. Three bins contain 573 bu. of wheat. The Ist has 110
bn. more than the 3rd and 53 bu. less than the •2nd. How many
bushels are there in each bin?
11. The cost of 5 bu. of oats and 8 bu. of wheat is $(>.80 and
the cost of a bu. of wheat is 33 ct. more than a bu. of oats.
Find the cost of a bu. of oats.
12. A box contained 286 marbles, red, blue, and white.
There were 192 red and white, and 199 blue and white. How
many of each kind were in the box ?
IV. AVERAGES.
The Aggregate of a nuni])ei' of qnantitios of tlio
.same kind is their entire number, or sum.
The Average of a number of quantities of the
same kind is the quotient arising from dividing
their sum by the number of addends; thus, the
average of 4,^8 and 9 is (4+8+9)3, or 7.
EXERCISE C.
Find the aggregate of the following: —
1. 47, 275, 368, 495, 784 and 6.
2. 571, 0, 100, 367, 2461, 78, 96 and 10.
3. 6746, 89745, 3689, 4875 and 78964.
Find the average of the following : —
4. 5 and 9; 7 and 13; 4, 8 and 15.
5. 9, 12, 16 and 19; 0, 7, 12, 15 and 21.
6. 26, 37, 49 and 60; 27, 0, 0, 16, 25 and 28.
7. A man trolling caught three fish; the 1st weighed 16 lb.,
the 2nd 11 lb., and the 3rd 15 lb. Find their average weight.
8. A's age is 45, B's 30, C's .35, D's 60, E's 70 years. What
is the average of their ages?
9. A man sold goods in six days to the following amounts:
$80, $75, $92, $64, $210, $193. What did his sales average per
day?
10. Seven houses are worth, respectively, $10000, $12000,
$8500, $7525, $4260, $4180, and $3200. What is their average
value I
ittl
76
ARITHMETIC.
EXERCISE CI.
1. Tho avpi'njjo woipht of 9 boys is 73 \h. 't oz. Find tlieir
nfXfiff'di^tt* weipfht.
2. The nvornge speed of a triiiii for 1*2 hours is 21 mi. 120
rd. Find the distajiee travelled during that time.
3. A farmer sells loads of wheat havinj? an averapje of 45
bu. 30 lb. per load. Find the value of tho loads at 75 ct. per
liushel.
4. A woman sells 12 turkeys of an averjipe weipfht of 13 lb,
8 oz. What did she receive for the lot, turkeys being worth H
ct. per lb.
5. A farmer brought to market a load of 15 hogs of an
average weight of 2 ewt. 35 lb. What was the aggregate
weight of the hogs?
0. The aggregate weight of turkeys is 113 1)». I oz. What
is the average weight of a ttirkey?
7. A train goes 333 mi. in 10 lir. What is the average speed
per hour?
8. In one of the classes in a school the aggicgate attendance
for the week was 225. What was the average attendance each
of the five days ?
9. A earns $3900 in a year. What does he earn each week,
there being 52 wks. in a year.
10. The aggregate weight of 24 tubs of Itutter is 591 lb. Find
the average weight of a tub.
EXERCISE Cll.
1 . Bouglit 1 cow for $36, and 2 others for $30i a piece.
What was their average cost ?
2. A grocer mixes 9 lb. of sugar at 5 ct. a jmund with IS lb.
at 8 ct. a pound. What is a i)Ound of the mixture worth?
3. A jeweler mixes 20 oz. of gold 18 carats fine with 12 oz.
10 carats fine. How fine is the mixture?
4. A grocer sold 7 lb. of tea at 55 ct. per lb. and 21 lb. at 35
ct. per lb. What was the average price?
5. A grocer mixed 20 lb. of sugar of a certaiji kind with 40
lb. worth 9 ct. per lb. The whole was worth 8 ct. per lb.
What was the price of the first kind of sugar?
6. I bought 500 bu. of wheat, part at 70 ct. per bu. and the
rest at 75 ct. per bu. The average price was 72 et. per bu.
How many bu. of each kind did I buy?
AVER AUKS. 77
7. The ftvcrnj^c iM'i^lit of 4 boys is 5 ft. 1 in. Wluit \h t\w
iK'i^'lit of u fifth boy, tlie uv«'i'ag«' hei^'lit of the five being 4 ft.
11 hut
K. The aggregate weight of ') men is 800 lb. Tlie aggregate
weiglit of tliree of them in ,'iJli lb. Find the average weight of
the otlier two.
9. A ])erson mixes 1 lit. of his best eoiTee with ') lbs. at Is.
4d. a lb., and produei s a mixture wortli Is. 4id. a lb. What is
the priee of liis best eoffee/
10. If 1") lb. of sugar are bought at 4d., jind 24 lb. at 6^d.,
iind if the two quantities ar«' tlien mixed and sold at 7d., how
much will be gained/
EXERCISE cm.
1. The weights of some hogs are as follows: 250, 320, 27'),
H22, 415, 2i:{, 244, 214 and 195 pounds. What is the average of
tiieir weights atid their aggregate weight?
2. In 1898 the value of hay and clover grown in the counties
bordering on Lake fhie was as follows: — Essex $5;J019.'{, Kent
$()9;{773, Elgin $(539646, Norfolk $404300, Haldimand $597953,
and Welland $559775. VV^hat was the average value of this
croj) per county?
3. If a doz. eggs weigh 1 lb. 8 oz., what is their average
weight?
4. A merchant mixes 4 lb. of coffee worth 32 et. a pound 3
lb. worth 35 ct. and 2 lb. worth 41 ct. What is the mixture
worth a pound?
5. Of candidates for office, 7 were 20 yrs. old, 12 were 22, 12
were 23, and 1, 24. What was the average age of the
candidates?
6. A drover bought 30 cows at $22 a head, 40 at $25 a head,
30 at $28 a head. What was the average price per head?
7. A merchant mixed 24 lb. of sugar at 5 cents a pound, 30
11). at 6 ct. and 26 lb. at 10 ct. What is the average price of
the mixture?
8. A merchant bought 2000 lb. of wool at 47 ct. ])ev
pound, 3000 lb. at 43 et., 5000 lb. at 49 et. and 8000 lb. at 45 ct.
Wliat was the average cost i)er lb. ?
9. In a factory a certain number of men receive $13 each
per week, 4 times as many receive $9 each per week, and 10
times as many receive $5 each per week. What is the average
weekly wage per man?
10. A goldsmith combined 8 oz. of gold 21 carats fine, 12 oz.
22 carats fine, 18 oz. 20 carats fine, with 28 oz. of alloy; required
the fineness of the composition.
'"ikS
CHAPTER V.
FACTORS, CAINCELLATIOIN, MEASURES. AND MULTIPLES.
I. FACTORS.
Whole Numbers, or Int('<?t'rs,are oitlior Odd or Erf h.
An Odd INumber is a nimihcr not cxactlv ilivisihlo
by 2, as 7, J), &(\
An Even Number is a nnnibcr oxactlv divisible bv
2, as H, 10, &i',.
A Factor of a iiuinbcr is a number wliieh will
divide the given iminber exactly, as 2, 3, 4 or 6 is a
factor of 12.
A Prime Number is one which has no integral
factors, ex(^ept itself and ouf, as 13.
A Composite Number is one which has other
integral factors than itself and one, as 12.
The Prime Factors of a composite number are
the prime numbers which, multiplied together, prodm^e
that number; thus, 2, 3 and 5 are the prime factors
of 30.
EXERCISE CIV.
Find the prime factors of the following: —
1. 12 56 84
2. 196 231 252
.3. 876 948 1052
4. 1095 1113 1127
5. 1202 1214 1218
Find the prime numbers in the following: —
(i. 781 797 821
7. 1157 1187 2067
8. 2543 2521 2007
9. 2273 23:!9 2417
10. 3397 3197 3013
78
30.
384.
1059.
1156.
1555.
1437.
2117.
2013.
2967.
3119.
OANCKLLATION.
79
EXERCISE CV.
rind tho prime fuetors common to the following: —
140 and .'JH.").
4129 and 1001.
H8S and 948.
1.
4.
().
7.
r)() and 70
10.~> and 'J:M
.')y.') and ir»47
4K4 and 470 (548 and r)40.
7120 and 748 9()0 and 912.").
Write the numbers less than 100 of wiiich 3 i8 a factor.
Write the numbers between 700 and 800 of which 1 1 is a
factor.
8. Find the larpjest factor otlier than the number itself of
each of the following? numbers:— (JO, I'Jf), 825, r)79, and 88(5.
9. Find three prime numbers that will divide each of the
following:— 30, 105, 385, 1001, 3553.
10. Resolve the followinp; into as many pairs of factors as
possible:— 60, 150, 100, 240, 3(i0.
II. CANCELLATION.
Cancellation is tlin process of rejecting erinftl
fjKitors from both Dividend and Divisor, and thereby
greatly shortening the operation of Division.
EXERCISE CVI.
1. Divide 15X16X18X20 by 5X8X3X4.
2. Divide 7X24X30X35 by 14X36X70.
3. Divide 60X66X80X90 by 15X20X88X180.
4. Divide 75X85 X 120 XI 14 by 57X102X125.
5. Divide 48X54X60X72 by 36X54X18X80.
6. Divide the continued product of 7, 8, 9, 12, 18 and 24 by
the continued product of 3, 4, 6, 6, and 6.
7. Divide the continued product of 16, 18, 20, 24, 25 and 27
by the continued product of 4, 9, 30, and 36.
8. A lot is planted with potatoe. There are 75 rows; each
row has 120 hills, and each hill has on an average 16 potatoes.
How many bushels are there, if it takes 20 potatoes to fill a
gallon?
9. Five pieces of cloth, each containing 60 yd., worth $1.50
per yard, are exchanged for 6 pieces, worth $1 per yard. How
many yards are there in each piece of the latter?
10. A bicycle rider goes at the rate of 10 miles per hour for
12 hours a day during 16 days. How many days must another
ride at the rate of 8 miles per hour for 6 hours per day to go
as far?
80
ARITHMETIC.
III. MEASURES.
A IVIeasure of n number is one of the factors of
that number.
A Common IVIeasure of two or more numbeis is
a factor common to the {^iven numbers.
The Greatest Common IVIeasure (G.C.M.) of
two or more numbers is the largest factor common to
the given numbers.
Numbers tliat have no common factor otlier than
one are said to be prime to one an otlier.
EXERCISE evil.
Find the G.C.M. of:
1.
i
12 and
56
48 and 128
65 and 91.
2.
2
10 and 455
230 and 506
210 and 294.
3.
288 and
360
352 and_384
336 and 884.
4.
27,
36,
108
32, 48, 128
56, 63, 315.
5.
75,
225,
500
210, 462, 546
546, 462, 882.
0.
216,
360,
405
168, 132, 352
146, 365, 219.
7.
36o,
511,
803
192, 576, 1760
671, 781, 1441.
8.
G39,
873,
747
808, 568, 1112
455, 403, 481.
9.
352,
992,
672
550, 770, 1210
154, 210, 420.
0.
luOl,
1365,
1820
715, 1001, 1287
1615, 969, 2261.
EXERCISE CVIII.
1. What is the length of the longest pole that will Pleasure
84 ft., 56 ft., and 70 ft.?
2. What is the length of the longest stick that will measure
15 ft. 7 in. and 18 ft. 5 i.?
3. What is the largest number that will divide 202 and 266
so as to leave 7 and 11 as remainders respectively?
4. What is the greatest equal length into which throe trees
can be cut, the first being 84 ft. long, the second 105 ft., and
the third 119 ft.?
5. What is the greatest width of carpet that will fit three
rooms — the first being 18 ft. wide, the second 22 ft. 6 in. wide,
and the third 29 ft. 3 in.?
6. A rectangular field 611 ft. by 364 ft. is fenced with rails
of equal length, and this the greatest possible. The fenc^
being straight, what is the length of a rail?
MEASURES.
81
7. A farmer has 441 bn. of oats, 567 bu. of wheat, and 315
bu. of rye. He wishes to make exact loads of the same
number of bushels of each kind of grain, and have as few loads
as possible. How many bushels will there be in a load?
8. Three debts of .$200, $1250 and $300 were paid with bills
of the same denomination. How might the debt have ])een
paid? How was it paid if the bills were the largest possible?
9. B has $620, C $1116, and D $1488, with which they agree
to purchase horses at the highest price per head that will allow
each man to invest all his money? What will be the cost of
each horse?
iO. How many rails will Inclose a rectangular field 14599 feet
long by 10361 feet wide, provided the fence is straight, and
7 rails higl>, and the rails of equal '' ngth, and the longest that
can be used?
EXERCISE ex.
Find the G.C.M. of the following: —
1.
1008 and
1026
1225 and
2247
2761 and
3263.
2.
1391 and
2247
1866 and
3421
1957 and
2987.
3.
4004 and
5772
4427 and
7219
7813 and
9015.
4.
2542 and
5487
4735 and
6629
3029 and
3961 .
5.
2951 and
3477
4559 and
7003
4055 and
7299.
6.
8128 and
8472
5544 and
8008
7956 and
9724.
7.
15444 and
13068
69615 and
92872
23673 ami
60203.
S.
45H62 and
29026
43155 and
81564
53712 and
659(51 .
9.
15249 and
27807
30429 and
88641
18577 and
20006.
10. 13230, 44100, and 118125
720100, 913330, and 211109.
EXERCISE ex.
1. Find the G.C.M. of 1365 and 1785, and from this find all
tlu' common measures of these two numbers.
2. Find the G.C.M. of 37 d. 13 hr. and 55 d. 5 hr.
3. Find the G.C.M. of 7 mi. 259 yd. and 11 mi. 407 yd.
4. Find the G.C.M. of 6 bu, 1 pk. 1 gal. and 10 bu. 3 pk. 1 gal.
5. What is the largest number that will divide 2000 leaving
a remainder of 11, and 2708 leaving a remainder of 17?
6. Find the greatest laimber that will divide 13956 and
14565, and leave a remainder of 7 in each case.
7. Find the greatest number tliat will divide 2293, 4245 and
."):U8, and leave iemainders 18, 20 and 23 respectively.
S. Whiit is the largest number of men amongst whom 209
.'ip])]es and 3(51 oranges can be distributed, so that every man
gets as many apples and as many oranges as any other man?
Ei
11*
82
ARITHMETIC.
9. Two masses of silver, weifjhing 1169 oz. an;l 139.'? oz.,
respectively, are eacii to be made, without loss, into medals of
the same weij^ht. What is the weight of the largest possible
medal?
10. A farmer has 1134 sheep and 1260 lambs. He forms them
into separate flocks, with the same number of animals in each
flock. The flocks being the largest possible, how many animals
are in each?
IV. MULTIPLES.
A IVIultiple of a imml)or is the product ()l)t}iined
by multiplying tlie given number by any whole
number.
Thus, if 7 is multiplied sueeessively by 1, 2, 3, 4, .">,
&(^, the products 7, 14, 21, 28, 35, &c,., are multiples
of 7.
From this, it follows that every multiple of a
number is exactly divisible by that number.
A Common IVIultiple of two or more numbers is a
iium))er which is one or more times each of the given
numbers.
Thus, 24 is a common multiple of 2, 3, 4, 6, 8, &c.
The Least Common Multiple (L.C.M.) of two or
more numbers is the least number that is one or more
times each of the given numbers.
EXERCISE CXI.
Find the L.C.M. of the following:—
1.
4,
6, 8
6, 8,
10
2.
5,
15, 25
25, 30,
40
3.
5,
7, 9
12, i:^,
17
4.
12,
IS, 24, 30
18, 30, 30,
42
f).
32,
48, ()4, 72
30, 40, 50,
CO
6.
14,
18, 20, 21
51, 187, 1.53,
105
t .
10."),
198, 242
312, 429, 572,
715
8.
510,
,^)95, G80
432, 840, 693,
(iOO
9.
19;')),
2001, 3451
2041 , 8470,
3423
10.
1554,
1058, 18058
4410, 7350,
7875
8, 10, 12.
36, 48, 60.
13, 15, 19.
24, 36, 42, 56.
60, 66, 72, 77.
203, 429, 494, 570.
287, 451, 455, 715.
253, 345, 414, 495.
2743, 400l», 4199.
2001, 4278, 4495.
MULTIPLES.
88
9;i oz.,
jdals of
possible
ns them
in eac'li
animals
3, 4, r>,
lultiples
>le of a
ibers is a
:lie given
6, 8, &(^
of two ov
} or more
10,
12.
48,
GO.
15,
19.
i, 4'2,
56.
), 72,
77.
), 494,
570.
1,455,
715.
>, 414
495,
4()0it,
4199.
4278,
4495
EXERCISE CXII.
1. Find the L.C.M. of the first six even nuni])ers.
2. Find the smallest number of apples that can be arranged
in gi'OU])s of 8, or 9, or 15, or 20 each.
.'J. Find the L.C.M. of the prime numbers between 4 and 18.
4. Find the L.C.M. of all the odd numV)ers between 8 and 16.
5. What is the least number from which 16 and 24 may each
be taken an integral number of times?
(). Find the least number that can l)e divided by 7, 20, 28
and ;J5 respectively and leave 3 as remainder in each case.
7. What number is the same mi Itiple of 7 that 1962 is of 9?
8. Divide the L.C.M. of 23949 and 26610 by their G.C.M.
9. What is the shortest piece of wire that can be cut into
exact lengths of either 6 ft., 8 ft. or 10 ft.?
10. Wliat is the capacity of the smallest cistern the full
contents of which will exactly fill a fourgallon, a tengallon
or a fifteen gallon measure a certain number of times;
EXERCISE CXIII.
1 . What is the smallest delit that can ]>e ]>aid with an exact
number of 2dollar, or 4dollar, or 10dolIar i>ills?
2. What is the gresitest weight of which 1 t. 19 cwt. 4H 11).
iind 4 t. 14 cwt. 47 lb. are multiples?
'.). What is the greatest weight of which 2 t. 4 cwt. 18 lb.
and 5 t. 4 cwt. 34 lb. are multiples?
4. How often does the L.C.M. of 5, 12, .36, 42 and 84
contain the G.C.M. of 7266 and 8022?
5. A rides at the rate of 6 miles per hour, B at the rate of
1(1 miles per hour, and (' walks at the rate of 3 miles per hour.
Find the shortest distance each may go in an integral number
of hours. .
6. What is the least number which divided by 8, 9, 10 and
12 respectively gives in each case a remainder of 5?
7. What numbers less than 200 leave 2 .as remainder when
divided by 3, or 4, or 5, or 6.
8. What is the smallest quantity of wheat that can be taken
lo market in either 20, 25, 30, or 40 bushel loads?
9. The prodiu't of four consecutive numbers is 43680. What
lire the numbers;'
111. One pound Avoirdupois weight contains 7000 gr. and one
pniind 'i'roy weight 57(50 gr. Find the least weight whicli can be
expressed integrally in l)oth Troy and Avoirdupois pounds.
■ •,^1
CHARIER VL
FRACTIONS.
I. DEFIINITIOINS, INOTATIOIN AIND INUMERATIOIN.
A Fraction is a number whieh expresses one or
more equal parts of a wJiole, or unit.
A Common or Vulgar Fraction is expressed by
two num))ers, one above and the other below a short
horizontal line; thus *, ro, iiud /a are Common, or
Vulgar frjietions.
The Denominator is the nuniber below the line,
and shows into how many equal parts the whole, or
unit is divided.
The Numerator is the number above the line, and
shows the number of equal parts in the fraction.
The numerator and denominator are calle'i the
Terms of the fraction.
A traction indicates also the quotient arising;, irom
dividingr the numerator l)v the denominator. Thus
4
f means
i. Four of the parts when a unit is divided into
five equal parts,
ii. The quotient when four is divided by live,
iii. Onefifth of tour units.
tXERCISE CXIV.
Express in fif;«i!'ps: —
I. Twothirds;
'J, Five ei^.iths;
;{. Sixsevenths
'ihree fourths ; Four fifths.
Fivenintlis; P''ivetwelfths.
Sixtlnrteeuth: ; Sixseventeenths.
4. Seventwenty 3i'!its; Sevtntwelfths; Seventhirtyseconds.
84
ii\
Ml
oi
«>
b<i
1
rioiN.
s one or
•essecl by
w a short
union, or
the line,
wlioU', or
line, and
tion.
;alle<l tlie
Isin^^ ii"f>»^
,r. Thus
Ivided into
)V tive.
lis.
llt'ths.
Iiteeuths.
lirty seconds.
REDUCTION.
Write in words: —
5. f
1
4
A.
6. i\
H
il
H.
7. H
H
^1
il.
Explain tlie meaning of
the following
fnietionB: —
8. f in.
f ft.
B a.
$t\ .
9. I hr.
H
1 3
21
1^\.
10, 1 cord.
H cwt.
Ub.
h t.
85
II. REDUCTION.
A Proper Fraction is one of which the nunier
iitor is less than the denominator, as j;, L
An Improper Fraction is one of whili the
numerator is equal to or greater than the denomin
ator, as r, V .
A mixed Number is a number which consists of
the sum of a whole number and a fraction, as 21.
A fraction is in its lowest terms when the numer
ator and denominator are prime to each other.
Similar Fractions are those that have a common
denominator, as f , f , i and V".
When the terms of a fraction are both mutti
plied by the same number or are both divided by
the same number, the value of the fraction is
not altered.
A Simple Fraction is one in w^hich the terms
are ])oth whole numliers and which expresses one or
more of the equal parts of unity, as f, .
A Compound Fraction is one which expresses
one or more of the equal ])arts of a fraction, as I of
3, a or T.
A Complex Fractio^i is one in which one or
i 4 2]
'Mm
l>otli terms 'are fractirTis, a.
■>, Oj, Si;,
•Ar^. ^>
86
ARITHMETIC.
EXERCISE CXV.
Redupe to improper fractions: —
1.
2i
4J
21
43.
2.
ek
7i
81
41.
3.
51
6*
8 A
9.^.
4.
18 i
192
2U
25L
5.
43 i\
101 1
1411
262V5.
6.
163 t*j
275 ^
4611^
403^1.
7.
20711
H.lO^r
908 y
78U].
8.
310A
5694 3
678,V:t
6982V0.
9.
1001, V
OCrin
8080f,l
7000 i,V,
10.
7018A
705?!!?
368 ln
37^1 01.
EXERCISE CXVI.
1. .John has two apples. To how many boys can he give
half an apple?
2. Among how many jrirls must 5 melons be divided 'lat
each may receive i of a melon r
;>. How many fifths are there in ii api>les?
4. How many persons will 5^ cords of wood supply, if each
one receivjs i cord?
5. A gave $i to each one of a number of boys. He gave
away $151 . How many boys were there?
6. Express both '1 and 7 as fractions with denominator 15.
7. (^liunge 48 to ninths and 57 to tenths.
8. What fractions with denominator 24 are equivalent to 3,
5, 8, and 12, respectively?
9. A walked a mile each quaricr hour. He walked for 3i
hours. Hi w far did he go?
10. To make badges i yd. 'oug for n :;lass, 5^ yd. of ribbon
are needed. How many pupils arc tiiere in the class?
EXERCISE CXV5K
Reduce to whole numbers or to mixed numbers: —
1.
f
1 5
8
3.
S 5
4.
Hi
¥/
¥
¥.
V
.{ 5
T2
H
u.
w
8 «H
^5
REDUCTION.
87
i),
G.
mm
i.
H.
!).
10.
H31
I 35
H (Ml
1 1 ff
4 » t »
24
76 84
2:1
8 :< 6
4 1
925
21 f mi.
54 I
1 2:1
6 01
700 1
830 1
fill '
764
3 1
gal.
cords.
9 7 8
1 5 I
5 2 3 1.
52.7
6 89 7
1 9 3 f
6 8 1
« 7
^V da.
36 9
TT
yd.
1 (I n I)
7 3 .
17 18
1 I 3 3 •
76 84 9
223 1
8 5 6 7
8^3 •
253
S
6 94
TT
11).
oz.
EXERCISE CXVIII.
1. How much money has John who has $'/?
'J. If a basket of peaclies holds i bu., how many ])ushels are
tliere In ;{69 baskets?
15. A walked from X to Y at the rate of a mile each i hr.
He walked h^ hr. How far is it from X to Y?
4. A druggist has 97 psiekages of medicine, eaeh weighing
h lb. How many pounds does the medicine weigh?
5. How many bushels of wheat are there in 964 bags, eaeh
oontaining i bu.?
6. Which is the he.ivier — 786 packages, each holding i lb.,
or 6'J9 packages, each holding i lb. ?
7. Express ^ in., fs lb., H: oz., eaeh as a whole inimber.
8. A bottle holds i gal. of wine. How many gallons are
there in 5 doz. such bottles?
9. The perimeter of a rectangular room is ^ ft. It is' four
feet longer than wide. Find the length and width of the room.
. 10. A farmer sold a load of oats consisting of 79 bu. at $i
per bushel. How much did he get for the load?
EXERCISE CXIX.
1.
Reduce i,
i and  ,
each to twelfths.
h
r and i,
twentyfourths.
3.
f,
t and 1,
eighteenths.
4.
3
f and A,
twentieths.
5.
!,
f and A,
thirtieths.
G.
f and 1,
twentyfourths.
7.
i
fV and IL
thirtieths.
s.
f,
1 and i
forty seconds.
5).
5
8,
i\ and i\,
fortyeighths.
0.
5
rV and H,
sixtieths.
iii
88
ARITHMETIC.
EXERCISE CXX.
1. llediKH'
'>
3.
4.
5.
6.
7.
8.
9.
10.
1.
^1.
3.
4.
5.
G.
7.
i.
9.
10.
1 2
30
4 4
26
.id
2 6
4(1
1 4
4ft
66
93
68
1
T55
20
3 5
n
u
25
*0
4 4
80
1 5
3 5
51 T
9 1
3?f
and
and
and
and
and
find
and
and
and
and
is,
4 9,
\l
38
20
97r,
1 4 3
34 1 ,
316
6 24,
each
to fourths.
' tifths.
sevenths,
ninths,
eleventlis.
eighteenths,
twentieths,
twentyfourths,
rhirtytirsts.
fiftyseconds.
EXERCISE CXXI.
Supply numerators in =t?
1 (
4 = 33
l=TTr
I 2
16=4
84
14 4 = T?
Supply denominators in =*®
" " "535
II =
it " "11154
12 =
it a "81
12 =
" " 4^8 2
3
6
5
9
6
13
15
25
T 5 _
1 
7 _
11
H
6
TT=
8
^4 =
3 8
'8
=7T
m
'T
T
. 28
.12 1
.7 2.
.1
6
■a. ;
t
1
1 1 
1T = 5"5
1 4
an
5 5
TS2 =
1 I
1 s —
y 6 3
it =
9
2Tt =
9
TS =
1^
44
feXERCiSE CXXII.
Reduce to equivalent fractions in lowest terms:
1.
1
2.
H
3.
80
TTJ
4.
AV
5.
3 2
T57
6.
4» 2
7.
2 6 40
2])To
8.
1242
2 3 2 ;t
9.
56 8
TT f T
10.
3 1
10 9^3
9
T2"
27
4?
9
T5S
1 5 9
5TT
19 2
3 1
2 7 5 5
3 3TF
3 6 2
IT 9 3
2 112
T T TT 4
2 2 7 7
2 8971
42
¥8
72
25
2 09
21 5
36 5
"5TT
1428
T530
26 5 1
326 5
"9¥T0Tr
2 6 194
8 1
3
2 14 4 12
20 4 —
7
28.
3 6
63.
1 5
2J5
22 1
2ff0.
3 1 6
T4 6 •
1 144
170 •
226 8
3444.
47 7
6T9^D.
6 53 9
T¥7g^3
3 6 73
IS.
lis.
^nths.
^ths.
fourths.
firsts.
iconds.
^— n
1 t _44
1 S =
19 6 3
n ^^
« H 1
2fi =
9 3
Id— •
14 4 12
2 4=^"
1
28.
36
6 3'
1 5 »
221
3 1 6
T4 fi
ll 44
22 6 8
3 4 4 4 •
4 '•05
6 53 9
T 2¥¥3 •
3 6 13^
HKDUCTION.
89
EXERCISE CXXIII
•
Keduee to
equivalent f ruet
IOI18 having leant common
denominator:
1.
1 and i
H and
5
1 6
A
and ].
2.
'\ and 2\
5 and
2\
A
and n.
3.
2 and 3
i and
1
6
i
and J .
4.
3 and I
7 and
5
9
A
and "6.
5.
I and 9
": and
A
i
and A.
6.
i\ and TT
A and
iPi
A
and 2^.
7.
6 Jtnd h
i\ and
i\
f\
and 2^.
8.
A and t\
9 and
n
A
and li.
9.
iV and 11
1 1 and
2 3
2t
U
and 42.
10.
U and A
2 8 and
'h
24
and 12.
EXERCISE CXXIV.
Keduee to equivalent fractions with least common denominator;
1.
t,
2.
I
3.
A.,
4.
6
'1»
5.
A,
6.
i\,
7.
A,
8.
8
T5,
9.
1,
10.
9,
5
12
4
25
6
1
T2,
1 1
T8,
A,
ii,
11
5
1 H»
A,
and
t\
and
^V
and
U
n
and
11
and
u
and
A
and
tV
and
A
and
M
and
1 3
14
1 1
T8
1 1
^4
1 1
36
EXERCISE CXXV.
3
I»
2
Tf,
3
19)
2
5»
3
4,
1 1
1 &,
1 7
24?
1 7
2 ,
5
I 1 ,
1 H
2 6?
3
14
6
TJ
5
7 8
5
T,
1 7
2 0,
1 3
2f,
5
'IT,
5
t,
23
4 5'
and
and
and
4
46'
2
8
2T
tV
1 1
14
1 3
24
1 1
2f
2S
I 8
and
and
and
and
and
and
and
1 II •
1 1
4 2
1 9
24
1 5
28
A.
1 3
71
Which is tlie greatest and which the least of the following
fractions?
1.
2.
3.
. 4.
f, I and f
4 ,
i and .
17 6 .,,,/] 5
21, T ana 6
f,
A and I.
4, Ti and U
1,
A and 1 .
A, At, 2'8 and
1 1
3 6
At,
U, U and 11
90
AIUTHMKTIC.
Armn^«' the followinp: fnictioiiH in onlcc (tf lunpfnitiuU' : —
\L ki, U and A A A 11 1 1
7.
1
1 1
B 1
3)) t
3
3«
» 1
t\ Jiiid
1 it, JO HlUl HO
24,
4
I's, 1^8, 2 6 and U
.•ind U.
I'^s, L^. and U.
H. Find a fniftion with 00 for (Icnominutor intcnnt'diatc in
valiH' Ix'twcon I and J;.
y. Find a fraction with H4 for dcnoniiniitor ^'rcater than f;
and k'HK than ".
10. Find a fraction witli 72 for denominator as much Ush
tlian g as it is j^rcatcr tlian i'^^.
EXERCISE CXXVI.
Kcduce the following eonijtound fractions to
1.
2
3.
4.
5.
G.
7.
8.
9.
10.
of
G
1 1
I of ^
^ Of H
i of 1 I
of
1
2
J
2
IT
4
1
2
O
fi
of I
of 4^
of 3G
of^ ofl
I of i I of A
8
If
lof iij
I of A
4 of ^^
I<'f4^
i of r)G
I of I of
f of I of
9
2 5
implc! ones:
of g.
of {i.
of if.
of h
of il.
of 4L
of 72.
of I
of
1
t
5
I
1
6
7
8
6
t
5
.5
,'5
I 1
of 1 1 .
of n.
21 of G5 of 13 of 10^ 81 of m of lOi (,f 7 J
Find the sum of
III. ADDmOIN OF FRACTIOINS.
EXERCISE CXXVII.
1.
^ •
3.
4.
f).
6.
7.
8.
9.
10.
A,
IT, IT
tV,
fV,
iV
1
IT,
A,
t\
4
5,
3
4,
/.r
i
A,
41
I
1
6,
4
t,
tV,
If
if,
H,
II
H,
15
4 4 ,
H
f, 5, 9
1
T,
S
IT,
2_
? 6,
2
T,
.3
T,
4
¥)
^\,
M,
f,
2
3^,
1
7,
5
«,
5
6,
1 1
T4,
1 9
3
4,
3
5,
3
"f
8
IT
8
^S
H
5
t\
1 3
?8
9,
4
4
TST,
3
!^,
3
4,
5
6,
X
h I
2
T3,
5
3 ,
4
T,
O
M
5,
T'fT, tI,
0, 8,
t\.
9
f¥.
If.
9
■3^8.
t\.
20 .
4
■2T.
9
TI
ADDITION OP FnAOTIONS.
91
HI
EXERCISE CXXVIII.
!U1 11
udi'i.
nd \l
tMliiitc ill
T than il
MH'h less
es: —
1
5
a.
[9
Of H
L' " 2
S o
f 71
i,
5
f\,
A
A,
A
1,
If
■f,
9
^8
2
5»
iV
If,
H
M,
A
i,
A
f,
A
1.
Add i
to i
< to li
i to^
2,
iv'M li
to i
\ t.) iV
I to ,',
8.
Add ;;
to A
S to A
8 i... H
8 to 1 J
4.
Add g
t«» 2^
1 to 1
4 to l^
T).
Add 1
to A
if to A
Vf to A
G.
Add A
to A
A to A
A to iV
7.
Add /,
to .'^T
A to A
A to i\
S.
Add I
to ,\
i torV
} to ,^6
9.
Add 1
to •?
4 tog
i to A
10.
Add U t<) {3
n to 11
Htoll
EXERCISE
CXXIX.
Sini))
lify:
1.
l +,^
+ 1
+
1.
2.
3 +^
+ J
+
5
+ A.
3.
2 1 2
+ 2^«
+
5
+ A.
4.
1 1 4
8 +9
+ ^
+
r,
+ 1 +u.
T).
t + A
+ A
+
1
18
+ 21 +20.
G.
t2l +31
+ 71
+
.)!
+ C1.
7.
7i\ + 3 A
+ 4.^
+ G,^
1 +8A +GA.
8.
2:1 +3]
+ 4i
+
.)^
+ 21.
9.
11 + ^
+ 2A
+
7i
+ c.
10.
3i +9^
+ 7A
+
>■>
+ 42V.
EXERCISE CXXX.
1. John spent i of his money on Monday, i of it on Tuesday
and w of it on Wednesday. What part did he spend altogether?
2. A fanner has three fields; the first contains 10 acres, the
second 91 acres, and tlie third 9tij acres. How many acres had
he in all?
3. How many pounds of butter are there in four tubs weigh
ing respectively 274 lb., 24 lb., 30* lb., and 29A lb.
4. How man^' tons of coal are there in four loads weighing
respectively li t.. If t., Ira t. and larr t.
5. What fraction is that which exceeds S^ by i?
i:h
IMAGE EVALUATION
TEST TARGET (MT3)
1.0 !f" 1^
1.25
S *^ III
2.2
I.I 1.*^ 1^
1.8
1.4 nil 1.6
■y ^ *? />^
^'^ %. #
7
Photographic
Sdences
Corporation
23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 8724503
<V
iV
<^
^^
■\
C\
\
o^
'%
92
ARITHMETIC.
6. A weighs 172 lb. ; B weighs 5^ lb. more. How much
does B weigh?
7. What number is that from which if 4 J be taken the
remainder will be aff?
8. One man rode 17ts mi. Another rode 4A mi. farther.
How far did the second one ride?
9. A grocer has ii barrels of molasses. The first contains
JJ3i gallons, the second 45i gallons, and the third 35 gallons.
How many gallons are there in the 3 barrels?
10. On Monday A rode 35f mi., on Tuesday 40^ mi., on
Wednesday 361 mi. and on Thursday 20 r* mi.
ride in the four days?
How far did he
IV. SUBTRACTION OF FRACTIONS.
Subtract :
t^tK«
;idt CAAAI.
1.
i from f
f from 1
1 from V.
2.
4 from f
A from ii
f from .
3.
TIT from f
A from 1
f from .
4.
T*i from f
f from f 1
i from H
5.
1 fromi:
1 fromH
f from M.
6.
4 from 1
1 from^^
A from A.
7.
A from If
A from i
1 from U.
8.
U from U
A from H
fl from if.
9.
U from H
11 from H
A from Ih
10.
J from 2
f! from 3
4 froni 5.
Simplify
1.
._ EXERCISE CXXXII.
g — i ¥ —I
1 i
2.
f 1
A— A
lf.
3.
ll
AA
Hii.
4.
j\j\
Hi§
un.
0.
•sPt— /^
ilA
fiA.
Find the difference between;
—
6.
A and A
A and A
1 andA
7.
1 and il
A and A
li andM.
8.
TT and ii
^h and A
A and If.
9.
U and V2\
IS andl? '
11 andAV
10.
tV and tItt
41 and U
A\aiidI.
SUBTRACTION OF FRACTIONS.
93
ni
1^ mi., on
far did he
I is white, f red, and the rest green.
How
What
EXERCISE CXXXIII.
1. Henry had I of a dollar and spent I of a dollar,
much had he left?
2. Of a pole
part of it is green?
3. How much must be added to hi to produce '§?
4. How much does the sum of i and i exceed the sum of i
and i?
5. Subtract the difference between /g and tj from the dilTer
ence between ^V and /?.
6. The sum of two fractions is fj and one of them is H
Find the other.
7. Find the sum of the greatest and least of the fractions
\hi hri, 1, I, and subtract this sum from the sum of the other
two fractions.
8. A traveller went VV of his journey on foot, A by railroad,
and the remainder on horseback. What part of the journey did
he go on horseback?
9. Find the difference between the sum of i and ^ and the
Slim of ^5 and ^pg.
10. The sum of three fractions is MS Two of them are is and
■i;j. Find the third.
Simplify:
1.
2_
3.
4.
^
;).
6.
7.
8.
9.
10.
EXERCISE CXXXIV.
II
9 6
— Jj~^
— iff
T^
S^% 3A
6tV 2il
7/4 41
19 4f
£?1 S
04¥
32U5lf
Ml 161
41/2171
r:l 2
8A 5i*i
71 2
<T5 
2 A.
5i 41
71 
7tV.
7A 2/ir
StIt
2 A.
8t\ 3A
7A 
2 A.
4A 11
m 
5f.
36 12i*i
24 
3M.
4H 4il
21A
lOA
27A6i
mi
7iL
561 1711
48! 
161.
IGA^h
26^,
^Vs
EXERCISE CXXXV.
1. From a barrel of vinegar containing 31i gallons 14
gallons were drawn. How much was left?
2. From a piece of cloth containing 35i yards a merchant
cut 21 J yards. How much was left?
94
ARITHMETIC.
3. A man staited on a journey of 45 J miles, and travelled
28S miles. How far had he still to travel?
4. The sum of two numbers is 56i, and one of the numbers is
251. What is the other number?
5. If I have $437i, and pay out $341iV, how much have I
left?
6. From a farm containing 1648^ acres, 4J^ acres were sold.
How many acres remained in the farm?
7. John's monthly salary is $1661 and his average expendi
ture is $971 i. How much does he save each month?
8. What must be taken from 35i to leave 22?
9. The sum of two numbers is 26^^. One of them is 10^.
Find the other number.
10. From a barge load of coal consisting of 540i tons 375^
tons have been taken. How many tons are still on board the
barge?
EXERCISE
CXXXVI.
Simplify: —
1.
31
+4i
6f •
81 71 +U.
9
mm •
51
21
1
8 f +3! li
3.
lA
/^
.v
11 +5i fl.
4.
5^
+4t\
4i
15 3f 21.
5.
f?
+41
!
m +m 1/t.
G.
7\
2f
+5 7M
5oA4f n s^\.
7.
2G
51
61 2h
30 U fi h
8.
4^
3^
+5/T2f
151 101 +71 5tV.
9.
31
+41
7^jhdl
141 lOA41 +II/1
10.
3A
11
U +7A
8A 211 +41 8A.
EXERCISE CXXXVII.
1. From 144 lb. of sugar there were taken at one time
171^ lb. and at another 28r^ lb. What quu,ntity remains?
2. A cask of wine contained 42i gal.; of this 13f gal.
Y^ere drawn off, and 12 J gal. leaked out. How much remained
in the cask?
3. A grocer bought 89i lb. of tea; of this he sold 13i lb.
to one customer, 9i lb. to a second, and 12f lb. to a third.
How many pounds had he left?
4. What number must you add to the sum of 126 and 2401,
to make 5601?
MULTIPLICATION AND DIVISION OP FRACTIONS.
95
travelled
umbers is
ch have I
were sold.
5 expeudi
sm is lOU.
tons 375U
I board the
h
If li
n
:K
4
S 
3
"8 ■
3A.
:i 5tV.
one time
lins?
]s 13t gal.
remained
lold 13i lb.
Ito a third.
and 2401,
5. A man had to walk 97f mi. He walked 30j mi. the first
day, 33i mi. the second day, and finished the journey the third
day. How far did he walk the third day?
6. A drover bought 4 cows for $168i, and after paying
$341*0 for pasturage, he sold them for $203i. Did he gain or
lose, and how much?
7. James had $12?, and Jane as much, lacking $l\i. How
much money had they together?
8. Bought a quantity of coal for $140f , and of lumber for
$456L Sold the coal for $175i, and the lumber for $516i^. How
much was my whole gain?
9. A merchant had 3 pieces of cloth, containing, respec
tively, 19f yd., 36i yd. and 33f yd. After selling several yards
from each piece, he found he had left altogether 711 yd. How
many yards had he sold?
10. A merchant sold a customer 22i yd. of silk, 3i yd. of
paper muslin, li yd. of silesia, 5t yd. of cambric, and 5i yd. of
ruffling. How many yards were sold?
V. MtLTIPLICATIOIN AND DIVISION OF FRACTIONS.
EXERCISE CXXXVIII.
Multiply "
—
1.
h by 3
f by 4
i by 6.
2.
t\ by 5
t by 7
4 by 6.
3.
$A by 9
$41 by 6
$A by 8.
4.
A by 36
A by 26
1 by 24.
5.
i\ by 32
rV by 12
f by 16.
6.
f by 24
hi by 10
A by 12.
7.
TT by 22
4 by 21
1 by 36.
8.
1 by 27
A by 35
i by 27.
9.
A by 21
A by 25
U by 15.
10.
U\ by 20
4f by 14
31 by 24.
EXERCISE CXXXIX.
Divide :

1.
f by 2
if by 4
H by 3.
2.
M by 8
if by 7
tVt by 12.
3.
61 by 3
201! by 4
28U by 7.
4.
3411 by 17
27if by 9
54M by 6.
5.
6f by 9
4f by 10
15^ by 23.
I m
ml
P
06
ARITHMETIC.
Divide:
•
G.
2f by 5
61 by 6
10^ by 5. ^
7.
h hy 3
3 by 5
I by 4.
8.
^ by 9
1^ by 6
A by 5.
9.
n by 7
11 by 9
5]^ by 9.
10.
711 by 8
1
84f by 12
EXERCISE CXL.
36 A by 7.
Multiply: —
1.
6 byi
12 byl
20 b> 1.
2.
1 by!
I hyl
4 byi
3.
1 by!
1 byf
1 by 1.
4.
f by 4
t\ by a
1 by I
5.
i byil
f byf
f by V.
6.
f byV
V byl
1 by V.
7.
1 by^
M byH
i by U.
8.
if by 1
n by if
HI by A.
9.
Mby4
!4 byT%^
11 by If.
10.
H by 11
nt by n
EXERCISE CXLI.
V byV.
Simplify: —
1.
4^ x4^
51 x5
n x7i.
2.
51 xf)^
6f x6f
8f x8!
3.
61 x6f
71 x7
12xl2t
4.
^ xf xl
1 xl xlf
f x^ xH.
5.
1 x2x3
3i x? x5l
3i x4l XtV.
6.
21 xMxl
5i Xt\x3^
81 xA .x5i
7.
U xlhx^h
2f X 41x15
3 x7i xU.
8.
21 x3ix4f
3i xl xl?
lAxljVxf.
9.
$31 xtjV
$3ix/2
925 mi. x.
10.
$37ixir)
140oz.x2i
21 lir.xlL
EXERCISE CXLII.
1. Find the cost of 9i yards of cloth at $4i a yard.
2. When flour costs $6 a barrel, how much will 26f barrels
cost?
MULTIPLICATION AND DIVISION OP FRACTIONS.
97
by 5.
by 4.
by 3.
by 9.
rby 7.
by I.
by I.
by I.
byi
by
by
by II
5
8
5
i
111 by
S^
by
by
V
x7i.
x8!
x^
xH.
x4l xiV.
xrr X'")^
x7i xii
PtxIjVx^
If) mi. X 5.
hr.xla
lard,
ill 261 barrels
3; Find the cost of 51 dozen eggs at 121 ctH. a dozen.
4. John walks at the rate of H'i miles an hour, ilow far
will he go in 2i hourHf
;'). A piece of clotii contains KJi ydw. Find the cost of i of
the piece at $',H per yard.
6. If it takes If bu. of wheat to how an acre, how many
bimhels will it take to how 7s acrenlf
7. If a man earnn $\Vih per week, how much will he earn in
a year of 52 weeks ?
8. If one horse eats ? bu. of oats in a day, how many
bushels will 14 horses eat in G days?
9. A man owning X of 156 acres of land, sold i of I of his
share. How many acres did he sell if
10. At $95 per ton, wiiat will be the cost of i of § of a ton of
hayf
EXERCISE CXL!II.
1. A boy spent j of his money and had 96 ct. left. How
much had he at first?
2. If I buy ? of an estate for $18000, what should I give for
the whole of the estate?
',i. After going 121 miles I have still f o of my journey to go.
Find the total length of the journey.
4. Seven ninths of a post is in the mud and water. There
are 8i ft. in the air. How long is the post?
5. A traveller 'finds that 175 miles is A of the distance he
has to go. How far is his journey?
6. A man at his death left his wife $12500, which was  of
c of his estate. What was the value of the estate?
7. If f of a certain number is 42ro, what will } of lf of it be?
8. In a battle a general lost n of his army. He still had
;{4500 soldiers left. How many soldiers liad he at first?
9. John has read ^ of a certain V>ook. He still has 112
]»ages to read. How many pages are there in the book?
10. A person dying left i of his estate to his wife, rs of it to
his daughter and the remainder to his son. His son received
$16400. What was his estate worth?
Simplify: —
EXERCISE CXLIV.
1.
3.
4.
fx(l+2H
8x(3f)
(4H2)x2
(4^21) x2A
7x(62^).
(3J2f)xl.
(3i+2i)xU.
y» ARITHMETIC.
Simplify: —
,
.'). (i + l) of ,«,
(32^65'',) of lA.
G. (^ + ii)xl2
(2^3^4^x12.
7. (^Ul)x24
12x(2R4j3i).
8. i\ of U of Axa2
1x1 of 4 of A.
9. (4^2.1+51) of 4J
(^>f3iof )x2A.
10. (1 of n+2i of l?)of
A
(311 of U) of lA.
EXERCISE CXLV.
1. If a train of eai*s runH 22i mi. an hour, how far will it run
in Si hrs.?
2. A merchant bou^'ht 500 cords of wood at $2 per cord.
He sold 75i cords at $4i per cord and the rest at $5. Find his
gain.
3. A merchant purchased 150 yards of cloth for $675, and
sold I of it at a profit of $f per yard, and the remainder at a
loss of $^ per yard. How much did he gain?
4. There are 50i bu. of wheat in a bin. How n^uch remains
after sowing a field of 7^ acres at 2^ bu. per acre?
5. A bought 319 acres of land at $200 per acre; he then
sold 250^ acres at $250 per acre, and the remainder at $266J per
acre. How much did he gain?
6. From the sum of 3^ and 2i take their difference and
multiply the remainder by 2f .
7. What number added to 14f+?+^+4TSV+lH wiU malte GOT
8. Three men own a hou.p worth $6250; one owns VV. the
second ^ of it. What is the value of the share of the third?
9. A grocer bought 100 barrels of flour at $6 per barrel ; he
sold 49 barrels at $7i per barrel, and tixe rest at $7i per barrel.
How much did he gain?
10. A drover bought 64 sheep at $71 apiece; he then sold
30 of them at $6^ apiece, and the remainder at $8 apiece.
Did he gain or lose, and how much?
ivide :
1.
10 by 4
20by
3.
5 byf
4.
12 by tV
5.
16 by 3^
EXERCISE CXLVI.
6 by I
25 by i\
8 by I
25 by i
25 by 4
12byi
36 by A.
9 byT*t,
27 by I.
•) j.
3C by ^
;t 4
MULTIPLICATION AND DIVISION OP FRACTIONS.
99
Divide:

6.
42 by 6J
45 by ')l
7.
20 by 31
25 by 61
8.
3 by^
1 byl
9.
! byl
I by 1*5
10.
31 by liV
21 l)y 41
EXERCISE CXLVII.
Simplify
: —
1.
71 
4!
/. 
M
2.
i\ 
4
6
u 
II
3.
U 
fl
iSS 
U
4.
11 
41
8i 
12^
5.
iiA
12^
s\ 
2^
6.
33^ 
lOH
VA 
n
7.
6i 
2i
n 
n
8.
121 
31
4T«r 
51
9.
71 
41
51 
7^
10.
18 
2i
12fT
81
74 by 61.
42 l)y 5L
I byt.
JTbyli.
52 by 55.
J 
— Afif
HI
21 •
9J
TTT
301.
5^
181
8!
171
501
3.
4
lif
•Itl
31.
";8
2J.
i>S3
3 6.
8*6 .
EXERCISE CXLViei.
1. At $* per yard, how many yards of cloth can be bought
for f.*}U?
2. A man rode 37i miles in 4i hours. How far did he ride
in one hour?
3. A farmer sold 25f acres of land for $072. What was the
pi'ice per acre?
4. A vessel sails 464 miles in 26j hours. Find its rate per
hour.
5. A miller has 27i bushels of meal which he wishes to put
into bags, each bag to contain 2f bushels. How many bags
will be required?
6. If 3i pounds of beef cost 431 cents, what is the price of a
pound?
7. If a man travels at the rate of 271 miles an hour, how
long will it take him to travel 784i miles?
8. By what numb'^r must \Q\\ be ruultipliad to produce 1481?
9. A fivmer sowed 478i bushels of grain on his farm. If he
sowed 2^ bushels per acre, how many acres did he sow?
M
Si
S; ;
■I
100
AUITHMETIC.
10. A Mnuitoba faritipr thranlu'd 10127 IuihIu'Is of wheat.
This WHH ail av<'raKe yield of 127A ))UHlielH jun aore. How many
acres liiul he in wheat?
11. If the cost of carryinpf 'jr)?')^ biisliels of wlieat from
Winnipeg to Montreal is $31)4.9] , find the rate charged per bushel.
12. If a man can do a piece of work in 18 days l>y working
14!j hourH per day, in how many days can he do the same work,
if he works 8i hours each day f
l.'l. When 3')! bushels of potatoes cost $28.60, how much
should be paid for 4i bushels?
14. Find a number which divided by 3i, the quotient increased
by li, and the sum multiplied by 7i, the product is 54.
Simplify: —
EXERCISE CXLIX.
1. (r)+3UiJ
(831)U.
2. (8i3i)^U
4j(3^2l).
3. 7\^{,^,2\)
20 (5141).
4. (3n(3+i)
(4i2!)(442!).
5. (5H4^)^(.J^41)
(2U18t\)(2U+18A).
6. (_i+l).(H^l)
3?.5f of jV.
7. 201 x3i of Ty*„+21
(2Uli)(3ix5n.
8. (8lx3Ax2!)^3l
(2R3j)xl2^4i.
9. 1 of? of 24^ of 3i
(4i_3i)x8i^l()0.
10. 7i^(4l3l5i)
72i44f04«>3 .
EXERCISE CL.
{Simplify: —
1. hxl\xl
i of Kl of I
2. ixKll
KKii
3. 51 of 8xll
4. 5^ of 8121 of 3^
5. HI of ll of I
6. 816f+^ of I
7. f of fUlof IB
8. 3xl
9. (128f) of lA
10. T^?lix2A
51x8.1^21x3^.
7l6A6A7i.
f of U of 911 of
3i of If.
12!8t of lA.
12!8fxlf*T.
All of 2A.
3f
GOMPLKX FRACTIONS.
101
of wheat.
How many
VI. COMPLEX FRACTIOINS.
EXERCISE
CLI.
Simplify
1 "^^ •
1.
1"
3
4
6 *
2,
8
i
8
"4
9
3.
2\
r)i
4i
3i
4.
5.
413.^
7^5]
41+3^
7i+oi
6.
3l+4i
3112
G^+1,V
93 5
4 — J»
7.
1^ of 11
7h2}
11 of i\
^ of 3^
8.
2i of 2h
21 of U
li of 3
5^ of 31
9.
n
16
li of A of 3
t\ of 2A of H
10.
(2U)x2i
4h of 5lf2
i of Ih
4^ of r)iiof
EXERCISE CLII.
Simplify: —
1. (321+71 )f of t\.
(5i+3f)(945U.
(i^V+Uf fx)(/iriof+n.
rV(/oof H)xiS.UxU.
I of 9?^+3gr8To — Tlor.
6. 3j2^x4i4TV+3TV.
2.
3.
4.
5.
'•I
102
ARITHMETIC.
7. U2§x32+UUx38.
G]5i Girfji 3
9.
(
i+'
1
G'
+''!)iixJ5i.
3 4ft/ «i2
10. 2.^ of lii + ii
6 + 3 <>t H— bX 86
EXERCIltE CLIII.
1. What must be added to f ^+7J to make 10?
2. Subtract the sura of 4j{ and IJi from the difference
between 151 and .'i§.
3. Multiply :H+5f Vjy 4,^ of U and divide the product
by 81^.
4. Bv how ranch does the sum of i+i+i+a+u exceed the
sum of l+i+A+if^?
'). The sum of J of 1X2 and f of X4i of ^ in equal ^.o how
nnmy times their difference?
54x
G. The smaller of two numbers is ^ —  . ; and their difference
f of 4*
is . . Find the larger number.
7. What number divided by 4— i of Siif+i^ will make the
quotient 2f ?
8. The product is 124; the multiplier is 8f. Find the
multiplicand.
9. Find the sum, the difference, and the product, of ^j and
H; also find their quotient, making the greater fraction the
dividend.
10. What number multiplied by  of X3f, will produce ff?
VII. G.C.IVI. AND LX.M. OF FRACTIOINS.
EXERCISE CLIV.
1. Find the G.C.M. and the L.C.M. of A, M and U
2. What is the G.C.M. and the L.C.M. of i, ^ and H?
3. Find the G.C.M. and the L.C.M. of 4, 2f and 2f.
4. What is the length of the longest measure that can be
exactly contained in each of the two distances, 18f feet and 57i
feet?
G.C.M. AND L.O.M. OF FRACTIONS.
103
r difference
f>. Wlmt aio tlio longest Hectlons of wire fence, of equal
length, with which I citn enclose a triimgulnr plot whoHO sides
are respectively 'J'Jjf t'«'«'t, 'M\k f<"et, and !){) fe«'t? I low many
sections are recpiireil to enclose the n»'l(lf
(J. How nuiny times do«'s the L.C.M. of Hi, 48 and 5i
contain the (l.C.M. of these nunihersf
7. What is the smallest sum of money with wiiich I could
purchase a numl)er of sheep at I'Ji each, a number of calves at
$4i each, or a numher of yearlings at .$98 each? How many
of each could I purchase with this money f
H. A farmer has H'M buHluds of corn, ()7i bushels of rye, 70
busliels of wheat. He wishes to put this grain, withoiit mixing,
into the smallest numlxM' of bags, each of which shall contain
the same quantl^iy. Required the quantity each bag will contain
and the number of bags.
9. A merchant has three kinds of wine, of the first 1.34} gal
lons, of the second 128it gallons, of the third lloi gallons; he
wishes to ship the same in full casks of equal size; what is the
least number of casks he can use without mixing the different
kinds of wine?
10. A, B, atid C start at the same place and travel round an
island, A making the circuit in J of a day. B in ^ of a day, and
C in ^ of a day; in how many days will they meet at the start
ing place, and how many times will each have gone round the
island?
VIII. DEINOMilNATE FRACTIONS.
A Denominate Frj'ction is one in which the
primary unit of the fraction is a denominate number,
as I oz., f mi., 3 gal.
EXERCISE CLV.
Reduce each of the following to lower denominations: —
1.
£
^\s.
Is.
2.
$1
n
$f.
3.
It.
I'lr cwt
•
I lb.
4.
f mi.
Ird.
f yd.
5.
f A.
TT sq.
rd.
V'ff sq. yd.
6.
1 cd.
A cu.
yd.
^\ cu. ft.
7.
Ibu.
Ipk.
fgal.
8.
8 gal.
1 qt.
1 gal.
9.
i\ wk.
A da.
i% hr.
10.
r
tc.
6 °
I ;
I.
' ' HI
^r^K^/^jzsL^raf—
104
ARITHMETIC.
EXERCISE CLVI.
Reduce the following: —
1. 7 mi. 5 id. 1 yd. to incheH; 2 mi. 2 ft. to inches.
2. 7456 ft. to miles, etc.; 2745 yd. to miles, etc.
3. 3f mi. to inches; 7 rd. to inches.
4. 5 A. 7 sq. rd. to scj. inches; 98 sq. vd. 14 h({. yd. to sq.
inches.
5. 57896 sq. ft. to acres, etc. ; 100000 sq. ft. to acres, etc.
6. 2 A. to sq. inchei.; 3ri sq. rd. to sq. inches.
7. 4i t. to pounds, 2§ cwt. to ounces.
8. Ti mi. to rd., yd., etc.; i^ A. to sq. rd., sq. yd., etc.
9. 47212 sq. yd. to acres, etc.; 6912000 sq. in. to acres, etc.
10. 1 t. of water to gallons; 7000 gal. of water to tons, etc.
Find
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
EXERCISE CLVII.
the value of
T^i of $140.76; f of $50,40.
I of £3 7s. 6d. ; t of £1 8s. 4d.
I of 5 t. 8 cwt. 6 lb. ; I of 2 t. 15 cwt. 9 lb.
I of 7 mi. 35 rd. 1 ft.
^ of 3 mi. 45 rd. 3 yd. ;
f of 4 A. 50 sq. rd. 3 sq. yd. ;  of 2 A. 100 sq
I of 3 cd. 120 cu. ft. ; t of 12 cd. 72 cu. ft.
f of 3 bu. 3 pk. 1 gal. ;  of 2 bu. 2 pk.' 5 qt.
I of 7 gal. 2 qt. ; ": of 15 gal. 3 qt
rd.
f of 1 da. 8 hr. 40 min.
J of 15" 45' 18"; f of 17° 24' 36".
1^ of 8 hr. 33 min. 20 sec.
EXERCISE CLVIII.
If 1 ft. is the unit, what immber expresses 8 ft.?, 12 ft.?,
21 ft.?
If 2 is the unit, what number expresses 8?, 12?, 21?
What part of 8 is 2? Of 12 is 2? Of 21 is 2?
What fraction of 8 is 2? Of 12 is 2? Of 21 is 2?
1. Reduce I lb. to the fraction of a cwt.
2. What fraction of a pound is d.?
3. What part of a bushel is §^ gal.?
4. Reduce f yd. to the fraction of a rod.
5. Reduce i in. to the fraction of a rod.
6. What part of a pint is ufo bu.?
7. Reduce atho cwt. to the fraction of an ounce.
8. What fraction of $9f is $7i?
9. What part of 2 mi. 130 rd. is 1 mi. 30 rd.?
10. What part of a foot is ir/sBi) mi.?
APPLICATIONS OF THE xiEVlOUS RULES.
105
H(l. yd. to sq.
in. 20 sec.
EXERCISE CLIX.
1. Whftt part of a pound Tro> wt. is 10 oz. 13 dwt. 8 gr. ?
2. What part of £8 is U s.?
3. What fraction of a mile 74 rd. 5 yd.?
4. What part of 3i yards square is 3i sq. yd.?
5. What part of 5 weeks is 7 da. 23 h. 20 min.?
6. What fraction of a cubic yard is 7 cu. ft. 8G4 cu. in.?
7. What part is 26 gal. 2 qt. 1 pt. of 3H gal. ?
8. Reduce 35 rd. 3 yd. 2 in. to ihe fraction of a mile.
9. What part of a pound Avoirdupois wt. is 1 lb. Troy wt.?
10. Reduce 86 sq. rd. 4 yd. 5 ft. 127^3 in. to the fraction of
an acre.
EXERCISE CLX.
V. 91 sq. rd. 7 sq. yd. 5
sq. ft. 29 aq. in. to sq.
are equal to 432 lb.
1. Reduce 5
inches.
2. How many pounds Troy weight
Avoirdupois weight?
3. If a pint of milk costs 2i ct., how many quarts can be
bought for $8.45?
4. If a sheet of paper is 13i in. long and 8J iu. wide, how
many such sheets will be required to cover an acre?
5. The circumference of a buggy wheel is 7 ft. 4 in. long.
How often does it turn in 6 miles?
6. How many paces 2 ft. 8 in. long are there in 3 miles?
7. What is the cost of 12 bbl. of vinegar averaging 41 gal.
3 qt. 1 pt. at 12i ct. per quart?
8. Find the value of a pile of tanbark 100 ft. long, 39s wide
and 181 ft. high at $3.20 per cord.
9. A merchant paid $35 for 8 bbl. of chestnuts averaging 2
111). 3 pk. 2 qt. per bbl. He sold them at 5^ ct. per pint. Find
!iis gain.
10. Find the value of a pile of wood 225 ft. long, 5i ft. high
and Q'k ft. wide at $4 per cord.
IX. APPLICATIONS OF THE PREVIOUS RULES.
EXERCISE CIXI.
1. If a cubic foot of broken stone weighs 168 lb., find the
weight of 5 ed. 63i cu. ft. of such stone.
2. A pile of wood is 168 ft. long, 6 ft. high and 4 ft. wide.
How many corde are there in it?
3. What will a pile of stone 240 ft. long, 8 ft. high and 4 ft.
wide cost at $2.50 per cord?
II
\'^
106
ARITHMETIC.
4. What are 3 bu. of strawberries worth at 2 et. per pint?
5. A gardener sells 495 crates of berries, each containing a
bushel, at 2 ct. a pint. How much did he receive for them?
6. In 1896 how many days were there from Jan. 10th to Oct.
Drd, inclusive?
7. How many minutes were there in Jan., Feb. and March,
1899?
8. How many more minutes were there in Feb., 1896, than
in Feb., 1897?
9. What is the value of a barrel of syrup containing 29 gal.
li qt. 1 pt. at 9 ct. a pint?
10. How many poles each 7i ft. long, placed in a straight
line, will reach 2 mi. 280 rd.?
EXERCISE CLXII.
1. Divide 13 cwt. 63 lb. equally among 29 persons.
2. A pint of water weighs 1 lb. 4 oz. How many pints are
there m 22 t. 11 cwt. 40 lbs. of water?
3. If 178 cwt. 61 lb. are divided into 53 equal parts, how
many ounces are there in each part?
4. How many tons, cwt., etc., are there in one million
ounces?
5. How many parcels each weighing 2 lb. 12 oz. can be made
from 2 t. 9 cwt. 50 lb. of sugar?
6. Find the cost of 4 t. 19 cwt. 99 lb. of sugar at 5 ct. a
])ound.
7. How many ounces of iron are required to make 32 iron
bars, each weighing 2 lb. 7 oz.?
8. I bought 3 cwt. 19 lb. of tea for $127.60, what did I pay
per lb. for it?
9. Out of a box containing 3 cwt. 78 lb. of sugar, how many
2 lb. parcels can be made?
10. A railway truck weighs 5 t. 3 cwt. On it are placed 97
iron bars each weighing 3 cwt. 76 lb. Find the total weight in
pounds of the truck and bars?
EXERCISE CLXIII.
1. How many grains in 11 silver medals each weighing 4 oz.
5 dwt. 6 gr.?
2. If 7 silver medals each weighing 10 dwt. 13 gr. are melted
and the silver divided equally among 11 persons, how many
grains would each have?
3. In 2468 grains of gold dust, how many ounces are there?
4. In a silver box weighing 10 oz. 16 dwt., how many grains
are there?
APPLICATIONS OF THE PREVIOUS RULES.
107
er pint?
ataining a
■ them?
3th to Oct.
nd March,
1896, than
ling 29 gal.
. a straight
18.
[ly pints are
[ parts, how
one million
lean be made
at 5 et. a
ake 32 iron
at did T pay
r, how many
placed 97
tal weight in
re
'ighing 4 oz.
\ are melted
how many
Is are there?
Imany grains
5. How many grains of gold will be required for 12 orna
ments each weighing 1 oz. 18 dwt. 12 gr.?
6. Reduce 58376 grains to lbs., oz., etc., Troy.
7. How many forks averaging 2 oz. 9 dwts. each can be
made from 5 lb. 1 oz. 5 dwt. of silver.
8. How many lbs. of silver in 270 spoons, each of which
weighs 1 oz. 13 dwt. 8 grs.l
9. Express 4040789 grains in lbs. oz. dwt., etc.
10. A pound Troy contains 5760 grains and a pound Avoirdupois
7000 grains. Find how many pounds Troy there are in 94 lb.
8 oz. Avoirdupois.
EXERCISE CLXIV.
1. How many inches are there in a mile?
2. A lake is 112 fathoms in depth; what is its depth in
inches?
3. A wheel is 13 ft. 9 in. round. In turning 768 times, how
many miles does it pass over?
4. Find the cost of 20 miles of telephone wire at 35 cents a
lb. supposing a lb. stretches 80 ft.?
5. Find the cost of 4 miles of barbed wire if 4 feet cost 8c.
6. What will it cost to survey 25 miles of road at 25 cents
for every 66 feet?
7. The distance from London to Harrisburg is 61 miles 224
rods. How long will it take to walk that distance at 32 rods
per minute?
8. How many inches are there in 5 times 4 mi. 319 rd. 5 yd.
1 ft. 6 in.?
9. How many more inches are there in 3 times 7 mi. 1759
yd. 2 ft. 2 in. than in 4 times 3 mi. 319 rods 5 yd. 6 in.?
10. A boy going to school walks 126720 inches every day.
How far will he walk in a school year of 220 days? Answer in
miles, etc.
EXERCISE CLXV.
1. At 40 cents a gallon what would be the cost of 5 bbl.
syrup, each containing 36 gal.?
2. A man bought a hhd. (63 gals.) of molasses for $18.90
and sold it at lOe. a pint. How much did he gain?
3. 1 bought a bushel of chestnuts for $4.80. What will be
the cost of 13 qts.?
4. A gardener has 13 bu. 2 pk. 1 gal. 2 qt. of strawberries.
How many quart baskets will be needed to hold them?
5. If 376 gal. 3 qt. 1 pt. of milk be divided among 9 charities,
how many piuts will each receive?
I ■i
i; '
f if
108
AHITHMKTIC.
6. A man bought 14 bags of beans, each containing 2 Vm. 2
pk, for $21, and sold them in boxes of 1 bu. 3 pk. eacli, so as
to neither gain nor lose. Find the price per box.
7. How many loads of apples of 27 bu. 3 pk. each can be
bought for $53.28 at 48e. per bushel?
8. What is the value of 324 bags of beans, raeh containing 2
bu. and 1 pk. at 70c. a bushel?
9. A milkman started with 10 gal. of milk. He sold i pt. to
each of 52 people and a pint to each of 50 others ; how much has
he left? Ans. in quarts.
10. Reduce 143 bu. 3 gal. 3 qt. 1 pt. of wheat to pints, and
find the value at H cents a pint.
EXERCISE CLXVI.
1. A farmer travels .!00 miles in 8 days, liow many days will
it take him to go 4224000 ft.?
2. A man walked 13G miles in 45 hrs. 20 min., how many
feet did he go per minute ?
3. How many times is 195 yd. 1 ft. 8 in. contained in 1 mile?
4. A train goes 30 miles an hour, how many feet does it go
l>er second?
5. A rate of 22 yd. in 5 seconds is equal to what rate per hour?
6. A tank has 12000 gal. of water in it. How long will it take
to empty it, if 5 pints are emptied in a minute?
7. How many days of 10 hrs. each would it take to count
30,000,000 sovereigns at the rate of 100 per minute?
8. Find the cost of 3975 lb. bran at $1.44 per cwt.
9. A farmer paid a laborer $1.75 a day for the month of
August, what should he get if the month began on Wednesday?
10. Find the cost of 40 lb. of ice, delivered three times a
week from April 1st to October Gtli inclusive, at COc. per
hundred pounds.
EXERCISE CLXVII.
1. Find the difference in the cost of 17 bu. of wheat when
sold at Ic. per lb. or le. per pint.
2. A pile of 4 foot wood is 64 ft.
to contain 10 cords?
3. How many steps each 2 ft.
take in walking 3 miles?
4. A farm of 111 acres is divided into fields of 7a. ()4 s<. r'l.
How many fields are there?
5. How far can I walk in 10 hv. 45 min. at the rate of a
mile in 15 minutes?
6. How many more hours are there in January than in
February, 1896?
long. How high should it l)e
() in. ill length will a man
APPLICATIONS OP THE PREVIOUS RULES.
109
taiuing 
how many
7. How. many paces each 2 ft. 8 in. are there in 2J miles?
8. Rednce 3 weeks 19 hrs. 2") min. 15 sec. to seconds, and
lii'S weeks 6 days 19 hrs. 5 min. 45 see. to seconds, and divide
the larger quantity by the smaller.
9. The circumference of a wheel is 16 ft. (J in. lon^. How
often will it turn between London and Hamilton, 76 miles If
10. A coach wheel 10 ft. 9 in. round, turns 12 times in 10
seconds, at what rate per hour is the coach going?
EXERCISE CLXVIII.
1. Find the weight of a dozen and a half silver spoons each
weighing 4 oz. 4 dwt. 22 gr.
2. Add together .£:J7 17s. 4id.. £19 12s. lOid, £18.1 19s. .3d.
and £52 Os. Hid. and take £93 lv;s. 5d. from the sum.
3. Multiply 3 cwt. 3 lb. 3 oz. by 69 and subtract the result
from 11 tons.
4. A bicyclist travelled 50 miles in 3 hrs. 3 min. 20 sec.
What was his rate in feet per second?
5. A train travels 95 miles 1100 yd. in 2 hr. and 50 min.
How far does it go in 1 minute?
6. If I walk 350 yd. in 2 min. 40 sec. how long will it take
me to walk 560 yd.? What distance can 1 walk in 7 min. 28
sec. at the same rate?
7. How many yards per minute faster is the rate, 42 miles
an hour, than the rate 20 yards per second?
8. How many bags of sugar each holding 235 lb. are there in
6 t. 6 cwt. 90 lb?
9. A grocer buys 13 hhd. of sugar weighing 6 t. 8 cwt. 57
ib. How much did each weigh?
10. How many trees will be required to plant 27 a. 91 sq. rd.
22 sq. yd. 2 sq. ft. 36 sq. in., allowing 105 sq. yd. for each
tree ?
EXERCISE CLXIX.
1. How many more inches are there in 3 yd. 1 ft. 6 in. tlian
in 3 ft. 6 in.
2. Three men can cut 8 ae. 36 sq. rods in a day, how long
will it take them to cut 57 ac. 92 sq. rods.
3. How many days from March 13th, 1898, to July 3l8t,
1899, both inclusive?
4. How many miles will a boy walk to plough 6 acres turning
9 inches of a furrow?
5. A man bought 3 bu. 3 peeks of nuts at 75e. a peck and
sold them at 10 cents a quart. How much did he make?
r <f3
no
ARITHMETIC.
6. A farmer in tlie North West had 4H(> acres of wliejit, and
the averaj^e yiehl was 27 bus. 'A pks. G qts. 1 pt! i>er a'.'re.
What will the whole be worth at GO et. i)er bushel ?
7. The price of broadcloth at lOs. 8d. per yd, is jCUG 128.
How many yards are there of it ?
8. A boy bought a bushel of nuts for $1 and sold them at 5
ct. a quart. How much did he gain f
9. If sound travels at 1144 feet per second, how long would
it take to travel to the moon, a distance of 240500 miles?
10. If a wheel turns 780 times in going over 1 mi. 1G85 yd.
What is the length of its circumference?
EXERCISE CLXX.
1. What 's the difference in weight between .3 dozen silver
table spoons weighing 5 lb. 9 o/.. 8 dwt. and as many silver tea
spoons weighing 1 lb. 9 oz. IG dwt. 18 gr.
2. How many times is 391 yd. 4 in. ccntainbd in 2 mi,?
3. If a man walk i mile in 5 minutes, how many hours will
it take him to walk 36 miles at the same rate?
4. Find the number of days between Sept. 23rd and Jan.
11th, one of these days included.
5. A man walks 1 mi. 47 rd. in 20 minutes how long will it
take him to walk 123 mi. 276 rd.
6. How many boards each 11 ft. 6 in. long and 10 in. wide
will be required for the flooring of a room 23 ft. long and 17 ft.
6 in, wide?
7. How many turns will a wheel 3 yd. 2 ft, 3 in. round make
in passing over 198 miles?
8. How many silver spoons weighing 1 oz. 18 dwt, 12 gr.
can be made from 23 oz. 2 dwt, of silver?
9. What is the rate per hour of a horse that travels 18 mi.
1620 yd. in 3 hr. 4o min.?
10. Find the cost of 260 lb. of tea at 3s. 3fd. per lb. If 20
lb. of it be spoiled, how much is gained by selling the remainder
at 48. lid. per pound?
EXERCISE CLXXI.
1. How much oats will it take to seed 87 acres, using 2 bu.
1 pk. 5 qt. to the acre?
2. A miller ground 7845 bu. of wheat. How many barrels of
flour did he obtain, provided each bushel yielded 39 lb. 3^ oz.?
3. A and B togeth<r bought a web of silk; A piid for ,\ of
it and B for the remainder. The difference between their shares
in 5i yd. What is the share of each?
APPLICATIONS OF THK PRKVIOUS Kfl.KS.
Ill
4. If A travels 24 mi. 198 id. 4 yd. in (5 )ir. 30 min., how far
will he go in 9 hr. 45 min.?
5. A field 80 rods long contains 1;') acres, while another field
of the same width contains 9 acres: wliat is the length of the
latter field?
0. A lady bought 15 yd. of velvet i yd. wide. How much silk
I yd. wide must she buy to line itf
7. Mrs. Brown wishes to carpet a room 18 ft. long by 15 ft.
G in. wide, with Brussels carpet I of a yard wide, at $1.25 a
yard. How much will it cost her?
8. If 4^ lb. of pepper cost $2.15, what will .30 lb. cost?
9. If 30iV tons of iron cost $1728, what will 7ii tons cost?
10. If drk tons of copperas cost $333J, what quantity of
copperas should be received for $500.
EXERCISE CLXXII.
1. If A of a barrel of flour costs $2.25, what will a whole
barrel cost?
2. If T^ lb. of a drug costs $2.52, what is the value of ^ of a lb. ?
3. If 41 tons of coal cost $28, what will 15 tons cost?
4. When $8 are paid for If yards of broadcloth, how much
must be given for 8 yards?
5. Sold 7i^ busLjls of apples for $7.28. What should I
receive for 19t5 bu.?
6. How many yards of muslin, at 62i ct. per yard, must be
given in exchange for 34 bu. of sweet potatoes, at 50c. per
bushel?
7 How many pounds of btitter at 18f ct. per pound, should
be exchanged for 40i yd. of calico at 12i ct. per yard?
8. If a man works Si hr. a day, he can finish a piece of work
in 12J days. How many hours per day must he work to com
plete it in lOl days?
9. If ^ of a yard of ribbon cost $, what will 5 yd. cost?
10. Paid $7888tt, for 83A acres of land. What sum did I pay
for each acre, and what would be the cost of 7 acres?
EXERCISE CLXXIII.
1. How many parcels each weighing 41 lb. 8 oz. can be made
up out of goods weighing 1 ton, and what weight will be
remaining?
2. How many pounds of sugar at 6i cents a pound will pay
for 12 dozen eggs at 16S^ cents a dozen?
3. If a man can drive lOf miles in H hours, how far can he
drive in 5f hours?
tA
112
AlilTHMKTlf.
4. How many yards of cambric  yd. wide will it take to line
14 yards of (;l(;tli li yd. widt*?
5. After selling? 'H of his sheep to n, drover, and Jt of the
remainder to hia neififhbor, a farmer has 100 left. How many
were there in the Hock at first if
(5. A road to the top of a hill has a rise of A of a foot in 10
feet. How many feet is the total elevation of the hill, if the
length of the roud is 2 miles?
7. From 120 A. of land 32lf A. are soM to one man and J of
the remainder to another. How many acres are unsold?
H. A grocer buys 'M lb. of tea at 48 ct. a pound, and '}0 lb.
at 64 ct. a pound, and having mixed them sells 40 lb. of the
mixture at oG ct. per pound. At what price per lb. must
he sell the remainder that he may neither gain nor lose?
9. A gentleman gave i of his estate to his wife, I of the
remainder to his oldest son, and f of what then remained to his
daughter, who received $750; required the whole estate.
10. A man has 4 lots containing 4 A., 6fB A., 9i A. and lli^
A. respectively. He wishes to divide each lot into the largest
sized building lots possible, each lot to contain the same area.
How much land will each building lot contain?
EXERCISE CLXXIV.
1. A wine merchant bought a pipe of wine (126 gal.) and
bottled it into an equal number of quart, pint, and halfpint
bottles. How many bottles of each size had he?
2. At $6.40 a cord, what is the value of two piles of wood,
each 4 ft. wide and li yd. high, but the one 2i rd. in length,
and the other 15i yd.?
3. From two fields 482 bushels of corn are gathered. The
first field yields i as much as the second. How many bushels
does each field yield?
4. What must be paid for a pile of wood 25 ft. long, 3^ ft.
high, and 6f ft. wide at $4^ per cord?
5. If lOi lb. of milk make a lb. of cheese, find the value at
9 ct. per lb. of the cheese made from 350 tons of milk.
6. A cistern 7i ft. long and 5i ft. wide contains 3321 eu. ft.
What is its depth? How many gallons of water will it hold?
7. At 12 cents per cubic foot, what will be the cost of a
block of stone 9 ft. long, 5i ft. wide, and 4 ft. thick?
8. A father divided a piece of land among his three sons
thus: he gave 12i acres to the first, I of the whole to the
second and to the third as much as to the other two together.
How many acres were in the piece of land?
APPLICATIONS OF THE PREVIOUS RULES.
113
9. A man bequeathed $37000 to his family. He gave i to his
wife, i to his son, and divided the rest equally among 5
daughters. How much did each daughter receive f
10. A young man lost i of his money in betting on races, jt
of the remainder In stock jobbing,  of what was left by invest
ing in foreign bonds, and has now $1750 left. Find the amount
of his property at first.
sq.
was
rd. were
divided
wide,
EXERCISE CLXXV.
1. From a tract of land containing 365 A. 90
sold 110 A. 110 sq. rd., and the remainder
equally among 5 persons. Find the share of each
2. In digging a cellar 24 ft. long and 10 ft. wide, 1860 cu.
ft. of earth were removed; how deep is it?
3. If a pile of bark 24 ft. 6 in. long, and 4 ft. 6 in,
contains 9ooi cu. ft., how high is it?
4. A gentleman sent a silver tray and pitcher, weighing 3
lbs. 9 oz., to a jeweller, and ordered them to be made into tea
spoons, each weighing 1 oz. 5 dwt. How many spoons should
he reefeive?
5. A man having a piece of land containing 3844 A., divided
it between his two sons, (r'.ving to the elder 22 A. 60 sq. rd.
more than to the younger. How many acres did he give to each?
6. A and B own a farm; A owns ^ of it and B the re
mainder. The difference between their shares is 15 A. 68i sq.
rd. How much is B's share?
7. The forward wheels of a wagon are 10 ft. 4 in. in circum
ference, and the hind wheels 15i ft. How many more times will
the forward wheels revolve than the hind wheels in running
from Boston to New York, the distance being 248 miles?
8. What will be the cost of plastering the walls and ceiling
of a room 36 ft. long, 26i ft. wide, and 15 ft. high, at 21 cents
a sq. yd., making no dedtictions?
9. A man has a piece of it.nd 201 1 rods long and 41 J rods
wide, which he wishes to lay out into square lots of the greatest
possible size. How many lots will there be?
10. A gentleman gave J of his property to his son James; i
of it to his son William ; ^ of the remainder to his daughter
Mary; and the balance to his wife, Mary received $2243.26 less
than James. What was the amount divided, and how much did
each receive?
m
EXERCISE CLXXVI.
1. A can dig a fi^ild in 5 days. B can dig it in 4. If both
work together, what part of the field will they dig in one day?
;«
114
ARITH;ilI::TIO.
2. A can do a piece of work in six days which B can do in 8
days. Tliey work together at it I'or 2 days. How much of the
work remains to l>€< done?
'.i. A can mow a piece of grass in 4 days, and B can do it in
2 days ; liow long will it take both working together to do it *
4. A and B together can do a piece of work in 18 days, l>nt
with the assistance of C they do it in 12 days. In what time
can C do it by himself?
5. A and B together can do a job in 7 days, b«it it would
take A alone 12 days to do it. How long would it take B alone
to do it?
6. A and B together can do a piece of work in 20 days. A
can do it alone in UG days. After A lias worked 3 days alone,
how long would it take B to ftnish it alone?
7. Three men can do a piece of work in 4 days; the first can
do it in 15 days, and the second can do it in 12 days. How long
will it take the third to do it?
8. A can do a piece of work in 3 days, B can do it in 4 days,
and C can do it in 5 days. How long will it take them to do it
together?
9. A can mow a field in 10 days, B in 8 days, and C in 5
days. When working together, how many days will they need?
10. A can build a wall in 8 days, B in C days, and C in 5
days. A and B worked together for 1 day, when they were
joined by C. How many days will they need to complete the
remainder of the work?
11. A and B working together can mow a field in 10 days; A
and C can do the same work in 9 days ; and B and C in 12 days.
In what time can C do the work alone?
12. If 4 men or 20 boys can do a piece of work in 12 hours,
in what time can 3 men and 30 boys do the same work?
13. If 5 men, 8 women, or 12 boys can do a piece of work in
20 hours, in what time can 1 man, 2 women and 3 boys do this
work?
14. Three men are employed to dig an acre of land. A can
dig 40 sq. rd. in 6 days, B can dig 60 sq. rd. in 8 days; and C
can dig the whole in 16 days. If all begin to work together, in
what time will they dig the acre of land?
15. A can dig a garden in ')l days; B can dig the same garden
in 4f days. If they begin to dig together in what time can they
dig the entire garden?
16. A can do a piece of work in 6j days; B can do the same
work in 7i days and C can do it in 8^ days. A works alone at
the job for 2 days when B begins and the two work together for
a day. Then C joins them and they all continue until the
work is done. How long does A work?
an do in 8
ueh of the
an do it in
to do it?
S days, i»ut
I what tiiue
lit it would
ike B alone
20 days. A
days alone,
the first can
, How long
it in 4 days,
hem to do it
, and C in 5
1 they need?
and C in o
\n they were
loniplete the
^1 10 days ; A
in 12 days.
Jin 12 hours,
lork?
le of work in
jboys do this
land. A can
lays; and C
I together, in
Isame garden
Ime can they
lo the same
[rks alone at
[together for
\e until the
CHAPTER VII.
DECIMALS.
I. DEFIINITIOINS, INOTATIOIN AND INUIVIERATIOIN.
When the numltcr 10000 is divided by 10, tiiequotient is 1000.
When 1000 is divided hy 10, the quotient is 100.
' When 100 is divided by 10, the quotient is 10.
When 10 is divided by 10, the quotient is 1.
When 1 is divided by 10, the quotient is ra and ir ritten .1.
Wiien .1 is divided by 10, the quotient is Too am is written
.01, etc.
Such nnin])ers as .1, .01, .001, .34, 5.7, etc., are
called decimals, or deeiiiial fractions.
Decimals, or Decimal Fractions are fractions in
which the unit is divided into 10, 100, 1000, etc.,
equal parts.
A decimal is expressed by writing the numerator
of the fraction with a point so placed as to indic^ate
the order or place of the decimal.
This i)oint which separates integers from decimals
is called the Decimal Point.
When there is a i>art of the nunil^'r to the left of
the i)oint, this is Cc'Ucd the integral part, and that
to tiie riglit, the Decimal part, of the given numl)er.
The following table shows the relation of the various orders
ov plaees to the right iind left of the unit's place to each other,
tliiis the order tens is lirst to the left of units, the order tenths
is iirst to the right of units; the order hundreds is secoml to
the left of units, the order hundredths is second to the right of
units, et".
115
no
aimtiimktk;.
Notation ank Nr.MKitATioN 'I'ami.k.
i
o
r.
C lu
O TS
fQ K
a
o
<■*
a
H
4
a
o
H
a
W
XI
a
'/J
a
o
H
01
7:
a
a
o
ja
H
a
a
W
]() 9 K 7 () T) 4 ;{
a
^
22  .2 ^
a • ^j a
I
ra
"3
a
•
a
a
a
•/.
a
1
,2
1— ii
■/I
a
a
H
1
a
a
a
• p4
1
a
0;
a
^
0)
• ^
a>
H
W
H
H
W
?^
H
I
a
o
iNTKCiKKS.
. 1» ;; 4 ;') <) 7 H I) 10
i
Decimals.
EXERCISE CLXXVII.
Koiul or writ*' in words: —
1.
.9
.45
.75
.08.
2.
.17.')
.087
.006
.209.
3.
'J.OG
7.001
10.07
9.207.
4.
.:5875
.0562
.0083
.0006.
15.
l.()31
1.315
48.007
87.0006.
G.
201.201
78.567
100.001
709.224.
7.
612.612
13.0108
700.625
5.6006.
H.
10000.001
1000.0001
100000.01
1000000.1.
9.
200.2006
2002.006
20020.06
20.02006
10.
78965. 4.*{2
789.65432
7896.5432
789654.32.
EXERCISE CLXXVIII.
Write in fi^ires: —
1. Three limidretl siiid twentyfive, and seven tentlis.
2. Four hundred and sixtyfive, and fourteen hundredtlis.
3. Ninetythree, and seven liundredths.
4. Two hundred and tiiirteen thousandths.
5. One tliousand, and six tenthousandths.
Thirtysev^n, and seventytwo thousandths.
Seven Inindred and eighteen tenthousandths.
Two liundred and forty thousand, and four hundred and six
thousandths.
9. Fiftysix million, and fiftysix jnillionths.
10. Seventy million, and seven millionths.
6.
( .
8.
AnniTION OF DKCIMAL8.
117
J
a
•
o
X
^4
*•
• r*
tt4
■/!
_o
1^
1
/
xa
'»— ;
fl
S
*j
• ^4
01
■»>
•<
o
?^
o
1
PI
• •^
S
7
H
J)
10
VLH.
.08.
.209.
9. '207.
.000(5.
87.000().
709.224.
r).()00().
1)00000.1.
20.02006.
1789654.32.
Miths.
lundredtlis.
tidred and six
Add togt'tlier: —
1.
359.6
35.964
520.
43.7
.876
1.01
II. ADDITIOIN.
EXERCISE CLXXIX.
7.04
3«).475
90.007
0.689
367.
7.82
200.
1.01.
36.010
19.00!).
7.7
178.6.
84.09
6.83.
785.3677
20.761.
6.005
.84.
2. 18.79, 147.072, 856.709, 185.8761, 397.05784.
3.
4.
3.584, 387. <), 5.894003, .00397, 8.889.
6.
7.
8.
8939, 8.939, 89.39, .89.39, .00089.39, 893.9.
56.6794, 5.76, ..579, 342.1, 34.21, 7000, 9.7646.
47.21, .946, 154.172, .000457, 17.46, 173, .05409.
4.71, 3.967, 17.10845, .04075, ().154, 99.876.
27.16, 47.148, 9, 9.2387, .()047(), .0853, 78.
9. $47.19, $27.15, $364.10, $.75, $4,085, $65,075.
.10. $7,009, $7, $871, $.065, $1,005, $21,075, $6,675.
EXERCISE CLXXX.
Sini)dify: —
1. 64 + .78 + 479.543 + 66.8 + 3^5.4876.
2. 34.084 + .088 f 96.7854 + 78 + 42.89.
3. 9.3 + .04 + 8.0067 f 778.7 + 47.0.393.
4. .365.84 4 19.07 + 17.8 + 78 + 584.3671.
5. 729. + 2.3788  35.68 + 7806.7 + .379.
6. 19.7864 + 3987 + .9 + 577.17 f 93.8 + .48.
7. 9.7 4 64.36 + .587 + 97 + .00487 + 54.7.
8. 76.54 + 3896.0484  77.3456 + 68 + 78.99.
9. 87.4785 + 78 f .84 + 37.84672 + 18.75.
10. 3698 + 786.4 + 7 + 4.9 + 36.847 j .099.
EXERCISE CLXXXI.
1. A man lias in one field 27.9 aeres; in another, 45.755
acres; in a tliird, 135.125; and in a fourth, 73.625. How many
acres has he in all?
2. Add together two hundred and nine thousand, and fortysix
millionths; ninetyeight tliousand two hundred and seven, and
fifteen tenthousandths; fifteen, and eight hundredths; and
forty nine ten thousandths.
3. What is the sum of the following numbers: twentyfive,
and seven millionths; one hundred and fortyfive, and six
hundred and fortythree thousandths; one hundred and seventy
five, and eightynine hundredths; seventeen, and three hundred
and fortyeight hundredthousandths?
:m
118
ARITHMETIC.
4. A merchant bought at one time 23.75 yards of cloth; at
another time, 57.375 yards; and at another, 34.6875 yards. How.
many yards did he buy in all ?
5. A farmer sold 2.875 tons of fodder; 8.3125 tons of oats;
5.4.55 tons of hay, and 7.625 tons of clover. How much did he
sell in all?
6. Add the following numbers: fiftynine, and fiftynine
thou'andths; twentyfive thousand, and twentyfive ten thou
sandths; five, and five milliouths; two hundred and five, and
five hundredths.
7. What is the sum of 304 thousandths, 5103 hundred 
millionths, 61032 millionths, 413 hundredthousandths, and
603 ten thousandths?
8. Jones bought 4 loads of hay, weighing 1.475 tons, 2.085
tons, 1.516 tons, and 1.424 tons, respectively. How many tons
are there in all?
9. What is the sum of fortynine, and one hundred and five
ten thousandths; eightynine, and one hundred and seven
thousandths; one hundred and twentyseven millionths; and
fortyeight tenthousandths? J
10. What is the sum of three, and eightet.'n ten thousandths;
one thousand and five, and twentythree thousand and forty
three millionths; eightyseven, and one hundred and seven
thousandths ; forty nine ten thousandths ; forty seven thousand,
and three hundred arid nine hundredthousandths?
III. SUBTRACTION OF OECIIVIALS.
EXERCISE CLXXXII.
1.
From
Take
From
Take
From
Take
7.84
3.67
39.3 *
1.6789
7.6
2.847
81.01
27.08
5.
1.678
3.842
1.9678
36.006
21.783
76.89*
7.397.
2.
6.1
1 .99999
41.7
21.9767.
3.
.0067
.0009
7.
1.345.
4. From 8, take 2.7689; from (5.5, take 2.378.
5. From .8, take .347; from ()!), take 7.9684.
(). From 25, take 12.789; from 17, take .0007.
7. From 100, take .0001; from 10, take .01.
8. From 87.1, take 5.6789; from 1, take .87654.
9. From 74.8, take 37.456; from 5.08, take 1.675.
10. From 385, take .0076; from 1001, take 7.0006.
SUBTRACTION OF DECIMALS.
119
Simplify: —
1.
7— :5.45()
»>_
2.5—1.7859
:j.
8.275—5.185
4.
70.5— .0375
5.
9.008— 4. 75G3
G.
10— .0005
7.
.75— .075
8.
600— 6.r)()
9.
4— 3.87G5
10.
100—3.145
17—6.435.
5.1 — .7^45.
3— .214.
17—9.0067.
1— .0001.
25—3.675.
785— .785.
1— .175.
3.65—1.19.
7.89646—6.9.
EXERCISE CLXXXIII.
15—2.34
.36— .0897
2.0132—1.25
6.4—3.876
2— .745
100—99.875
735—7.85
5— .275
■ 28—2.8795
5 — .5555
EXERCISE CLXXXiV.
1. From seventy three, take seveiitythree tliousandths.
2. From twentythree hundredths, take three hundred and
seven ten thousandths.
3. From three hundred and sixtyfive, take fortyseven ten
tliousandths.
4. From seven thousand, and seventeen millionths, take
.0004125.
5. From one million, take one millionth.
6. From eighteen thousandths, take five hundred and nine
teen millionths.
7. From three million, and one millionth, su, tract one tenth.
8. From one thousandth, subti'act one millionth.
9. From fiftythree, and ninety thousandths, take ten, and
three hundred thousaTuiths.
10. From seven thousand and seven, subtract seventyseven,
and four thousand and seven hundredthousandths.
Simplify: —
EXERCISE CLXXXV.
1. 25.000315 — .00045 + .2801 — 16 + 21.001.
2. 8.14 f 38.124 — .9175 — 16.28 + 46.
3. 16.945 — 2.994387 — .06735 — .0007 f .953 + 0.8.
4. 7.654327 — .3793080 f 9.06990 — .00999 + .345.
5. 78 — l(i.45 — 32.08 — 11.709 f 24.305 \ 7.09.
6. 100 f 1.005 — 41 — 36.008 — 21.07 f 1.225.
7. 84 — 7.(59 f 9.0S9 — 3.425 — .S25 — .006.
8. 1.6 f 7.92 f 6.859 — 3.9999 — 2.5554 — .0(;4.
9. 75  25.8 f 36.08 — 25.755 f 42.375 — 21.875.
10. .008 j 10.01 — 3.5876 — 2.8497 f 7.854 — 2.345.
li
120
ARITMHETIC.
EXERCISE CLXXXVI.
1. A farmer owning 957 acres of land sold at one time
225.7 acres; at another, 175.45 acres; and at another, 327.375
acres^ How many acres did he still have?
2. A merchant, having $1000, invested it as follows, viz. :
$145.75 in calico; $275.56 in shoes; $95.25 in hats; $156,375
in broadcloths, and the remainder in groceries. How much did
he invest in groceries?
3. A is to tiavel 597 miles in 3 days. The first day he
travels 196.4 miles, and the second day 201.25 miles. How
many miles must he travel the third day?
4. A man received the following sums: $27.40, $68.75,
$810.47, $381>.59, and $2.20. He paid out the following sums:
$78.67, $129.72, $119.46, and $3.88. How much had he left?
5. A man owning 875 acres of land divided it among his
four sons as follows: to tlie first he gave 213.65 acres; to the
second, 192.375 acres; to tlie third, 206.625 acres; and to the
fourth, the remainder. Wliat was the fourth son's share?
6. In 1897 tlie rainfall in Ontario for six months was as
follows:— April, 2.52 in.; May, 3.38 in.; June, 2.83 in.; July,
5.36 in. ; August, 2.62 in. ; and September, .83 in. How much
did the rainfall during the second three months exceed that
during the first three?
7. A gardener sold his cabbages for $212,875 and his
turnips for $118.33. The cost of raising the cabbages was
$119.75, and the cost of raising the turnips was $99,875. What
was his profit on the two crops?
8. A speculator, having 57436 acres of land, sold at different
times 536.74 acres, 1756.19 acres, 3678.47 acres, 9572.15 acres,
7536.59 acres, and 4785.94 acres. How much land had he
remaining?
9. From a hogshead of sugar containing 397.25 lb., a grocer
sold parcels as follows: 110.25 lb., 64.5 lb., 14.25 lb., 29.375
lb., 39.23 lb., and 16.33 lb. How much was left?
10. A flagstaff is made up of two parts, the upper part being
27.84 ft. long, and the lower part 57.86 ft. long. If the loer
part is set 11.97 ft. in the ground, how many feet of the whole
staff are above tlie ground?
11. Four men dug a ditch. The first dug .123 of it; the
second .234 of it; and the third .343 of it. How much of it did
the fourth man d' jf?
12. On Monday the mercury of a barometer was 30.356 in.
high. It fell .017 in. and .15,3 in. during the next two days.
During the next four it rose .008 in., .027 in., .231 in., and .018
in. On the seventh day it fell .132 in. Find its height at the
end of the seventli day.
MULTIPLICATION OF DECIMALS.
121
IV. MULTIPLICATIOIN OF DEC1IV1ALS.
Multi
1.
o
.3.
4.
5.
G.
7.
H.
J).
10.
EXERCISE
ply:—
4.8 by 4.2
3.5 by 3.5
4.5 by 3.58
240.5 by .25
32.7 by 2.35
G1.76 by .071
.0009 by .0009
.0068 by .0062
7.006 by 4.05
CLXXXVII.
5.4 by 5.G
12.7 by 12.3
.37 by 4.3
.45 by .21
.009 by .07
.6101 by .061
.084 by .086
.0125 by .0125
75.6 by 75.04
7.007 by 7.007
1.0001 by .001
7.1 by 7.9.
10.8 by 10.2.
5.25 by 3.75.
.27 by .0009.
12.5 by 12.5.
.1234 by 1234.
.073 by .077.
.075 by .075.
245 by .245.
34.56 by .008.
Simplify: —
EXERCISE CLXXXVIII.
1. 72.5 X .006
2. 37.654 X 13.45
3. (2.45 + 3.08) X .0024
4. 3.075 X 80 X .15
5. .008 X .019 X 25000.
G. .0525 X 10000
7. (101 f 10.1) X 101
8. 1.0005 X (3.4 + 5.66)
9. .0003 X .003 X .03
10. .012 X .0012 X 12000
8.45 X .008.
7. 0805 X 5.0006.
(7  1.234) X 5.65.
895 X .475 X .004.
123 X 12.3 X 1.23.
.0927 X 1000.
(7 — .564) X 8.5.
7.245 X (75 — 36.45),
1000 X .0006 X 8.
64 X .125 X .004.
EXERCISE CLXXXIX.
1. Multiply 123.456 by 10; by 100; by 1000.
2. What is the product of one thousand and twentyfive,
multiplied by three hundred and twentyseven tenthousandths?
3. Multiply one hundred and fiftythree thousandths by one
hundred and twentynine millionths.
4. Multiply five thousandths by seventythree hundredths.
5. Multiply three hundred and fiftysix thousandths by one
hundred and forty five tenthousandths.
6. Multiply 4.5 by 10; by 100; by 1000; by 10000.
7. Multiply eiprht hundred and fortytwo thousandths by five
hundred thousand.
8. Multiply'one hundred and seven thousnnd, and fifteen ten
thousandths by one hundred and seven tenthousandths.
M
1>)0
AKITHMETIC.
9. Multiply twenty five tenthousamlths by two hundred and
seventy five, and fourteen hundredths.
10. Multiply thirtyfour millionths l»y twentysix tenmil'
lionths.
EXERCISE CXC.
1. If a nnm can walk 27.25 miles in a day, how far can he
walk in 7.;') days at the same rate?
2. A cubic foot of water weighs 02.5 pounds. Whsit will be
the weight of 7.25 cubic feet?
:J. What is the profit on one million yards of cotton cloth at
$0,007 per yard?
4. How many solid feet are there in a pile of wood 7.3
feet long, 5.7 feet wide, and G.5 feet high?
5. A roller 4.15 feet in circumference makes 208.4 revolu
tions in passing from one end of a field to another. Find the
length of tha field.
G. A is .875 times as old as C, and C is 1.08 times as old
us B. B is 25. How old is A?
7. If one cubic inch of pure water weighs 252.458 grains
Avoirdupois, how many grains will 1728 cubic inches, or one
cubic foot, weigh?
8. A and B start from the same place at the same time, and
travel in opposite directions, A travelling at the rate of 22b
miles per day, and B at the rate of 24.04 miles per day. How
far apart will tliey be at the end of 12.45 days?
9. From a cistern containing 27G5 gallons, 56.25 barrels, of
31.5 gal. each, are drawn off. How many gallons remain?
10. A man made a journey as follows: He travelled 7.75
hours by rail at the rate of 22.75 miles an hour, 9.875 hours by
stage at the rate of G.75 miles an hour, and 11.75 hours on foot
at the rate of 4.G2 miles an hour. What was the length of the
jourf^iy?
V. DIVISION OF DECIMALS.
EXERCISE CXCI.
ivid
e: —
1.
.8 by 2
8 by .2
2.5 by .05.
2.
12 bv .06
124 by .31
.09 by .003.
3.
.08 by 5
.9 by .12
1 by .125.
4.
.51 by .015
.005 by .020
.375 by .025.
5.
.008 by .04
.12 by .0000
.004 by 2.5.
G.
155 by .0025
.00025 by 25
25 by .30025.
7.
272.G3G by 6.37
281.8585 by 3.85
9.6188 by 3.40.
8.
40.1975 by 54.35
.014274 by .001
345.15 by .075.
9.
3.0 by .00000
75 by 10000
4.30 by 10000.
10.
216.32 by .00512
5058 by .00i23
4.110 by .0075.
DIVISION OF DECIMALS.
123
iidred and
tenmil
fav can J»6
tiat will be
on cloth fit
wood 7.IJ
iA revolu
Find the
iraes as old
1.458 grains
has, or one
le time, and
rate of 22
day. How
1 barrels, of
eraain?
ivelled 7.75
75 hours by
Durs on foot
ngth of the
Simplify: —
1. 01.04
EXERCISE CXCII.
by .05.
by .003.
by .125.
by .025.
by 2.5.
by .)0625.
by 3.46.
by .075.
by 10000.
by .0075.
3.
4.
5.
G.
7.
8.
9.
10.
(JO. 25 H 3.125.
.0045 : 225.
5.007 — 375.
154.28 ^ .0004.
(28 + 11.75) ^ 1.25.
1.2 X .7 ^ 12.5.
100 X 4.0125 r .004.
(7.89 — 3.0111) ^ .015.
12"— (.832 — .757).
11.25 X 11.25 ^ 937.5.
4.30
9005 — .049
327.6 r 0.25
10 — .0004
(0.05 + 3.75 — .0048) > .4
.06 X .08 H 3.2
8 ^ .025 X .01
12 ^ (.015025 + .040875)
(.06 + .006 — .00000) ^ .06
3.225 — .75 X .01
EXERCISE CXCIII.
1. Divide one hundred and fortyseven, and eight hundred
and twentyeight thousandths by nine, and seven tenths.
2. What number must be multiplied by .0017 to give 595?
3. By what must .7847 be divided to give 1.9 for quotient?
4. Divide seventyfive thousand eight hundred and one by
two thousand two hundred and ninetyseven tenthousandths.
5. What is the quotient when 10.9536 is divided by 1000
times .4564?
6. Divide three hundred and twentythree tiiousand seven
hundred and sixtyfive by five millionths.
7. Divide 123.45 by 10; by 10( ; by 1000; by 10000.
8. What is the sum of the quotients of 24 by 9.6, of 42.75
by 11.4, and of 17.85 by 4.2?
9. The product of three numbers is 2.94294. Two of these
are .21 and .11. Find the third number.
10. Divide seven, and five tenths by one hundred; by one
thousand; by ten thousand.
EXERCISE CXCIV.
1. If 25 men build 154.125 rods of fence in a day, how
niueh does each man build?
2. There are 16.5 feet in one rod, and 5280 feet in a mile.
How many rods are there in a mile?
3. How many bushels of clover seed at $6.25 a bushel will
Itay for 25 barrels flour at $10.5 per barrel?
4. A man has 324 bushels of apples which he wishes to init
into barrels containing 2.25 bushels each. How many ) ."Is
will be required?
5. Tlere are 31.5 gallons in a barrel. How many barrels
can be tilled from 2756.25 gallons?
■i
124
ARITHMETIC.
6. A speculator bonglit 78.2') acres of land for $9781.25,
and sold it so as to gain $3.50 an acre. How much did he get
per acre?
7. A man bought a farm containing 64.5 acres for $177.'1.75.
How much did he pay per acre?
8. Twenty five hundredths of a farm cost $3000. Find the
cost of .9 of it.
9. If 20.5 acres of land produce 322.875 bushels of wheat,
what is the yield per acre?
10. If a train goes at the rate of 24.75 miles per hour, how
long will it be in going 128,7 miles?
VI. REDUCTION OF DECIMALS.
EXERCISE CXCV.
Reduce the following decimals to vulgar fractions in
lowest terms: —
their
1.
.35
.48
.25
.125.
2.
.625
.75
.375
.64.
3.
.016
.225
.875
.035.
4.
.275
.575
.0375
.005.
5.
.068
.024
.175
.0175.
6.
.99
.021
.123
.003.
7.
2.75
4.76
7.45
5.. 36.
8.
3.25
9.75
12.725
5.064.
9.
6.0125
16.075
7.875
11.625.
10.
5.3125
2.1875
7.9375
9.6875.
EXERCISE CXCVI.
Reduce the following vulgar fractions to decimals: —
1.
i
o
5
8
8.
t\
4.
h
5.
A
C.
1 8
TJ5
7.
4^\
8.
i%z
9.
T5
10.
1 31
625
3
11
40
q89
o 1 1
H
SI
40
1 1 1
nil
«J4
711
441
15 25
3
tV.
1 3
Iff.
1 8
33
4 (J
2 1 1
73 9
'40
8/5.
311
625
APPLICATIONS OF PREVIOUS HULKS.
126
EXERCISE CXCVII.
Expiess each of the foUowiiif? as oonipound iiuinlior.s: —
1.
£.79002.')
2.
.83125 cwt.
3.
.787") mi.
4.
.907") A.
n.
.9370 on. yd
G.
.875 bu.
7.
.875 gal.
8.
.495 da.
9.
.975°
10.
.0125 fathom.
£.705025
.08745 t.
.2525 mi.
.881 25 A.
7.875 ed.
2.375 bu.
5.175 ^'al.
7.875 wk.
2.8475"
17.875 rra.
EXERCISE CXCVIIi.
£1.809375.
3.8975 t.
21.30875 mi.
13.4375 A.
0.75 cu. yd.
5.475 bu.
7.75 gal.
9.95 wk.
17.3875°.
7.75 gro.
FiX])ro'ss oMoh of the following as a dofimal of its highest
deuominatiou: —
1. £1 10s. Od.
2. 9 t. 17 cwt. 8 lb.
3. 7 mi. 35 rd. 2 yd. 2 ft. 3 in.
4. 9 A. 48 sq. rd.
5. 7 cd. 112 cu. *t.
0. 7 bu. 3 pk. 2 qt.
7. 27 gal. 3 qt. 1 pt.
8. 3da. 13hr. 24min.3Gsec.
9. 3'^ 52' 39"
10. 5 nn. 17 qr. 18 sheets.
£7 13s. 7.1d.
5 t. 14 cwt. 7i lb.
Gmi.28rd.2yd. 1 ft. 11.04 in.
7A.45sq.rd.8sq.yd.4.23sq.ft.
7 en. yd. 18 cu. ft. 972 cu. in.
5 bu. 3 pk. 4 qt. 1 pt.
14 gal. 1 qt. 1 pt.
2 wk. 5 da. 9 lir. 4G niin. 48 sec.
17° 7' 25.5".
24 grs. 9 do 55.
VII. APPLICATIONS OF PREVIOUS RULES.
EXERCISE CXCIX.
1. What will l>e the cost of filling in a street GOO ft. long
Mild (55 ft. wide, averaging 4i ft. below grade, at $.52 a cubic
yard?
2. Goliath of Gath was 6i cubits high. What was his
luiglit in feet, the cubit being 1 ft. 7. 108 in.?
3. What will be the cost of the wood that fills a shed 20 ft.
long, 10 ft. wide, and 8 ft. high, at $4.75 a cord?
4. Which will contain more — a box 5.5 inches long, 4 iiichcs
\\idc, and 4.25 inches deep, or one 0.5 inches long, 4.5 inches
\\i<t(', and 3.5 inches deep?
5. How much gold may be obtained from a ton of quart/;
'uck, if it yieWs .0010 of its weight in gold?
126
ARITHMETIC.
G. At ()7i «'ents per eu. yd., what will be the cost of iligging
a cellar 15.5 ft. long, 12 ft. wide, aud 5 ft. 4 in, deep?
7. How many yards of carpeting 1 yard wide will b« required
to cover a tloor 33.5 ft. long aud I22i ft. wide?
8 What is the cost of slating a roof 52 ft. lU in. long, each
side being 20 ft. wide^ at $15.25 per square, a scpiare being
100 sq. ft.?
9 If 1 cu ft. of water weighs 1000 oz., what will be the
weight of the' water iu a cistern 8.5 ft. long, U ft. 3 in. wide,
and 3 ft. 9 in. deep?
10 At $13.60 per square, what will be the cost of tinning
both" sides of a roof 36 ft. 6 in. in length, and each side 18 ft.
9 in. in width, a square being 100 sq. ft.?
EXERCISE CC.
1. If 11.8 A. of land cost $236, what will 20.7 A, cost at
the same rate?
2. Find the cost of 8725 ft. of boards at $12.50 per
thousand?
3. A drover bought sheep at $3.37i a head, and sold them
at $3.87i a head, and gained $37.50 by the transactions. How
many sheep did he buy?
4. What is the cost of 24 ewt. 87 lb. of sugar at $6.50 per
hundredweight?
5. The contents of a chest of tea weighing 87.5 pounds are
made up into an equal number of 1 pound, i pound, and i
pound packages. How many packages are there of each kind?
6. What would 7 bales of cotton cost, each bale weighing
537.5 pounds, at $0.11 J a pound?
7. Boys in playing hare and hound run 3.875 miles. The
hares drop a piece of paper every 5.5 feet on the average.
How many pieces do they drop?
8. A merchant sold 4 pieces of matting, each containing
35.5 yards, at $0,375 per yard. How much money did he
receive ?
9. Divide $47.10 among 6 men and 11 youths, giving a youth
0.525 of a man's share. What is each man's share?
10, The great pyvitmid of Clieops measures 763.4 feet on eacli
side of its base, which is square. How many acres does it
cover?
EXERCISE CCI.
1. Bought land at $62.50 an acre, and sold it again at $75
an acre, thereby making $846,875. How nuiny acres vvei'(
bought ?
2. If .875 of a man's age is 35 years, what will .7 of his
age l.>e?
APPLICATIONS OF PREVIOUS RULES.
127
i ve(iuued
long, each
tare being
nil be the
1 in. wide,
of tinning
side 18 ft.
A. cost at
$12.50 per
d sold them
tioiis. How
at $6.50 i»ev
pounds are
[ound, and i
f each kind?
ale weighing
miles. The
the average.
Ih oontaininp;
}oney did he
iving a youth
foet on each
lucres docs it
afi;ain at $7.>
ly acres wert
LiU .7 of his
;{. If .75 of a ton of steel rails is worth $7i!, wluit is the
value of 275.875 tons?
4. Divide 1(5. .'14 into two parts, so that one i)art may be
1.50 larfrer than the other.
5. A ujan spent .875 of his money and has $1.29 left. How
much had he at first?
G. Bought G7.75 acres of land at $62.50 an acre, and hoUI
the lot for $5081.25. Was there a gain or loss? How much was
gained or lost on the whole, and how much an acre?
7. Divide $133.26 between A and B so that A may have
$18.48 cents more than B.
8. What number is that which, being diminished by 2.75,
the remainder, multiplied by 4.6, and the product, increased
by 6.75, gives 70?
9. How many cu. ft. of water will pass under a bridge every
12 min. if the stream is 125.125 ft. wide and 4.8 ft. deep, and
flows at the rate of 2.5 mi. per hour?
10. Two men who are 17.82 miles apart start at the same
time to walk towurds each other, one at the rate of 3.27 mi.
per hr. and the other at the rate of 3.48 mi. per hr. How i
will each walk before they meet?
EXERCISE ecu.
1. What is the price of 20 joists, 10 ft. long, 6 in. wide, and
2 in. thick, at $25 per M. ?
2. What is the cost of 576 fence boards 16 ft. long and 9 in.
wide, at $14 per M. ?
3. During a week the barometer stood as follows: — On 3
days at 29.46 in., on 2 days at 30.05 in., on the other two days
at 29.48 in. and 30.85 in. What was the average for the week?
4. In walking 3.6 mi. a girl took 7040 steps. What was the
average length of her step?
5. Find the average of 2.6, 2.37, 3.025, 2.973, and 0.516.
6. Find the G.C.M. and L.C.M. of 2.25, 3.375 and 2.8125.
7. How many boxes 4.5 ft. by 3.25 ft. by 2.875 ft., outside
measurement, can be stored in a room 52 ft. by 36 ft. by 345 ft. ?
8. If a block of English oak 3i ft. long, 2 ft. l)road, and 1.75
ft. thick, weighs 710.5 lb., find the weight of a cu. ft. of
English oak.
9. What will be the cost of painting the walls of a room, at
$.30 per sq. yd. the length being 19 ft. lOi in., the breadth 16
ft. 1* in., and the height 10.25 ft.?
10. A merchant fails in business and his assets pay $.425 on
the dollar. How much does a creditor receive to whom he owes
$453,60?
. i
I Tr
128
AKITHMKTIC.
EXERCISE CCIII.
1. Fiml llin sum of tlic su?n, <lilT«n'<'ii(M<, mid lu'odiid of
seven, iiiul t\voutytiv«5 Imiulredths iiiul tlirco, uud eif^htyfoiii'
ImiidiMMlths.
'J, Find tho sum of the sum, dilferunco, jn'oduct, and two
quotients of l.G and 4.
I{. .5 tiincH the sum of two nnmhers is 35.25 and one is 2.8
more than the other. Find the numbers.
4. Two ni<Mi toj^etlier eliopped 50.75 cords of wood and one
cliopped 1.45 cords more than the other. How much did each
ciiop?
5. Two men are 120.25 miles apart. They walk straij^ht
towards each other and when they meet one has gone 7.75 mi.
less than the other. How far has eaeli gone?
G. If a merehant deposits !)!;i75. 50 in a bank at onetime, ami
$487.75 at another, how much will remain after he has with
drawn $17().;{7 and $340.83?
7. Bought 1 ])arrel of flour at $8.50; 3 })ushels of corn at
$.505 a busliel; 24.5 jmunds of sugar at 8.ic. a pound; 3 gallons
of molasses at 37ie. a gallon; 2 pounds of tea at 624c. a
])ound; pounds of cotfee at 35e. a pound ; 15 pouiuls of rice
at 8c. a pound; and 4 pounds of butter at 22c a pound. What
was the cost of the whole?
8. A guinea is 21 shillings. Reduce 7i guineas to the
decinuil of £10.
9. A stick of square timbor is 17.5 in. wide by 13.5 in.
thick. What length must be cut off to contain 7 cu. ft.?
10. What must be the length of a plot of ground, its breadth
being 70.23 yd., to contain 232.848 sq. rd.?
11. Divide $302.50 among A, B, and C so that A may receive
1.5 times us much hh the otiier two together, and B, 1.75 times
as much as C. Find the share of each.
12. In sinking a shaft it is found that .375 of it passes through
earth, .075 of it tlirough shale, and the remainder through
solid rock. The shule is 90 ft. deep. How much of the shaft
is in the solid rock?
13. A stick of square timber 32.5 ft. long, 2.5 ft. wide, and
1.125 ft. thick, weighs 4387.5 pouiuls. Another stick of the same
kind of timl)er is 21.75 ft.
long,
1.875 ft. wide, and 1.25 ft.
thick. How much does <he second stick wiMgh?
14. A piece of work can l)e done by A in 17.5 days; by B in
22.5 days; and l»y (' in 15.75 days. If A works alone at it for
5.5 days and is then joined by B and C, how long mus^ the
three work together to finish the remainder?
M
CHAPTER VIII.
PERCEINTAGE.
The expression Per Cent. (L.itiii per ceiitiiin)
nnnuia for, or hij tlic Inindnd.
A Rate Per Cent, denotes u eerluin mmiber of
liuiidredths, as G per cent, denotes 1 0,7 or .00; 4 per
eent. denotes liyOr .0075.
Tlie symbol " „ is used for the phrase per cent.
EXERCISE CCIV.
Express the following as hundredths: —
1. )% 7% 10% 1.)%
'2. 7i% (U% 12i% 20%
Express the following deeimuls in percentage: —
;{. .05 .07 .1 .17
4. .055 .0725 .105 .125
27%.
50 % .
.1725.
Express the following — (1) iis decimals, and (2) as common
fractions in their lowest terms: —
O. '070
5%
8%
lGf%
# 10%
37J%
12.i%
75%
G. 1U%
Express as hundredths and also in percentage
20%,
87^%.
I
t\
S. 3
i
i
4
8 .
Express the following as fractions in their lowest terms: —
9. 4% 40% 80% 15% :{0%.
10. •m% Gi% Si% 5§% G2i%.
r29
PI
KJO
ARITHMETIC.
Kiihl IIh' following:
I. :\'/ro\'^HM
li. 4'/f> (tf lOOiicros.
i't^^fi <»r 'J.')!) words
U)% of ")()() Itoys
20% ofsUl";')!)
I7r of 200 men.
2)i% of $2(500
n.'.T^'of 270yil.
U)''r of $7.M
;{.
4.
T).
(>.
7.
s.
!).
10.
EXERCISE CCV.
r)%of!»!ioo
H%of 2r)0 A.
C)'/t' of "mO vvonlH
100'? (if 79
io7'> of !)<:{r>o
2r)%or7r>0 mi.
•i'^ of 400 yd.
12.i% of 400 11.
X]k'/r of 7r)0 slu'cp.
2')7f of lOiiO mty.
S7i% of lG()4yil.
7% of !fir»oo.
U>7 of 75 A.
(i'V of !)00 COWH.
10% of I'tOyiirds.
7.')% of 00 JMIIH.
r^% of .1(200.
H,^%of<)GOnu'U.
('))}% of 4r)0co\vs.
;57i % of r)7GI»ooks.
22^ % of .1!720U.
EXERCISE CCVI.
Find thf rjitc ix'r cent, equal to t'lich of the following: —
1 . $5 IMT !i«2r)
2. 1 hr. per 10 lir.
Wliat per eeut Jh: —
3. 8 of IG?
4. 3 ft. of GO ft.?
i). 240 lb. of 1 ton?
G. 24 da. of 480 da. ?
$8 i)er !i!80
5 lb. per 1 cwt.
$1;') per $G0.
$G0 per .$480.
20nii.of 4.')0mi.?
880 ft. of :i mi.?
$<)G of $1920?
5 qt. of 10 gal.1
$.") of $40?
7 mi. of 100 mi.?
84 men of 1200 men?
50 men of 80 men?
Find the difference between the following: —
7. 'M7o of $100 and f of $100; G0% of 200 A. and J of 20f) A.
8. t of 80 lb. and 50 % of 80 lb. ; I of 80 gal. and 80 % of 80 gal.
Find the sum of the following: —
9. $40 and 5% of .$40 $100 and 7% of $100.
10. $G0 and 50% of $G0 50 mi. and 10% of 50 mi.
EXERCISE CCVII.
1. A f.irmer having 1200 sheep lo.st 37% of them. How
many did he lose?
2. A lawyer collected $2575 for a merchant, charging 4% for
liis services; what was his charge?
3. A ship loaded with 1875 bales of cotton was overtaken by a
storm, and the sailors threw overboard 12 per cent, of the
cotton; how many bales were lost?
4. In a warehouse 1920 boxes of tobacco were stored; the
warehouse haviiig taken fire, 15% of the tobacco was burned.
How many boxes were burned?
PKRPF.NTAOK.
VM
f). A iniin'M inoniuc is (I'lSOO ii y«'ur, (if wliit'li \iv piiys 1)1%
for lioiiso rent. Whiit. r«'iit iloos Ik* pay f
(5. A iiiiiii owns 'J I'lirms. Tli«' first contuiiis .'H!0 A. iiii*l tli«'
ikiiiiImt (tl" iicrcs in tin second is l.'td'f of tlif ininilxr of iicrcs
in tin* lirst. Find the nnniltcr in tlic st'cond farm.
7. If copjHT ort' yields {]% of pure metal, how many jto.in.'s
of copper will lie obtained from I t. of ore*
S. A l>on^'ht ;{*J() acres of land, and sold (ilii"/ of it. JJow
many acres did he sell?
!». In an orchard of 900 trees, '.V.\h% are peach trees. How
niiiny peach trees are there in th.* orchard?
10. A nnm havin<; 11250 bu. of wheat, sold 'Sf/r of it. How
mnch did he sell 1
EXERCISE CCVIII.
I. A man has an income of .$4000; he spends {>'>% of it.
How much does he save?
'2. A lionse post .fOTOO and 20% of the money is ])aid at nnee.
How much still remains unpaid?
'A. \ man has a farm of 200 acres. He sells 40% of it in
viliaj^e lots. How much has he left?
4. A man bouf?ht a farm for $;{000. How much must he sell
it for to fi;ain 12i% on his outlay?
r>. A speculator invested !i!3r),400 in stocks and lost 168^% of
his investment. How much had he left?
(). A shepherd luid 5,800 sheep b>it lost 15% of them in a
snow siorin. How many had he left?
7. In a seliool 420 pupils are enrolled, 45% of v/hom are
tioys. How many girls are enrolled?
5. The population of a certain city is 18775. What will it be
ill one year from this time if it jrains 8% ?
i>. If 5% is deducted from a bill of $755, how much will pay
the bill?
10. A farmer having a flock of 1200 sheep lost 27% of them,
Wliiir per cent, of them, and how many sheep, had he left?
EXERCISE CCIX.
1. A cask contained 42 gallons of vinegar, and 14 gallons
leaked out. What per cent, was left?
2. In an orchard of 4000 trees, 80 died. What per cent,
if'tnained?
;{. In a school of 50 j)upils, 10 are absent. What per cent.
are ]»resent?
4. A merchant bouglit shoes at $2 a pair, and sold them at
f'> a pair. What per cent, of the cost did he gainf
^Ul
132
ARITHMETIC.
f). A mnii bouglit a hoisc for Jt^'Jlf) mikI soM liini l"<>i' $ll!)4.
VVIiiit per cent, of llio cost tlitl lie f,';iiii.'
(i. ir ;i niercluint houj:;lit tc:i at .")(» ct. per Ih. and sold it at
44 ct. pw lb., wliat is his loss ]»('!• cent. .'
7. A workman's wages arc reduced from ^lOawick to fj<7..1(l.
Find the per cent, of decrease.
H. A collector cliarged t^2').i)2 for collecting ^',^24. What rate
percent, did he charge?
9. A man's income is $840 a year and his expenses .toCO.
What per cent, of his income does he save?
10. A and B engage in partnership. A invests ifoGOO and U
$8400. What per cent, of the capital does each invest?
EXERCISE CCX.
1. The aver.age attendance in a school was 5(5; this is 80%
of the nnmher enrolled. How many were enrolled?
2. A bookkeeper spends ^WO per year, which is 24% of his
salary. Required his salary.
3. I have bought two ]»uilding lots. For the one I paid $.300,
which was GO per cent, of what I paid for the other. What
did I pay for the latter ?
4. A young farmer owns J520 acres of land, which is 40% of
the land his father owns. How mucli has the father*
5. A man had 24 sheep killed ])y dogs, which was 5^% of
his flock. How many siieep had he at lii'st?
C. A gentlennm pays $49;") for the rent of a hon^;e, which is
at the rate of 11 per cent, of the vahie of the house. What is
the value of the house?
7. A schoolboy in one week reiid 450 lines of Latin, which
was 75% of the number in tiie book. How many lines had he
still to read?
8. A clerk spent 00% of his salary for board, 20% of it for
clothes, 11% for books, and saved $117. What was his salary?
9. A wool grower sold 3150 head of sheep, and had 30% of
his original flock left. How many sheep had he at first?
10. The number of pnpils belonging to a certain school is 48(5,
which is 8% more than belonged a year ago. How many
belonged to the school a year ago?
EXERCISE CCXI.
1. A grain dealer had 7000 busliels of grain; 17% was oats,
30% wheat, and the rest l»arley. How much barley had he?
2. A man bought a horse for $85 and sold him foi' $90.10.
What per cent, did he gain?
PERCENTAGE.
133
:?. Increase $450 by H% of itself, and decrease $450 l)y S'fr
(>r ilselt', and find the difference between tlie I'esults.
4. Find tliu dill'ereuco between 40 ^fc of $12200 and (JO'r of
$ir)(H).
5. A farm contains IJilO acres; 15% of it cost $'J<S pei acre,
2i)'''r' cost $;{5 per acre, and tlie rest $40 per acre. \Vliat was
the total cost?
G. A f?rocer sells 128% more j^ranulated than loaf su^ar. Ho
sells 38275 lb. of loaf sugar in the year. How much granulated
sugar does he sell in a year?
7. A music dealer bought ?> pianos at $250 each. He sold
one at a gain of 'AQ7o, another at a gain of 40%, and the thir<i
at a loss of 20%. What was his net gain?
8. A drover sold cows and sheep for $9180. Ho received for
his sh"ep 70% of what he got for his cows. What did he get
for the cows?
i). A young man having received a fortune deposited 80% of
it in a bank. He afterwards drew 20% of his deposit, and then
had $57(50 in the bank. What was his entire fortune?
10. I sold my farm for $5000 and made 25%. What per cent.
should I have gained, or lost, if I had sold it for $3500 1
EXERCISE CCXII.
1. How many rods are there in 8i% of 121 miles?
2, What ^•um of money, increased by 8]t% of itself, will
ii mount to $403?
',',. What is the quantity 71% of which is 12 ounces?
4. A train which runs 45 miles per hour has its rate increased
by G;i%. How far will it then run per hour?
5. A library consists of English and classical books. The
imniber of English books is 2135, which is 7Gi% of the whole
niinilier of books. How many books does the library contain?
(). In a r(\giment of 9G0 men of English, Scotch, and Irish
(liscent, 40% of the whole are Irish, and3G8^%are Scotch. How
ninny are of English descent?
7. The sum of two numbers is 3901 and one of them is 71%
more than the other. Find the numbers.
S. A nuin owning 75% of a foundry sold 40% of his share to
"lie man and 33^% of the foundry to another. What per cent.
<it' llii' foundry did he still own?
!). Tlif population of a city in 1891 was 15048, being 41%
I'loie tnan in 1881. What would have been the population in
I'^Ol, if there had been a decrease of 4i%?
10. If water expands 10% when it becomes ice, by what per
cent, does ice contract when it b(;comi'S Wiiter?
' ';!
CHAPTER IX.
APPLICATIONS OF PERCENTAGE.
I. TRADE DISCOUNT.
,. Discount is a sum deducted from the face of a
bill, debt or note.
Trade or Commercial Discount is a sum deduc^ted
from the catalogue or list i)rices of goods.
The terms Catalogue Price, List Price, Gross
Price and Invoice Price all denote the same thing,
viz., the price entered in the catalogue of the goods.
The Net Price is the List Price diminished by the
discount.
An Invoice is a bill of goods purchased at one
time.
EXERCISE CCXIII.
1. Find the discount off the following bills: —
Invoice price $i')Q, discount 2')%.
Invoice price $570, discount 37i % .
2. Find the net price of goods bought as follows: —
Invoice i)rice $'SG'), discount off 20%.
Invoice price $756, discount off 33i%.
3. The discount off a bill is $27 ; the rate of discount is 25%.
Find the bill.
4. The rate of discount is l(}i% and the discount is $17.50.
Find the list price of the goods.
5. The discount off a bill of goads is $45; the rate of dis
count is 20%. Find the net price of the goods.
6. The rate of discount being 33i% and the discount being
$75, find the net price of the goods.
7. Find the rate of discount on goods bought as follows: —
Invoice price $;)G0, discount allowed $1(!.20.
Invoice price $420, discount allowed $157.50.
8. Tlu^ net price of goods is $270. The rate of discount
being 25%, lind the list price.
i;i4
TRADE DISCOUNT.
135
is(h1 at one
tt> of discount
9. A doalor paid fpG20 for goods at 22^% off. Find tlio list
]»ri('(' of the goods.
10. I am eliarged $2.r)0 for a book, wliicli the bool\seller says
is '.iVI^'/o less tliau it cost liim. Find tlie cost.
EXERCISE .CCXIV.
1. Find tlio net price of goods bouglit as follows: —
Invoice price $^75, discount off 20% and 10%.
Invoice price $800, discount off 25% and 10%.
Invoice price $800, discount off 20%, 10% and r)%.
Invoice price $1640, discount off 25%, 10% and 5%.
2. What is the net cost to the purchaser of hardware
invoiced at $815 and subject to a discount of 20%, 10% and 5% ?
15. A's list price for pocketknives is $9 per dozen, 20% anil
')% off. B's list price is $9.50 per dozen, 25% and 10% off.
How much will be saved by ordering 24 dozen knives from B
rjitlier than from A?
4. At what price must goods l)e marked to sell for $2.72
after allowing 15% discount?
5. At what price are goods listed that sell for $18 after
allowing 20 and 10 off?
f). If goods cost $3.60, what must be the invoice price to
allow discounts of 25%, 20% and 10%?
7. At what price must goods which cost $216 be listed to
give 25% gain after allowing 25, 20 and 10 oft'?
S, At what price must goods which cost .$1.52 be listed to
f.ave 121% gain after deducting discounts of 20%, 10% and 5%?
9. What single discount is equivalent to a discount of 25%
ami 10%?
10. What single discount is equivalent to 25%, 20% and
10% off?
tXERCISE CCXV.
1 . What is the difference on a bill of $425 between a
discount of 50% and a discount of 30% and 20%?
2. A bookseller wishes to mark a book wliich cost $2.00 that
he may allow a discount of 25% and still make a profit of 20%.
What must be the marked i)rice?
.'{. What direct discount is equivalent to a discount of 20%
and 10%?
4. A bookseller buys at a discount of 20%, 10% and 5% off,
and sells at list prices. What per cent, profit does he make?
5. The selling price of an article was $25 when the rate of
^'aiii was 25%. Find its cost pricef
• i. It' $1.40 is gained by selling goods at 25% altove cost,
liiid what selling price would make t)u^ rate of gain 35%.
i. 'J
136
ARITHMETIC.
7. An invoioo wns $fiK), trsulc dlsooujit 20 ami f) off. Find
tli(^ cost ol' tlic j;()»>«ls.
S. A dciilci' Ixtu^lii !i l>()<»k, list prico $1 .00, iit n discount of
2i)'/tJ, itiid iit'terwiii'ds sells tlio book jit $1.00. VVh.'it ]>('i' cent,
docs lie j^iiin?
9. What is tlic not amount of a bill for $720, discounts
being 2'), 10 and ") off?
10. A man jmrchasos goods, list prico $080, discounts being
'S:ik%, Vl}.% and I07r. Find llic not amount of the bill; also,
a single discount e(iuivalent to these three.
II. PROFIT AND LOSS.
Profit and Loss, as a ooinmcrci.'il toim, donotes
the ^i\u\ or loss ill business tniusac^tioiis.
Profit is tlie amount l)y wliieli the sellin<^ pi'iee
exceeds the cost price.
Loss is the amount by wliicli tlie selling; price falls
short of the cost price.
The Rate of profit or loss is usually expressed as
a certain i)erceutage of the cost pric(\
EXERCISE CCXVI.
1. Find the i)rofit or the loss on the following: —
Cost $0, selling i)rice $8; cost $15, selling price $2^.
Cost $115, soiling price $113.50; cost $75.50, selling price,
$77.
2. Find the gain or the loss per cent, on the following: —
Cost $G, selling price $8; cost $80, selling price $125.
Cost $7.50, selling price $9; cost $100, selling price $95.
3. Find the profit or the loss in the following: —
Cost $100, gain 10"^ ; cost $500, loss 8%.
Cost $G5, gain 8% ; cost $450, gain 33^%.
4. Find the selling price iu the following: 
Cost $40, gain 7i% ; cost $80., loss 6i%.
Cost $120, loss 15%; cost $75, gain 33^*^.
Find the cost price iu the following: —
8elling price $110, gain \0% ; selling price $210, gain 5%.
Selling price $40, loss 33i% ; selling price $84, gain l(Sl7o .
Helling price $05, gain 8;^% ; selling price $72, loss 25%.
Find the cost in the folloAvinji:: —
5.
Profit $3, gaiTi 10%; profit $8, gain 5%,
Jjoss $5, loss 20% ; loss $50, loss 8%.
PROFIT AND LOSS.
la?
r» off. Find
discount of
lilt pel' et'iit.
:(), discovmtS
counts behif?
Hi bill; also,
■m, (lonotes
(T price falls
expressed us
X)Y
ice $2r>.
selling ])net',
bllowing:—
price $125.
ug price $1)5.
I<210, gain 5^c.
U, gainlG^^o.
r2, loss 25':^.
I':'!
I
■I
7. A iloek of slieep increases from 88 to 110 in a year. What
is tlie gain per cent.?
H. Bought books for $420, and sold them for $357. Find
my loss per cent.
[). If Mr. Jones buys a farm for $3875, and sells it for $3720,
wiuit per cent, does he losef
10. If I buy i)aper at $3.50 a ream, and sell it at 25c. a
(juire, what is the gain per cent.?
EXERCISE CCXVil.
1. A merchant sold cloth which cost $1.75 per yard so as to
gain H%. Find the selling iirice.
2. Goods which cost $735 ,vere sold at 20% gain. Find the
selling price.
3. At what price must goods be sold to lose 12%, if they
cost $13.50.
4. Bought a house for $3500, expended $750 in repairing it,
iuitl then sold it so as to lose 15% on the whole cost. What
did I receive for it?
5. Sold goods at a loss of 20%, an actual loss of $59.50.
What was the selling price?
0. Find the selling price of goods by which there is a loss of
2'r and an actual loss of $55.50.
7. A farmer bought 35 A. of land for $1750, and sold it at
20% gain. How much did he get per acre?
8. Mr. Smith bought a house for $5000 and spent $400 more
for repairs. He sold it at 15% gain on the whole cost. What
was his profit?
9. A quantity of wheat whieli cost 72 ct. per bu. Wfis sold
lit a loss of 20%; the total loss was $1290. How many
Imshels were there?
10, A grocer sold potatoes for $10.10, gaining 15%. If he
had sold them for $18.20, how much would he have made above
the cost price?
EXERCISE CCXVIII.
1. A set of jewelry was sold for $140 at a gain of 25%.
What did the set cost?
2. A ]>roduco deahn sold a sliipinciit of wlu^it at a loss of
'^'r", realizing as the net proceeds $S170. What was the cost!?
•>. A miM'cliant sold rye at 15% gain. His profit was $2(5.70.
How much did he receive for the ry»!?
4. A man gained 24% by selling land for $lit5 more than lu)
jniid for it, liow much Uiti he receive for the laud?
4
138
AHITHMKTIC.
'). TiMi COWS were sold foi $()!)(), at a ^i\\u of 15^. Fov how
mticli per lufiul, oil tlie iivernge, should tliey have Im'cii sod to
6. A merchant lost 25'^ by selling flour at $0 i)er barrel.
If he had sold it at $9 per barrel, what would have been tlie
gain per cent. ?
7. 1 sold a liorse for $240 and lost 20%. For what should I
have sold him to have gained 10%?
8. A building lot was sold for $1840, at an advance of 15% on
its cost. What would have }»een the gain per cent, if it had
been sold for $2240?
D. I bought a lot of goods for 1;")% below market price, and
sold them for 15% above market i)rice. What per cent, did I
clear?
10. Sold my carriage at 30 per cent, gain, and with the
money bought another, which I sold for $182, and lost 12i per
cent. How much did each carriage cost me?
III. COMMISSIOIN.
Cominission is the compensation received by an
agent for transacting (pertain kinds of business. It is
generallj^ reckoned at a rate per cent, on the money
involved.
The agent is variously known as Commission
Merchant, Broi<er, Collector, Factor, &c.
In selling, the Commission is reckoned oh the
money received by the agent.
In buying, the Commission is reckoned on the
money paid by the agent.
EXERCISE CCXIX.
Find the commission on the following: —
1. $450 at 4% $300 at 2*%
$1200 at 4A% $5700 at 3g %
Find the commission on the followiiig: —
2. $2500 at i% $044^ at i%
$3000 at li% $4800 a" 5%
3. An agent received a consignmeui of flour, .vliich ho sold
for $3750. What was his commission at H%?
4. My agent in Chicago has purcliased whert for me to the
amount of $7728. What is his commission at 14 per cent. ?
$575 at 4J%.
$1875 at 4^%.
$3000 at i%.
$8400 at i%.
)r what should I
)ned on the
COSIMISSION.
i;. Find the rate of oo '^**^ ^^^ i^e cVjJ,; *^, ^"^' ^'^eeived
,, ,^: ;^" '^Sent sold 'no vd'^nJ''^^ '^''''^
l"^' "Ot proceeds flic™ ""vli; "f/^' "' 25 at. pe,. Ih „. .
4 Find t, '""'=™"»'»sionf ^ *° "«' <>«■■'«■ *2334.5o:
.."io,, U2i'i STJS: """•"' ^"i' ere sold when the com
EXtRCISE CCXXI.
m
140
AKITIIMETIC.
12. A Hour nn'ivluiiit rcniltM to lils aj^riit in ('hiciif^o $;J71)(i, for
tlu' imrcliiisc of j^ijiiu, iiftc^r dediu'tiiij^ the eomiiiissioii at 4"r ,
How imu'li will tliu Hf^«Mit exptMul for his einployci, and what will
l>o the coininiHsionlf
J{. A miller sent liis Montreal apont $9270 to }>e invested in
flour, after deductinj* liis eonnnission of ii'/r . What was the
conuuission?
4. Hent to my apjent in Boston .$:?8Lir) to l)o invested in
French prints at $.15 per yard, after deducting? his commission
of '2 % . How many yards shall I receive ?
5. An agent received $2040 to be invested in sugar at .'Ji ct.
l>er pound, after deducting his commission of 2%. How many
pounds did he buy?
(5. What weight of wool at 40 et. a lb. can he bought for
$1722 by my agent, after deducting his commission of 5% ?
7. I sent $2G7H to my agent to invest in calico at 5 ct. per
yard after deducting his commission at 3%. How many yards
did I receive?
8. A si)eculator received $:{290, as the net jiroceeds of a sale,
after allowing a commission of 6%. What was the value of the
property?
9. A hiwyer collected 75% of a debt of $1200, and charged
5% commission on the sura collected. What did the creditor
receive ?
10. I sent a quantity of dry goods into the country to be sold
at auction, on commission of v% . What amount of goods must
be sold that my agent may buy produce with the net proceeds,
to the value of $3500, after retaining his purchase commission
of 4%1
IV. IINSURAINCE.
Insurance is n contract wliercby one jmrty, in
consideration of a certain snm, guarantees another
party aj?ainst loss by fire or accident.
The Premium is the sum paid for the insurance.
It is always a certain percentage of the sum insured.
The Policy is the written contract, j?iven by the
insurer to the insured.
EXERCISE CCXKII.
Find the premium on the following: —
1. $ 850 at 1% $1200 at f% $ 900 at 1%.
$1500 at ?.% $3200 at f%
ijiOOOO ?it .70% ijio^OO ut .80%
T. ("i
$8000 at .75
$G(iOO at .()Oii%
Vf) ,
INSURANCE.
141
;j7<U), for
1 at 4'^.
what will
^.est('«l in
was tlio
vestcfl in
)unnissi(m
V at 3i <'t
How many
l)0uslit for
f 5%?
vt 5 et. poi"
many yavdsJ
Is of a sale,
ralue of the
md charged
the creditor
1
to he sold
jroods must
, proceeds,
commission
party, in
another
insnrance.
11 iiisnred.
/en by the
)0 at S '^r .
«)() at .75 % .
loo at .U0^%.
2. Kind tlie cost of insurin<? ]>ropt'rty wortli linOOO at },% ,
if i of the vahu' is insured.
;{. A insured his house for 1 y(Mir for $8000 at the rate of
i%, and his furniture for sfHOOO at tlie rate of 1%. W'iuit was
the total >reniiuni?
4. A cotton factory worth $25000, and tlie machinery and
stock wortli ifltoOOO, are insured for i their value, at i%. What
is the premium?
5. A cotton factory and its machinery, valued at $75000, are
insured at ,"; per cent. What is the yearly premiuT»'? and if it
should be destroyed, what loss would the insurance company
sustain?
G. What will be the cost of insuring 4000 bu. of wheat worth
75 ct. a bushel, at i% ?
7. The lioyal Insurance Company took a risk of $16000, for
a premium of $280. What was the rate of insurance?
8. A company charges $20.25 for $2700 insurance. What is
the rate charged?
9. I have goods worth $37560, which I insure for i of their
value, paying $262.92. What is the rate?
10. The sum of $280 was i»aid for the insurance at i of its .
value of a storehouse worth $40000. What was the rate
ciiarged?
EXERCISE CCXXIII.
1. At 1^%, how much insurance can be effected upon a store
for $128?
2. For what sum was a house insured, if the premium paid
was $24 and the rate of insurance ^ % ?
3. A company charged $225 for insuring property at l^%
premium. What was the value of the policy?
4. A man pays $87.50 for the insurance of house at %, and
$50 for the insurance of furniture at li%. If both are
destroyed by fire, hosv much will he receive?
5. Find the cost of insuring ^ of the value of 6000 bbl. of
Hour worth $9.60 a barrel, the insurance being reckoned at %.
6. A vessel and cargo, valued at $35000, are insured at f per
cent. Now, Tf this vessel should be destroyed, what will be the
actual loss to the insurance company?
7. I insure a factory for one year, at ro%, for i of its value.
'J'lie premium is $270. How much is the factory worth?
8. I buy a house for $8000, and get it insured for f of its
value, at S%. If the house is burned, what is my loss? What
is the loss of the insurers?
142
AUITIIMKTIC.
9. All insiinmco compiiiiy, Iiaviii;^ taken ii iisk of $20000 nt
1%, rciiiHured ♦SdOO ut ^'.o with iiiiotlici' (•((inpaiiy, :iihl .f(J()(l()
at 'i% with iiiKtthir. it' no loss ofcms, wimt docs tlic first
company ^'i'" '
10, A lmii«liiif< wortii $1,10000 is insured in three eonipjiiiies;
in tlie lirst for ^UwOOO, in tlie second for $;jr>000, iind in the tiiird
for $40000. For what is eaeii company liable in case of damaj,'e
to the extent of $10000 f
V. TAXES.
A Tax is ti sum of niouey levied on the i)ersoii,
property or income of iudividiuils for piiblie i)in'poses.
Taxes on property or income tire nn^koiied at Ji
certain rate per cent, of tlie assessed vtiliie of the
property or income, or at Ji certtiin number of mills
on the dollar.
Taxes are of two kinds: — Direct Taxes jind
Indirect Taxes.
Direct Taxes are levied by the Province, Town
ship, Town, or City.
Indirect Taxes are called Duties and nre levied by
the Dominion.
Customs Duties are levied on articles imported
from other countries.
Excise is a duty on articles manufac^tured in tlie
country itself.
Duties are either Ad Valorem or Specific.
An Ad Valorem Duty is reckoned at a certain rate
l)er cent, of the cost of the goods in the country from
which they have been imported.
A Specific Duty is a fixed sum levied on the
quantity of goods without regard to their y.ost.
EXERCISE CCXXIV.
1. Find the tax on $4500 at 12 mills on the dollar.
12. Find the tax on property assessed at $7r)00 at 2%.
3. Tlie law exempts $700 of income from being taxed.
What does A, whose salary is $12000, pay when the rate is 15
mills on the dollar?
TAXES.
143
lilt' thinl
^ person,
purposes.
)1UhI «it Jl
ue ot tlio
f of luiUt^
axes and
ice, Towii
e levied by
s imported
Hved ill tlie
fic.
'ertain rate
luutry f I'om
ied ou tlie
Icost.
liar.
lat 2%.
Ibeing taxed.
Ihe rate is 1^^
4. Kind tlio duty (mi fiiriiitiiir, the invoice prifo ol' which is
$l7.")n, :it :i()%.
.'». A hMi'dwan* nicnditiiit iniports «'uth'ry to thi vahic of
$1:17'). What duty must he pay at :U)'i i
(». What is the duty (»n a case of sardines couXaiMiu^ 410
boxes at 5 et. per box?
7. Kind the duty on KOO Ih. of snfjjar oaiuly worth r» et. i)er
Ih., the speeifie duty lieinj,' i et. i>er Ih. and the ad valoniu
duty [iiS % .
H. What is the rate of taxation, wlien property assessed for
$'J7r)() pays $:{H.r)() tax?
9. Wiuit is the rate of taxation, wlien .+ 1120 is the tax upon
$U<)00?
10. Find the rate of taxation, wlien $'J8 is the tax on $1(500.
EXERCISE CC\XV.
1. Wliat is the assessed "■itlue of pro])ertv on whieh the tax
is $:U.r)0 at lli mills on the dollar?
2. The rate is 16J mills on the dollar. A's income tax is
$29.70. What is A's income, $700 of it being exempt?
15. The expense of buildinj? a public bridfjje was $17(58, which
was defrayed by a tax upon the proi)erty of th.^ town. Tiie
rate of taxation was 3i mills on one dollar. What was the
valuation of the property?
4. The duty upon stockings is 35%. What is the invoice
cost of stockings upon which $35.56 duty is paid?
5. What is the invoice cost of goods upon which .$025 duty
is paid, if the duty is reckoned at 25%?
6. If a tax of $12350 is to be raised, and the collector
receives 5% for collecting the taxes, what sum must be levied?
7. What sura must be assessed in order to raise a net amount
of $.5501.50, and pay the commission for collecting at 2%?
8. In a certain section a scho ilhouse is to be built at an
expense of $9600, to be defrayed by a tax upon property valued
at $153(5000. What shall be the rate of taxation?
9. In a school section, a tax of $375 is levied for the
sn])port of schools. What is A's tax on a valuation of $4000,
the entire valuation of the district being $00000?
10. A town is to be taxed $23200 on an assessed valuation of
$2900000. What is A's tax ou au assessed valuation of
$14275?
[rl
"l^Bi
144
AltlTllMRTlC.
VI. SIMPLE INTEREST.
Interest is imuicv p<'ii<l tor llic iisr of iiHUHy.
Ttie Principal is the smn lor Ihr iis«> of wliicii
interest is paid.
The Amount is tlic sum of tlii> Principjil mikI
Interest.
The Rate of Interest is tlie rate per cent, of
tlie principal allowed for its use for one year.
Interest, is either Simple or Compound.
Simple Interest is tlie sum <'liarji:ed foi* the use
of the IM'ineipal oidy.
Compound Interest is intei*est re(!koued on the
principal and mIso on tlu' aeerue(l interest as it falls
dut^ from period to period.
EXERCISE CCXXVI.
1. Find till! iiitert'st on the following: —
$m) at 6% for I yr. if^'JOO at 4% for 1 yr.
$ir)() iit 4% for () nio. ^'AH) at ;')% for ;{ mo.
IIJ.'jU iit (5% for 4 mo. ^■i')0 ut 4% for (J mo.
t>. What will l>e the interest on $;U)0 for 5 mo. at G%?
15. Tf !fi;5r)0() Itorrowed money is re]>aid in 7'A (lays, how much
interest should he paid, money being worth HVr ^
4. Find the simple interest on $4800 for 1 yr. 5 mo. at !S% .
n. Find the interest on ^'2i){) for G mo. at 8% .
(I. What is the interest on i^HO'.i for J}') days at tho rate of 7%
per annum?
7. Find tlie interest on $S7() for 10") days at G%.
8. Find the interest on .$17512 from June '.i to Oct. IG at (>% .
9. What interest is due on $584 from March 7 to August li)
at 5%.?
10. Find the interest on $131.40 from Sept. 5, 1899, to March
7, 1900, at 7'^r.
EXERCISE CCXXVII.
Find the amount of the following: —
Principal, Kate. Time.
1. $ 8712 G % 10 mo.
2. $ 9412 G % 15 mo.
3. $]S9(i 7 % 17 mo.
8IM1'IK INTKKKST.
115
[Mil i>»»(l
.('lit. of
the ^^^^
i\ (n\ the
IS it fulls
)r W mo.
)v () nio.
, how mxich
mo . at T) /f •
rate of l^c
[t. IG Jit (•)%•
Ito August 19
[99, to March
Ime.
mo.
mo.
mo.
4.
n.
0.
7.
8.
$511
$408.80
$17'J8
$(iO
7 ^ .liiiH 'J to Off. 1:..
5 ^r April I, 1851!), to .hiii. 1^1, liMlO.
7 rf .hily ;{, 18!»!», t(. F«l.. !{, 1!)00.
(5K^ 1 yr. 'J 1110.
8 'ir 1 VI'. '.] nu).
<>. J. Ay<T li:iM I). How's note Cor !f!l8'jr.. «liit«'(l Dec. L'S),
181M); \lmt in the iimoiint Oct. !», I'XIO, iit (J per cent.*
10. I*. K'vc's his iiot«', Aii^rnst (itii, IS!)!>, lor .flOiC), interest iifc
7^'r; he piiys tlic note iiiid interest May 17lh, I'.MMl, how niucli
did he pav?
EXERCIS^E CCXXVIII.
What is th(» rate jtei' cent, wiieii
1. The interest on $4'yO for 1 y. is ^'27'!
12. The interest on .f!>.")0 for 1() nio. is $88ji ?
;{. Tiie interest on !f!:i80 for 1 yr. 4 nio. is $'J2.80?
4. The interest on Mil for 75 da. is ^^71
5. $480 amounts to lllO in 1 yr. f
(5. .$()00 amounts to $()i;{.75 in 5 nio.f
7. $ll(i8 amounts to .$in»5.()0 in II.") da.?
8. The amount of $1022 for 2(50 days is $10.')4.7r.?
9. The interest on $80:{ from June 10 to Dec. 2 is $2;{.K»?
10. The amount of $87(3 from April 10 to Dee. 1 is $!)0!j.84?
EXERCISE CCXXIX.
Find the time in wliich
1. Tiie interest on .$45(5 at (]% will be $27.:}(i.
2. The interest on $540 at 4J% will be .$:{(5.45.
:i. The interest on $840 at G% will l»e $(5:5.45.
4. The interest on $1.')00 at 7% will lie $4:5.75.
5. The amount of $1(500 at 5i% will be $l()(i(5.
G. The amount of $750 at 7% will lie $785.
7. The amount of $2920 at M% will be $2901.40.
8. Tlie interest is ill,, of the jirincipal at 4.1 Cir.
9. The amount of $7:53.(55 will be $751.74 at 0^.
10. A j.rincipal of $i:514, loaned May 12, 1S99, at 5.]^^;, will
amount to $1328.85.
EXERCISE CCXXX.
Find the prineii)al that
1. I'roduces $24.:;0 interest in 1 yr. at 4.?'^.
2. i'rodiices $;;!». :;o interest in I yr. mo. at 4%.
:5. Produces $21.25 interest in G mo. at 5%.
m
" I IV
146 ARITHMETIC.
4. Produces $22.50 interest in 1 yr. ;it tii%.
f). Produces $.56 interest in 1 yr. 4 mo. at ^%.
6. Produces $22.50 interest in 8 mo. at 4i%.
7. Produces $12.96 inteest in 90 da. at 6%.
8. Produces $56.25 interest in 225 da. at o%.
9. Produces $6.48 interest at 6% from June 5 to Dec. 2.
10. Produces $lu5 interest at 7i% from April 15 to Oct. 7.
EXERCISE CCXXXI.
Find the pvineipal that
1. Amouiits to $265 in 1 yr. at 0%.
2. Aruounts to $496 in 1 yr. 4 mo. at 5%.
Amounts to $596.70 in 1 yr. 6 mo. at 7%.
Amounts to $595.40 in 8 mo. ut 6%.
Amounts to $li{91.50 in 1 yr. 1 mo. at 5%.
Amounts to $424.83 in 9 mo. at 5i%.
Amounts to $796 in 1 yr. '.i mo. at 5%.
Amounts to $1782.60 in 85 da. at 7i%.
9. Amcant> to $3735.50 from June 3 to Dee. 10 at 4i%.
10 Amounts to $3338.50 from April 17 to Dec. 3 at 6i%.
3.
4.
5.
6.
7.
8.
Vli. COMPOUND INTEREST.
EXERCISE CCXXXII.
Find the compound interest and the amount of
1 . $800 at 5 ^ , compounded annually, for 3 yr.
2. $2500 at G% , com])ounded annually, for 3 yr.
3. $1250 at 4'~r, compounded lialfyearly, for 18 mo.
4. $8000 at '}9h, compounded iinnually, for 4 yr.
5. $10000 at 12%, comi)Ounded quarterly, for 1 yr.
Find the jcineipal which will ])roduce
6. $648.90 interest at 6%,' compounded annually, for 2 yr.
7. $151.32 interest at 5%, compounded annually, 'or 3 yr.
8. $927.27 interest at 6'!^: , jompounded halfyearly, for 18 mo.
9. How much j^i'cater is the cf)mpound inicrcst on $1200 foi'
2 yr. Jit 6'^f ,. conipounded yeiirly, tlian the sini])le interest for
the same tinu'?
10. ilov niiich juri'ciitcr is the coinpouinl interest on $SO00 for
2 yr. ill, lO'/i, coiniiouiidctl halfyc;ti'Iy, thiin the simple interest
for the same time .'
BANK DISCOUNT.
147
Dec. 2.
to Oct. 7.
at 4*^0.
3 at 6i%.
18 mo.
a*.
fov 2 yv.
'or '^ yv.
irly, forlHi'if»
u ;„ $1200 for
ilo interest lor
it on i^«'"^'^ *''^';
V,uil»»« interest
Vm. BANK DISCOUNT.
Bank Discount is the charge made by a bank for
advaiudng the payment of a note not due. It is equal
to tlie simple interest on the face value of the note,
for the time between the date of buying the note and
iho. time it falls due. The banker deducts the dis
count from the face value of the note and pays the
balance, which is called the Proceeds of the Note.
A Promissory Note is a promise in writing, made
by one person to another, to pay on demand, or at a
designated time, a specified sum of money.
The Maker of the Note is the person who signs
the note.
The Payee is the person to whom, or to whose
order, the note is made payable.
The Holder is the person who has legal possession
of the note.
The Face of the Note is the sum for which it is given.
The Maturity of a note is the time at which it
becomes legally due.
Days of Grace are three days whi(^h elapse from the
time specified in tlu^ note for its payment until it is
legally due. The time that elaj^es between the day of
discounting the note and the day of maturity, called
the term of discount, includes the days of grace.
A Negotiable Note is one which is made payable
1<) bearer, or to the order. of the payee. It can be
sold to another. If payable to bearer, no endorsement
is necessary. If i)ayable to the order of the payee, it
must be endorsed by him before being disi)osed of.
The Payee endorses the note by writing his name
across the back of the note.
PROMISSORY NOTE.
$;{oo.
Toronto, Uay 18, 1900.
Sixty (lays aftoi' date I promise to ])ay Xicliolas Walsli,
or
(irdcf, iJilJOO, value received.
John Biuck.
Tliere arc three parties to a draft: —
The Drawer, the person who makes the diai't, —
the person who ordei'S the m(Mi(^y to be paid.
1 
148
ARITHMETIC.
The Payee, the person in wliose favor it is drawn.
The Drawee, the person on whom it is (h'Hwn.
If the draft is ae(;ei)ted, the Drawee l)eeoines the
Acceptor.
DRAFT.
$100. Toronto, Jan. ]5tli, 1900.
Ten (liiyH aftoi sif^ht i)ay to the order of James Mills the sum
of one hundred dollars for value received, and charj^e the same
to the amount of
Thomas Lovkll.
To John Smith, Esq.,
Merchani;, London.
In the above draft, Thomas Lovell is the drawer; John
Smith, Esq., is the drawee; and James Mills is the payee^
EXERCISE CCXXXill.
1. Draw a note due in 3 months with interest at 0% per
ann., (1) payable to John Smith or bearer, (2) payable to John
Smith or order, (3) payable to John Smith.
2. Draw a note payable on demand.
3. Write a note for the following: — Face $250; time 3 mo.;
interest 4% per ann.; maker James Jones; payee Thomas
Harris.
4. Write a note payable at a bank for the following: — Face
$.")(); time 3 mo.; interest 5% per ann.; maker Thomas Jones,
payee Wm. Meadows.
5. W^iat is the cost of a sight draft in Montreal for $750, at
i% premium?
6. What is the face of a draft which can be purchased for
$1500, at 1 % premium?
7. Suppose that Porter & Jones of Montreal, owe you $350.
Write out a sight draft on them for that sum in favor of the
Bank of Commerce.
EXERCISE CCXXXIV.
Find (1) the day of maturity, (2) the term of discount, and
(3) the proceeds of the following: —
Date of Note. Face of Note.
$657
$803
$182.50
$5021
$511
$) 1(5.80
1.
April
17,
1899
2.
Oct.
20,
1899
3.
Sept.
15,
1899
4.
May
11,
1899
5.
Aug.
23,
1899
(1.
June
20,
1899
Time.
Discounted.
Kate.
3 mo.
May 1
8 %.
4 mo.
Dec. 15
7 %.
(5 mo.
Dec. 28
•5 %.
4 nio.
.Inly 31
G %.
!>() dii.
Oct. 25
r^}<%.
(iO da.
lune 28
7li%.
•
STOCKS AND Dl VI DKNDS,
149
(Iniwu.
wu.
iiies the
», 1900.
s the sum
tho siuno
LiOVKLIi.
ver; John
at f)'"/" P*^i'
ble to John
\me 3 nio. ;
ree Thomas
ins:— Faee
Hiias Jones,
[for !i;7r)0, at
Liehased for
■(> yon $350.
It'avor of tUt!
tsconiit, and
Imtetl. Kate.
1, S '>.
15 7 ^'■.
'>S '5 % •
31 %.
25 5i'^.
oy 7 i % ,
7. Find the face of a note wliieli will realize !f31K.50 when
diseonnted 4 mo. Iti^fore maturity at (5%.
K. Mr. Jones lias a })iil for $5(58.80 to pay. He f^ives iiis
note for 3 mo. whieh discounted at 5% on the day of inaiUiii^ just
l>rodiKM*s tliis sum. Find the fae(* of the note.
9. Find tlio proeec'ds of the following notes: —
$19()L'i'*,A,. Toronto, July 1>G, 1899.
Four months after date I promise to j)ay to the order of
James (Jillis one thousand nine hundr<Ml and sixtytwo hA,
dollars at tin* Ontario Bank, for value received.
Discounted Aug. 'J(5, at 7%. John Dkmaukst.
10.
.HIOOGiV... Winnipeg, April 19, 1899.
Nin(^ty days after date we promise t' pay to the ord(M' of
Kiii}^ & bodge one thousand and sixtysix iVo dollars at the
])oiiiinion Harik, for value received. (!ask & Sons.
Discounted May 8, at G%.
IX. STOCKS AND DIVIDENDS.
An Incorporated Company is n iiurn})(a" of per
sons einpovvered by law to act as a sin^lo individual.
Stock is the eapitnl of an incorporated company
or the money borrowed ))y a government.
A Share is one of tlie (Hjnal i)arts into which
sl(M'k is divided. Sometimes the share is $200, or
$100, or $r)0, etc. Any sum may be agreed upon.
When the i)rice is quoted it is always on the })asis
of $100 of stock.
A Certificate of Stock is a statement showing
that th(^ party therein named owns a certain numl)er
of shares of the capital.
The Par Value of sto(;k is the value nanKul on Ihe
face of the certificate.
The IVIarket Value of stock at any time is what
it can be bought or sold for at that time.
Stock is at a Premium, or Above Par, when Hk;
mai'ket valu(^ is greater than the i)ai' value. It is at a
Discount, or Below Par, when tin; mai'ket value is
l<'ss tliau the par value.
^4i
a;
150
ARITHMETIC.
Dividends jire the profits from tli<^ ))usiTiess oi'
compaiiies distributed from time to time amoiijif the
stockliolders as percentages upon the par value of the
stock.
A Bond is an obligation to pay a um of money
at a certain time with interest at a fixea rate at stated
l)eriods.
EXERCISE CCXXXV.
Find the value of the following: —
1. $7000 stock in the 4 per cents, at 103.
2. $r^'>00 Bank of Ontario stock at 130.
3. $4850 Bank of Commerce stock at 145.
4. $650 Standard Bank stock at 192.
5. $3400 scock at 78 i.
No. of shares.
6. 25 shares Imperial Bank
7. 45 shares Bank of Commerce
8. 75 shares Dominion Bank
9. 40 shares Bank of Montreal
10. 20 shares Ontario Bank
EXERCISE CCXXXVI.
How much stock can be bought with
1. $588 in the 3 per cents, at 84?
2. $5300 in Imperial Bank stock at 212?
3. $3220 in C.P.R. stock at 92?
4. $5733 in Toronto Railway stock at 102s?
5. $5500 in War Engle stock at 250?
How many shares of stock can be bought as follows?—
Sum invested. Per value of share. Sellinj; prictj
Par value.
$100
$50
Sel
ing price
190.
145.
$50
260.
$200
255.
$100
130.
6.
7.
8.
9.
10.
$650
$5200
$576
$588
$900
$100
$200
$50
$25
$40
130
260
192
84
150
EXERCISE CCXXXVII.
VVhiit incotiic is made from investing as follows: —
1. $5200 ill stock at 130, pjiyiiig 5"!^ diviileiid?
2. $5390 in stock at 2694, paying 12% dividend:'
STOCKS AND DIVIDENDS.
151
3. $3600 in stock ut 144, paying 8% (livi«l«'iidF
4. $1350 in stock ut 135, payiiif? lOTi dividend?
5. $28(53 in stock at 102i, paying' 4% dividend?
What rate of interest is made by investing? as follows: —
(5. In British America stock at 125, paying 7% dividend?
7. In Dominion liank stock at 270, payiiifjj 12% dividend?
8. In London Pjiectric stock at 120, paying? (>% dividend?
1). In Traders Bank ^^tock at 112i, paying 6% dividend?
EXERCISE CCXXXVIII.
What sni. nust })c invested to produce an income of
1. $350 from stock at 130, paying a 5% dividend?
2. $550 from stock at 242, paying a 10% dividend?
3. $500 from stock at 141f, paying a 7% dividend?
4. $720 from stock at 173, paying an 8% dividend?
5. $660 from stock at 104i, paying a 6% dividend?
How many sliares of stocl< must l)e bouglit to j>r()duce tiie
following incomes: —
Par value of stock. Dividend.
50 12%?
400 20%?
40 10%?
50 6%.?
EXERCISE CCXXXIX.
1. I received $880 from a 5i per cent, dividend. How much
stock do I own?
2. I receive $279 as my share of a 4J% dividend. How
iiKiiiy shares^ at $50 each, do I own?
3. A lady receives $1200 dividend at 7%. 'Required th(*
uinouiit of stock she owns and the number of shares, valued at
$25 each.
4. A owns 85 shares of ruilioad stock, at $100 a share, attd
receives a dividend of $080. What was tiie rate of dividend ?
5. Find tiie rate of dividend ]»aid l)y a railroad when a
holder of 240 shares, at $100 a share, receives $1722.
(). Mr. .Tones owns 25 sliares, .'it $50 a share, and receives a
li;ilfyearly dividend of $43.75. What was the halfy(^arly rale?
7. A has 40 shares, $50 each, of stock in a bank, wliicii
ilfclares a dividend of 5%. What is A's dividend?
8. How much income will be obtained iinnually by investing
■f^iMO in (;% bonds, selling at HI)?
!•. Find the sum refjuired tor :in iMV«'stnient in a 4% stock,
;il !>.S.i, to produce iin income of $200 a year.
Income
0.
$360
7.
$5600
8.
$880
•J.
$1500
\i ■ '?■?■■
152
ARITHMETIC.
EXERCISE CCXL.
1. If money is worth 7%, whut ouglit a stock tlmt regularly
pays S% a year to sell for?
2, What must be the price of a T)^ stock in order that a
buyer may receive G% on his investment?
n. IMoney l»ein,<? worth 41^, what ought to l»e paid for stock
that regularly pays 12% per annum ?
4. If an H% stock is wortli ]')0, what rate of interest will a
purchaser receive on his money ?
5. How much stock must be sold at V2'.i, brokerage i, to
produce $2949?
6. What must l)e paid for 40 shares of stock $25 a sliare,
selling at 142i, brokerage!?
7. How many shai'es of stock, $50 a share, at 72, i%
brokerage being paid, can be bought for $1825?
8. What sum must be invested in 6 per cent, gas stock, at
84, to produce an annual income of $2100?
9. The security being equal, which is the better investment
— 5 per cent, stock at 125, or 4i per cent, stock at 115?
10. A owns $5000 stock, which pays a dividend of 7%. How
much must B invest in a stock which pays 6i% dividend so
that his income may be $50 more than A's?
X. EQUATION OF PAYMENTS.
Equation of Payments is the process of fiiuliiij?
the time at which several debts due at different tiiiK^s
may be paid without k)ss of i?iterest to either the
debtor or the creditor.
The Equated Time is the time at whicli the
several debts may be caiK^elled by one payment.
EXERCISE CCXLI.
1. The interest on $100 for 10 days is equal to the interest
on what sum for 1 day? for 2 days? for 5 days?
2. The interest on. $250 for 12 days is equal to the interest
on what sum for 1 day? for 2 days? tor 3 days? for 5 days? for
8 days? for 10 days?
3. A loaned me $000 for 10 days. For how long should I
allow him the use of $;J75? of $1200? of $1500? of $3000?
4. T borrowed from P> $200 for 4 months, $300 for G montlis,
and $400 for 7 months. How long should I lend him $1800 to
repiiy the favor?
5. T .7we to A $500, >;iyjil>Ie in (! moiitlis. and $400, due in
15 mouiUs. When may 1 pay the whole in one payment ?
EQUATION OF PAYMENTS.
168
Ito the interest
n. I owe to B $80, due in 2 da. ; $60, due in 8 da. ; $40, due
in lOda. ; and $100, due i;i 12 da. Find tiie c'(Hiated time of
imynieut.
7. A del>t of $200 is due in (50 da.: $r)0 is paid 12 d.i.
Ix'foi'o it is due, and $1(M) is paid 24 da. before it is due. When
should the balance be paid?
8. A man bon{?ht a farm on .Ian. 1st, 1900, and is to pay
$(500 casli, $000 in 2 mo., $800 in 6 mo., and $1000 in 12 mo.
Find the equated time of payment.
0. On Jan. 1st, 1900, a man jijave 3 notes, the first for
$r)0(), ])ayable in IJO days; the second for $400, payable in
()(] days; the third for $G00, payable in 90 days. What was
the average term of credit?
< (
4
o
l\ i!400, due in
EXERCISE CCXLII.
1. Find the averaj?e term of credit for the following l)ills: —
(a) $100 due in 2 mo. (/>; $100 due in 1 mo. (c) $700 due in .') mo.
;K)0 " 4 " 200 " 2 " IJaO
200 " 7 " 300 " 3 " 550
400 " 8 " 400 " 4 " 400
2. A grocer buys $400 worth of goods at 90 days, at the end
of 00 days he pays $200. Find when the balance should be
paid.
3. If I buy goods for $3200 and agree to pay 1 in 3 months
and tlie rest in 5 months, but afterwards decide to pay all iu
one sum. When should I pay it?
4. A note for $800 is to be paid as follows:— i at once, I in 6
months, and the balance in 8 months. When could it all be
piiid together?
5. What is the average date for paying three Vjills due as
follows:— March 31st $400, April 30 $300, May 30th $200?
G. On Jan. 25th, 1899, a grocer sold goods for $1340, i
l>!iyable in 90 days; i in 120 days, and the balance in 150 days.
Wiuit was the equated date of payment?
7. I bought goods for $600; i to be paid at once, } in 4
months, and ts in 6 months. At what time may the whole be
\KiuU
H. A owes a sum of money, of which ^ is payable at 30 days,
■■ at GO days, and the rest at 90 days. What is the equated time
tor the payment of the whole?
9. A man purchased real estate, and agreed to pay i of the
jivife in 3 months, i in 8 months, and the remainder in 1
year. W^ishing to cancel the whole obligation at a single pay
ment, liow long shall this payment be deferred?
<n
m
!il
1
CHAPTER X,
PARTNERSHIP.
Partnership is tlie association of two or more
persons in business, witli an agreement to share the
profits and losses.
Partners are tlie persons associated in business.
The Association is called a Company, a Firm, or a
House.
The Capital or Stocic is the money or property
invested in the business.
'< EXERCISE CCXLIII.
1. B and C gain in business $1050. B's stock was $1500
and C's $2000. What share of the gain should each get?
2. A and B are partners. A furnished $840, and B $1030
capital. Find the share of each of $432 profit.
3. A and B agreed to do a work for $260. A worl<ed 27
days and B 25 days. How should the money be divided?
4. A, B and C rent a pasture field for $275. A puts in 17
horses, B 26 horses, and C 12 '"orses. What share of the. rent
should each pay?
5. A, B and C engage in business. A puts in $3600, B
$1700, and C $4800, and they gain $2424. What share of the
gain should each get?
6. A and B engage in business with a capital of $6000. At
the end of the year, ,i. gets $208 and B $272 gain. What was
the capital of each?
7. A, B and C enter into partnership. A puts in $2325,
B $3250, and C $4625.. A gets $465 for his share of the gain.
What should B and C receive respectively?
8. The capital of a firm consists of $40000, of which A
contributes $14000, B $17000, and C the rest. Divide $5000
profits among them in proportion to the capital of each.
9. A, B, C and D form a partnership. The capital of each
is $4500, $2300, $1900, and $1100 respectively. They lose $1568.
What is A's share of the loss?
10. Divide $9282 among A, B, C and D, giving A 10% more
than B, B 10% more than C, and C 10% more than D.
154
or property
Partnership.
EXE.7CISE CCXLIV.
155
7 weeks 'Vi^n^ i'"'" '^ P»«tiJre for .*4/) *
, •• A and B take ., . '"'*''''^
i"'^ *7;io, be divided ' '" ^'^>'« ^ovv .iji'.r*" f"/ 10
cows (or mo. How ,.?. , ' • ^' ^" cow, w •, "° ^ Pi'ls in
"o i B ^Jt.^'"™." Partnership. T^ ?'"■'' "">■'
^ A and B form n * °"
"rtidJ^f »«»« »o. °^iv? ?S "L1o"'^'h*?S
.Ii.l B joi;;" '• ""«' """"y months befJ^e'C: ' ■•«<'™1 """
9. A and R f >''■'"■ *
«'"<» and B $mT " P»rt"erahip for „ y,„, , ^ ^,.
CHAPTER XI.
IINVOLUTIOIN AND EVOLUTION.
I. INVOLUTION.
A Power of n iniuilx'i* is tlic product <>l)taiiio(l ])y
taking the imnilM'r a number of times us a factor.
Involution is \\w proct^ss of raisinj? a iiiurioer to a
power.
Tlie Index or Exponent of a power is a Hjfun;
placed at tlie ri^lit and a little above the iminher to
show how many times it is used as a factor; thus, 5",
2 is the exponent.
The Square of a number is the product obtained
])y using tlie number twice as a faetor.
The Cube of a number is the product obtained
by using the number three times as a fac^tor.
4 X 4 = 4** = IG, or, tlie'Jnd power, ors(niiU'('(jt'4.
4X4X4 = 4*^ = ()4, or, the 3rd power, or cul)e of 4.
4X4X4X4 = 4* = 256, or, the 4th power of 4.
4X4X4X4X4 = 4"^ = 1024, or, the nth power of 4.
EXERCISE CCXLV.
Write tlie following as powers nvl find their vjilues: —
1. 2X2X2
2. r)X5X5
.•J. ixixi
4. 2iX2i
5. .IX.IX.I
C. .12X.12X.12
2X2X2X2
5xr>XoX5
ix*x*x*
;jix3ix:{i
.03X.03X.0:{
.15X.15X.15
;}x3x:jx;5x3.
5xr)X 5X5X5.
6 /\ u /N 6 '^ n /^ r. •
4iX4iX4iXv^.
.05X.05X.05X.05.
2.5X2.5X2.5X2.5.
"Write the factors of the following powers and find their pro
ducts: —
7. 2^ 3* 4^
8.
ar
(f)^
(i)^
9.
i.'^V
(.05)
(.001)''
10.
(2i)«
iuy
(5i)*.
156
INVOLUTION AND EVOLUTION.
157
bXERCISE CCXLVI.
.S(uiir«' llir following iiumber.s: —
for.
r.bt'i" to a
i\imbt'V f<>
thus, r>,
t obtuiiuHl
t obtained
rs(iu!in'of4.
or cube of 4.
i: 4.
f 4.
Is : —
l5X5X'>.
:X4*X'.*.
iooX.OoX.O').
.5X2.5X2.5.
Ind their pvo
3
,5/
.001)'.
:5i)*.
1. 19
45
86
93.
2. 101
504
906
708.
3. 75.G
40.8
97.5
7.96.
4. *
♦
i
A.
5. 4i
7h
9i
V2L
ibe the following
numbers : —
G. 9
19
41
91.
7. 101
110
506
909.
8. 30.5
4.55
78.4
6.97.
9. 1
A
H
\t.
10. 2i
5i
31
71
EXERCISE CCXLVII.
Kiiise the following numbers to the powers indicated: —
1. 9^
5='
25^
l6^
2. (.09)''
(.ir
y
(2.5)«
(.33)3.
3. (t)«
(1)
I
(2i)»
(3i)^
Find the value of
4. 452
24
?
88*
(If)".
5. S''XS"
7*
X7'*
12''X12'^
(i)''x(^)^
0. 12'' ^12'*
a*
H'
J23^2''
9^3^
7. 10^5'
(2
5)«
■{.IV
i^y^av
(3.5)«^(.5)»
S. What power of )i number is the product of the first power,
the second power, and the third powerf
9. If the fifth power of two be multiplied by the third power
of two, find the resulting number.
10. What power is the square of the cube of the fourth
power?
11. Of what number is 7009 one of the two equal factors?
12. Of what number is 5050 one of the three equal factors?
13. Find the number of which one of its four equal factors
is .002.
14. Show that 3G'' = 2*X3^
15. A field is 48 rods long and 32 rods wide. Fiud the area
of a square with an equal perimeter,
168
AUITliMETIO.
II. SQUARE ROOT.
The Square Root of a numbot' is oik; of its two
equal tactors, tlms G is the s(nuir(i root of 36.
The stiimn; root of a nuniljcn is iiidif^attnl by th«
radical sujn J, or by tlie fra(!tion A written above and
to the right of tlie number.
EXERCISE CCXLVIII.
Find the square root of the following: —
1.
SI
i)
i:{G9
8.
iimi
4.
U
5.
ni\
6.
.01
7.
.061009
121
:ji;{6
98596
.0025
.001225
144
4096
655:36
684 I
1 2 r
.0009
.oo:i;u54
225.
6561.
277729.
1 a 2 6
5411.
T H (t a •
.0S41.
.0256.
Find the value of the following
8. (144)^ (A)^
Find the following: —
I
Ki) ^ \^2a) V81 '^ V 1 Off
9. v/9.3025 i/. 010404 /. 326041 >/. 0000316969.
Find correct to 3 decimal places the square root of
10. 5 .5 .9 .009.
EXERCISE CCXLIX.
1. Find the two equal factors of 240100.
2. What number must be multiplied by itself to produce
2450,Vff.
3. Resolve 10252804 into two equal factors.
4. The area of a square lawn is 576 sq. yd. What is the
length of one side?
5. Tlie area of a square is 40 acres. Find tho length of one
of the sides in yards.
6. How many rods long must the side of a square field be to
contain 250 acres?
7. Find the side of a square equal in area to a rectangle
whose sides are 544 ft. and 136 ft.
8. What will it cost to fence a square farm coritainiug 160
(icres at 25 ct, per vo^i
OUBK KOOT.
ir>j»
f its two
iO.
id by tli«
ibove aiul
225.
()')()!.
277729.
1 2 'J 5
6 4 1V
T 6 » »^.
10 rt & •
.0841.
.02r)(5.
JW^'J
19B
)000:U69(i9.
)f
.009.
[if to produce
What is the
length of OIK
lare field be to
^0 a rectaiigh'
hontainiug lO^J
!>. Tin i«lo of 11 H»U!ir<> licld is !Mi rods Ion;;. l'iinl lli«t
Iciij^th of i\w si(l(* of II sciuarc (Muitiiiiiiii^ 2i tiiiifs jih iiiiicli.
10. A s<iiare lnwii contuin.s ll(i(J4 sq. yd. What will it rost
to fciK'e it at $.7 > per yd. If
EXERCISE ecu
1. A nMtaii>?)iIar KardiMi contains IS7r> h(. yd., and it is '.i
tiiiics as long as it is widi^ Find its length and width.
2. A rectanjfUJMr pird<<n contains 2 acres, atid it is ;') times
as long as it is wi(h». Find its Icnj^tli and width in yiirds.
3. A s(iuaro yiird is divided into 57(5 ecjuiil squares. Find
tlio length of a side of each.
4. A field is 12 rd. sqiuire. How lotig is the side of another
square field containing 1 s<j. rd. more than twice th«» first?
5. Find the number of rails, each 12 ft. lon^, re(uired to
Itnild a straight fence 6 rails high round a s(iiiare lOA. field,
allowing the rails to overlap 1 ft. f
(). The rroii of a square field is 122i acres. A rectjtngiiliir
Held containing the same area is 4 times as long as it is wide.
Find the number of rods in the hngtii of this field.
7. llaw many yards of fencing are required to enclose a
sfpiare farm containing 832A. 105 n(\. rd. ?
H. A square bin has a capacity of 1800 cu. ft. and is 8 ft.
deep. What is its length?
9. The side of a square field it; 171 yd. loiif; and of another
square fiold 140 yd. long. Find the length of the side of a
s<. field as large as both together.
10. The i)erimeter of one square is 3840 yd. and .)f another (i()88
yd. Find the perimeter of a square equal in area to both of
them.
III. CUBE ROOT.
The Cube Root of a iiii]ri])er is one of its three
equal factors; thus, 4 is tho cube root i;f 64.
T\u' cube root of a number is indicat(!(l by f, or
)ty file fraction ^ written abov(i and to tlie rij^lit of
tile numl)er.
EXERCISE ecu.
Resolve the following nnnibers into prime factors, and from
these find their cube roots: —
1.
216
512
729
1728.
«)
3375
4096
5832
93«1.
3.
15625
13824
21952
35937.
4,
42871^
T17649
166370
175616,
1(50
AUITIIMKTId.
Extnu't llio (MiVx' ro(»t of tlu^ follnwlu'':
f).
4in;j
G.
14,SS77
7.
io:j():u)1
S.
3 4 :i
"2 1 y 1
9.
.001
rji(i7
2or);j79
];5()7();}i
7 ','
T) « f)
.0001210
24:}8!>
:5007():!
4S'j()Soa
£ 7 4 4
1 1 r> 1 ti
ir)GO.S9(5
Find tlio ciihc) root corrc'ct to 'A (liM'iiuul pliicos of
10. .8 .08 .008
jjOCm:}.
3r)7911.
G7;")1"J()9.
1 .'i .•! 1
f> a :n 9 •
47832.147,
CXERCISE CCLII.
Find the followint^: —
1. f'lilG'JS f .Oir)G25 fl.8G08G7 f I012.0480G4.
2. (92G1)^ (8i:W0^ (373i¥5)'' (480it;l)^
3. Tiu' product of tluvo oqnul fii 'ors is ,3980.977. Find
the factors.
4. Uequirod i\)e rnKn'rur of squnro feet in ono faee of a
cubical bloelt wliose contents aie 40r)224 cu. ft.
5. What is the entire snrftice of a cube whose cnl>ieal
coiitents are 912(573 (Mil)ie ft.?
G. A cubical cistern liolds 4913 cu. ft. JIow deep is it?
7. The edf?es of a rectanfjjnhir solid are IGO iii., 2;") in., and
54 in. respectively. Find the edj^e of a cube of the same
volume.
8. The contents of a cube arc 97.33G cu. in. Find the ed^e
' of a cube that contains 8 times as niucli.
9. A rectanf^ular l)loc]i of stone with a square end is 8 times
as long as it is wide and contains 27 cu. ft. Find its length.
10. The contents of two cul)es are respectively 53;')9.37o and
5.3r)937i') cu. in. Find the dilference between the lengths of
their edges.
11. Find the total lengtli of the edges of a cube containing
5005)5 cu. inches.
12. What nnist be the edg(^ of a cubical bin that shall contain
as many bushels as a bin 10 ft. 5 in. long, 5 ft. 4 in. wide,
and 2 ft. 3 in. deep ?
13. Tile product of tliicc numbci's is 2304. The second is
twice the first and the third is onethird of the second. Find
the first inimlter.
14. A rectangular room "ont.i" < 13;'<24 cu. ft. Its width is H
of its length and its lieiglil is h .' il:; width. Find its length.
:.o(»r)3.
3r)7'.)U.
G7r)ii:()'J
1 ;{ :( 1
5 « :t 1 •
47832.147.
CHAPTER XIL
/1012.0480G4.
480itS)^.
80.977. Find
ono faee of a
whoHo cul)ical
idccp is it?
u., 2') in., and
of tho same
Find the od}?e
end is 8 times
Id itH lenj?tli.
]y MiVJ.:^.") and
tiie lengths ot
lube containing
lit sliall contain
ft. 4 in. wide,
Tlic second i^
second. Fi»"'
Its widtii is H
hiid its length.
MENSURATIOIN.
A Triangle is a plane figure Ijounded by thivv,
straight lines.
An Equilateral Triangle is one whieh has its three
sides equal to one another.
An isosceles Triaiigie is one whieh has two sides
('((ual to eaeh other.
A Right Angled Triangle is one which has a
riglit angle.
The Hypothenuse is the side of a right angled
triangle, whieh is opposite to the right angle.
The Base and the Perpendicular of a right
angled triangle are the sides that (contain the right
angle!.
A Quadrilateral is a i)lane figure Ixmnded ))y four
.<iruiglit lines.
A Parallelogram is a qnadii lateral, the opposite
sides of whieh are i)arallel.
A trapezoid is a quadrilateral with oidy two
sides ]){irallel.
A Rhombus is a (piadrilateral whieh has its four
sides ('(pud to one another.
A Trapezium is a (quadrilateral, whicdi has none of
its sid(\s i)arallel.
A Circle is a plane figure bounded l)y a enrved
line ealhul the circumference, every point of whi(di
is equally distant from a point within called the
centre.
The Diameter of a (urcle is a straiglit line i)}issing
thi'ough the centre and t(!rniinated Ixjth ways l)y
the cinnunference.
161
I
162
ARITHMETIC.
The Radius ot n ciivle is a straiglit line drawn
from the (tcMitre to the eircumfereiice,
A Right Cylinder is a solid, bounded by two
(eir(;ulai*) plane faees and a eui'ved faee, every part
of whieh is the same distanee from a straiglit line
joining the eentres ot the plane faees.
A Right Pyramid is a solid, bounded by a plane
fa(;e enelosed by three or more straight lines, called
the bfi^e, and as many triangular plane faees as the
base has sides.
A Right Cone is a solid, bounded by a circular
l)lane faee, (tailed the base, and a cnirved face tapering
from the circumference of the base to a point.
A Sphere is a solid, bounded by a curved face,
every i)art of which is equally distant from a i)oint
within it called the centre.
EXERCISE CCLIII.
1. Find the area of a square whose side is 39 yd.
2. How many square feet are there in the surface of a table
7 ft. 8 in. long and 3 ft. 10 in. wide?
3. A rectangular grass plot 25 yd. by 20 yd. has a gravel
walk 4 ft. wide round it. Find the area of the gravel walk.
4. The sides of a rectangular field are 525 ft. and 84 ft.
Find the side of a square of the same area.
5. A rectangular field contains .78 A. It is 3 ch. 25 1. long.
Find its width.
6. Find the area of each of the pai'allelograms, one of whose
sides and the perpendicular distance between it and the opposite
side are respectively as follows: —
(a) Side 17 in., perpendicular 131 in.
{h) Side 3 ch., perpendicular 1 ch. 80 1.
(c) Side 3 yd. 1 ft., perpendicular 2 ft. 8 in.
7. The parallel sides of a trapezoid are 48 in. and 56 in.
long respectively, and the perpendicular distance between them
is li ft. Express the area in sq. ft.
8. The base of a parallelogram is 75 rods long, and it con
tains 7i acres. Find its width.
y. The area of a square field is 40 A. Find it? side.
10. A grass plot in the form of a parallelogram is 125 ft.
long and ;$G ft. wide. Find the cost of levelling and sodding it
at 10 ct. per sq. yd.
MENSURATION.
163
drawn
by two
ivy part
gilt line
a plane
;s, called
iS as the
I ciroAilar
! tapering
it.
rved f'lce,
II a point
1.
je of a table
lias a gravel
.vel walk.
. and 84 ft.
i. 25 1. long
)ne of whose
the opposite
, and 56 in.
between them
and it con
pide.
im is r2r> ft
liul sodding it
EXERCISE CCLIV.
1. Draw figures repiesenting the following triangles, and
find the area of eacli, the base and perpendicular upon tlio btcx
from the opposite angle being rospectivoly : —
{a) 24 ft. and 15 ft. G in.
(h) 21 yd. 1 ft. 10 in. and li yd. 10 in.
((0 2750 1. and 380 1.
(d) 20 ch. and 365 1.
2. The area of a triangle is 875 sq. in. Tlie length of 1!i(?
perpendicular from an angle to the opposite side is 3;' !ii.
Find the length of this side.
3. The arc^a of a triangle is 34 sq. ft. 63 sq. in.; its base is
14 It. G in. Find the perpendicular from the opposite angle
upon the base.
4. A triangular field contains 1 a. 24 sq. per. The per
]i<'ndi('ular from an angle to the side opposite it is 4 rd. long,
llow long is this side?
5. A 3 C D is a ti'apezium. The diagonal, AC, is 100 ft.
long. The perpendiculars, frini 1) and B ujon AC, are 30 ft.
and 56 ft. respectively. Find the area of the trapezium.
6. In 5, if the diagonal is 65 yd. and tlie two perpendiculars
27i yd. and 38i yd., find the area.
7. The longest diagonal of a quadrilateral is 49 yd. and the
perpendiculars let fall on it from the remaining angles are
9 ft. 6 in. and 13 ft. 10 in. Find the area.
8. Draw the trapezoid A B C D, AB and CD being the
]i;irallel sides and being 48 yd. and 56 yd. long respectively.
The perpendicular distance botv/een them is 10 yd. 2 ft. Find
tlie area of the trapezoid.
9. The parallel sides of a trapezoid are 19 ft, and 23 ft., and
the altitude is 9 ft. Find the area.
10. The area of a trapezoid is 1155 sq. ft. One of the parallel
sides is 84 ft. long and it is 16i ft. wide. Find the length of
the other parallel side.
EXERCISE CCLV.
Note. — In the following examples tt = 3t.
1 . Find the circumference of circles wliose diameters are
] 1 in. ; 1 ft. 9 in. ; 3 ft. 6 in. ; 5 yd. 1 ft. 4 in. ; 7 yd. 2 ft. 4 in. ;
4 ch. 76 1.
2. Find the diameter of circles whose circumferences are
5 eh. 39 1.; 4 rd. ; 12 rd.
1 ft. 10 in.; 4 ft. 7 in.; 20 yd. 6 in.;
i ft. 10 in.
3. A boy can walk round a circle in 1 hr. 17 min. At the
same rate, how long will he take to walk along the diameter?
164
ARITHMETIC.
4. Two bicycles liiive wliools 2 ft. 11 in. and .T ft. G in. in
diameter respectively. If they start from the same i>lace, and
each wheel lias made 1000 revolutions, liow far will one lie
ahead of the other f
i). A coach wheel turns .330 times in travellinj? one mile.
Find the diameter of the wheel.
6. A locomotive is moving at the rate of (50 miles per hour.
The diameter of the driving wheel is 4 ft. How many times
does it turn in a second?
7. The radius of a circle is 8 ft. Find the perimeter of the
semicircle.
8. To enclose a circular garden, there are required 5L*8 yd.
of wire fencing. How long is the radius of the garden f
9. The diagonal of a square is 4 ft. 1 in. Find the circum
ference of a circle circumscribed about the square.
10. The radius of a circle is 5 ft. 3 in. Find the length of
an arc of 20^: of 30' ; of 50°; of 60°; of 100°; and of 110^
EXERCISE CCLVI.
1. Find the area of each of the following circles : —
Diameter, 35 in. ; 42 in. ; 70 in. ; 84 in. ; 105 in.
Circumference, 44 in. ; 06 in. ; 77 in. ; 110 in. ; 308 ft.
Radius, 7 in. ; 3i ft. ; 4 ft. 8 in. ; 5 ft. 3 in. ; 21 c!'.ains.
2. How many square yards of oilcloth will be required to
cover a circular floor 17 ft. 6 in. across?
3. Find the circumference of a circle whose area is 3.85
acres.
4. The radius of a circle is 84 inches. Find the radius of
another circle of half the area.
5. Two circles, the radius of each being 7 in., are placed on
the surface of a circle whose radius is 14 in. Find the number
of square inches not covered.
6. A cow tethered can feed over 2i acx*es of ground. How
long is the rope by which she is tied?
7. A circular field contains exactly one acre. Find the lengtli
of the fence which encloses it.
8. Find the number of grass sods, each 15 in. by 12 in.,
that will cover a circular piece of ground 21 ft. in diameter.
9. A circle 18 in. in radius has one 34 in. in diameter
inscribed within it. Find the area of the part of the largf
circle without the smaller one.
10. Find the cost of making a path 7 ft. wide round ;i
circular pond whose perimeter is 352 yd. at $1 per sq. yd.
MENSURATION.
165
EXERCISE CCLVII.
1 . b'iiul the hypotl;eiiuso of oucli of tlio following right aiiglfd
trituigloH whose base uud perpendicular are respectively :
(«) i:i ft., 84 ft. (c) 1032 ft., 574 ft.
{b) 408 ft., 500 ft. ((0 598 ft., 300 ft.
perpendicular and hypothenuse are respectively:—
(a) 40 yd., 530 yd. . (c) 117 ft., 125 ft.
(b) 1450 ft., 1900 ft. {(l) 270 yd., 300 yd.
2. Find the bases of the following rigiit angled triangles
whose
3. Find the perpendicula of the following right angled
triangles whose base and hypothenuse are respectively:—
{a) 050 ft., 794 ft. (c) 50 yd., 394 yd.
{b) 240 ft., 818 ft. {(I) 272 ft., 353 ft.
4. A boy is 21 mi. due south from his home; he travels 20
mi. due west. How far is he then from homef
5. A ladder is 37 ft. long and leans against a building with
its foot 12 ft. from the wall. How far from the ground will its
top rest against the wall?
0. A garden ■ the form of a rectangle is 210 ft. long and
170 ft. wide. How far is it from any corner to the one
diagonally opposite it?
7. How far is it from the diagonally opposite corners of a
cube 12 in. long?
8. How far is it from the diagonally opposite ©orners of a
box 8 ft. long, 6 ft. wide and 5 ft. deep?
9. A ladder 26 ft. long stands upright against a wall. How
far must the bottom of It be pulled out so as to lower the top
2 ft.?
10. Find the cost of fencing a field in the form of a right
iingled triangle, its base being 105 yd. and the perpendicular
208 yd. long at 10 ct. per yd.
EXERCISE CCLVIII.
1. Find the volumes of the cubes whose dimensions are as
follows: ik in. ; 3i in. ; 2 ft. 5 in. ; 1 yd. 1 ft. 1 in.
2. Find the surface of each cube in the last example.
3. A rectangular log is 18 ft. long, 18 in. broad, and 14 in.
thick, find — (1) its volume, (2) its surface.
4. A block of marble is 10 ft. long, 5 ft. 3 in. broad, and
'i ft. thick. Find — (1) its volume, (2) its surface.
5. The surface of a cube is 2400 sq. in. Find— (1) the
Ifiigtli of its side, (2) its volume.
(). How much will it cost to excavate the basement of a
sclionihouse 27 ft. long, 20 ft. wide and 8i ft. deep at 25 et.
l»er eu. yd.
iTT"
166
ARITHMETIC.
7. From the log, in examjde 'S, 2i eu. ft. are cut off. What
h^igth of log is left? v
S. A room 11 ft. high is half as long again as it is wide, and
its cubical space is 47G8i eu. ft. Find its length and breadth.
9. A gallon contains 277.274 cu. in. Find the length of a
cubical box that holds 10 bushels.
10. A cubic foot of water weighs 1000 oz. and a gallon 10 lbs.
How many gallons are there in a rectangular cistern 6 ft. long,
5i ft. wide, and 8 ft. deep.
EXERCISE CCLIX.
1 ■ Find the volume of each of the cylinders whose length
and diameter are respectively: —
(a) 8 ft. and 14 in. (c) 10 ft. and 7 ft.
(6) 12 ft. and 3 ft. G in. {(I) 20 ft. and 2 ft. 11 in.
2. Find the area of the curved surface of each of the
cylinders in example 1.
'.\. A well is 15 ft. deep and its diameter is 3 ft. (5 in. How
many eu. yd. of earth were taken out in digging it?
4. A circular slmft is 90 ft. deep and 3 ft. in diameter.
Find the cost of sinking it at $2.80 per cu. yd.
5. Find the total surface of the cylinders in example 1.
6. How much curved heating surface is there in a steam
pipe 1 in. in diameter and 350 ft. longf
7. A pillar 21 ft. high and 18 in. in diameter, supporting a
building, is to be decorated at 25 et. per sq. ft. Find the cost.
8. A cylinder contains 11 cu. ft. and is 14 ft. long. Find
its diameter.
9. It costs $11.88 to paint the curved surface of a pillar 18
ft. high at 63 et. per sq. yd. Find its diameter.
10. Find the number of eu. ft. of iron in a water pipe 12 ft.
long and 2 ft. 6 in. in diameter, the iron being 2 in. thick.
EXERCISE CCLX.
1. A square pyramid is 16 ft. high, and each side of the
base is 4 ft. 6 iui long. Find its volume.
2. A triangular pyramid is 12 in. high, and the sides of the
base are 29 in., 52 in. and 69 in. Find its volume.
3. The slant height of a cone is 10 ft., and the circumference
of the base is 15 ft. Find the area of the curved surface.
4. A cone is 3i ft. in diameter. Its slant height is 6 ft.
Find the area of the lateral surface.
5. The slant height of a conical spire is 45 ft. The circum
ference at the base is 30 ft. Find the cost of painting it at
45 ct. per sq. yd.
MISCELLANEOUS EXERCISES.
167
G. Find tlio volnmo of a cone 35 in. in diameter at the base
and GO in. in hcij^ht,
7. A cone is 48 ft. lii^li; its volume is 138G en. ft. Find —
(I) the area of the basts (2) the eircuniference of the l)ase.
8. JTow many yards of canvas 4 yd. wide will be required
for a eonieal tent L51 ft. in diameter ami 15 ft. high?
9. Wliat is the volume of the largest possible cone, cut out
of a cubical block whose edge is 7 ft.
10. 'I'he radius of the base of a cone whose height is 5 ft. is
11 in. Find the slant 1; eight.
EXERCISE CCLXI.
1. Find the surface of each sphere of the following
dimensions: — {a) Kadius, '^i in.; (h) diameter, 3^ in.; (c)
circumference, 44 in. ; {d} circumference, 88 in.
2. What will it cost to gild a globe 28 in. in radius iit 3G ct.
per sq. ft.f
3. The surface of a sphere contains 24G4 sq. ft. Find its
radius.
4. The surface of a sphere contains 5544 sq. ft. Find its
circumference.
.^». Find the volume of each sphere of the following
dimensions: — (a) Radius, Gin.; (6) radius, 12 in.; (c) diameter,
14 in. ; {(I) circumference, 22 in.
G. Find the volume of a sphere whose surface is 1386 sq. ft.
7. A cubical block of wood 3 ft. long is formed into the
largest globe possible. How much wood is cut away?
8. A solid metal sphere G in. in diameter is melted and
formed without loss into a cylinder 3 in. in radius. How long
is tlie cylinder?
9. A solid metal sphere 12 in. in diameter is melted and
formed without loss into shot i in. in diameter. How many
siiot are there?
10. How many balls i in. in diameter can be made from a
cubic block of lead 5i in. long?
IMISCELLAINEOUS EXERCISES.
EXERCISE CCLXII.
1. Each equal side of an isosceles triangle measures twice
as much as the base. If the base is 48 ft. long, find the altitude.
2. Find the base of a triangle whose area is 5280 sq. yd. and
lieiglit 120 yd.
3. The perimeter of an isosceles triangle is 153 yd. and each
"f tlie equal sides is f of the 3rd. Find (1) the base, (2) the
iiiea.
lOfl
AniTIIMRTir,
4. Twfi siilcs of ii Iriiiiifrlc iin> 'J IS It. tiiid 241 ft. loup nnd
tli*> iMTiit'iidK iiliii' from tli(> iiii'lii«l<Mi tiii^lo upon tlir llrtl sitlo 'in
I'JO ft. I'MikI tli<> :tni si(l«>.
5. Tlic top of a poi<> ih ln'ok(<n olT hikI striUcs tlio ^roiiiid 15
ft. from the foot «^ tlu' polo. V'wul i\w wliolo loii>;tli of tlu' polo
supposing ♦' • bi'Oi\( II j>ioco to l»o ;{!► ft.
(5. Kiml ,>r< .)f iiii otpiihitoral triimj^lo whoso wido is 10 ft.
7. A stici ft. 1. .i^r pliicod upii^ lit in Ww ground is found
to Piist )i sluidow 4 ft, ' ni. lon^. V> hut is the hoi^ht of a polo
tlnit casts a shadow IJH it. lonj^if
8. A foot jtath fjoos alonj; two adjaoont sid<^s of a I'ocfiinjjio.
Ono sido is llMiyd. and tho otiutr 147 yd. lonR. Find tho savinj^
in distan('(« by f^oiii^ iilon^ Uw dia^oiuil instt^ad of tlio sidos.
9. Tho pt»riinotoi' of a s((U!iro is 748 in. and of anolhoi' is '.VM't
in. Find tiio poriniotor of anothor o(inil in area to tlit othor
two.
10. There are two rootanf?ular fields of (^qual iirea. Tho
adjacent sides of one are 1)45 yd. and IU44 yd. lonj;. Tho lonj^or
side of tiie othor is 1KJ4 yd. lonj^. Find tln^ shorter sido.
EXERCISE CCLXIII.
1. How long is tho edge of a cube whose surfjico is 11094
sq.ft.?
2. A triangular field contains one acre. A ])eri)endicular
drawn from one corner to the side opposite measures 40 yd.
Find this side.'
3. The volume of a cube is 37 cu. ft. 64 en. in. Find the cost
of painting it at 33^ ct. i)er sq. ft.
4. A has two circular plots of ground 100 ft. and 20 ft. in
diameter, respectively. How many times is one as large as the
other?
5. What must be the circumference of a circular lake which
shall contain nr part as nnich surface as a circular lake I'M
miles in circiimference?
6. What is the distance through the opposite corners of a
square yard? .
7. Find the perimeter of a rectangular plot of land whose
length is 2i times its width, if it contains Oi acres.
8. A ladder 20 ft. long reaches to the top of a wall when the
foot is 13 ft. from the wall. How much does the ladder project
above the wall, when its foot is 5 ft. from the wall.
9. If a c. ft. of marble weighs 2.71(5 times as much as a en.
ft. of water. Find the weight of a rectangular block of marble
9i ft. by 2^ ft. by 2 ft. (A cu. foot of water weighs 1000 oz.)
10. The sides of a triangular field are 350 yd., 440 yd. and
750 yd. in length. It rents for $31.50 per annum. Find the
rent V^^' Jicre.
MISCELLANEOUS EXERCISES.
169
EXERCISL CCLXIV.
Kind tli(^ li'ii^tli
!. Tli(f pfrinu'lcr of ii H(ttni(Mr<;lo is 'Mi ft.
of tlio (litiiiiotiM*.
'J. VViiioli will carry tin* liirKOKt lunoniit of water two '.i in.
tikt or ono 4 in. tile, the speed hc/mf? the same in each ease?
',]. Find the diamet<M' of a eirele ecjual in area to a rectanj^ht
whose sides are K)4 ft. by Kl ft.
4. A cireular pond Hli ft. in diameter has a walk 4 ft. wide
round it. Find the area of the walk.
5. A tower \i'H ft. hij;h stands in the middle of • stream 144
ft. widen How lon{» is tlie distance from the she t' the foot
of the llaj,' staff upon the top of the tower.
(5. Find the ar(^a of a trapezoid whose parall. . nidis are 178
ft. and 14(5 ft. and the perpendicular distance between them
sri ft.
7. Find the area of a pond whose circumference is 204 ft.
H. A H (! 1) is a quadrilatcual figure. AB 400 ft. lon^,', liC
'J0:{ ft., CI) '.im ft., DA 195 ft. The anf^ios at A and C are
rif^ht aufjfles. Draw tlui figure and find its area.
9. A trapezium is dividcMi into two triangles by a diagonal
40 ft. long. The difference in length of the perpendiculars
from the opposite angles on tlio diagonal is 7 ft. Find the
difference in area of the triangles?
10. The differetu'o between the circumference and the
diameter of a circle is 45 in. Find the area of the circle.
EXERCISE CCLXV.
1. ABCI) is a trapezoid. AD and BC are the parallel sides
and are '.V2 ft. and 40 ft. long, respectively. AB is 16 ft. long
and (M) 18 ft. BA and CD are produced to meet in E. Find
th(^ length of EB and EG respectively.
2. Find the aroa of a quadrilateral field wlioso diagonal is 40
rods and the perpendiculars on this diagonal from the opposite
angles 14 rods and 2U rods, resi)ectively.
.'J. Find the aroa of a trapezium whose diagonal is 108 ft. long,
one perpendicular on the diagonal from the opposite angle
being 42 ft. long, the other, 50 ft. long.
4. The area of a circle is 44 sq. ft. Find the difference
between the areas of the circumscribed and inscribed squares.
T). The side of a square field is 40 rods long. Find the
li'nii,tii of the side of a square field that contains (I) 4 times as
nuuh land; (2) 9 times as much; {[i) 5 times as much.
0. The perimeter of a rectangle is 104 in. and the difference
in length of the two adjacent sides is 22 in. Find the area of
the rectangle,
170
AKITIIMKTIO.
7. The Idisc (»r ii friiiiigic is 07 ft. long iiiul i\w <lifT«<rriK'«> in
loii^tli of llm oilier two sidcH is li ft. TIk' (listiiiico Itctwt'cn tlio
middle of the Imse mid tin perdciidiciiliir let full from the v«'i*ti
cal allele on Ihe base is ."Ji fl. Find (1) the other sides of the
triangle, (2) the length of the perpeiidieiihii'.
H. The lieight of a tower on a river bunk is ir)4 ft. Tie
length of a line from the top of the tower to tin' opposite bank
is 170 ft. Find the breadth ol' the stream.
t). Find the surfaces of the cubes whosi* contents are 1)201 cii.
in. ttud IDGH.'] e. in. respectively.
10. A man has a circular lawn 75 ft. in diameter. What is the
length of a string that as radius would des<'ribe a circle contaiu
iug 9 times as much ground.'
EXERCISE CCLXVI.
1. A circular garden contains 24(5400 s((. ft. A pole ])lnced
in the centre of tlie garden is broken and the top just reaches
the odge of the garden. Find the heiglit of the piece still
standing, tlu^ length of the broken part being 287 feet.
2. A cylinder is 14 ft. long and 7 ft. in diameter. Find (1)
the area of the curved surface and (2) the area of the entire
surface.
3. What is the length of a stone wall that will enclose an
acre of land in the form of a circle'/
4. How many men can stand on an acre of laud allowing 12
sq. ft. to each?
5. What length of wire without loss of metal may be drawn
from a globe 6 in. in diameter, the diameter of the wire being
iTo of an in.?
6. The area of a rectangular field is 5 acres and the fence
that encloses it is 120 rods lung. Find the length of the sides
of the field.
7. A stick of square timber 24 ft. long contains 90 e. ft.
What must have been the diameter of the tree from which it
was hewn?
8. A square tank holding 4500 gal. of water is 5 ft. deep.
Find its length.
9. What is the cost of lining a watercistern .'5 ft. long, 2 ft.
deep and 2 ft. in. l)road, with sheet lead of 10 l)>. per square
foot at $9.00 per cwt., there l)eing no lid.
10. What is the cost of painting a t'onical spire whose slant
height is 120 ft. and circumference at the base GO ft., at 8 c.
per sq. yd.?
EXERCISE CCLXVII.
1. Three squares contain respectively 36, 04, and 576 sq. ft.
Find the length of a side of that square which Juih tin jirop:
pqual to four times their sum,
MI8(;KIiLANE()UH KXKRCISEH.
171
[•net! in
i>en the
,. v»'i'ti
I (it the
t. Tie
tv bank
!)201 en.
lilt is the
contiiin
,le placed
,t rcachrrt
»iuce Htill
Find (1)
the entire
snelose an
llowinj; 12
be drawn
^vire being
the fence
the sides
[s 90 c. ft.
which it
a ft. deep.
lon^^ 2 ft.
I per square
Lvhose shmt
ft., at 8 c.
57G eq. ft.
2. What in llie hiiRth of a perin'tHlicuhir I<'t fall from any
nnj,'le of an equilateral triangle to its opposite side when this
siile is 12 yd. louj^?
.'5. How many elmins are there in the side of a field in the
torm of an (>(piilateral trianj^le, containing; 24 acres?
4. The len>,'th of a rectangle is 12 chains. What is its
Ineadth to contain 4 acres?
f). The sides of a iectangle are 77 yd. and ;i2 yd. What is
the diameter of a circle of ecpial areaf
(i. The liase and perpt^jidicular of a right angled triangle are
44 ft. and (>'.i ft. respectively. Find the diameter of u circle of
equal area.
7. The l)a«e and i)erpendicular of a right angled triangle are
respectively, IIOH ft. and 87") ft. long. Find the diameter of a
circle equal in area to the triangle.
8. The side of a square is 15 ft. long. What is the length of
the diameter of the circumscribed circle?
9. The length of a stick of timber is 24 ft. ; its breadth is 3
ft. and its thickness 2 ft. 9 in. Find the area of the entire
surface.
10. Find the volume of a cylinder 21 inches i i diameter and
20 ft. in length.
EXERCISE CCLXVIII.
1. Find the area of the surface of a sphere lii ft. in
diameter.
2. The side of a cubical box is 20 in. long. Find the
length of its diagonal.
;$. The volume of a cube is 4096 cu. in. Find the length of
its diagonal.
4. A room 18 ft. high is quarter as long sigain as it is wide and
its cubical contents are 20250 cu. ft. Find its length and
breadth.
5. Find the weight of a metal disc 7 ft. in diameter, and li
ft. thick, if a cubic foot of this metal weighs 371 lb.
6. How many planks each 13i ft. long and lOi in. wide will
cover a platform 54 yd. long and 21 yd. wide?
7. A cii'cular plate of lead 2 in. in thickness and 8 in. in
diameter is converted without loss into spherical shot each of
.05 in. in radius. How many shot does it make?
8. If a cube of lead the edge of which is 1 in. long weighs 9
oz., find the weight of a cube of lead whose edge is 3 in. long.
9. A solid sphere of iron 12 in. in diameter is melted and
cast into a hollow cylinder 7 in. in radius, Hovv long is the
cylinder, the iron being 2 in. thick.
10. A sphere 5 in, in diameter weighs 75 oz. Find the
weight of a sphere 4 in. in diameter iP^^i^ ^^ paaterial 2b%
heavier than the other,
CHAPTER XIII.
THE METRIC SYSTEM OF WEIGHTS AIND MEASURES.
The Metric System of Wciglits and Measures is
])ase(l upon the deeimal m'n\v of notation.
It is used in seientifie treatises, aiul lias heen
adoi)ted ))y most of tlie nations of p]uroi>e
and South America.
Its advantages are: —
(I) It is easily applied. All the opera
tions are the same as in simple numbers.
^ (2) It does away with Reduijtion, Addi
2 tion, Subtraction, Multiplication and Divi
I sion of Compound Numbers.
I (3) Its general introduction would
g greatly facilitate commerce and exchange,
II giving all nations a universal system of
g weights and measures.
I The fundamental Unit is the Metre,
rt From this all the other units of the
1 system are derived, hence the namc^ IVIetrlc
7 System.
2 The principal units of the system are as
I follows: —
I The unit of Length is the Metre, which
^ is 39.37 inches.
The unit of Capacity is the Litre, which
is .2201 gallons.
The unit of Weight is the Gram, which
is 15.43 grains.
The unit of Surface is the Are, which
is J19.6 so. yd.
173
01
^
9 :
01 L
Q 
^^ I
« :
Cl 
T^ 
CO
1 C4
THE METRIC BY8TEM.
173
\SUBES.
liis 1h'<'^^
lio optva
ion, A(Wi
and Divi
(^^i would
cxcluinKf,
svsteiu of
Tli(< Metri<; Syslcni is entirely (UmmiiihI. The siib
iniiltiples siiid multiples of the unit tin; denoted l>y
the t'oliowinj^ prefixes : —
Milli = .001
Ceiiti = .01
Deci = .1
Deka = 10. ^timew,
Heeto = 100.
Kilo = 1000.
Myria = 10000.'
a metre.
a litre.
1 a gram.
[liix aru.
LINEAR MEASURE.
10 millimetres (mm.) = 1 centimetre
10 ceiitimetreH (cm.) = 1 decimetre
10 decimetreH (dm.) = 1 metre
10 metres (m.) = 1 dekametre
10 dekametres (Dm.) = 1 hectometre
10 hectometres (Hm.) = 1 kilometre
10 kilometres (Km.) = 1 myriametre
Note. — 1 metre = 39^ in. nearly; 70 yd. = G4 metres nearly.
1 kilometre = 1 100yd. nearly ; 8 km. = 5 mi. nearly.
.01
metre.
.1
1.
10.
100.
1000.
10000.
48.3 mm.,
(1) as centimetres, (2) as decimetres.
EXERCISE CCLXIX.
1. Read the following:— 37.5 m. ; 12.7 cm.
7.H05 Dm. ; 9.7 dm.
2. Express 4560 mm.
(;{) as metres.
3. Express 1.87 Dm. — (1) as metres, (2) as millimetres, (3)
IIS centimetres.
4. Simplify .789 m. + 78.9 cm. + 7856 mm. + 1897 km.
5. Simplify .845 Km. — 6457 cm.; 6.59 cm. — 54.87mm.
6. Simplify 768.4 cm. X 12; 3.7896 dm. X 789.5.
7. A ]>ook is 3.2 cm. thick. If the average thickness of the
leaves is 05 mm., find the number of leaves in the book.
8. Tilt 'Ircumference of a wheel is 6.3 m. in length. How
often will such a wheel turn in going 173.88 Km.?
1>. Find the cost of 27.84 m. of cloth at $2.75 per metre.
10. The Mont Ceuis tunnel is about 12.22 Km. long. How
iimny miles is this?
H. Find the cost of building a railroad 37 Km. 47 m. long at
*irtOOO a kilometre.
12. How often will a bicycle wheel 225 cm. in circumference
turn in going from Toronto to Hamilton a distance of 63 Km.?
174
ARITHMETIC.
SQUARE OR SURFACE MEASURE.
100 sq. millimetres (sq. mm.) 1 sq. eeiitiiii(>tie=^ .OOdl sq. metre.
100 sq. centimetres (sq. cm.) 1 sq. decimetre == .01
100 sq. decimetres (sq. dm. )l sq. metre = 1. "  1 centare.
100 .sq. metres (sq. m.) 1 sq. dekiiiiietre 100. " =1 are.
100 sq. dekametres (sq. Dm.) 1 .sq. liectometre  10000. "=1 hectare.
100 sq. hectometres (sq. Hm.) =1 sq. kilometre =1000000.
NoTK.— The ML, ceutiire juid hectare are used only in land
measure.
The are is slightly less than 4 sq. rods.
The hectare is slightly less than I2i acres.
EXERCISE CCLXX.
1. Convert 287G345 sq. m. into hectares.
2. How many arts are there in 3.7850 sq. Km.?
3. Write 5.7536 sq. ni. as sq. centimetres; as sq. millimetres.
4. How many sq. metres are there in 2.34' 7 sq. Km.?
5. How many sq. centimetres are there in .0542 sq. m.?
6. Write as one quantity in sq. metres 3 sq. Km. + 3 sq.
Hm. ■} 3 sq. Dm. f 3 sq, m.
7. How many ares are there in a rectangle 200 metres long
and 50 metres wide?
8. How many sq. metres are tliere in a rectangular floor
0.8 m. long and 4.8 m. wide?
9. What will be the cost of 5 sq. m. of sheet tin at 5 mills
a sq. decimetre?
10, How many bricks, each 20 em. long and 10 em. wide,
will be required to pave a sidewalk 3.3 m. wide and 1.7 Km.
long?
MEASURES OF CAPACITY.
1000 cu. millimetres (c. mm.)=l ci. centimetre = .000001 cu. metre.
1000 cii. centimetres (c. cm. )=l cu. decimetre = .001 " =1 litre.
1000 cu. decimetres (c. dm.)=l cu. metre =1. " =1 stere.
Note. — In measuring wood a cul)ic metre, called a stere
(st.), is used; 30 steres = 1 "ord nearly.
In measuring liquids the cubic decimetre, called a litre. In
used.
In measuring grains, fruits, etc., the hectolitre is r.sed.
The numeral preiixes are used with the litre af with tln'
metre.
EXERCISE C'JLXXI.
1. How many steres of wood are there in a p'ie 29 m. long,
1.25 m. wide, and 2 m. high?
2. What will 17.3 HI. of Wiieat cost at $0 25 a dekalitre?
'^HE METRIC SVSTEM.
only in land
10 cm. wide,
and 1.7 Km.
ed a litre, is
175
.01
.1
, '^ 'f^W J.lfUlv )it,.,.w .,„ ., ^'
'"ll."' i .i m!'*l„" j"'i "•■; ''l«t will „„ ti,, ,.„,. „f ,. .
JO deei^^rams 1]?/) Z J ^^««iS''fim =
JO grams ^A^/ ^ .J ff^'fim :^ j
.NOTR.A cubic cenfilT ^'^'^^'^'am == ,000.
1  am  L, ^,,.,^j,^g
AJ<.,„,.„,„ = ,, ,, ^,„,',>;',;« «™= 1 o... Avoi... ,.e„W..
K'UO kilograms ^ 22 evvt  w
A "tre of water weig],, l" 7uL ""'' ^' "^^*"« to".
A eiibie metrfl nC . ^^^'ogram.
metie of water weighs looo 1n
J Write 5 Kg .^ j^''^''''*^^ CCLXXII.
4. Express oT7" ' "'^ ^^"t'>''am?s.^'' ^ «^nt,grams and 5
. ''■ ^^'^lat is thetl ^'""''' «« f'entigrams
,^;ram.? ''*''*^^««o«tof .67225Kg of o. •
^ ''^ "l"'"" at G2,l et. per
ffJ'fun.
^!v*C^
17G
ARITHMETIC.
1). (Jivo llic w»'if,'lit ill milli<j:riuiis of a pill wlion n, mass
wcij^liiiij^ 21.7 K '^ iiiiiclc into 70 pills.
10. Wliiit decinuil is ;") K '^ <'K <**^ <>"<' l<iloj?riim?
EXERCISE CCLXXIII.
Write* tlio following: —
1. {a) Write 7 dekametres, 2 decimetres and f) centimetres
as nieties.
{h) Write H hectolitres, 8 litres and 7 decilitres as litres.
((') Write If) ares, 9 declares and 8 milliares as ares.
(d) Write 27 kilograms, ',i decigrams and 7 centigrams as
grams.
2. Mercury weighs 115. f) times as much as water. Find the
weight of 44 litres of mercury.
;j. Marble weighs 2.7 times as much as water. Find the
WH'ight of a rectangular block of marble 2.5 m. long, 1.75 m.
wide, and 4 m. thick.
4. If silver weighs 10.5 times as much as water, how many
coins, each weighing 5 grams, can be coined from a cubic
decimetre of silver?
5. If alcohol is 80% as heavy as water, find the weight of
485 com. of alcohol.
0. How many steres of wood are there in a pile 50 m. long,
1.1 m. wide, and 2 m. high?
7. What is the ])rofit on 75 hectolitres of potatoes, l)ought
at 7 francs a hectolitre, and retailed at 1 franc a dekalitre?
8. How many hectolitres of apples, at $1.25 a hectolitre,
should be given for 5 dekasteres 5 steres of wood at 75 ct. per
stere ?
9. A druggist having .75 Kg. of quinine 'makes up 500 pills
containing 2 decigrams of quinine each. How many grams ho,s
he left?
10. A farmer, having 4 hectometres of wire fence, uses a
portion of it to enclose a field 50 metres square. How many
metres has he left?
11. What will be 'the profit on 10 g. of calomel, bought for
50 ct., if sold in powders of 5 dg. at 5 et. each.
12. A train runs 47.5 Km. per hour. How many miles does
it go in 6 hr. 24 rnin.
i;5. How often can a cup, holding 3 ci., be filled from a
vessel containing 14.:?1 1. of water?
14. How many rolls of wall pjiper, 10 m. long and .5 m
wide, are needed to paper the walls of a room, 6.3 m. long, 4.2
m. wide and 3.2 m. high?
lien a mass
centimetres
r. Find the
CHAPTER XIV.
^'SCELLANE^ EXERCISES
»• CfRCULATrNO DECIMALS
Recurring Decimals. '"^'"'*^' Circulatinq o,
A Terminating Decimal
 't I.mited number ornH^^^^^^^ ^^^'^'^^ ^'^^'^'"cls
i>*'"'^ as .375, .()()24 ^^''''"^^ ^^•^>"' the DeoimaJ
A Circulating Decimal ,
''«'"''^n or set of tinn^, /• "' ^" ^^'^^^^'^^ ^h. su,m.
same order as ^n'7'7 ' ''''^^^'^^I'dUy reeurs in
,.,.TheRepete„d.«.,,„,eor.,;,«^„.,.,_,„,.,^,_
.^Circulating DeclmaU . ' ■•^*'**
M.xed arc„?atl^g'7?eclmals""""'' " "' ^^^ ,..,„
'^""'l'"'e tho foil • ^•'^^'*^'SE CCLXXIV.
1.
J
3"
4
Si
fl
H r,
Ti r.
*.
^\^!'f^
178
AKITIIMETIC.
5
7
^r
^
t\
iV
n
S 1
22
S6
2 8
AV
14T
■1V4
^VST
4 r, i»
6
111
DOT
14U 8
.Vt
o 4
'>. 1
4. i\
5. I
6. 11
7. H
8. If
y. 84
10. 2 88
EXERCISE CCLXXV.
Reducn the followiuK to vulgar t'nietions hi their lowest terms:—
1. '
1
1 J.
1
T 1 •
1 .{
1 4.
1 1
"44f •
29
Tift.
8
21 .
8 9 1
"17 7 (r .
2 7 7
"I37ff.
.5 .17 .;i6
2. .018 .627 .OOU
3. .054 .'h'i .1376
4. .945 .423 .78;i
5. .9801 .923076 .142857
6. .954 .527 .3si
7. .7852 .103G .01(59
8. .G59(') .00()75 .24376
9. .7954 AWAh 2.297
10. 4.00(i 5.o6() 7.00(5
EXERCISE CCLXXVI.
Simplify the following: —
1. .23 + .234 + .2345 + 5.7 + .12345.
2. .1(5 + .792 + .21431 + S)iS + .5(5.
3. 25.12;i — 15.(53; l9.io7 — 5.043.
4. .574 — .2rx; .574 — .25.
5. .754 + .213 — .(5S47 + .45()i — .00(5.
G. .(53 X 2.5; 2.15 X 3.204.
7. .1(5 X .72; .75 X .75 X .75.
S. .339  .72; .SI — 2.3.
i). 2.7;!<5 — 4.3; 51. SI — 5.18.
1<>. 4.37 X .27 —2.18; .154 — 2 X 11.25.
.210.
.144.
.296.
.261.
.285714.
.24390,
.01315.
.3857142.
7.675.
Ta O
7.
«« jrVVv^ <":
CIRCULATINO DEC^IMALS.
179
At terms: —
)714.
m.
6.
)7142.
75.
7.
EXERCISE CCLXXVII.
1. The product of .9, .19 and a third factor is 2.1. Find
the third factor.
2. What must be multiplied by .809523 to produce .liif
3. Without dividiufif, .vrite the decimals equivalent to rooryt
7 1 7L 7.1 7 1 _Xl_ 7_1_
UUU) OUO) UOd> WIMIOJ UOOO) llttUU*
4. What two numbers are those the sum of which is
.l!)i and the greater exceeds the less by .128?
"). Without dividing, state what kind of decimal each of the
following are e<iuivalent to: — I, ^, n, ^, i\, v, A, T.
G. Simplify .(5518 ^ .140 X .225 + 5 — .15.
7. Simplify .7 of £3 + .2i of 5s. + .:!(') of lid.
8. Simplify .38 of 9 t. + .144 of 37 lb. — .45 of 3cwt. 74 lb.
9. Simplify .375 of 16 mi. + .40 of 198 rd. + .35 of 4^ yd.
10. How many tons, cwt., etc., are there fn .375 of 185 t. ?
EXERCISE CCLXXVIII.
1. Describe the vulgar fractions whose equivalent decimals
are finite.
2. Why do I, 1, ro, "/o> ¥u, iso and fi i)roduce finite decimals?
3. How many figures will there he in the decimals equivalent
to ixij s, :T2? and airo.
4. Why do §, ^, n and ;\^ produce infinite decimals?
C,. How many figures will thcic lie in the nonre)eating
part of the decimals, equivalent to §, j, jij, H> and ^ff?
(). Whether is 7.45()48 more accurately represented by
7.450 or by 7.457?
7. Show that .005 X .005 X .04 X .04 = .0002 X .0002.
8. Show how a numl»er may be multiplied or divided by 10,
100, 1000, etc., by merely shifting the decimal point.
9. Su]»pose unity represents .0015, what decimal will
represent .0002?
EXERCISE CCLXXIX.
1. A father, dying, left .518 of his property to the elder of
his two sons, and .518 of the rest to his younger, and the
n'Uiiiinder to his wife. The older son received $1900 more than
the y(,nnger. What did the elder son receive?
'.'. A reservoir is 03, ;j ft. long and 48.5 ft. wide. How many
•'ultf ft it of water must be ]iumped out of it to make the
uider sink 3 it.?
180
ARITHMETIC.
;j. Divide $G54.50 amonp A, B and C in proportion to the
numbers 1.3, 2.5, and 2.7.
4. A man, after spending .4 of his money, found that .6 of
the remainder was $40. How much had he at first?
5. Multiply the sum of 1.5, .6 and .75 by the difference
between .26 and .15, and divide the product by 43.5.
6. A man on a journey goes .6 of it by train, .18 of it by
street ear and walks the remaining distance in 1.6 hours at the
rate of 3 miles an hour. How far is the distance?
7. The area of a square field is 72.9 acres. How long will
A require to walk around it at the rate of 3.3 miles per hour?
8. A grocer buys tea at 30c. ; twice as much at 33.3c. ; and
three times as ranch at 36. 6e. per lb. He mixes the three kinds
tojijuther and sells the mixture at 40c. per lb. Find his gain
p( r cent.?
9. Subtract .08 from .08 and divide the remainder by .625.
II. PROBLEMS RELATIING TO WORK DONE.
EXERCISE CCLXXX.
1 . If A and B cnn do a woik in f of a day, and B alone can
do it in 2i days, how much more does A do than B in 1 day?
2. A can do a work in i day; B can do it in i day and C in
i day. How long will it take if all begin working together to
do the entire work?
3. A can do a work in 4i days; B can do it in 3^ days.
Wi^h the help of C the work can be done in li days. In what
time can C do the work?
4. A's working power is t of B's working power. How long
would A take to do what B dtfes in 12i days?
5. B liikes I of the time that A takes to do a work. What
fraction of B's working power is A's working power?
6. A and B take 18 days to do a work, A doing twice as
much as B. In what time could each do the work by himself?
7. .V, B, and C can do 5 of a work in 3i days, A doing half
as mucli as B and twice as much as C. In what time could
each do the woi'c by himself?
8. If 10 men can do a work in 15 days, how soon after cora
meticing v.mst 4 additional men be employed so that the work,
may bo done in 12 days?
CLOCK PROBLEMS.
181
9. A can do a work in 27 days, and B in 15 days. A works
at it alone for 12 days; B then works alone for 5 days; then C
finishes the work alone in 4 days. In what time could € do the
whole work by himself?
10. If 5 men or IG boys cau do a piece of work in 15 hours,
in what time could 3 men and 48 boys do the work ?
11. If the times taken by A, B, and C to do a work are as 1,
2, and 3; and tof^ether they cau do the work in 20 days, in
what time could each do it by himself?
12. A does ^ of a piece of work in 12 days. He then calls in
B, and they finish the work in li days. How long would B
take to do the whole work l>y himself?
13. A and B can together do a work in 14 hr. 56 min. A
alone can do it in 28 hr. In what time could B alone do it?
14. A can do a work in 3 hr., B in 2i hr., and C in 3i hr.
In what time will it be finished by the three, if B begin i hour
after A, and C 22i miu. after B?
15. If 2 liorses do the same work as 3 mules, how many
horses along with 7 mules will be required to draw 9i tons the
same distance in the same time that G horses and 5 mules cau
draw 7 tons?
16. A can do a work in 12 days ; B can do it in 15 days and C
in 10 d.iys. They all begin to work together but A stops 2 days
and B 1 j days before C who finishes the work. How long does
each one work?
17. A can do a piece of work in 7i hr. ; B can do it in 8i hr.
If tliey do it together and the work is worth $2.10, what sum
ouulit each to receive?
III. CLOCK PROBLEMS.
EXERCISE CCLXXXI.
1. The hands of clock are together. In what ti' *o will they
be 11 minute spaces apart? 22 minutespaces apart? 27i
minute  spaces apart ?
2. The minutehand is 16i miiuitespaces behind the hour
hand. When will they be together?
3. At what time between 3 and 4 o'clock are the hands of a
watch together?
4. Find the first time after 6 o'clock tliut the hands of a
clock are at riglit angles.
5. The hands of a clock are opposite each other at 6 o'clock.
At what time will they l)e togetluM* for the first time?
6. Find the first time after 5 o'clock that the luinds of a
clock vviU be 3 minute spaces apart.
182
ARITHMETIC.
7. Fiiul the times between 6 and 7 o'clock wlien the linnds
of u watch are 8 minutespaces apart.
8. Find the time after 8 o'clock when the hands of a clock
are («) together; [h) at right angles; (c) opposite each other.
9. Find the times Lotween 9 and 12 o'clock when the hands
of a watch are together.
10. Find the first time after 5 o'clock that the hands of a
watch are equally distant from the figure five.
EXERCISE CCLXXXII.
1. Find the first time after 4 o'clock that the hands of a
watch are 48° opiri.
2. Tlie hands of a watch are 18° ajjart for the second time
after 3 o'clock. Find the time.
3. Find the first time after 6 o'clock that the minutehand
is midway between the hourhand and the figure six.
4. Two clocks are together at 12 o'clock. One loses 8 sec.
and the other gains 7 sec. in 24 hours. \Vh('U will one be half
an hour ahead of the other and what time will each show?
5. Two clocks are together and show correct time at noon.
One loses 5 see. and the other 7 sec. in 12 lir. When will one
be 5 minutes faster than the other?
6. A clock loses 5 sec. in 24 min. At 9 p.m. on ^Monday
it is 17 min. fast. When will it show coriect time?
7. A watch set accurately at 12 o'clock indicates 5 min. to 5
at 5 o'clock. What is the exact time when the watch indicates
5 o'clock.
8. One clock gains 2 min. in 12 hr., and another loses 2
min. in 24 hr. Tliey are set right at noon on Friday. What is
the time indicated by each clock when one appears to have
gained 8.i minutes on the other?
9. A clock which was 1.4 min. fast at quarter to 11 p.m. on
May 2, was 8 min. too slow at 9 a.m. on May 7. When was it
exactly right?
10. A watch showing correct time at noon on Tuesday gains
3 min. 40 sec. in 24 hr. What is the correct time on Saturday
evening when it is 10 o'clock by the watch.
IV. PROBLEIVIS IINVOLVIfNO VELOCITY.
EXERCISE CCLXXXIII.
1 . How many feet per second is equal to a rate of 30 miles
l)er hour?
2. ITow many miles per hour is equal to a rate of 50 ft. per
second?
THE SUM AND DIFFKRENCE OK TWO NUMBERS.
183
3. A train 22 rods lonp' i)aHS08 a post in 11 socondH. At
wliat ratt< per hour is it moviiif??
4. How loiif^ will a train GO yd. in length, moving .'JO miles
per hour take to pass another 50 yd. long standing on a sidingf
5. A railway train moving at the rate of 49 miles {»er hour
goes 7 miles while a coach goes 2 miles. How long will it
require the coach to go ;{.36 miles?
6. A is walking 4 miles an hour, and B, who is 4 miles ahojid
of him, is walking 3i miles an hour in the same direction as A.
How long will it be before A overtakes B?
7. A starts from Sarnia to walk to London, u distance of GO
miles. At the same time B starts from Londoti to walk to
Sarnia. If A goes 4J miles per hour and B ',ii miles per hour,
how far from Sarnia will they meet?
8. In a mile race A can beat B >)y 80 yd. and C by 87 yd.
By how much can B beat C in a mile race?
9. In a mile race A can beat B ])y 22 yd. and B can beat C
by 11 yd. How many yards start can A give C that there may
be a dead heat?
10. If the hands of a clook coincide every G5 minutes, how
unich does the clock gain or luse in a day?
V. PROBLEMS IINVOLVIINO THE SUM AND DIFFERENCE
OF TWO NUMBERS.
EXERCISE CCLXXXIV.
1. The sura of two numbers is .'565; their difference is 83.
Find the numbers.
2. A man rows at the rate of 7 miles per hour down a
stream which flows at the rate of li miles per hour. Find his
rate of rowing against the current.
3. A man can row 8 miles down stream in 2 hours, but he
takes 3 liours to row back to the starting point. Find the rate
of the stream.
4. If a man rows 10 miles in 21 hours against a stream, the
rate of \ylnch is U miles per hour, how long will he be in
rowing 3 J miles down the stream?
3. A man rows 15 miles down stream in 21 hours and up in
4 hours. Find his rate of rowing in still water.
G. A can row a distance down stream in 15 minutes and the
same distance up i,i 20 minutes. Wliat is the distance, the
rate ot the stream being 1 mile per hour?
"• A man rows on the still water of a canal one mile in 15
iiin. Tie then reaches the river and rows down stream U miles
"I the next 15 min. How long will he take to return to the
startingpoint?
!!'
184
ARITHMETIC.
H. IIow far can a man who rows 4 miles per hour in still
water row up strenm, which Hows nt the rate of 2 miles per
hour, so that he may be 2 hours before he returns to the Vioat
house?
9. A crew can row down a stream a eertain distanee in 2
hours and back the same distanee in .1 hours. Comi)are the
rate of rowing in still water with the rate of the stream.
10. If A can row (ii^ miles in 2h hours against a strenm flow
ing H miles an hour, how long will it take him to row 12 miles
with the current?
EXERCISE CCLXXXV.
1. A skated G miles at the rate of 10 miles an hour with the
wind and returned against it in 50 minutes. Find tli»' rjito of
the wind i)er hour.
2. Two trains moving on parallel traeks in opposite direc'
tions, and respectively 110 yd. and 8s yd. long, pass each other
in ;') sec, and, when moving in the same direction, the faster
l)asses the other in 45 see. Find their rates in miles per hour.
',]. A train 110 yd. long, moving i mile a minute, meets
another on a parallel tiack, moving 40 ft. per see. and passes it
in 8 sec. Find the lengtii of the second train.
4. If telegraph poles are 88 yd. apart, and one is observed
to pass the window of n r.iilway car every 4 sec, at what rate
pc hour is the train moving?
5. An express train going 57 miles an hour passes a station
5i min. after a freight, going 38 miles an hour. When will the
express overtake the freight?
6. A train going 30 miles an hour passes a man walking in
the same direction at 3 miles per hour in 10 sec. Find the
length of the train.
7. The whole time taken by a train 150 yd. long in crossing
a bridge at the rate of 25 mi. per hour was 20 sec Find the
length of the bridge.
8. If a train 88 vd. long overtakes a person walking at the
rate of 4 miles per hour and passes him in 10 sec, what is the
rate of the train in miles per hour?
9. If a train 110 yd. long meets a person walking on the
railway at the rate of 5 miles per hour, and passes him in 8
sec, what is the rate of the train in miles per hour?
10. A train 352 ft. long overtakes a man going in the same
direction at 4 mi. per hour and ])asses him in 15 sec Shortly
after it passes a man walking in the opposite direction in 9
sec. At what rate per hour is the second man walking?
11. A train 88 yd. long takes 10 sec to cross a bridge 44 yd.
long. At this rate, how many hours will it take the train to
go 180 miles?
REVIEW EXERCISES FOR THIRD CLASS.
185
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;
VI. REVIEW EXERCISES FOR THIRD CLASS.
EXtRCISE CCLXXXVI.
1. Two pieces of elotli of the wjuno length cost $r);{.G4 iiml
!}!(J9.lL!, respectively. Tlu* price of the hist was !)!i.4y u yiucl.
What wjis the price of second per yard?
2. Three l)iif,'s couttiiued 025 nuts. The first bag contained 25
more than the other two together; and the second contained 5U
more than the third bag. How many nuts are there in each
bag?
3. A man living on $700 a year for 6 years finds that he is
exceeding his income and then lives on $500 a year for 4 years
and finds he is just out of debt. What was his income?
4. How often can £3 17s. lOid. be subtracted from £288 4s.
lid., and what is the last remainder?
5. A boy had the same num])er of five, ten, and twentyfive
cent pieces, and had $6.80 in all. How many pieces of each
kind had the boy?
<). Find the largest number that will divide '{65, 540, and
1140, leaving as remainders 20, 17, and 13, respectively.
7. A, B and C have JC53 Os. 8d. among them. B and C have
£40 2s. 8d. ; A and C have £29 10s. How much has C?
8. How many l)oards 15 ft. long will build a straight fence,
(i boards high, around a field 120 rods long and 30 rods wide?
9. A man ploughs a furrow 8 in. wide the whole length of a
field in 6 minutes. How many hours will be required to plough
a ridge 16 ft. wide?
10. A farmer's wife sold 8 pairs of ducks at 75 ct. a pair and
13 pairs of chickens at 50 ct. a pair and received payment in
•sugar at 16 lb. for 1 dollar. How many pounds did she receive?
EXERCISE CCLXXXVII.
1. Into a veetangular cistern, the bottom of which is 8'ft. by
6 ft., water is pouring at the I'ate of 500 gal. per hour. How
long will it take to fill the cisl rn to a depth of 4 ft.?
2. Divide $25.75 among 10 men, 8 women, and 7 boys, giving
each man 50 ct. and each woman 25 ct. more than each boy.
3. A agrees to trade apples at $2.50 per bbl. for cloth at
$1.75 per yard. What is the least numbers of barrels that can
be exchanged for an integral number of yards?
4. The quotient is 7469; the divisor is 728, and the remainder
is 19. If the dividend remains unchanged what divisor would
give as quotient 5320 and remainder 411?
5. A and B ran a race. B had a start of 20 yd., but A ran
3 yd. while B ran 2 yd. and won by 5 yd.
the race?
Find the length of
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186
ARITHMETIC.
U. If 30 men do a piece of work in 24 diiys working 10 hours
a day, in bow many days would 25 men do the sunie piece of
work, working 9 hours a day?
7. The hind wheel of a wagon is 12 ft. in circumfereneo and
turns 7480 times in going from one village to another. How
many miles are the two villages apart if
8. A man bought 120 A. of land for $7800. He sold 30 A.,
gaining $10 per A. and 45 A. at a loss of $15 per A. At what
price per A. must he sell the rest to gain $300 in the whole
transaction if
9. A farmer sold 250 animals (sheep and pigs) for $1720.
He received $8 for each sheep and $6 for each pig. How many
were there of each If
10. The cost of 5 coats and 4 vests is $33.25, each coat
costing $1.25 more than a vest. Find the cost of a dozen coats.
EXERCISE CCLXXXVIII.
1. A bankrupt paid $2.50 out of $4 on onehalf his debts and
$2 out of $4 on the other half. Altogether he paid away $7200.
How much did he owe?
2. A man buys 128 gal. of wine at $1.70 per gal. How
much water must be added to gain $33.40 on the outlay by
selling the mixture at $1 per gallon?
3. A farmer sells 9 horses and 7 cows for $1200 and 6 horses
and 13 cows for the same sum. Find the price of 3 horses and
8 cows at the same price.
4. A person bought 475 apples at 5 for 6 ct. and another lot
at 8 for 5 ct. He paid altogether $10.20. How many of the
latter kind did he buy?
5. A divided a field 40 rods lon^j .md 24 rods wide into lots,
each 165 ft. long and 66 ft. wide and sold all for $1800. Whnt
price did A get for each lot?
6. A grocer bought 60 chests of tea weighing 40 lb. each for
£280 and sold it at 3s. 6d. per lb. How much did he gain?
7. What is the value of a pile of cord wood 60 ft. long, 8 ft.
wide and 8 ft. hi^h at $3.25 per cord?
8. Find the greatest unit of time by means of which 23 hr.
2 min. 36 sec. and 46 hr. 8 min. 55 sec. can both be expressed
as integers.
9. Divide $1078 among John, Thomas, and Henry, so that
John has 5 times as much as Thomas, and Thomas 8 times as
much as Henry.
10. A farmer planted 60 rows of corn. Each row had 240
hills and 5. hills produced one quart. The crop was sold for
$50.40. What was the price per bushel?
REVIEW EXERCISES FOR FOURTH CLASS.
187
EXERCISE CCLXXXIX.
1. Find the cost of o.irpetinf? a room 18 ft. loiij? iiml 13 ft. G
in. wide with carpet 2 ft. 3 in. wide at 75 et. a yard.
2. How much rope will it take to tie a box in the ordinary
way, tlie box beinj? 4 ft. by 3 ft. 2 in. by 2 ft. 8 in., allowing? 1
ft. G in. for the knot if
3. The average height of four boys is 4 ft. 7 in.; but if
the height of two others be considered, the average height of
the six will be 4 ft. 5 in. Find the average height of the other
two.
4. If 5 lemons are worth 4 oranges, and 2 oranges are worth
3 apples, find the price of 15 lemons when apples are worth 10
ct. per doz.
5. Find the smallest number of rails of equal length that can
be used without cutting to make a straight fence 6 rails high
around a rectangular lot 1089 ft. long and 1375 ft. wide.
G. The product of four consecutive numbers is 212520. Find
the uumbers.
7. On counting out the marbles in a bag by 3 at a time, or
by 4 at a time, or by 5 at a time there are always 2 over; but
on counting them 7 at a time there are none remaining. Find
the least number of marbles there could be in the bag.
8. At 25 et. per sq. yd. find the cost of painting a close
board fence G ft. high round a rectangular lot 40 yd. long and
20 yd. wide.
9. How many shingles 4 in. wide and 4 in. exposed to the
weather would be required for a roof 35 ft. by 25 ft. ?
10. A bale of hay is 3 ft. long, 2 ft. wide, and 18 in. thick.
A car 33 ft. long, 8 ft. wide, andG ft. high requires 2G400 lb.
to fill it. Find the weight of one bale?
VII. REVIEW EXERCISES FOR FOURTH CLASS.
EXERCISE CCXC.
1. A farmer bought two farms of 130 A. each for $19500.
What was the cost of an acre of each, if 2 A. in one are worth
3 A. in the other?
2. In going to town the front wheel of a carriage makes 2G4
turns moi^ than the hind one. If the former is 10 ft. and the
latter 12 ft. in circumference, how far does the carriage go?
3. A laborer is to receive 95 ct. and his board each day he
works, and pay 45 et. for each day he is idle, to pay for his
board. At the end of 100 working days he receives $7G.80.
How many days did he work?
188
ARITHMETIC.
4. Wliieli is tlie pjreater cost and by how much: — feiieiiig a
lot 40 Y(l. long and 30 yd. wide at 1.') ct. a foot or liuildint? a
wall< round it 4i ft. wide at 29 et. i)er sq. yd.?
5. A water tanlt without a lid, IG ft. 6 in. long, 7 ft. 6 in.
wide, and 7 ft. deep, is lined with zinc weigliing 8 lb. to tlie
square yard. Find the cost of the zinc at $4.90 per cwt.
6. Fourfifths of a merchant's goods were destroyed by fire;
I of the rest were injured. He sold the injured goods at 1 cost
for $840 and the uninjured for $300. There being no insurance,
find his loss by the fire.
7. A sum of money in 5 yr. at a certain rate per cent,
simple imprest amounts to $1131 and to $1339.80 in 9 yr. Find
the sum and the rate per cent.
8. A goldsmith manufactured 2 lb. 3 dwt. 8 gr. of gold into
rings, each containing 9 dwt. 16 gr. He sold them for $8.75
each. How much did he gain, gold being worth $18 per oz. ?
9. If 150 men can do a work in 40 days, how soon after
ccmmeneing the work must 60 additional men be employed so
that the work may be done in 34 days?
EXERCISE CCXCI.
1. A legacy of $4500 is left to three persons in the propor
tion of 2, 3, and 4. What should each receive after deducting
the legacy duty of 10 % ?
2. A man paid $2580 for 85 head (horses and cattle) , there
being t^i Jis many horses as cattle, and the cattle cost $8 less per
head than the horses. Find the cost of a horse.
3. A farmer sold a load of barley, weighing 3024 lb., when
barley was 46 ct. a bushel. In weighing the ,?rain, the dealer
made a mistake and took it as rye, and paid 55 ct. a bushel.
How much did the farmer gain or lose by the mistake?
4. A county map is drawn on a scale of 2 in. to the mile
and covers a surface 4 ft. by 2i ft. How many acres are there
in the county?
5. A rectangular field whose length is to its width as 4 to 3
contains 10 A. 268 sq. rd. Find its dimensions.
6. A bookseller sold a book 16% below cost. Had he
received 50 ct. more for it, his gain would have been 4%.
Find the cost of the book.
7. A stone wall, under a building 24 ft. longer than wide,
contains 8550 eu. ft. This wall is 10 ft. high and 2i ft. thick.
Find the dimensions of the building.
8. A father gave his son $128.50. This was 66%'of what
^he father had left. How much money had the father at first?
9. The amount of a note for 1 yr. 9 mo. at 6% simple
interest was $391.17. What was the principal?
( I
REVIEW EXERCISES FOR FOURTH CLASS.
189
10. A farmer agreed to pny his hired man 8 sheep and $180
for one year's work. The man quit work at the end of 7 mo.,
receiving the sheep and $80 as a fair settlement. Find the
value of each sheep.
EXERCISE CCXCII.
1. A and B earn $4.02 in 7 days; A and C, $7 in 10 days;
and B and C, $8.36 in 11 days. How much did each earn per day?
2. A hare is 80 leaps before a hound, and takes 4 leaps while
the hound takes 2, but 2 of the hound's leaps equal 5 of the
hare's. How many leaps will the hound take to catch the hare?
3. A sells goods to B at a gain of 12%, and B sells the same
goods to C at a gain of 15%. C paid $3155.60 for the goods.
What did the goods cost A?
4. Find the time a train 184 yd. long, running 21 mi. per
hour, will take to pass another on a parallel track 135 yd. long,
going in the same direction at the rate of 16 mi. per hour.
5. A hor^e and lot are together worth $4750. Twice the
value of the house is equal to 17 times the value of the lot.
Find the value of the lot.
6. If a grain dealer by selling 416 bu. of oats for $277i
loses 10%, at what rate per bu. should he have sold the oats to
gain 8%?
7. A man mowing giass travelled 4 mi. per hour. In 72
min. he cut 2i, A. What width did the machine cut?
8. I bought .2000 lb. of sugar, part at 7 et. and part at 10
ct. per lb. Had I bought all at 8 et. per lb., it would have
cost $13 less than it did. How many pounds of each kind did
I buy?
9. The area of a rectangular field whose breadth is i of its
length is 15376 sq. yd. Find its dimensions.
10. A hall 60 ft. long is to be carpeted. It is found that by
stretching the carpet lengthwise any one of 4 pieces — f yd.,
1 yd., li yd. and li yd. wide respectively — will exactly fit the
hall without cutting anything from th« width of the carpet.
Find the cost of carpeting the hall with the narrowest piece at
$1.10 per yard.
EXERCISE CCXCIII.
1. A train going 30 mi. an hour passes a man going in the
same direction at 3 mi. an hour in 10 sec. How long is the
train?
2. A and B enter into partnership. A puts in $4900 rnd B
$1400. B receives 6% of all the profits for management. The
rest is divided in proportion to the capital invested. What is
A's share of $450 profit?
I
190
ARITHMETIC.
3. In a long division example the dividend is 1768479, and
the successive remainders from the first to the last are 127, 180,
166, 28. Find the divisor and the quotient.
4. What is the prime cost of a yard of clotli, if selling it at
1% gain brings $1 more than selling it at 11% loss?
5. Twentyfive animals (cows and calves) cost $427.75, but,
if the number of cows and calves is reversed, they would cost
$303.50. A calf being worth $5.75, find the cost of a cow.
6. A and B rr . a two mile race; A wins. If B had run one
third faster, he would have won by 22 yd. Compare their rates
of running.
7. A can dig 36 postholes in a day; B, 32; and C, 30.
What is the smallest number of postholes that will furnish an
exact number of days' labor for each working alone, for any
two, or for all three working together?
8. A, B and C together invest $4860 in wheat. A invests
twice as much as B, and C invests twice as much as A and B
together. They gain 40% on their investment. What is each
person's share of the gain?
9. If my income of $1150 is reduced by taxation to $1063.76,
what is the income of another who has $1554 left after paying
his taxes?
10. A sold two city lots at the same price. On one he gained
20% and on the other he lost 20%. He lost $30 by the transac
tion. Find the cost of each lot.
VIII. REVIEW EXERCISES FOR FIFTH CLASS.
EXERCISE CCXCIV.
1. What is the least number by which 2016 must be multi
plied to become a perfect cube? What will be the cube root of
this cube?
2. Divide $1650 into two parts such that the simple interest
on one of them, at 4i% for 3 yr., would be equal to that on
tae other for 2i yr. at 5 % .
3. A man bought a horse and sold him at 10% loss. If he
had received $45 more for it, he would have gained 12i%.
What did the horse cost?
. ,. ... (.201 .102)'^
4. Simplify ^201)^' (102)^"
5. A marked goods at an advance of 40%, but in selling
them a false b.alauce was used, by means of which he gave 14
oz. to the pound. His total gain being $240, find the cost of
the goods.
REVIEW EXERCISES FOR FIFTH CLASS.
191
6. The amount of a sum for a certain time at 8% is $336,
and at 7i % for the same time it is $330. Find the sum and
the time.
7. A solid sphere of iron 12 in. in diameter is melted and
oast into a hollow cylinder 6i in. in radius and 8 in. long. Find
the thickness of the iron in the cylinder.
8. A hare takes 4 leaps to 3 of a greyhound; but 2 of the
hound's are equivalent to 3 of the hare's. The hare has a start
of .'iO of its own leaps. How many leaps must the hound take
to catch the hare?
9. A clock loses at the rate of 8i see. per hour when the
fire is alight and gains at the rate of 5r5 sec. per hour when
the fire is not burning. Upon the whole it neither gains nor
loses each day. How long in the 24 hours is the fire burning?
10. A walks a distance at a certain rat'*. If he had walked
1 mi. per hour faster, his time would have been f of what it
was. If he had walked 1 mi. per hour slower, he would have
taken 4 hours longer than he did. Find the distance.
EXERCISE CCXCV.
1. A man buys wine at $3.20 per gallon; 20% leaks away.
At what price per gallon must he sell the remainder to make
20% on the outlay?
2. A's income is derived from the proceeds of $227.5 at a
certain rate per cent, and $2700 at 1% more than the former
rate. His total income being $425, find the rates.
3. A grocer has two kinds of tea. By selling the first kind
at 45 ct. a pound, he gains 25%, and by selling the second at
42 et. per pound he gains 40%. If he mixes them in equal
quantities and sells the mixture at 43i ct. per pound, find his
gain per cent.
4. A shipment of wheat was insured at 2#% to cover three
fourths of its value. The premium was $44.07. The wheat
being worth 80 ct. per bushel, find the number of bushels there
were in the shipment.
5. In a constituency having 3200 voters, A received 23 votes
for every 25 votes received by B, and was defeated by 124 votes.
How many did not vote?
6. How fast is a locomotive going when the small wheel,
which is 4 ft. in diameter, makes 180 revolutions per minute
more than the large wheel, which is 7 ft. in diameter?
7. Ten men can do a work in a certain time, but 7 men
would require the same time and 7 days more to do the same
work. How long did it take the ten men to do it?
.1'
it'
192
ARITHMETIC.
8. There is a j?ras8 plot in the form of a ciicle 145 yd. in
rrjIiiiH and a carriage drive round the outside of it 4 yd. wide,
llnvv many cu. yd. of gravel will be required to cover the drive
to the depth of 8 inches?
9. A can do a piece of work in 10 days; B, in 12 days; and
(% in 15 days. They all begin to work together, but C stops
2 days and B li days before the work is finished. A finishes
the work. How long does he work?
10. Divide $2699.10 among A, B, C and D, so that A may
have 12% more than B; B, lOVo more than C; and C, 5% more
than D.
EXERCISE CCXCVI.
1. A farmer raised 3105 bu. of oats in 2 years. He had 30%
more the first year than the second year. How many more
bushels had he the first than the second year?
2. The breadth of a room is half as much again as the
height, and the length is twice the height. It costs $33.60 to
paint the walls at 30 ct. per sq. yd. Find the dimensions of
t''t» room.
.".. Iron weighs 7.112 times as much as water. How many
i" = ft. are there in a ton of iron?
4. A person holding $5000 of 5% stock and $7600 of 6%
stock sold the first at 110 and the second at 115, and reinvested
the proceeds in 4*% stock at 89. Find the gain or loss in his
income?
5. How many oranges must a boy buy and sell to make a
profit of $12, if le buys at the rate of 5 for 3 et. and sells at
the rate of 4 for 3 ct. ?
6. The price cif gold is £3 17s. lOid. per oz. A compound
of gold and silver, weighing 18 lb., is worth £637 78.; but if
the proportions r^re reversed, it would be worth £259 Is. Find
the value of silver per oz. and the proportion of gold and silver.
7. A drover bought sheep at a certain price per head. He
sold I at a gain of 20%, n, at a gain of 15% and the rest at a
loss of 10%, and gained, on the whole $217. How much did he
pay for the sheep?
8. A rows 30 mi. and back in 12 hours, and he finds he can
row 5 mi. with e stream in the same time as 3 mi. against it.
Find the rate ot the stream.
9. If the time past 3 p.m. is to the time past 1 a.m. as 4 to
1, find the time.
10. The sides of a rectangle are in proportion of 5 to 6, and
it contains I A. Find the cost of painting a close board fence
6 ft. high around it at 45 ct. per sq. yd.
RRVIKW KXKR(MSK8 FOR FIFTH CLASS.
193
5 yd. in
d. wide.
;he drive
ays; aud
; stops
k. ftuishes
it A may
5% more
B had 30%
lany more
lin as the
A, $33.60 to
aensions of
How many
7600 o£ 6%
re invested
loss in his
to make a
md sells at
compound
7s. ; but if
l9 Is. Find
and silver.
head. He
\\e rest at a
luch did he
Ifinds he can
against it.
la.m. as 4 to
5 to 6, and
Iboard fence
EXERCISE CCXCVII.
1. Find the area of ii sciiiuro inscribed in a circle 48 ft. in
diameter.
2. Tlie n«'t proceeds of the sain of 1000 tons of hay at $20 a
ton after deducting !t!875 for freiglit, etc., were $18325. What
rate of commission was charged?
3. From a cask of wine onefourth is drawn off, and the cfi' '<
is filled up with wat« r: onefourth of the mixture is then dra
off, and tlie cask again lilled up with water; after this process
has been repeated four times altogether, what fraction of the
original quantity of wine will be left in the cask?
4. A wall whose height is i of its length, and whose thick
ness is i of its height, co.itains 625630/4 eu. in. Find its
thickness.
5. Express as a vulgar fraction, and also as a decimal, the
difference between 25.135 X 13aT and 61.375 X b^.
6. Calculate the ratio between the values of gold and silver,
if from 2 lb. of standard gold are coined 89 guineas, and from
1 lb. of standard silver GO shillings, yi of standard gold being
alloy, and A of standard silver.
7. A grocer bought 1500 lb. of tea and sold 300 lb. at 45 et.
a pound, making 12i% profit. Find the price at which he
must sell the remainder per pound to gain 20% on his outlay.
8. A merchant bought 240 yd. of silk. He sold i of it at
2')% gain; i of it at 20% gain; rnd tlie remainder at 15% loss,
and received $800 in all. How much did the silk cost him per
yard ?
9. How mtich less will it cost to fence a square field of 40
acres than a rectangular one of the same size, 90 rods long, at 81
ct. a rod?
10. By selling $1000 of 3 per cent, stock at 95 and reinvesting
the proceeds I increase my income $10 a year. If the dividend
on the new investment is at the rate of 8%, what is the price
of the stock?
EXERCISE CCXCVIII.
1. A rectangulsr field contains 27 A. 48 \\q. rd., and 13 times
its length is equal to 21 times. its breadth. How many rods of
fencing will be required to enclose it?
2. A buys $18300 of 3% stock at 75 and pays for it with
money loaned at 8% per annum. At the end of a year he sells
out and his gain is $122. At what price did he sell the stock?
3. A bought cloth at 20 ct. and the same quantity at 30 ct.
per yard. He sold all at the same price per yard so as to gain
as much per cent, on tlie one kind as he lost on the other kind.
Find the selling price and the total gain or loss per cent.
194
ARITHMETIC.
4. The area of the two larger walls of a room is 810 sq. ft.;
of the two smaller, 024 sq. it.; and of the floor, 884 sq. ft.
Find the dimensions of the room.
5. The road between A and B, distant 15 miles, poes over a
hill whose summit is 15 miles from A. Two men set ont at the
same time from A and B, the former going 4 miles per hour up
hill and 5i down, the latter 3i uj) and 4i down. IIow far will
tile slower have to go when the faster reaches B?
0. A pond A. in area is frozen over to a dej>th in. If a
cubic fcot of water weighs 1000 oz. and ice is nt »^ heavy as
water, find how many tons of ice there are on the pond.
7. A man bought 03 sheep. He sold J of them at 15% gain;
y of them at 50% gain; and the rest at 25% loss. His total
gain was $15.40. How much did he pay for the sheep?
8. A's present age is to B's as 9 is to 5, and 23 years ago
the proportion was 10 to 3. Find the present age of each.
9. If gold can be beaten out so thin that a grain will form a
leaf of 50 sq. in., how many of these leaves will be required to
make up the thickness of a sheet of paper, the weight of a cu.
ft. of gold being 1215 lb. and 400 sheets of paper being 1 in.
thick?
10. If 5 men, 4 women, and 3 boys can complete a piece of
work in 150 days, what time would it take 9 men, 15 women
and 18 boys to do twice as much, the parts done by each in the
same time being as 3, 2, and 1, respectively.
EXERCISE CCXCIX.
1. The perimeter of a serai'jireular flowerbed is 00 ft. How
many plants will it contain, allowing 1 sq. ft. to each plant?
2. A sold a farm to B at 15% Joss; B sold it to C at 10%
loss; and C sold it to D for $3786.75 at 10% gain. How much
did the farm cost A?
3. A can row 4i miles an hour in still water and he finds he
can row a distance down stream in onethird of the time he can
row back again. Find the rate of the stream per hour.
4. How much tea at 48 et. a pound must be mixed with tea
at 60 ct. a pound to form a mixture of 180 lb. in which the
value of the different teas will be equal?
5. A grocer buys coffee at $34 per ewt.
per ewt. He mixes them in proportion of 5
lb. of coffee and sells the mixture to gain i of the cost.
much does he charge i)er pound?
6. A town levied a tax for a bridge which cost $2520.
Allowing 4% for the cost of collection, wliat sum wa^j levied?
and chicory at $10
lb. of chicory to 7
How
REVIKW EXERCISES FOB FIFTH CLASS.
195
) sq. ft. ;
4 sq. ft.
es over n
ut at the
V hoiiv up
V fur will
in. If a
, heavy as
id.
].f>% gain;
His total
p?
yoawi ago
each.
will form a
required to
lit of a cu.
being 1 iu.
a piece of
15 women
each in the
60 ft. How
eh plant?
,0 C at 10%
•How much
. he finds he
time he can
_our.
xed with tea
u which the
liicory at $10
chicory to 7
cost. How
eost $2520.
;a,.i levied?
7. A merchant's debts amonntrd to $5000. Onolialf of liis
stock was sold at '.i\i7c discount and tin* rest at 12i% discount.
His creditors received G2i% of what was owing them. Find the
value of the goods.
8. White cedar weiglis 20 lb. to the cu. foot, while a cu. ft.
of water weighs (iiii 11). A kind of iron is 7.492 times as heavy
as water. Wliat thickness of iron will be of the same weight as
a 9 in. plank of white cedar, their lengths being equal?
9. A cube contains n.']90025 en. in. Find to four places of
decimals the differeiice between the lengths of the edge and of
the diagonal.
10. Two men formed a partnership. A put in $10000, and B
$10000. They lost $2080 and their capitals were reduced
accordingly. They then took in (! as partner .ith $18000.
They gained $4716. How much should each receive?
EXERCISE CCC.
1. A merchant mixes wine at $'i a dozen with wine at $3.60
a dozen. He sells the mixture at $4.32 a dozen at a gain of
26%. In what proportions are the two kinds mixed?
2. It is between 4 and 5 and the hands of a watch form with
a line joining their extremities an isosceles triangle, each of
whose angles at the base is half the third angle. What is the
time?
3. I bought an article and sold it at a loss of 20%. If the
cost had been 10% less and the selling price $13 more, I would
have gained 25%. Find the cost.
4. The expense of carpeting a room was $45. If the breadth
were 1 yd. less the cost would be $36. Find the breadth.
5. Seven pounds of tea being mixed with 4 lb. of a better
quality the mixture is worth 88 ct. per pound. What is the
value of each kind, the difference of values being 22 et. per
pound?
6. I buy two houses for $5850 and sell one at a loss of 8%
and the other at a gain of 10% and neither gain nor lose on the
whole transaction. How much did each house eost?
7. The sides of two squares are 2321 ft. and 23i ft.
respectively. Find the side of a square whose area is equal to
the sum of the areas of the other two squares.
8. If 175 men and 240 boys do in 1330 days the same
amount of work as 603 men nnd 1005 boys in 350 days, compare
the average daily work done by each man with that done by
each boy.
ill
190
AUITIIMKTIC.
!>, Ill tin* ('«'iitrt» of n room 121 ft. sqmirc, thero is ii sqiiiire
<'iir»«*t. 'V\w rt'Ht of the fIor>r is covon'd with oilcloth. The
oirpct mill thf oilclotli post rcspcctivM'Iy $.40 and IMi ct. p«'r
H(. .v<l. ; and tln' wliolf cost of carpet iiiul oilcloth is .fJtO.CiO.
FimI the width of the oil cloth.
10. Tliicc nicrchaiits enter into partnership. I'he fiist, A,
jmts in $W\{) for (5 months; the second, li, a certain snm for 12
months; and the third, (', ff<)40 for ii certain time when the
accounts vver* settled. A leceived .$1200 for his stock and
j.roHt, H $2400 for his, and C $1040 for his. What was H's
Htock and (''s time?
EXERCISE CCCI.
1. If tlie telcfjraph poles at the side of a railway are GO yd.
apart, what fraction of the true speed will the error bo in
rt'ckoninj; the speed of the train to be twice as many miles ptr
hour as the train passes poles per minute.
2. A and B f?o to nnirket and biiy tofjfether 80 lb. of meat at
10 ct. per lb. A takes HO lb. and B the rest. Upon examin
ation, they a{?ree that A's meat is worth i ct. per lb. more than
B's. How nnich must each pay for the meat.
;{. A merchant borrowed $1300 at .3^% and at the same time
$1790 at ^i7r and j)aid both loans when the sum of ])rincipal
and interest was $3202.50. How long did he keep the money?
4. Two circular gold plates each 1 in. thick and (5 in. and 8
in. in diameter, respectively, are melted and formed into one
j)iate also 1 in. thick. Find its diameter.
5. A merchant sold 400 yd. of cloth,
it he gained 10% and r>% on the remainder.
S% gain, he would have made $21 more.
l)er yard.
C. Find the cost price of 3 per cent, stocks, so that if $3(5000
be invested, the income may be $1140 after paying an income
tax of 5 ct. on the dollar.
7. If James can do S^ of a work in 8 hr. and John can do f
of the remainder in 2 hr. and Charles can finish it in 40
minutes. * What time would all take working together?
8. A piece of metal weighing 1410 lb. has been formed by
compounding three metals in quantities which, by measure, are
as 5, 3, 2; but the weights of equal volumes of them would be
as 7, 11, 13. What weiglitof each of the component metals has
been used?
9. Divide $5600 into 4 parts, sucli that the respective
interests on the 1st at 2^ per cent, for 4 months, the 2nd at 3
per cent, for 4 months, the 3rd at 4 per cent, for 5 months, and
the 4th at 5 per cent, for G months may be the .same.
On one fourth of
Had he sold it at
Find the cost price
REVIKW KXKRCI8ER FOR FIFTH 0LA8S.
197
HOtiare
» ct. »»'r
first, A,
11 for VI
rhim the
:()('k imd
was H'H
ro GO yd.
•or bo iu
miles ptr
f meat at
II examin
more tlian
same time
f principal
he money?
■) in. and 8
into one
fonrth of
sold it at
cost price
it
it $:U)000
an income
n can do I
it in 40
f?
formed by
easuve, are
1^ ^^•ould be
; metals has
respective
llie 2nd at 3
iionths, and
10. In a niih' rjH'c, A starts at U70 paccH of 48 inohes ])er
minute, and li 'MO paces of 44 inclies per minute. After 4
minut«'s, H (uickeiiM his pace to II'JO. Siipposiiifi; A eontinueH
at his (irij^iniil rate. VVIiich wins, l»y how much, and in what
time?
EXERCISE CCCII.
1. I'Mnd the dilTerence between the areii of u triaiif^N' wliose
sides are IDI ft., 0 ft. and 44 ft., respectively, aiul that of an
e(iuilate.'al triangle of the same perimeter.
2. Divide $;r)GO among A, B, (', and 1), giving A 'M% of
D's sinire; C, '.M% of A's share; and B as much as A and C
toj^ether.
:j. A sold a lot which cost $1875 and gained Gi% of the
selling price. He sold another which cost $1200 at H% gain on
the cost price. His whole gain was $221. Find the selling
price of each.
4. A farmer holds two mortgages for $14000 and $34000
rt;spec(ively, which bring in $2000 interest each year. 'V\w
rate on the latter is i% higher than that on the former. Find
the rates.
ii A buys tea at '){)c. per pound and the same quantity of a
l»etter quality. He mixes them and selfs the mixture at GGc.
l)er pound and thus gains 20% on his outlay. Find the price
of the second kind of tea.
G. After a certain number of men had been employed on a
piece of work 24 days and had half finished it, IG men more
were set on and the remaining half was completed in 16 days.
How many men were employed at first?
7. A sets out to walk to a town at 3 miles an hour; B on a
hicycle sets out with him at 12 miles an hour. On reaching the
town B rests half an hour, and after riding 40 minutes on the
return journey meets A. How far is the town distant from the
starting point?
8. A banker increased his capital 10% per annum and in 4
years, the interest for one year at 4% on the capital he then
had was $3GG0.25. Find his original capital.
9. The minutehand of a town clock is 9 feet long. Find
the time after twelve when its extremity has moved over 11 ft.
on the dial.
10. If $5 be allowed as discount off a bill of $125 for a certain
time, what should be the discount if the bill had twice as long
to run, (1) at simple interest, (2) at compound interest?
ANSWERS.
10
5.
10
10
4.
9.
4.
9.
4.
9.
10
5.
9.
6.
G.
Ex. IX. 1. 49 et. S. $47. 3. 209 bu. 4. 87 mi. 5. 124 mi.
945769. 7. 969 yd. 8. 1367 mi. 9. 786. 10. 1668 pages.
Ex. XIV. 1. 303. 2. 354 A. 3. 272 marMes. 4. 158 mi.
$7353. 6. 1273 animals. 7. 885 trees. 6. MCXVII. .9.46391.
. 226.
Ex. XV. 1. 40 marbles. ^. $45. 3. 870 pages. 4. 300 mi.
1000 et. G. $1900. 7. $270. S. 98 et. 9. 208 mi. i^. $7856.
Ex. XVI. 1. 9054. 2. $9000. 5. 814 baskets. 4. 106 ft.
170 ct. 6. $129. 7. 144 et. 8. 500 ct. 5. 160 A.
. 90 sheep ; $389.
Ex. XVII. 1. $999:! . 2. $350. 3. 197795. 4. $52948276.
3617 sheep. 6. 510 mi. 7. $100. ^. $120. 9. 195 et.
. 3666.
Ex. XVIII. 1. 76 mi. 2. 1159620. 3. $45000. •
1171460 oranges. 5. $3811. 6. 78. 7. $31839. ^. $12085.
$33820. 10. $33020.
Ex. XIX. 1. 1990977. 2. 72720, 147720. 3. $18565.
154 yd. 5. 31136. 6. 131 et. 7. 365 days. 5. 12413.
1832. 10. $140900.
Ex. XXI. I.Ul cows. ;?. 40 chickens. 5. $23.
113 pages. 5. 272 gal. 6. $150. 7. 254bbl. ,5. 1232 sheep.
433 A. 10. $1200.
Ex. XXVII. 1. 74. 2. 286032. 3. 6319267. 4. 32299.
676. 6. 2714. 7. 526084. 8. 2578. 9. 6667315. 10. 141998.
Ex. XXVIII. ^. 89 sheep. ^.$257. 5. $468. '^. 24168 bu.
$1779. 6. $2168. 7. $49. .9. 1432 mi. 9. 162482.
. 158677 cows.
Ex. XXIX. i. $807. ^.39 marbles. 5. 13999 men. 4. $.3816.
351636 min. 6. 439 pages. 7. $21506957, 8. 6300836 ft.
117993. 10. 83849884 lb.
Ex. XXX. 1. 27 ct. 2. 288. 3. $11993. 4. $35. 5. 1642.
89 yr. 7. 983 yr. .?. 3688 it. f^. 1325 votes. iO. 3969356.
Ex. XXXI. Z. 45. ^.$198. '?. 215bu. 4. $3250. 5. $32.
$107950, 7. $7178. 8. 5mi.,13V7'1. 9. 225 mi, 10. 2210.
Ex. XXXII. i. $245. 2.1950. 3. Ut7 A. 4. 45 yr., 38 yr.
Loss, $2410. 6. Jas. 31, Jno. 26. 7. 4o A. 8. 70 da.
18 marbles. 10. 211V 1, 14896, 18691.
198
ANSWERS.
199
Ex. XXXIII. 1. 6746. 2. 129G8. 5. 1606. 4. 2658225.
5. 6529. 6. 925358. 7. 2534. 8. 73699. 9. 2155. i^A 8453.
i/. 23718. 12. 74128.
Ex. XXXIX. 1. 1200 mi. ^. $195625. 3. 607488 oz.
4. 1632000 mi. 6. 63168 et. 6. 702 trees. 7. 2920 mi.
8. 95424 hills. 9. $130455. 10. 75087 lemons.
Ex. XL. 1. 1530000 ct. 2. 32076 yd. 3. 2368 nails.
4. 62640 mi. 6. 171216 ia. 6. 383600 ct. 7. 482040 ct.
8. $204000. 9. 525600 min. 10. 5285484 papers.
Ex. XLI. 1. 43050. 2. $2241190. 3. $5. 4. 553 ct.
5. $516. 6'. Gain, $32. 7. 94720 ct. *. 2472 ct. 9. 1037 mi.
i^. Loss, $83.
Ex.XLII. i. 172484. ^.233189. 5.1062347. 4.67419143.
5. 15403465. 6. 2016978981. 7. 1123193115. 8. 63096033.
9. 50700. 10. 14254.
Ex. XLIII. 1. 55986805. 2. 1516. 3. 62985. 4. 9989001.
5. 7051253. 6. $30613. 7. 57415 ct. 8. 15725910 A.
9. 703 stocks, 8436 sheaves. 10. 99693084.
Ex. XLVII. 1. 16, 28, 44, 88 yd. 2. $121. 3. $75.
4. 329 bbl. 5. 142 lb. 6. 524 lb. 7. 15065 lb. 8. 532 pk.
9. $7625. iO. 379 t.
Ex. XLVIII. 7. 480 mi. ^. 1760 yd. 5. $13. 4. 13 hr.
5. 30 ct. 6. $32. 7. 57 persons. *. 362 mi.
U. 11625000 mi. a min. 10. 5642 pence.
Ex.LII. i. 6540. ^.391525. 5.489673. 4.150287. 5.481.
6'. 4798. 7. 61. 8. 378. 9. 9605. 10. 228689.
Ex. Llll. 1. 134 da. 2. $2003. 5. 2640. 4. 29603 lb.
5. $658. 6. 160sq. rd. 7. 327 mi. *. 275 persons. 9.168 1b.
10. 9 da.
Ex. LIV. 1. 179 mi. 2. 96934 yd. 5. 19 mi. 4. 64 bu.
5. 51 bu. 6. 245 bu. 7. 144. 5. 75 c. yd. 9. 207 bbl.
^<?. 704 cd.
Ex. LV. 1. 119. 2. 910. 5. 83. 4. 1331424. 5. 45. C. 27.
7. 14839. .?. 811. 9. 41. iO. 23849.
Ex. LVI. 7.7469. ^.23. 5.631229. 4.323603. 5.150321.
0. 66. 7. 245. ,?. 119025. 9. 767561. 20. 336.
Ex. LVII. 1. 840 steps. 2. 14668. 5. 2380277. 4. 1249.
5. 962556. 6. 179538. 7. 253440 in. ,S. 20063110804. .
9. 35643910. 10. 40160 ct.
Ex. LVIII. 1. 91132497. 2. $288. 3. 1145348. 4. 6029.
5, 30595. 6. 815. 7. 99368. .9. $254. i^. 1420799. 10. 224(1 ct.
Ex. LIX. 1. $336. ^. 18 et. 3. $5 each. 4. 2632 ct.
5. 200 ct. 6. $50. 7. $1620. 5. 485 sheep. 9. 11657397.
10. 8 yr.
v^
illl
200
AKITHMKTIC.
6'.
C.
6.
4.
8.
6.
5.
10
5.
9.
Ex. LX.
960 et.
1. 2552,
7. 72 et.
2. 18480 et.
8, $4800. !K
S. 95 et. 4. 42.
113. i<^. 203.
5. 10624.
Ex. LXI. i. 27 ct. 2. 10 ct. .■?. 21 mi. 4. $51. 5. $150.
30 yd. 7. 21 dresses. 8. 1728 bu. 9. 11 br. ^6*. 579000 lb.
Ex. LXII. i. 21da. ^. 95da. 5. 20 da. ^. 27 da. 5. 18da.
15 men. 7. 45 men. 8. 6 men. 0. 240 men. lU. 225 men.
Ex. LXMI. 1. 16, 20. 2. 20, 30. 3. 39 bu., 46 bu.
42 yd., 58 yd. 5. 44, 50. 6. 12 yr., 15 yr.
Ill votes, 129 votes. 5. 67 mi., 90 mi. lU
Ex. LXIV. 1. 8458. 2. 181357. 3. $3570.
$16. 6. 240 ct. 7. $6. *. $135. 9. 170.
Ex. LXV. 1. 33148. ^. 5607 ct. 3. 10 ct.
21450 et. 7. 19 gal. ^. $170. 9. 2046 et.
Ex. LXVI. 1. 120 pieces. ^. 159 pieces.
1800 ct. G. 11 stacks. 7. 302304 ct. ^.
17 hats.
Ex. LXVII. 1. 36405 bu. 2, 202878 ct.
Gain, $161. 6'. 38400 lb. 7. 5355 ct.
36 1b. 10. 1953.
Ex. LXVIII. 1. 1580712.
7. 19, 28.
192, 195.
4. 264 mi.
10. $46836.
4. 17. 5. 47 ct.
10. $468.
5. 9 et. 4. 21.
500 A. 9. 60 bu.
3. 23 lb. 4. $2028.
8. 4860 et., 90 et.
2. 148 mi. 5. $2277. 4. 1862 et.
5. $2688. 6. 150 boys. 7. $31104. 5. 86 A., $42. 9. 132 head.
10. 114 mi.
Ex. LXXIII. 1. £83 12s. 9d. ; £74 18s. lid.; £810 2s.
2. 74 cwt. 64 lb. 3oz. ; 127 t. ewt. 72 lb. ; 56 1. 1 ewt. 281b. 3 oz.
3. 82 yd. 1 ft. 9 in. ; 18 yd. 2 ft. 4 in. ; 58 yd. ft. 9 in.
4. 16 bu. 2 pk. 6 qt. ; 32 bu. 3 pk. 5 qt. 1 pt. ; 133 gal. 2 qt. 1 pt.
5. 38 gal. 3 qt. ; 32 da. 18 hr. 51 min. 56 sec. ; 7 wk. 4 da. 2 hr.
45 min. 3o sec.
£3 3s. 9d.: £19 9s. 3d.; 4 cwt. 22 lb. 10 oz.
6.
7.
S.
9.
10 t. 15 cwt. 63 lb. ; 3 yd. 1 ft. 5 in. ; 47 yd. 1 ft. 3
8 bu. 3 pk. 6 qt. ; 2 qt. 1 pt.
41 see. ; 1 wk. 5 da. 7 hr. 14 min.
yd. 18 e. ft. 1483 c.
in.; 51 e. yd
in.
45 see. ;
2 e. ft.
28 bu. 1 pk. 7 qt. ;
2 da. 18 hr. 8 min.
6° 50' 39".
10. 30° 53' 49"; 31 c.
1488 e. in.
Ex. LXXIV. 1. £66 9s. 2d. ; £454 14s. ; 136 ewt. 67 lb. 1 oz.
2. 61 1. 13 ewt. 31 lb. 8 oz. ; 211 yd. 2 ft. ; 967 yd. ft. 3 in.
3. 23 bu. pk. 1 qt. 1 pt. ; 95 bu. 3 pk. 2 qt. ; 34 gal. qt. 1 pt.
4. 187 gal. 2 qt.; I.i9 da. 11 hr. 33min. ; 46 da. 13 hr. 34 min. 56 sec.
5. 123° 53' 39"; 422° 17' 20"; 86 c. yd. 22 e. ft. 967 e. in.
6. £20 98. 5d. ; £5 3s. lid. ; 7 ewt. 85 lb. 14 oz.
7. 2 t. 10 cwt. 64 lb. 9 oz. ; 12 yd. 1 ft. 11 in. ; 9 yd. ft. 11 in.
8. 4 bu. 3 pk. 6 qt. 1 pt. ; 8bu. Opk. 1 gal. 1 qt. ; 15 gal. 2qt. Ipt.
.9. 4 gal. 1 qt. 1 pt. ; 164 hr. 26 min. 24 see.; 187 da. 21 hr.
55 min. 57 see.
10. 19° 15' 42"; 125° 9' 24"; 19 e. yd. 22 e. ft. 969 e. in.
ANSWERS.
201
Ex. LXXV. 1. 13; 32. 2. 400; 35. 3. 49; 42. 4. 77; 720.
.5. 325; 64. 6, 1856; 375. 7. 90; 35. 8. 2880; 156.
.'>. 78; 1680. 10. 1120; 303.
Ex. LXXVI. i. 4 ft. 8 in. ;g. 504pt. 5. 744hr. 4. 131,36oz.
5. £116 168. 3d. 6. £54 13s. 4d. 7. 11 ft. 6 in. ; 6 ft. 6 in.
S. 107° 40' 38". 9, 353. 10. $529.20.
Ex. LAXVII. i. $27. 2. 1301. 5. $104. 4. 3080 yd.
5. $164475. 6. 342 min. 7. 37 lb. 14 oz. ,S. 15 t. 9. 3000 gal.
10. $551760.
Ex. LXXVIII. i. 45t. ^. 60 spoons. 5.108. ^.15 pages.
5. 42 mi. 60 rd. 6. £110 10s. 7. £9 78. 6d. .S. $54.92. 9. 60 yd.
iO. 15 ct.
Ex. LXXIX. 1. 95 gal. 2 qt. 1 pt. ;g. 12 gal. 2 qt. 1 pt.
S. 278 bu. 36 lb. 4. 23 bu. 13 lb. 5. 5 min. 15 see. past 8.
6'. 4 lb. 4 oz. 16 dwt. 7. £3 17s. lO^d. 8. 288 lb. 9. $2919.
26*. 15 lb.
Ex. LXXX. 1. $44.70. 2. $153. 5. $8778.50. 4. $134.09.
5. $297.45. 6. $153.27. 7. $17.81. ^. $49.97. 9. $2.56.
i(?. $58.95.
Ex. LXXXI. 1. $290. ^. $2.79. S. $7.25. 4. $311.48.
.5. $221.81. 6. $5.32. 7. $21.80. 8. $42.70. 5. $13.94.
iO. $71.91. 11. $13.54.
Ex. LXXXII. 1. 10 in. ; 14 in. ; 22 in. ; 16 in. 2. 56 ft.
:?. $45. 4. 250 boards* 5. $3.40. 6. $700. 7. $256.
S. 14080 yd. 5. $1440. 10. 120 ft., 40 ft.
Ex. LXXXIII. 1. 1224 sq. ft.; 1216 sq. ft.; 5616 sq. ft.
^. 9 A. ; 10 A. ; 15 A. ; 42 A. ; 15 A. ; 19 A. S. 18 sq. ft.
4. 11 sq. yd. 5. 2304 sq. yd. 6. 200 sq. yd. 7. 112 sq. in.
8. 1056 sq. ft. 9. 2000 sq. ft. 10. 24 sq. ft.
Ex. LXXXIV. 1. 18 ft. 2. 54 ft. S. 40 rd. 4. $290.
0. $150. 6. 500. 7. 72 ft. 8. $940. i>. 360 ft. 10. $660.
Ex. LXXXV. 1. 40 yd. ,?. 60 yd. S. 32 yd. 4. 70 yd.
5. 196 yd. C. $57.60. ' 7. $13. 8. $130. y. $24. if. $12.60.
Ex. LXXXVI. ?. 6; 9. ^.8. .?. 16. ^.8. 5.10. 6.72 yd.
/'.48 yd. .§.$58.80. r>. $88. iC. $110.
Ex. LXXXVII. 7. 80 sq. yd. 2. 168 sq. yd. S. 224 sq. yd.
4. $9.12. 5. $40.02. 6. 82 sq. yd. ; 91 sq. yd. ' 7. $23.60 ; $26.20.
<V. $21; $23. 9. $:59; $41 ..'50. if. $70.20; $76.14.
Ex. LXXXVIII. 1. 160 yd. 2. 288 yd. .^. 448 yd. 4. 96 yd.
J. 348 yd. C. 82 yd. 7.396 yd. 5.144 yd. .^>. $5.85. if . $16.25.
Ex. LXXXIX. 1. 9 ft. ; 24 ft. ; 24 ft. ; 24 ft. ; 40 ft. ; 24 ft. ;
12 ft. 2. 3300 ft. S. 4200 ft. 4. 2220 ft. 5. 7680 ft.
6'. 768 ft. 7. 1650 ft. 8, 10000 ft. 9, $300, 10. $540.
202
ARITHMETIC.
Ex. XC. 1. 2880 c. ft. 2. 210 c. ft. 3. 60 c. yd.
4. 210 c. yd. 5. 4032 lb. 6. $40.50. 7. 13600 c. yd. v
8. 109 e. yd. 1 c. ft. 9. 2376 c. ft. 10. $1380.
Ex. XCI. 1. 30 cd. 2. 63 ed. 3. 30 cd. 4. $84. 6. $216.
6'. $75.25. 7. 80 ft. ,S. 5 ft. D. 8 ft. id?. 224 ft.
Ex. XCII. 1. 7 ft. 2. 11 ft. S. 24 ft. 4. 3 ft. 6. 112 ft.
6. 18144. 7. 192 ft. «. 40 ft. 9. 30 in. 10. 17 ft.
Ex. XCIII. 1. 32 ft. ^. $40.25. 3. $1080. 4. 1120 lb.
5. 32 t. 6. 48 t. 7. 1760 c. yd. 8. $792. 9. $1440. i<?. $72.
Ex. XCIV. 1. $32.64. 2. 220 yd. 5. 3600 sods. 4. 3 ft.
5. 90 c. ft. 6. 33 mi. 7. 15 ft. 5. 9 ft. 9. 36 8q.yd. 10. 5 ft.
Ex. XCV. 1. $17; $23. 2. 19 yd.; 30 yd. 3. 36; 48.
4. $48.75; $50.25. 5. $27000; $23000. r>. $215; $160.
7. $425; $371. 8. 271 mi.; 237 mi. 9. yu5; 361.
iO. $4500; $1250.
EX.XCVI. 7. $5120; $1280. ^. 2064 bu. ; 2311 bu. 5. $2726.
4. 361 yd.; 242 yd. 5. 297; 315. 6. 462; 534.
7. 24 ed. 39 e. ft. : 27 cd. 89 c. ft. 8. 9 A. 115 rd. ; 10 A. 45 id.
9. 4 mi. 275 rd. 10. 1 t. 8 ewt. ; 2 t.
Ex. XCVII. 1. 30; 90. 2. 254; 508. 3. 23 yd.; 92 yd.
4. $2450; $9800. 5. $75; $168. 6. $145; 462. 7. $3450; $10500.
5. 30 rd.; 90 rd. 9. $126. 10. 1240; 3737.
Ex. XCVIII. 1. $36; $48. ^. 60 bu. oats; 150 bu. peas.
3. 17. 4. $7800; $11700. 5. 275; 330. 6. $20; $40; $60.
7. 30; 45; 75. 8. 6. 9. $420; $140; $560.
10. $10940; $3020; $2450.
Ex. XCIX. 1. $8; $10; $13. 2. 170 lb.; 152 lb.; 134 lb.
3. 150 yd. ; 125 yd. ; 169 yd. 4. 2400 lb. ; 2200 lb. ; 1800 lb.
5. 127 lb.; 100 lb.; 175 lb. 6. 60 mi. ; 25 mi.; 40 mi.
7. 81 rd. ; 45 rd. ; 123 rd. 8. 256; 378; 452. 9. $450; $531 ; $612.
10. 180 bu. ; 233 bu. ; 160 bu. 11. 32 et.
12. 87 red, 94 blue, 105 white.
Ex. C. 1. 1975. 2. 3683. 3. 184019. 4. 7, 10, 9. 5. 14, 11.
6. 43, 16. 7. 14 lb. 8. 48 yr. 9. $119. 10. $7095.
Ex. CI. 1. 6.59 lb. 13 oz. 2. 256 mi. 160 rds. 3. $204.75.
4. $17.82. 5. 35 ewt. 25 lb. 6. 12 lb. 9 oz. 7. 33 mi. 96 rd.
8. 45. 9. $75. iO. 24 lb. 10 oz.
Ex. Cll. i. qj32. ;?. 7 ct. ,?. 15 carats. 4. 40 ct. 5. 6 et.
6. 200 bu. at 75 ct., 300 bu. at 70 ct. 7. 4 ft. 3 in. 8. 139 lb.
9. Is. 7d. 10. 4s. 9d.
Ex. cm. i. 272 lb., 2448 lb. ;g. $570940. 5. 2oz. 4. 35et.
5. 22 yr. 6. $25. 7. 7 ct. 8. •*6 ct. 5. $6.60. 10. 12 carats.
ii
A17SWERS.
203
[. 6. $216.
5. 112 ft.
1120 lb.
:0. 10. $72.
. 4. 3 ft.
yd. 10. 5 ft.
16 ; 48.
L60.
bu. 5. $2726.
; 10A.45rd.
. ; 92 yd.
3450; $10500.
bu. peas.
0; $60.
lb. ; 134 lb.
.. ; 1800 lb.
mi.
i; $531; $612.
9. 5. 14, 11.
3. $204.75.
mi. 96 rd.
et. 5. 6 ct.
8. 139 lb.
loz. 4. 35 ct.
10. 12 carats.
Ex. CIV. 1. 2, 2, 3; 2, 2, 2, 7; 2, 2, 3, 7; 2, 3, 5.
;?. 2, 2, 7, 7; 3, 7, 11; 2, 2, 3, 3, 7; 2, 2, 2, 2, 2, 2, 2, 3.
S. 2, 2, 3, 73; 2, 2, 3, 79; 2, 2, 263; 3, 353.
i. 3, 5, 73; 3, 7, 53; 7, 7, 23; 2, 2, 17, 17.
5. 2, 601; 2, 607; 2, 3, 7, 29; 5, 311. 6. 797, 821. 7. 1187.
^. 2543, 2521. 9. 2273, 2339, 2417. 10. 3119.
Ex. CV. 7. 2, 5; 5, 7. ^. 3, 7; 11, 13. 5. 7, 17; 2, 2, 3.
4. 2, 2; 2, 2, 3, 3, 3. 5. 2, 2; 5. ^. 30; 25; 275; 193; 443.
0. 2, 3, 5; 3, 5, 7; 5, 7, 11; 7, 11, 13; 11, 17, 19.
Ex. CVI. 1. 180. 2. 5. 5. 6. 4. 120. 5. 4. 6. 1008.
7. 2400. ^. 900 bu. 9. 75 yd. iO. 40 da.
Ex, evil. 1. 14; 16; 13. 2. 35; 46; 42. 3. 72; 32; 4.
4. 9; 16; 7. 5. 25; 42; 42. C. 9; 4; 73. 7. 73; 32; 11.
5. 9; 8; 13. 9. 32; 110; 14. iO. 91; 143; 323.
Ex. CVIII. 1. 14 ft. 2. 17 in. 3. 15. 4. 7 ft. 5. 2 ft. 3 in.
G. 13 ft. 7. 63 bu. 8. $1, $2, $5, $10, or $50. 9. $124.
10. 26880 rails.
Ex. CIX. i. 18; 7; 251. 2. 107, 311, 103. 3. 52, Prime, 601.
4. 31, 947, 233. 5. Prime, 47, 811. 6. 8, 616, 884.
7. 1188, 13, 13. 8. 46, 21, 9. 9. 897, 1323, 1429. 10. 315, 19.
Ex. ex. 1. 105; 3, 5, 7, 15, 21, 35, 105. 2. 2 da. 5 hr.
3. 1 mi. 37 yd. 4. 3 gal. 5. 117. 6. 29. 7. 25. 5. 19 men.
9. 7 oz. iO. 126.
Ex. eXI. 1. 24; 120; 120. 2. 75; 600; 720. ,
3. 315; 2652; 3705. 4. 360; 1260; 504. 5. 576; 600; 27720.
6. 1260; 8415; 16546530. 7. 10890; 17160; 205205.
8. 14280; 166320; 22770. 9. 1190595; 27945372; 885989.
10. 12018233514; 110250; 620310.
Ex. eXII. 1. 120. 2. 360. 3. 85085. 4. 6435. 5. 48.
6. 143. 7. 1526. 8. 90. 9. 120 ft. iO. 60 gal.
Ex. eXIII. 1. $20. '2. 141 lb. 5. 94 lb. 4. 30. 5. 30 mi.
6.365. 7.62,122,182. 5.600 bu. 9.13,14,15,16. i<?. 1008000 gr.
51
r).
7.
8.
9.
10
s.
5.
7.
.9.
Ex. CXV. 1. f; V; V; V 2 V; l
V;V; ff; %¥. 4. V; V; ¥; ^F
4JLQ . 508.23 3.S2T3 /? 8449. 4 41 8
30
^.
^9. 4^^
TT : ff; T5"; i^T n. ^s
519L. 68861. 36449. 19126
13 33 1. 44 3 99. 5.9881. 1.60689
1.102 2. 71041. 18 3 821. 101001
.2 8 114 1. 49880 3. 288161. 110 8 61
>
46664 .
84 80
Ex. exvii. i.
oi.
7,1!; 5; 51*4; 5A. 4. 9A;
5fA; 4iAA; 6,¥,; 13f:^. 6
34 ; 2.
(9 17. oB ,
^ 16M: 33i§; .35^.
4,^^a„; 260i; 163¥3 ;. 1,W:<
20h§; 9ff; Sfltf ; 342^2^^. 8. 334^3; lOOrg; lOeVy ; lO^^u
'>'^M; 45f gal.; 53f da. 50* lb
10. 7M mi. ; 24f? cd. ; 2lH yd. ; 63^ oz.
204
ARITHMETIC.
Ex. CXVIII. 1. $4i. 2. 92i bu. 3. 4i mi. i. 16.V lb
6. 321* bu. 6. Latter by ij^ lb. 7. li in.; 7 lb.; 25 oz.
S. 7i gal. y. 20 ft. ; 16 ft. 10.. $19.75.
Ex. CXXII. i. i; I; f; i. ^.
A; /s; I. 4. J; l;il; i^.
3.
0.
&.
10.
2.
3.
4.
5.
6.
7.
8.
9.
6 .
iVr;
i; /s; I
AV; 11;
I; "
^1;
i; I;
4. J;
5 3 9
8jir; ij.
13. 829
gCr; T33T
A;
3 .
6»
'y 8.89.
' • 9 ; jt;
i^.
A;
H;
5.
841 .
68T;
1 . 4
s; 1
1 .
3;
e;
II.
6 fi 3 9
T29 6 5.
V,
63
13 «.
i.
Ex. CXXIV.
12 6 2 4 3 6_ .
TSO", TS^T, T60 >
8 4 2 3 3,
liii lir, T¥4>
2 16 14 1 8 0,
2 5 3» 8Jf3» ^5?
8 0^
6 2,
]8 8ff,
J 8
TTf,
39 .
15
"A;
Tg
110 1 1
9 0, f f , I
42
¥8,
3 6.
■98»
8
A2
600
64
84
Tffff,
^/l 22
10. ^9,
4P
fl, fl, !l, II; il, H, h, It
" 102
HI,
Hi Mi
If.
86
18 10
3 0_ 14
— TTT?
4*0.. 8 8_
10 8 19 2
66 . log.
TffF; T?o,
rrff, rrs, yrs"
6. 3 .120 198. 3 2 4.
99, ff9 , ¥9"; 4 5(r,
f3
ITT, ¥^¥,
10
TUTT,
tVtt,
1 2 1
626
96
TSTF.
1 32
Tff"8,
84
39
3150
¥30".
9
Ex. CXXV.
i^.
I;
3
ro
i; h
5. 1: 2;
13.1 li.3
It; i2r«.
"30'
d.
36
1 4>
13
«?
91 25.
29'^
23f.
ft A. 5.
6.
6.
4'
mi.
/. •T2 0. <*• 35»
iZ Q 71
30 ^' S1)0«
9.
114/2 gal.
8. t\'
Ex. CXX^^I. .?. h ;
Ex. CXXVII. 4. 2; 1; 2.
7. IH; li^.; 2A<
^0. im;2A^o; iSt^
Ex. CCXIX. l.\\l. i
6. 24t. 7. 35i^. ,?. 17^0.
Ex. CXXX. 1
6. 178/„. 7. f.}.
Ex. CXXXIII.
& 'T kl. O
5 4' ' • 1 2 O • O
Ex. CXXXIV.
"2 8 , UjjHU.
14f; 23 ,i,; 20,^,
9. 17f; m?, 31M. i<?
Ex. CXXXV. /. m gal. i?. 13f yd.
5. $95f^. (;. l.>9^i}A. 7. $68f. .?. 13,\.
Ex. CXXXVI. 1. U; lA. 2. 3i; SH.
4. 6; 9/s. 5. 4; 5^1. 6. 1?; 34§. 7.
«. 2H; 7i^9. 9^ 10; llA. i<9. 8^; in^.
Ex. CXXXVII. i. 97M lb. ^. 16i gal.
6. 33i miles. 6. Gained $la%. 7. $23j.
iO. 37M yd.
iO.
6.
288, 1024.
1^9, 2r2.
2.>
O 119, oli. . ol^£
y. T»?; •isi; ^440.
1 73 4
1 S 36 • * •
10. 26i§.
llll^ lb
*3B0» ^'
O li!7
73
20
'8 ,
jlB
•Jl 1
•'1 3«
59
200'
7
^)»
23
60
. 4.
10. 132i mi
5
11
5.H
too
f; 1
4 ^^3 • 4. ft . 4
*• «>17 , ti 1 ? '^i
3'
7. 1
48 .
5 39 ,
OQ '3 .
5.
133
21
14 ,
17
144
13 . 10^5^1
84 » i"l 40
10A_.
1143 ,
6
13 ^A
Ol 7 . 12 63.
2T, 1288'
^. 2G*i; 2011 ;
lOy^.
T5
16i"
.9.
«4 mi.
6
Yb
a IQl.
<5 • I 1 O 1
111; 27H
4. m.
\'^n. lO.lQii}
4i.
3. 54 lb.
5.
$94H.
4.
9.
193H.
18i vd.
ANSWERS.
205
i lb.
oz.
6 3,
h
2i?t
40»
8, 1024.
5. jSTbo
7 3
«< i 2 O •
\2i mi
foo*
5.i
11
?oM; iOt^.
4. 30ft.
:?0. 164s}t.
4i.
4. 193H
9. 18i yd.
4.
H.
3.
0.
9.
.«.. . 1 1 . 1,1
1 > ■'■To > T'f'
Ex. CXL. i. 4; 9; 8. 2. tI; ^r; M. 5. t; H; M
m, i%. 6. A; f ; 4i. 6. ^; Gl; 5f. 7. h: I; H.
i'. 8; f; n. 10. h T%; 35.
Ex. CXLI, 1. l»Oi; 30fV; 5GA. ^. 30*: 42^; 72H.
42^; 5(iA; 15ttU. 4. i; t^; A. 5. 15; l(i*; 9*.
U; 11; 20. 7. U; 195; 16i. 5. 31i; 2A; 1.
$1^; $i; i>55 mi. 10. $558; 324 oz. ; 3 hi*.
Ex. CXLII. 1. $39i^. 2. $159lt. ^. 71c. 4. 8i mi.
$13i. 6. 12k^ bu. 7. $1733i. ^. 36 bu. 9. 47 A. i<?. $4.
Ex. CXLIII. 1. $1.68. 2. $30000. 5. 85 mi. 4. 37^^ ft.
385 mi. 6'. $105000. 7. 257. .S. 39100 men. 9. 210 pages.
$65600.
Ex. CXI IV. 1. 21; 24i. 2. 18; U. 3. 17ir; 7.
4. 3^1 U. 5. ,J\; 3^ G. 7; 20. 7. 10; 40. 8. 2f; tV.
y. 3i4; i. ic^. 1; 2i^.
Exc CXLV. 1. 1851 mi. 2. $1012. 5. 59. 4. 32H bu.
10
5. $170861. G. 10. 7,
37 im
^. $3125. 9. $43i. iO. Gain, $12.
Ex. CXLVI. 1. 14, 16, 15. 2. 36, 55, 44. 3. 8f, 14, 24f.
4. 171. 31i, 30f. 5. 4f, 5.^4, 6^. C. 6, 1^%, llf}.
7. 5i 4, 7i. .Sf. lao, laS, it 9. ih, 2i, If. ^ 3, i, U.
Ex. CXLVI I. 7.11;
TT>
111 <? 1 1 IB. S. y 1 1 11 1 a
2if, 12. 4.
^. 231, 16. 9.
h
^' 5) »■, T" i'" ii> It* k). G. 3i8» It, l54» 7. 2i, 6, 8.
^. 31, h, 3i. 5. 1§, t, 2. ii^. 7f, A, 5i.
Ex. CXLVIIi. .*. 37* yd. 2. 8 mi. .9. $26i. 4
5. 10 bags. G. 12i et. 7. 28 hr. 8. 8M. 9. 217i A.
10. 370i A. ii. 15i ct. 12. 32 da. 13. $3.60. i4. 20.
Ex. CXLIX. 1. 7^, 4. :^. 3J, 3f
r ol 2.5 /I 5. 4>a6 w jl _S,_
•'• "T, aaa. o. 7, sT. /• *1i> ii5»
Ex. CL. 1. 1^, 3i
i^' H(H «4« 'J' 10) *jT«
Ex. CLI. 7. 5f, i. 2. n, U.
/; 11 3 /; 1 14. /y 9I .jA o
Ex. CLII. /. 144§. 2. 2. 5.
17f mi.
2H.
1 1
6 O > 1 « •
2. 3i, 30. 3. 54, 66J. 4. 6,
7. i, 5i. ,?. lOA, f. 9. 5H, *.
IB.
1 ra> li. •^^ 2 1 » 3
13
7 1
7. 15i. V?. 43 1^
Ex. CLIII.
7. 101. ,?. U. 9
Ex. CLIV. 7.
9. h.
\h.
9. 11, 40. ' 10. 4,
I. 5. 7i. C. 4x^„.
2.
1 11
i. TJ.
^.
10.
4.
36 •
lUi. 1»
6
r3
3B ;
30 fj
T3» >*
4.
5. 6H.
2 1 6 J • iB
7_ . 21
T3i5 >
4, ^0. 5. 2.
10. f.
4^5 ; 60.
e. 35.
4. 2h ft.
5. 5tft.; 19. G. 60. 7. $112i. 8. 3S bu., 51 bags. 9. 59.
10. 6 da; A, 10 times; B, 15 times; C, 8 times.
Ex. CLV. 1. 16s., 3M., 4id. 2. 87i et., 80 ct., 75 ct.
3. 17 cwt. 50 lb., 7 lb. 8 oz., 14 oz.
4. 213 rd. 1 yd. 2 ft. 6 in., 3 yd. 2 in., 2 ft. 6 in,
5. 128 sq. rd., 22 sq. yd., 2 sq. ft. 117 sq. in.
y"'
2Qe
ARITHMKTIC.
6. 96 e. ft,, 11 e. ft., 432 c. in., r)04 c. in.
7. 2 pk. 1 gal., 1 K'll H qt., 'A (jt. if. 3 qt. 1 pt., li pt., 3i qt.
.'/. 4 da. 21 hr. 'Mi niin., 7 lir., 2.') min. 10. 40, 288 , 16'' 40".
Ex. CLVI. 1. 444.')4() in., 12(5744 in.
^. 1 mi. i:{l rd. 4 yd. 2 it. G in., 1 mi. 179 rd. 1 ft. 6 in.
3. 237600 in. luuOi in. 4. 31637628 aq. in., 3860136 sq. in.
5. 1 A. 52 Hq. rd. 19 sq. yd. 8 sq. ft., 2 A. 47 sq. rd. 9 sq. yd.
3 sq. ft. 36 »q. in.
6'. 16727040 sq. in., 131868 .sq. in. 7. 9600 lb., 3800 oz.
8. 14") rd. 2 yd. 1 ft. 6 in., 93 sq. yd., 10 sq. vd. 108 sq. in.
!). 9 A. 120 sq. rd. 22 sq. yd., 1 A. 16 sq. rd. 9 sq. yd., 3 sq. ft.
10. 200 gul., 35 t.
Ex. CLVII. /. ,$82.11, $28.80. ;?. £1 Hs. 3id., £1 2s. 8d.
3. 3 t. 12 ewt. 4 lb., 1 t. 11 cvt. 48 \h.
4. 2 mi. 197 rd. 5 yd. 9 in., 2 mi. 270 rd. 4^ in.
5. 1 A. 135 rd. 22 yd. 8 ft. 51 in., 2 A. 16 rd.
a. 2 ed.59eu.ft., 10 ed. 60<?.ft. 7. 3 bu. ^gjil., 2 bu. pk. 4 qt.
8. 5 gal.,, 13 gal. 1 pt. 9. 23 lu. 20 min., 5 hr. 26 min. 40 see.
10. W 30' 12", 14" 30' 30".
Ex. CLVIII. 1. tItt owt. 2. &AS. 3. iV Ini.
i.
A i'<^. •^. liir i"<l.
A. 10. { ft.
0. 1 1>I.
7. i oz. .S. U.
Ex. CLIX. 1. ^ 11).
iW. 6. A on. yd.
2. lb.
/. lit.
.7. m iiii. 4. T*J
c'v. I mi. .'y. ^^^
557561.
10. $300.
$3.84.
i>. $21.51.
5.
10. i\ A.
Ex. CLX. 1. 34940585. 2. 525 lb. 3. 169 qt. 4
5. 4320. 6. 5940. 7. $251.25. 8. $1837.J. i>. $44.20.
Ex. CLXI. 1. 118188 lb. 3. 31 i cd. ■?. $150. 4
5. $633.60. 6. 267 d. 7. 129600 min. ,?. 1440 min.
10. 2024 poleo.
Ex.CLXII. i. 471b. ^. 36112 pt. 5. 5392oz. 4. 31t.5ewt.
5.1800. 6'. $499.95. 7. 1248oz. A'. 40et. 5.189. id>. 467721b.
Ex. CLXIII. ^. 22506 gr. 5. 161 gr. S.ohho?.. 4. 5184gr.
/J. 11088 gr. C. 10 D). 1 oz. 12 dwt. 8 gr. 7. 25. 8. 37i lb.
y. 701 lb. 6 oz. 6 dwt. 5 gr. 10. 114 lb.
Ex. CLXIV. 1. 63360 in. 2. 8064 in. 3. 2 ml. 4. $462.
5. $428.40. 6. $500. 7. 10 hr. 17 min. 8. 1584000 in.
0. 506898 in. 10. 440 mi.
Ex. CLXV. ?. $72. .?. $31..50. ,?. $1.95. ^. 438 baskets.
5. 335pt. 6. $1.05. 7.4. .S'. $510.30. .9. 2 qt. iO. $13T.74i.
Ex. CLXVI. 1. 32 da. 2. 264 ft. 5. 9. 4. 44 ft. 5. 9 mi.
G. 320 hr. 7. 500 da. cV. $57.24. .9. $47.25. 10. $19.44.
Ex. CLXVII. 1. 68 et. 5. 5 ft. 3. 8184. ^. 15. 5. 43 mi.
G. 48 hr. 7. 4620 paces. 8. 43. .9. 24320. 70. 8f mi.
VNSWERS.
2U7
pt., 3i qt.
16'Uo".
i in.
sq. in.
. 1) sq. yil.
oz.
< sq. in.
I., 3 sq.ft.
;i 28. 8d.
i.0pk.4qt.
[iiin. 40 sec.
bu.
4. T5'
144
4. 55756^
0. ^6*. $300.
4. $3.84.
. iy. $21. ni.
31t.5ewt.
JO. 467721b.
4. 5184 gr.
h*?. 37i lb.
4. $462.
in.
basliets.
to. $137,741.
It. 5. 9 mi.
519.44.
5. 43 mi.
1 4 mi'
4. 6(5 mi.
9. .■?. 12 hr.
Ex. CLXVIII. 1. 6 lb. 4 oz. H dwt. 12 gr. 2. £200.
5. 10 cwt. 80 lb. 1 oz. 4. 24 ft. J. 990 yd.
6'. 4 min. 16 sec; 980 yd. 7. 32 yd. *. 54. 9. 989 1b. 70. 1271.
Ex. CLXIX. 1. 84 in. ;.^ 7 da. 5. 506 da.
5. 75 ct. 6. $8050.50. 7. 49 yd. ,y. 60 et.
!K 12 da. 20 hr. 20 min. 10. 4 yd, 1 ft. i in.
Ex. CLXX. 1. 3 lb. 11 oz. 11 dwt. 6 g. i
4. 110 da. 5. 36 hr. 6\ 42. 7. 92928. ,!;. 12 spoons. .9. 5/a mi.
iO. £43 Is. 3d. ; £6 8s. 9d.
Ex. CLXXI. /. 209 bii. 1 pit. 3 qt. S. 1569 bbl.
3. A, 131 yd.; R, 19i vd. 4. 36 mi. 298 rd. 1 ft. 6 in.
5. 48 rd. 6. 8f yd. 7. $62. ,?. $13.50. 9. $432. iO. Hi t.
Ex. CLXXI I. ./.s7.50. iJ. $1.76. 5. $96. ^ $49. 5. $19.12.
6. 27i yd. /". 27 lb. 8. 1.0 hr. 9. $8. 92 J. 10. $94.40, $660.80.
Ex. CLXXIII. /. 48, 8 lb. 2. 32 lb. 3. 42 mi. 4. 24 yd.
5. 450sheep. 6.176ft. 7. 58A. ^. 60ct. .9. $12000. 10. U A.
Ex. CLXXIV. /. 288. 2.$:]H. 5. 160 bu., 32U bu. ^. $20J.
5. $6000. 6. 8i ft,., 2079U gal. 7. $23.76. ^.100 A. 9. $4070.
10. $0250.
Ex. CLXXV. /. 50 A. 156 rd. 2. 7 ft. 9 in. 3. 8f ft.
4. 3 doz. .5. 181iJ A., 203^5 A. 6. 38 A. 91i rd. 7. 42240.
^. :!;6C.01. .9. 396 lots. iO. $13459.56; Jamr*' $3364.89; William,
S»}4486.52; daughter, $1121.63; wife, $4486.52.
Ex.CLXXVI. 7. all. ^. i\. 5. l^da. 4. 36da. 5. 16^ da.
6. 41ida. 7. 10 da. 8. Uf da. 0. 2h da. 10. lf da. 11. 21^ da.
12. £J hr. 13. 28f hr. 7^. 6^,^ da. 75. 2^ da. 16. 3^ da.
Ex. CLXXXI. 1. 282.405 A. 5. 307222.086446.
3. 363.536487. 4. 115.8125 yd. 5. 24.2675 t. 6. 25269.111505.
7. .42951303. 8. 6.5 t. .9. 138.122427. 10. 48095.139833.
Ex. CLXXXIV. 1. 72.927. 2. .1993. 3. 364.9953.
4. 6999.9996045. 5. 999999.999999. 6. .017481.
7.2999999.900001. .?. .000999. .9.43.08997. 70.6929.95993.
Ex. CLXXXV. 7. .30.280965. 2. 75.0665. 3. 15.635563.
4. 16.()799884. 5. 49.1.56. d. 4.152. 7. 81.143. 8. 9.7597.
.9. 80.025. 10. 9.0897.
Ex. CLXXXVI. 7. 228.475 A. ^. $.327,065. 3. 199.35 mi.
^.$963.68. 5. 262.35 A. 6. .08 in. 7. $111.58. 5. 29569.92 A.
9. 123.325 lb. 10. 73.73 ft. 77. .3. 12. 30.338 in.
Ex. CLXXXVIII. 7. .435; .0676. ^. 506.4463; 35.4367519.
'?. .013272: 32.5779. 4. 36.9; 1.7005. 5. 3.8; 1860.867.
6. 525; 92.;. 7. 11221.1; 54.706. 5. 9.06453; 279.29475.
9. .000000027; 4.8. 70. .1728; .032.
Ex. CLXXXIX. 7. 12.34.i56, 12.345.6, 12.3456. 2. 33.5175.
3. .000019737. 4. .00.365. 5. 005162. G. 45; 450; 4.500; 45000.
7. 421000. 8. 1144.90001605. 9. .68785. 70. .0000000000884.
208
AKITHMETIC.
4.
.V.
6.
8.
4.
9.
3.
4.
6.
G.
7.
8.
!).
10
3.
9.
4.
8.
6.
8.
5.
10
4.
7.
11
9.
Ex. CXC. J. 204.375 mi. il. 4'y'.i A'2') lb. 3. $7000.
270.40.) ft. 5. H64.H() ft. 6. 23. (52.') yr. 7. 4:{(}247.424 ^r.
r)yO.U28 mi. 9. 993.12;') gal. JO. 2y7.2r)37r).
Ex. CXCIII. /. ir>.24. ;.\ 3r)0000. 3. .413. 4. 330000.
.024. 6'. 647r)3(;t)0000. 7. 12.34r), 1.234.^), .12345, .012345.
10.5. 9. 127.4. 10. .075, .0075, .00075.
Ex. CXCIV. /. (5.165 nl. 2. 320 rd. 3. 42 bu.
144 bbl. 5. 87.5 bbl. 0. $128.50. 7. $27.5. 8. $10800.
15.75 bu. 10. 5.2 hr.
Ex. CXCVII. /. I.^s. 9fd.; 15h. 3(1.; £1 16s. 2id.
83 lb. 4 oz. ; 1 cwt. 74 lb. 14.4 oz. ; 3 t. 17 cvvt. 95 lb.
252 rd.; 80 rd. 4 yd. 1.2 ft.; 21 mi. 118 rd.
145 sq. rd. 6 sq. yd. 64.8 sq. in. ; 141 sq. rd. ; 13 A. 70 sq. id.
25 eii. ft. 540 eu. in.; 7d. 112 cu. ft.; 9 eu. yd. 20 cu. ft.
432 cu. in.
3 i>k. 1 gal.; 2 bu. 1 pk. 1 gal.; 5 bu. 1 pk. 1 gal. 3.2 qt.
3 qt. 1 pt. ; 5 gal. 1.4 pt. ; 7 gal. 3 qt.
11 hr. 52 min. 48 sec. ; 7 wk. 6 da. 3 hr. ; 9 wk. 6 da. 15 hr.
36 min.
58' .30"; 2" 5C' 51"; 17° 23' 15".
. 3 ft. 9 in. ; 17 rra. 17 qr. 12 sh. ; 7 gro. 9 doz.
Ex. CXCVIII. 1. £1..')25, £7.68125. 2. 9.854 t., 5.70375 t.
7.1109375 mi., 6.089 mi. 4. 9.3 A., 7.283 A.
7.875 cd., 7.0875 cu. yd. 6. 7.8125 l.u., 5.890625 bu.
27.875 gal., 14.375 gal. 8. 3.55875 da., 2.7725 wk.
3.8775% 17.12375°. 10. 5.8875 rm., 24.75 grs.
Ex. CXCIX. 1. $.3380. 2. 10.3826 ft. 3. $59,375.
The latter, 8.875 cu. in. 5. 3.2 lb. G. $24.80. 7. 83.75 yd.
$322.28. 9. 199218.75 oz. 10. $186.15.
Ex. CC. 1. $414. 2. $109.0625. 3. 75 sheep. 4. $161.6.')5.
50. 6'. $492.01875. 7.3720. A\ $53.25. 9. $i. i6^. 13.378A.
Ex. CCI. 1. 67.75 A. 2. 28 vr. 3. $26484. 4. 7.39, 8.95.
$10.32. 6'. Gain, $846,875, $12.50. 7. A., $75.87; B., $57.39.
16.5. 9. 1585584 cu. ft. 10. 8.6328 mi., 9.1872 mi.
Ex. ecu. 1. $5. 2. $96,768. 3. 29.83 in. 4. 2.7 ft.
2.2968. 6. .5625, 33.75. 7. 15360. 8. 58 lb. 9. $24.60.
. $192.78.
Ex. CCIII. 1. 42.34. 2. 17.3. 3. 8.45, 5.65.
26.1 cd.. 24.65 ed. 5. 64 mi., 56.25 mi. 6. $340.05.
$18.8325. S. .7875. 9. 4 ft. 3.2 in. 10. 92.4 vd.
, $181.50, $77, $44. i^. 660 ft. ^5. 2446.875 lb. i4. 4A da.
Ex. CCVII. 1. 444 sheep. 2. $103. 3. 225 bales.
288 boxes. 5. $216. G. 480 A. 7. 120 lb. 8. 200 A.
300. 10. 30 bu.
ANSWERS.
209
td.
)5lb.
\. 70 sq.
. 20 cu.
1(1
ft
1. 3.2
qt.
da.
1;)
hi
Ex. CCVIII. /. $1400. 2. $77(50. S. 120 A. 4. $:j:175.
6. $29500. 6. 4930 sheep. 7. 231 girls. 8. 20277. U. $717.25.
lU. 73%, 876 sheep.
Ex. CCIX. /. 061%. 2. 98%. S. 80%. 4. 50%.
5. '20%. 0. 12%. 7. 25%. H. 8%. y. 33i%.
10. 40%, 60%.
Ex. CCX. 1. 70. ;^. $2500. 5. $500. 4. 800 A.
5. 450 sheep. 6'. $4500. 7. 150 Hues. ^. $1300.
9. 4500 sheep. i(>. 450 pupils.
Ex. CCXI. /. 3290 bu. .^6%. 5. $72. ^.$20.
5. $12932.50. 6'. 48992 lb. 7. $125. H. $5400. U. $9000.
2(^. Lost, 12i%.
Ex. CCXII. 1. 330 rd. 2. $372. 5. 10 lb. 4. 48 mi.
5. 2800 books. 6'. 224 men. 7. 1880, 2021. 8. 11%.
f^. 13752. 10. 9A%.
Ex. CCXIIl. 7. $112.50; $216. 2. $292: $504.
5. $108. 4. $105. 5. $180. 6. $150 7. 4i%;374%.
^. $360. 9. $800. i6^. $3.75.
Ex. CCXIV. 1. $270, $540, $547.20, $1051.65. 2. $557.46.
3. $10.26. 4. $3.20. 5. $25. 6". $6g. 7. $500. 5. $2.50.
9. 32i%. iO. 46%.
Ex. CCXV. 1. $25.50. ^. $3.20. ,?. 28%. 4. 46.19%.
5. $20. 6. $7.56. 7. $850. .!?. $33i%. 9. $461.70.
10. $357, 47i%.
Ex. CCXVI. 7. 25%. «. 15%. 9. 4%. iO. 42f.
Ex. CCXVII. 1. $1.89. ^. $926.10. 3. $.38.28.
4. $3612.50. 5. $238. 6. $2719.50. 7. $60. 8. $900.
5. 9000 bu. 10. $4.20.
Ex. CCXVIII. 1. $112. ;g. $8600. 5. $204.70. 4. $1007.50.
5. $75. 6. 12*%. 7. $330. .^. 40%. 9. 35^.
i<?. $160, $208.
Ex. CCXIX. 3. $168.75. 4. $115.92. 5. $12.50. (. $19.38.
7. $13.50. .?. 3%. 5. U%. iO. 3%.
Ex. CCXX. /. 3%. 2. 2\%. 3. 3*%. 4. $14400.
5. $8400. 6. $2592.80. 7. 84ct. 5. $7200, $216. 9. 156 members.
10. $3264.
Ex. CCXXI. 1. $150. ^. $3650, $146. 3. $270.
•^. 25000 yd. 5. 6000 lb. 6. 4100 lb. 7. 52000 yd. 8. $3500.
». $897.75. iO. $4000.
Ex. CCXXII. 2. $80. 3. $66.25. 4. $225. 5. $675, $74325.
6. $22.50. 7. 11%. 8. %%. 9. i%. 10. %.
Ex. CCXXIII. 1. $16000. ;^. $3000. 3. $20000.
i/. $14000. 6. $420. 6. $34737. .50. 7. $40000.
8. $2040, $5960. y. $75. 10. $2500, $3500, $4000.
210
AKITHMETIU.
Ex. CCXXIV. /. ii.'>4. 2. $150. .?. 19.r>0. /. !fir)23.
5. $tjr)2.50. a. $22. 7. $1H. J^. 14 milln. 'J. 12i mills.
i^>. 17 J inlllH.
Ex. CCXXV. /. $2800. ;'. $2500. .i. $.544000. 4. $101. fiO.
6. $".)00. a. $13000. 7. $5075. 8. 6i inillH. U. $25.
10. $114.20.
Ex. CCXXVI. 1. $0, $8, $.'{, $7, $7, $9. 2. $9. ./. $50.
4. $:i40. 6. $10. 6'. $5.39. 7. $15.12. 8. $38.88.
f>. $13.20. 10. $4.0110.
Ex. CCXXVII. /. $915.00. ii. $1012.05. 3. $2084.02.
4. $074.01. 6. $531.65. 6'. $425,050. 7. $1859.04. 8. $66.
0. $1910.20. 10. $1154.04.
Ex. CCXXVIII. l.(S%. 2.1%. 3.H%. 4.61%.
6. Oi%. 6. 5i%. 7. 7i%. 8. 4i%. 0. 6%. iO. 6%.
Ex. CCXXIX. i. 1 yr. 2. li yr. .?. li yr. 4. 5 mo.
6. 9 mo. 6*. 8 mo. 7. 115 da. *. li yr. 9. 150 da.
10. 75 da.
Ex. CCXXX. 1. $540. i2. $055. 5. $850. 4. $360.
5. $840. 6. $750. 7. $876. *. $1825. 0. $219. 26?. $2920.
Ex. CCXXXI. /. $2.50. 2. $405. 3. $540. 4. $572.50.
6. $1320. 6. $408. 7. $750. 8. $1742. f>. $.3050. 10. $.3212,
Ex. CCXXXII. i. $126.10, $920.10. 2. $477.54, $2977.54.
5. $70.51, $1320.51. 4. $1724.05, $9724.05. 6. $112.55.09.
6. $5250. 7. $900. 8. $10000. 0. $4.32. 10. $124.05.
Ex. CCXXXIil. 5. $751,875. 6. $1485.15.
Ex. CCXXXIV. 1. $645.48. 2. $792.22. S. $180..50.
4. $.5579.42. 5. $508.69. 6. $115.48. 7. $325. 8. $570.
9. $1920.70. 10. $1053.77.
Ex. CCXXXV. 1. $7828. 2. $6760. S. $7032.50.
4. $1248. 5. $2669. 6. $4750. 7. $3262.50. 8. $9750.
9. $20400. 10. $2,600.
Ex. CCXXXVI. 1. $700. ;g. $2500. .9. $3500. 4. $.5600.
5. $2200. 6. 5. 7. 10. /?. 6. 9. 28. /fl. 15.
Ex. CCXXXVII. 1. $200. ;2. $240. 3. $200. 4. $100.
5. $112. 6. 5^%. 7. 4^%. ^. 5%. 5. 5i%.
Ex. CCXXXVIII. 1. $9100. «. $13310. 3. $11340.
4. $15570. 5. $11495. C. 60. 7. 70. 8. 220. 9. 500.
Ex. CCXXXIX. 1. $10000. ;?. 124. 3. $18000; 720.
4. %%. 6. 1%. 6. 3i%. 7. $100. *. $540. 9. $4925.
Ex. CCXL. 2. lUf. ;2. 83i. 5. 20Gf. 4. 5*%.
5. $2400. C. $1420i. 7. 50. 5. $29400. 9. 5%. 2^;. !!;)!00,
Ex. CCXLI. 4. 3 inc. 5. 10 mo. C. 8 da.
7. 60 days after the debt is due. 8. 6 mo. 9. 02 du.
ANSWERS.
211
^2i.
i, $101.60.
15.
.h $56.
184.02.
8. $66.
. 6%.
5 mo.
da.
JS360.
iO. $2920.
$572.50.
10. $:J212,
p4, $2977.54.
2.55.09.
24.05.
80.. 50.
?. $576.
50.
;9750.
4. $.5600.
U. $100.
I340.
I. 500.
720.
$4925.
10. t'WOQ.
Ex. CCXLII. 1. 6 mo., 3 mo., 4 mo. 2. 120 da. S. 4 mo.
4. 5 mo. 5. Ap. 23. 6. Il2i dii. 7. 3* mo. ,y. 70 da.
0, H mo.
Ex. CCXLIII. 1. B, $450; A, $600. 2. A, $189; B, $243.
3. A, $135; B, $125. 4. A, $85; B, $130; C, $60.
5. A. $864; B, $408; C, $1152. 0. A, $2600; B, $3400.
7. B, $650; V, $925. ^. A, $1750; B, $2125; C, $1125.
!). $720. /^. A, $2662; B, $2420; C, $2200; D, $2000.
Ex. CCXUV. 1. A, $17.50; B, $22.50.
5. A, $285; B, $150. ^ A, $25; B, $21; C, $54.
4. A, $75; B, $175; C, $330. 5. Equally.
6. A, $2200; B, $3000. 7. A, $1225; B. $875; C, $1050.
*. 4 mo. 9. $1480. /^. A, $8445.94; B, $4054.05.
It. $1800. 12. C, $16051^; 1), $1544^^; K, $1050.
Ex. CCXLVII. 7. 80; 15625; .512; 343. 8. 6th. .9. 256.
10. 24th. 11. 49126081. 13. 128787625000.
13. .000000000016. 15. 10 A.
Ex. CCXLVIII. 9. 3.05; .102; .571; .00563.
W. 2.236; .707; .948; .094.
Ex. CCXLIX. 1. 400. 2. 49j. S. 3202. ^. 24 yd.
5. 440 yd. 6. 200 rd. 7. 272 ft. 8. $160. .9. 144 id.
10. $324.
Ex. CCL. 1. 75 vd., 25 yd. e. 220 yd., 44 yd. .9. H in.
•/. 17 rd. 5. 1440 mils. 6. 280 rd. 7. 8030 yd. S. 15 ft.
.'>. 221 yd. 10. 7712 yd.
Ex. ecu. 9. .1; .06; 11.6; 36.3. 10. .928; .4308; .2; 1.709.
Ex. CCLII. 3. 35.3. 4. 5476 sq. ft. 5. 564.")4 sq. ft.
0. 17 ft. 7. 60 in. cV. 9.2 in. 9. 12 ft. ^^. 15.75 in.
11. 37 ft. 12. 5 ft. i5. 12. 14. 36 ft.
Ex. CCLIII. 1. 1521 sq. yd. ^. 29 sq. ft. 56 sq. in.
3. 1144 sq. ft. 4. 210 ft. 5. 2 ch. 40 1.
6". {(i) 229i sq. in. (/>) .54 A. (c) 20 sq. ft. 7. 5A' sq. ft.
5. 16 rd. 9. 80 rd. 10. $50.
Ex. CCLIV. i. {a) 186 sq. ft. (^) 318^ sq. ft. (c) 5A A.
id) 7A A.
i?. 50 in. 3. 57 in. 4. 92 rd. 5. 4300 sq. ft. G. 2145 sq. yd.
7. 1715 sq. ft. 8. .5541 sq. yd. .9. 203 sq. ft. 10. 56 ft.
Ex. CCLV. 1. 44 in.; 66 in.; 11 ft.; 51* ft.; 73i ft.;
14 eh. 961.
2. 7 in.; 17i in.; 19J ft.; 1 ch. 7U 1.; 7 vd.; 21 vd. 7 in.
^>. 24i min. 4. Ill rd. 1 ft. 10 in. 5. 5 ft. G. 72. 7. 4lf ft.
8. 84 yd. 9. 12 ft. 10 in.
10. 22 in.; 33 in.; 55 in.; 06 in.; 110 in.; 121 in.
212
ARITHMETIC.
Ex. CCLVI. 1. 9()2i Hq, in.; 138(5 sq. in.; 3850 sq. in.
5544 sq. in.; 8(502^ sq. in.; 154 sq. in.; 346i sq. in.
471f sq. in.; J)62i sq. in.; 7546 sq. ft.; 154 sq. in.
38i sq. ft. ; G8^ sq. ft. ; 861 sq. ft. ; 1386 sq. eh.
2. 26M sq. yd. 3. 88 rd. 4. 59.4 in. 5. 308 sq. in.
6. 62.04 yd. 7. 246.66 yd. cS'. 277.^:. U. 110 sq. in. 10. $838^
Ex. CCLVII. 1. («, 85; (/>) 650; (f) 1730; {d) 698.
2. (a) 528; (/>) 1230; (c) 44; (r/) 144.
5. (a) 456; (/>) 782; (c) 390; (<0 225. 4. 29 mi. 5. 35 ft.
6.274 ft. 7. 20.7J^in. ,?. 11.18 ft. .9.10 ft. i^>. $54.60.
Ex. CCLVISI. 1. 9H eu. in.; 34fi cii. in.; 14 cu. ft.; 197
cu. in.; 68 cu. ft.; 145 cu. iu.
2. 121i sq. in.; 63 sq. in.; 35a4 sq. ft.; lOOA sq. ft.
S. 311 cu. ft.; 99^ sq. ft. 4. 131i eu. ft.; 18U sq. ft.
5. 20 in.; 4^f eu. ft. 6'. $41i. 7. 16 ft. 8. 25i ft.; 17 ft.
9. 28.09 in. 10. 1650 gul.
Ex. CCLIX. 1. {a) 8f eu. ft.; (ft) 115i eu. ft.; (c) 385 cu.
ft.;. ((0 13311 cu. ft. 2. {a) 29* sq. ft.; (/>) 132 sq. ft.;
(c) 220 sq. ft.; (^0 183* sq. ft.
5. 5f^ cu. yd. 4. $66. 5. {a) 31^ sq. ft.; (6) 15U sq. ft.;
(c) 297 sq. ft. ; {d) 196 sq. ft. 101 sq. in.
6. 91^ sq.ft.. 7. $24.75. <f^. 1 ft. .9.1yd. i^. 14cu.ft.
Ex. CCLX. 1. 108 eu. ft.
2760 eu. in. 3. 75 sq. ft.
:>. 89^ eu. ft.
4. 33 sq. ft. 5. $33.75. 6. 19250 cu. in.
7. (1) 861 sq. ft.; (2) 33 ft. 8. 89.51 yd.
10. 61 in.
Ex. CCLXI. i. (a) 154 sq. in. (/>) 38i sq. in. (c) 616 sq. in.
id) 2464 sq. iu.
2. $24.64. ^. 14 ft. 4. 132 ft.
5. (a) 905eu. iu. {b) 3620teu. in. (c) 1437ieu. in. (d) 179lreu. in.
C. 4851 cu. ft. 7. 14f eu. ft. 8. 4 in. 5. 110592. 10. 2541.
Ex. CCLXII. J?. 92.9 ft. 2. 88 yd. 3. 68 yd.; 867 sq. yd.
4. 391 ft. 5. 75 ft. 6. 43.3 sq. ft. 7. 32 ft. 8. 98 yd.
9. 820 in. 10. 1120 yd.
Ex. CCLXI 1 1. 1. 43 ft. ,?. 242 yd. 3.
5. M mi. 6. 4.24 ft. 7. 140 rd. 8. 4 ft.
i(^. $3.30.
Ex. CCLXIV. 1. U ft. 2. 3 in. tiles.
4. 704 sq. ft. 5. 170 ft. 6'. 14175 sq. ft.
$22f. 4. 25.
9. 8063i lb.
3. 126 ft.
7. 5544 sq. ft.
8. 79194 sq. ft. 9. 140 sq. ft. 10. 3461 sq. in.
/. 80 ft. 90 ft. 2. 5 A. 3. 8232 sq. ft.
89.44 rd. 0. 1560 sq. in.
Ex. CCLXV.
4. 28 sq. ft. 5
7. 65 ft., 68 ft.; 60 ft
10. 1121 ft.
80 rd.; 120 rd.
8. 72 ft. 9. 2646 S(i. in.; 4376 sq. in.
sq. in;
H sq. in.;
4 sq. ill;
h.
'lO. $838 J.
198.
5. 35 ft.
$54.60.
u. ft.; 197
ft.
ft.
ft. ; 17 ft.
(c) 385 cu.
132 sq. ft. ;
L51i sq. ft. ;
lieu. ft.
rS sq. ft.
oil. ft.
;) 616 sq.
in.
I) 179"ncn
. 10. 2
. in
541
; 867 sq.
98 yd.
yd
4. 25.
3i lb.
ft.
sq. ft.
sq. ft.
)0 sq. in.
4376 sq. in.
ANSWERS. 213
Ex. CCLXVI. 1. 63 ft. 2. 308 sq. ft. ; 385 sq. ft.
S. 246.66 yd. 4. 3630 men. 5. 4800 ft. 6". 40 rd. 20 rd.
7. 2.18 ft. 8. 12 ft. 9. $28.32. 10. $32.
Ex. CCLXVII. 1. 52 ft. 2. 10.39 yd. S. 23.54 ch.
4. 'ih eh. 5. 56 yd. 6'. 42 ft. 7. 414.12 ft. 8. 21.213 ft.
5. 292i sq. ft. 10. 48i c. ft.
1. 38i sq. ft. 2. 34.64 in. 5. 27.71 in,
5. 1925 lb. 6'. 864. 7. 192000 shot.
Ex. CCLXVIII.
4. 37i It. ; 30 ft.
8. 243 doz. a. 12 in. i^. 48 oz.
Ex. CCLXIX. ;g. (1) 456 cm., (2) 45.60 dm., (3) 4,560 ni.
,9. (!) 18.7 m., (2) 18700 mm., (3) 1870 cm. 4. 1897009.434 ni.
5. 780.43 m. ; 11.03 mm. 6. 92.208 m. ; 299.18892 m.
7. 640 leaves. 8. 27600 times. 9. $76.56. 10. 7.6375 m'.
11, $555705. 12. 28000 times.
Ex. CCLXX. 1. 287.6.345 hectares. 2. 37856 ares.
3. 57536 sq. cm. ; 5753600 sq. mm. 4. 2341700 sq. m.
5. 542 sq. em. 6. 3030303 sq. m. 7. 112 ares.
8. 32.64 sq. m. 9. $2.50. 10. 280500 bricks.
Ex. CCLXXI. 1. 72.5 st. 2. $432.50. 3. 25800 1.
^. 23.375 c. m. 5. 2.604 m. G. 1.40 c. m. 7. 30 em.
8. 300 HI. 9. $275.31. 10. 8 ct.
Ex. CCLXXII. 1. 5037 j?. ; 503.7 Dj?. ;?. 3075 mg. ; 30.75 (Ijr.
5. 8070006.5 eg. 4. 2.756 Kg. ; 275600 eg. 5. 7.28 1. 6. $750.
7. 264.6 Kg. 8. $420.15625. 9. 310 mg. 10. .00504.
Ex. CCLXXIII. 1. (a) 70.25 m. (6) 808.7 1. (c) 15.908 a.
((0 27000.37 g.
2. 594 Kg. 5, 47250 Kg. 4. 2100 coins. 5. 388 g. «. 110 st.
7. 225 francs. 5. 33 HI. 9. 650 g. /^. 200 m. 11. 50 ct.
12. 190 mi. iJ. 477 times. 14. 13.44 rolls.
Ex. CCLXXIV. 1. .3, .45, .96, .765.
2. .4, .142857, .285714, .42857i.
3. .571428, .714285, .857142, .076923.
4. .230769, .384615, .692307, .63. 5. .83, .583, .9318, .9287514.
6'. .9428571, .954, .89285714, .15990.
7. .7083, .4196428571, .54861, .164772.
.S'. .44230769, .72li53846, .1392045, .3809523.
.'>. .20238095, .8270, .14076.5, .505067'*
10. .170138, .686789772, .35267857142, .20145.
214
ARITHMETIC.
1 1 16
1 n , 3r, TIT, 1 1 1
Ex. CCLXXV. i . § , H , T I , f 1 . ^
o2 1810 8 ^35 47 S9 89
«3 3T> 5T, i?, ?7. 4. ]JT, Til, 5T, 111
r9»1218 /J81198110
5. TIFT, TI, T, T. O. 8 2, 36, tz, 4 1.
^ 583 61 14 41 o 89 1 389 81
7 Tffff, 360", ^25, SffOTT. o. 44, T4g, iJSff, '10.
o 36 43 Oil 735 7/1 /1 f^l 72 r;5
^ 44, "SSff, ^Jf, 'IT tl' "ITSO, JT63, '353^, «^1S.
Ex. CCLXXVI. i. 0.60244. 2. 2.3060941229258.
3. 9.4H69; 14.0636727. 4. .32457; .32147. 5. .73231777.
6. 1.590; 6.893. 7. 339; .429. 8. .4675; .350649.
D. 63; 10. 10. .54175; 7.805.
Ex. CCLXXVII. 1. 10.5. i?. .42. 4. .161; .03.
6. 33.142857.7, £2 Os. 8. 6'. 3 t. 8 cwt. 35.3 lb.
9. 6 mi. 92 rd. 1.6 yd. 10. 69 t. 888.8 lb.
Ex. CCLXXVIII. 6. 7.456. 9. 13.
Ex. CCLXXIX. 1. $3780. S. 9215 cii. ft.
3. $132, $247.50, $275. 4. $100. 5. .0078125.
6. 33 mi. 7. .405 hr. 8. WA'^n. 9. .00129.
Ex. CCLXXX. 1. A. 2. h dii. S. 3* da. •^. 14.7 da.
5. L 6. A 27 da., B. 54 da. 7. A 19^ da., B 9da., C 39ida.
8. 4i da; 9. 18 da. 10. 4i hr.
11. A 361 da.; B 73i da.; C 110 da. 13. 15 da. IS. 32 hr.
i4. li hr. ^5. 8 horses. 16. A 3A da.; B 3^^ da.; C 5h da.
17. A $1.10; B $1.
Ex. CCLXXXI. 1. 12imn.; 24.min. ; 30 min. ^. 18 min.
3. 16ri min. past 3. 4. Wrx min. past 6.
5. 32 1\ min. past 6. 6. 24 min. past 6.
7. 24 min. past 6 and 41n min. past 6.
.9. (a)43i^i min. past 8, (?>)27A min. past 8, (c) lOi? min. past 8.
9. 49n min. past 9; 541*1 min. past 10; 12 o'clock.
10. 23 ra min. past 5. •
Ex. CCLXXXII. 1. 13A min. past 4. 2. 19fi min. past 3.
3. 3I23 min. past 3. 4. 120 da. ; 44 min. past 11 ; 14 min. pnst 12.
5. 75 da. 6. 36 min. past 6 a.m., Friday. 7. 5A min. past 5.
8. 5i min. past 9 p.m. on Tnesday, and 57i min. past 8 p.m.
9. 3 p.m.. May 3. 10. 43MH min. past 9 p.m.
Ex. CCLXXXIII.
5. 14 min. 24 see.
10. Gains 10/.,% min.
Ex. CCLXXXIV.
1. 44 ft. S. 34 A mi. 3. 22h 4.
0. 8 lir. 7. 33: mi. 8. 7h yd. 9.
i'l sec.
t J M ~
5. 41 mi. 0,
nil.
/. 224. 141. 2. 4 mi. ,1. J mi. ^. i hr.
7. 45 iiiiii. 6'. 3 mi. .V. 5tol. tO. '2k hr.
ANSWERS.
215
1 1 6
riT, T 1 1
n 5
1777.
14.7 da.
.,C 39^ilii.
3. 32 hr.
; C oh dii.
2. 18 mill.
mill, past 8.
lin. past '.5.
nil. pjist 12.
min. past 5.
ist 8 p.m.
4. 7i sec.
li. 4. i liv,
to. 2i hr,
Ex. CCLXXXV. 1. l! mi. 3. 45 mi., 36 mi. 3. 114 yd.
4. 45 mi. 5. 11 min. 6. 396 ft. 7. 94^ yd. .?. 22 mi.
9. 23i mi. 10. G'i mi. ii. 6 hr.
Ex. CCLXXXVI. 1. $1.92. 3. 325, 175, 125. 5. $620.
4. 74; 3s. 8jd. 5. 17. 6. 23. 7. £16 6s. ,S. 1980.
9. 2 hr. 24 min. it*. 200 lb.
Ex. CCLXXXVII. 1. 144 min. 2. Men, $12.50; women, $8;
boys,$5.25. 5. 7bbl. /. 1022. 5.75yd. 6'. 32da. 7. 17 mi.
8. $80. 9. 110 sheep, 140 pigs. 10. $51.
Ex. CCLXXXVIII. 1. $12800. 3. 123 gal. 5. $672.
4. 720 apples. 5. $75. 6. £140. 7. $97.50. 8. 223 sec.
•O. John, $880; Thomas, $176; Henry, $22. 10. 56 et.
Ex. CCLXXX!X. /. $27. 3. 26 ft. 6 in. 3. 4 ft. 1 in.
4. 15 ct. 5. 2C88 rails. 6. 20, 21, 22, 23. 7. 182. 5. $60.
,9. 7875 shingles. 10. 150 lb.
Ex.CCXC. i. $90,$60. 2.3m\. 5. 87 da. 4. Latter, 51 ct.
5. $20.0246. 6'. $8460. 7. $870, 6%. ,?. $2.50. 5. 19 da.
Ex. CCXCI. 1. $900, $1350, $1800. 2. $36. 3. Gain, 72 ct.
^.230400 A. 5. 49.90 rd, 37.43 rd. 6. $2.50. 7. 100 ft. by 76 ft.
8. $321.25. 9. $354. 10. $7.50.
Ex. CCXCII. 1. A, 30 ct. ; B, 36 ct. ; C, 40 et. 2. 160 leaps.
•S. $2450. 4. vm see. 5. $500. 6. 80c. 7. U yd.
8. 900 lb. at 7 ct. ; 1100 at 10 ct. 9. 248 yd., 62 yd. 10. $440.
Ex. CCXCIII. /. .396 ft. 2. $329. 3. Divisor, 547; Qiiot., 3233.
4. $4J. .5. $23.50. 6'. A's rate is to B's as 79 to 60.
7. 409036320 postholes. 8. A, $432; B, 216; C, $1296.
0. $1680. 10. $300; $450.
Ex. CCXCIV. 1. 294; 84. 2. $900, $750. 3. $200. 4. ,^,?, .
•5. $400. 6. $240, 5yr. 7. 2i in. ,?. 300 leaps. 9.9hv. 10. 2imi.
Ex. CCXCV. 1. $4.80. 2. 8%, 9%. 3. 31^%.
4. 3060,^j bn. 5. 224. 6. 60 mi. per hr. 7. 16j da.
10. A, $776.16; B, $693; C, $630;
8. 813i cu. yd. 9. 4fo da.
D, $600.
Ex. CCXCVI. 1. 405 bu. 2. 24 ft. by 18 ft. by 12 ft.
.?. 4.5eii.ft. 4. Gain, $14. 5. 8000 oranges.
6. 5Jts. ; 56 oz. gold; 160 oz. silver. 7. $2480.
5 U mi. per hv. 9. 20 min. past 4 a.m. 10. $217.80.
Ex.CCXCVII. /. 1152 sq.ft. :?. 4%. 3. i^^. ^.14.625 in.
5. I?; 675. G. 14.288 to 1. 7. 48jct. <S'. $3i. i?. $1.80. 10. 190.
Ex. CCXCVIII. i. 272 rd. 2. 111. 3. 24 ct. ; loss, A% .
4. Length, .34 ft.; width, 26 ft.; height, 12 ft. 5. 4^ mi.
6. 3G75§ t. 7. $441. 8. 63 yr. ; 35 yr. 9. 567 leaves. 10. 104 da.
216
ARITHMETIC.
Ex. CCXCIX. /. 213 plants. ;2. $4500. 3.2imi. 4.1001b.
5. 28 ct. 6. $2625. 7. $4000.
8. .384 In. (Note, their length and width being equal.)
9. 164.7114 in. 10. A, $1035; B, $1656; C, $2025.
Ex. CCC. 1. 2 to 5. 2. 13tV niin. past 4, or 30 min. past 4.
3. $40. 4. 5 yd. 3. $1.02, 80 ct. 6". $3250; $2600. 7. 233H ft.
8. 3 to 2. f?. 2i ft. iO. $1600; 15 mo.
Ex. CCCI. 1. A. 2. A, $2,901; B, $5.09f. 3. 10 mo.
4. 10 in. 5. $3. 6.90. 7. 3 hr. ,?. 5251b., 4951b., 3901b.
9. $2100, $1750, $1050, $700. 10. B, by 50 yd. in 4i min.
Ex. CCCII. 1. 141.4 sq. ft. 2. A, $600; B, $780; C, $180;
D, $2000. 5. $2000; $1296. 4. 4%;4i%. 5. 60et. 6. 32 men.
7. 15i mi. 8. $62500. 9. 11 J min. past 12. 10. $9r3 ; $9.
The End.
4. 1001b.
a.)
min. past 4.
7. 233H ft.
10 mo.
, 390 lb.
I min.
; C, $180;
6. 32 men.
>r3; $9^.