,M5:r.NRLF
^B 53S
M
c'C'-^
A
COMPLETE KEY
TO
NEW FEDERAL CALCULATOR,
OE
IN WHICH THE
METHOD OF SOLVING ALL THE QUESTIONS CONTAINED
IN THAT WORK IS EXHIBITED AT LARGE.
designed
to facilitate the labour of teachers, and assist
those who have not the advantage of a
tutor's aid.
BY THOMAS T. SMILEY,
TEACHER.
Author of an Easy Introdaction to the Study of Geography. Also,
of Sacred Geography, for the use of Schools.
PiaatrrtjjJxta:
PUBLISHED AND FOR SALE BY J. GRIGG, No. 9, NORTH 4th St.
AND FOit SALE BY BOOKSELLERS AND COUNTRY
MERCHANTS GENERALLY IN THE SOUTHERN
AND WESTERN STATES.
jo Mpi ^'Vnci-i -
Qcil & Mechanical Engineer.
aAtf FRANCISCO, GAL.
GiFT
Eastern District of Pennsylvania, to wU:
********* BE IT REMEMBERED, That on the ninth
I T g * day of May, in the forty-ninth year of the Tnde-
I * * t pendence of the United States of America, A. D.
********* 1825, John Grigg, of the said district, hath de-
Eosited in this office, the title of a book, the right whereof
e claims as proprietor, in the words following, to wit :
" A Complete Key to Smiley's New Federal Calculator,
or Scholar's Assistant; in which the Method of ►Solving all
the Questions contained in that Work is exhibited at large.
Designed to facilitate the labour of Teachers, and a?^sist
those who have not the advantage of a Tutor's aid. By
Thomas T. Smiley, Teacher. Author of An Easy Intro-
duction to the Study of Geography. Also, of Sacred Geog-
raphy, for the use of Schools."
In conformity to the act of the Congress of the Unitrd
States, entitled, " An Act for the encournj^tMncnt of learn-
ing, by securing the copies of maps, charts, and books, to
the authors and proprietors of sucii copies, during the times
therein mentioned." And also to the Act, entitled, "An
Act supplementary to an Act, entitled, ' An Act for tiie
encouragement of learning, by securing the copies of maps,
cuarts, and books, to the authors and proprietors of such
copies, during tlie times tlierein mentioned,' and extending
the benefits thereof to the arts of designing, engraving, and
etchings historical and other prints."
D. CALDWELL, C/erA:V ^/le
Eastern District of Pennsyhania.
Stereotyped by J. ilowc.
3L>
nSo
CONTENTS.
Paffc
Simple Addition,
-
Multiplication,
.
7
Subtraction,
.
10
Division,
.
11
Long Division, -
-
13
Compound Addition,
-
20
Compound Multiplication,
.
26
Compound Subtraction,
-
33
Compound Division,
-
43
Reduction,
.
43
Single Rule of Three, -
.
61
Double Rule of Three, -
,
69
Practice,
-
73
Tare and Tret, -
.
87
Interest, - .
.
94
Compound Interest,
-
100
Insurance, Commission and
Brokage,
104
Discount,
-
lOG
Equation,
-
109
Barter, -
-
110
Loss and Gain, -
.
112
Fellowship,
.
IIG
Kxchange,
-
119
Vulgar Fractions,
.
121
Decimal Fractions,
.
127
Position,
■-
132
Involution, or the Raising of Powers,
141
E/olution, or the Extracting
of Roots
1 "
t7>.
Alligation,
.
147
Arithmetical Progression,
.
149
Geometrical Progression,
-
151
Compound Interest by Decimals,
1.52
Annuities at Compound Interest,
ir;.3
Annuities in Reversion,
.
154
Perpetuities at Compound Interest,
ih.
Combination,
.
ih.
Permutation,
.
155
Duodecimals,
-
ib.
Promiscuous Examples,
"
*
158
iviS03795
EXPLANATION OF CHARACTERS.
Signs. Significations.
= • Equal; as 20s. =£1.
-f Addition, (or more) as 6-f 2=8.
— Subtraction, (or less) as 8 — 2=6.
X Multiplication, (or multiplied by) as 6 X 2=12.
-^ Division, (or divided by) as 6-f-2=3.
: : : : Proportionally ; as 2 : 4 : : 6 : 12.
^J or "^-J Square Root: as ^^64=8.
y Cube Root; as ^64=4.
A vinculum ; denoting the several quantities
over which it is drawn, to be considered
jointly as a simple quantity.
JOHN S. PI^ELL.
QoS & Mechtudcal Engineer,
HAJA JfkiLf^CiaCO,
A KEY
CATi,
Etit S-ettt iFeTretal ealculatot^
~mt9®9*^
SIMPLE ADDITION.
EXAMPLES.
(8) 4829
1234
6101
3014
5618
(9) 91769
14678
80032
71897
76989
(10)
(13)
(16)
876994
213678
482906
809769
376980
20796
335365
2760327
(11) 389261
789794
849798
487697
999996
948219
(12) 2136784
8297698
8297694
4897695
1234697
7092032
3769694
4976082
4569761
8213243
4876962
4876920
4464765
31956600
31282662
(14) 37856
975
1234
14
5612
2075
16287
(15) 378269
402607
702
1246
2132
45178
10276
141
5672
82971
34676
1459
427
12
64053
840410
125358
A 2
6
SIMPLE ADDITION.
(17) 14
16
23
29
80
31
100
293
(21) 365
807
660
25
37
101
1895
(24) 35 (
21
66
(18) 36
97
125
384
1176
1818
(19)
3797
9^
2
75
876
9750
(20) 205
20
340
970
367
1001
3403
14595
(22) 300
75
2
47
33
9784
20150
765091
1075047
(23)
tSES.
(27) 60
25
125
216
416
75960800
225000
140
76185940
Miles,
(28) 37
33
40
35
145
1870529
PRACTICAL EXEBC
25) 275 (26) 30
196 12
5
471 —
g47
Sheep,
(29) A's 34
B's 47
C's 64
135
(30) 25
15
40
9
89
(31) 8
15
19
12
64
bar. $
(32) 400 for 2000
550 2750
950
$4750
L
"*""
"~"
MULTIPLICATION. 7
MULTIPLICATION.
CASE L
EXAMPLES*
(8) 3948769768 (9) 87051298 (10) 976201698769
3 4 5
11846309304
348205192
488100849384{^
(11) 456978426976 (12) 8079698769 (13) 97698429769
6 7 8
2741870561856
(14) 28769842369
9
258928581321
(16) 5697698976845
11
'62674688745295
(18) 84976876989
12
56560891388
781587438152
(15) 769829769478
10
7698297694780
(17) 7029876956
12
1019722523868
(20) 4218 (21) 7S21
84358523472
(19) 9021681409671
12
108260176916052
(22) 87692 (23) 95698
4 5
8436
21963
350768
478490
(24) 10691 (25) 31078 (26) 109019 (27) 900078
6 7 8 9
64146
217546
872152
8100702
8
(28) 826870
10
MULTIPLICATION.
(29) 278976
11
(30) 12569769
12
8268700
(34) 39786948
197
3068736
150837228
CASE 2.
EXAMPLES.
(35) 4978829
408
(36) 8735698
570C
278508636
358082532
39786948
39830632
19915316
52414188
61149886
43678490
2031362232
7838028756
49845892788
(38) 49569876
4817
(37) 84016978
3761
(39) 9637842
9078
84016978
504101868
588118846
252050934
346989132
49569876
396559008
198279504
77102736
67464894
86740578
87492329676
315987854258
238778092692
(42) 11271
35
(40) 9786
13
29358
9786
(41) 8475
29
• 76275
16950
56355
33813
127218
245775
394485
'1
(43) 19004
305
MULTIPLICATION.
(44) 76976
489
9
(45) 84769
976
95020
57012
692784
615808
307904
608614
693383
762921
5796220
37641264
82734544
(46) 1978987
4809
(47)
49
9807094
6047
17810883
15831896
7915948
68649658
39228376
035470
9516948483
49496403418 1
(48) 37|00
2|00
CASE 3.
EXAMPLES.
(49) 4870
25|00
(50) 4087 00
906 000
740000
24350
9740
24522
36783
12175000
370282200000
(51) 876956
99 10000
7892604
7892604
868186440000
10
SUBTRACTlOJs.
CASE 4.
exampj.es.
(53) 8976
6
(54) 769G (55) 87698
9 V 9
(56) 20784
12
5,3856
69264 789282
249408 1
8
9 8
9]
430848
62337G ■■■ '^' 6314256
2244072
(57) 81207
11
(58) ^7696 (59) 75687
12 - 7
1 „ , ; . .
(60) 34075
6
893277
572352 529809
204450;
12
12 8
e'
10719324
6868224 4238472
1226700'
PRACTICAL EXERCISES.
(61) ^25
5
(62)15 (63) g250
4 7
(64) gl50i
4\
§125
(65) glOO
25
60 ^1750
{66) 18175
14
Or thus, 100
5
500
500
72700
200
5
g2500
18175
^2500
254450'
.i*»9®d«^
SUBTRACTION.
EXAMPLES.
(1) 859708
124978
(5) 0076048 (6)
5321478781
7940689
139876956
734790
1135359
392270922
-, ; ^ T-^l
DIVISION. 1 1
(7) 100000
84321
(8) 75381478 (9) 102070845
39040217 19768799
15671?
36341261 82302046
(10) 196 (
37
159
11) 487 (12) 875 (13) 967 (14) 1001
96 302 351 487
391 573 616 514
(15) 9765
1307
8458
(16) 87696 (17) 455692 "* (18) 1000000
10091 300120 1
77605 155572 999999
PRACTICAL EXERCISES.
(19) 25 (20)
8
75 (21)7896 (22)4875 (23)1240 375
42 4389 2976 1082 567
... .— .... .,_ 1 ,^10
17
33 3507 1899 ^158
_ Sum 1082
(24) 5487
2075
3412
325 (25) 25 containing 250
750 9 75
1000
16 175
2075 Sum.
.MH«Q9««»-
DIVISION.
EXAMPLES OF SHORT DIVISION.
,(7) 2)56789^
28394^
mn (8) 3)3729768769 (9) 4)469769876
^4 1243256256+1 117442469
, , - , , ^1
12
DIVISION.
(10)
6)849768769 (11) 6)756976874
169953753+4 126162812+2
(12)
7)87694213628 (13) 8)80269687
(14)
12527744804 10033710+7
9)376948769 (15) 11)876956788
(16)
41883196+5 79723344+4
12)4976876946782 (17) 12)89769762048769
(18)
(21)
414739745565+2 7480813504064+1
2)3976 (19) 3)8769 (20) 4)47876
1088 2923 11969
5)8767 (22) 6)9698 (23) 7)97899
(24)
1753+2 1616 + 2 13985+4
8)80409 (25) 9)981021 (26) 10)897697
10051+1 109002+3 89769+7
(27) 11)9876978 28) 12)4967844
897907+1 413987
PRACTICAL EXERCISES.
(29) 2)12 (30) 7)350 (31) 8)8736 (32) 3)3966
6 50 4)1092 1322
273
■ . ■
LONG DIVISION.
LONG DIVISION.
EXAMPLES.
13
(35) 13)875(67
78
95
91
(38) 28)1475(52
140
75
56
19
(41) 41)256976(6267
246
109
82
277
246
316
287
29
(36) 15)476(31
45
26
15
IT
(37) 18)958(53
90
58
54
(39) 31)4277(137 (40) 37)25757(695
31 222
117
93
247
217
30
335
333
227
222
(42) 48)337979(7041
336
197
192
59
48
11
14
LONG
DIVISION.
(43) 59)997816(16912
59
(44) 98)999987695(10203956
98
407
199
354
196
538
387
531
294
71
936
59
882
126
549
118
490
8
595
588
7
(45)1
^25)4697680424(3758144:
375
947
J (46) 396)387690204886(979015668
3564
3129
875
2772
726
3570
625
1018
3564
620
1000
396
180
2244
125
1980
554
2648
600
2376
542
2728
500
424
2376
3526
375
49
3168
358
LONG DIVISION. 1 5
C47) 876)4876020048769(5560232932 (48) 1478)8769820000402(5933576454
4380 7390
4960 13798
4380 13302
^37
5802 4962
5256 * 4434
5460 5286
5256 4434
2040 8520
1752 7390
2884 11300
2628 • 10346
2568 9540
1752 8868
8167 6724
7884 5912
2836 8120
2628 7390
2089 7302
1752 5912
1390
16 LO^
(49) S7G96)987G97G8720497(112G2
87696
\G DIVISION.
74501 (50)97680
89768214100(
30940
00O0)8976478976|000OC91896
87912
110737
87696
18527
9768
230416
175392
87598
78144
550248
526176
94549
87912
240727
175392
66377
58608
77696
653352
613872
)00(3242 Ans.
394800
350784
440164
438480
168497
87696
80801
(51) 1476980|00000)47
44
3588282
2953960
Rem
6343221
5907920
4353014
2953960
. 1399054
LONG DIVISION
.'
PRACTICAL EXERCISES. 1
(52)
45)9847(218
90
84
45
(53)
391)1259678(3221
1173
866
782
397
360
847
782
Rem. 37
658
391
Rem. 267
(54)
148)225476(1523
148
(55)
25)375(15 bushels.
25
774
740
125
125
347
296
516
444
Rem. 72
L=
B 2
18 LONG DIVISION. ||
(56) 75)87735840(1169811
75
127
75
(57) 49850)99700(2
99700
523
450
735
675
608
600 *
•
84
75
90
75
15 Rem.
When the divisor is the exact product of any two
; figures multiplied together.
EXAMPLES
(61) 5)9756 (62) i
7)l951-fl 1st Rem.
))8491
9)943+4
278+5 2d Rem.
X5
25+1=26
104+7x9+4=67
(63) 9)44767 (64)
7)92017
2)4974+1 Rem.
2487
1643+1x7+2=9
1
LO:SG DIVISION. 19
(65) 11)55210 {6G) 6)38751
9)5019+1 8)6458+3
Rem. — Rem.
557+6X11+1=67 807+2x6+3=15
(67) 12)99876 (68) 12)379^7
9)8323 12)3163+11
— — Rem. : Rem.
924+7x12=84 263+7x12+11=95
PRACTICAL EXERCISES.
(69) 5)3775 (70) 12)480 (71) 12)14400
5)755
Ans. 151
8)40
Ans. 5 fe
12)1200
Ans. 100
(72) 12)1800
6)150
(73) 12)396
11)33
Ans. 25
Ans. ^3
EXAMPLES IN ADDITION, MULTIPLICATION, SUBTRACTION
AND DIVISION.
(I) 50 (2) 40 10 (3) 25000
50 20 10 13000
100 2)20 20 2)12000
—25
Ans. 10 g6000
75 Ans. —
20
COMPOUND ADDITION. 1
(4) Bought 8200 Sold 3756 (5) 50)2450(49 mUes. Ans.
5000 4879 200
13200 8635 450
8635 450
Ans. 4565 1
(«)
Bought 24 bags, containmg 3000 fe
Sold 15 1736
Remains 9 bags, containing 1264 ^
(7) Days '365)2920(8 dols. per day. Yearly income 2920
2920 Spends yearly 1769
Savesper year $1151
i..
-^©a*.^
COMPOUND ADDITION.
l^'EDERAL MONEY.
EXAMPLES.
$
ct8, m, $ cts. g cis.
(2) 46
79
75 5 (3) 37 68J (4) 72 62-
37 8 95 371 85 87l
43
50 43 25" 20 12|
97
37 5 79 . 56} 45 ISJ
91 37'
g267
00 8 g255 87i 42 68|
g440 06»
COMPOUND ADDITION
21
$ cts.
g
cts.
i
' cU.
(5) 54 75
(6) 29
25
(7) 1
182
3^ 371
34
371
2
50
93 18|.
188
68|
871
149 871
603 68|
979 121
2194 181
265
1783
121
18|
1
93J
87o
68|
8579
56|
2
6
87i
372
87-
93i
g4012 18J
P
0887
06J
^
1
$
els.
$13
25
Ct8,
(8) 5
00
(9)
1
871
681
18
60
1
8
87^
433
1
18|
1
371
14
50
933
871
56J
5
371
87|
37f
3l|
7
20
00
STERLING MONEY.
121
^82
18|
$l_
683
EXAMPLES.
£ s.
d.
£
*. d.
£
*. rf.
(2) 7 9
6|
(3)
4
6 4
(4) 565
3 7
13. 7
47
19 7
382
13 5
4 5
2
159,
5 3
592
9 2
10 18
lOj
78
6 llj
856
259
17 3
9 8
Ans. 36 1
Ans.
289 18 IJ
An
3. 2656 1
3 1
22 <^03irOl ND ADBITIOX.
_—
£ S. d.
£ s.
d.
£ s.
d.
(5) 142 16 7 (6)
763 7
4
(7) 69 18
7
489 3 4
39 4
9
175 2
6
726 15 9
162 17
2
1582 19
4
573 4 '8
459 15
175 13
9
628 12 6
473 12
8
143 13
212
8
7
Ans.2560 12 10 Ans. 18^8 16
11
Ans.
£
2359 8
5
£ s. d.
s. d.
(8) 1776 12 8
(9)
985
4 9
412 16 5
186
13 4
369 7 2
1569
18 4
469 15 10
183
8
573 19 2
^
17 4
1987 14 8
7
4823 15 11
Ans.
EIGHT
2925
15
Ans. 10414 1 10
POIS WJ
AVOIRDU
T. cwt. qr. lb. oz, dr.
T. cwt. qr. lbs. oz.
dr.
(2) 7 11 2 16 4 13
(3) 12
16
1 19 15
15 7 3 8 16 7
114
io
2 12 4
13
138 19 1 12 8 13
72
4
2 24 14
3
42 8 3 19 12 4
176
15 .
3 4 15
11
357 6 2 8 3 3
Anp '^'^ft
7
2 6 1
11
Ans. 561 14 1 7 13 8
qr. lb.
z.dr.
T. cwt.
(4) 139 19
3 18 1
13 10
1754 10
2 11
2 14
27 , 3
14 11
13
13
Ans. 1922 6
.2 17
8 8
^^i;^^,;^;^^
COMPOUND ADDITION. 23
TROY WEIGHT.
lbs. oz.dwts.gr. lbs. oz.dwts.gr. lbs.oz.dwts.gr.
(2) 185 2 19 20 (3) 16 4 18 6 (4) 172 11 19 22
56 9 15 6 7 9 11 22 12 4 13 12
1472 11 2 17 163 7 12 18 ' 18 5 11 20
385 ^5 / .17 13 ' 119 11 13 18
1 10 Pl ■ 7 I*'* -. -— .. n ^ T^
., , . ,, , Am 901 ini'i'^^ 010 90
Ann c>i in ft T? 1«
APOTHECARIES' WEIGHT.
fe 5 3B^r. ife 3 3 9g-r. ft 3 3 B^r.
(2) 84 .7 6 12 (3) 18 1 12 (4) 182 3 10
■ 132 5 2 175 10 5 10 12 10 2 17
16 2 2 2 8 472 3 1 2 3 17 2 4 2 15
1427 6 7 19 11 7 2 10 2 1 19
Id 6 1 9 ■
Ans.667 1 7 2 5Ans.212 5 1 1 11
LONG MEASURE.
yd. ft. 171. L. m.f, p. yd. ft. in. L. m. f. p. yd. ft. in.
(2) 3 2 11 (3)172 2 3 19 2 2 4 (4)462 17 29 1110
119 000 14 1 3 000110110
20 8 12290010 4 1 2 28 1 2 9
31 10 0040000 000 13
627 00 032 3Ans.46703 140 5
Ans.20 1 1 Ans. 173 1 4 23 210 6
CLOTH MEASURE.
E. E, qr, n, E,F. qr, n,
(2) 72 3 2 (3) 19 2 3
536 2 1 728 1 2
847 1 3 142 1
1453 2 816
41 2 32 1 2
Ans. 2951 Ans. 1739
24 canrouAD addition
,
yd. qr.
(4) 19 2
14 2
32
3
142 3
na. E.
3 (5)
o
1
2
Fr.
143
17
172
182
132
72
qr. na,
3
2 2
1 1
1 3
3 2
1 1
Ans. 210
720
10
A. R. P.
(2) 487 2 17
25 3 28
e-V 32
45 1 16 .
26 29
LAND MEASURE.
A. r: p.
(3) 22 2
700 3^27
47 5
39
47 2 39
3 28
A
(4)
Ans
(
Ai
A. R. P.
(4) 132 3 25
654 C 17
462 3 25
16 4
1665 3 38
Ans. 652 1 2
Lns. 2931 3 '29
Ans. 858 19
hhd. gal. qt. pt.
(2) 385 42 3 1
27 36 2
132 17
729 25
163 47 2 1
Ans. 1438 43
T. h. gnl.qt.pt.
862 10 10
32 1
37 2
32 1
2 1
LIQUID MEASURE.
T. h. gal. qt.pt.
(3) 19 2 19
45 Oil
3 17 2
21 1
Ans. 65 1 58
863 39 1
DRY MEASURE.
B. p. qt.pt
(3) 754 2 5
469 2
385 2 7 1
375 1
3 2
B. p. qt.pt.
(2) 47 '2 4 1
635 3
247 3 1
285 2
734 2 5
B.p. qt.pt,
4) 144 3 2 1
.0120
3 1
462 3 1
72 5 1
Ans. 1950 7
Ans. 1985 1 1
18. 680 fi
COMPOUND ADDITION.
25
TIME.
F. m. w?. 6?.
h. m. sec.
F.
m, w, d. h. m. sec.
(3)
172 1
4 62 (4)
462
4 5 37 24
34 18
62
11 24
15 4 5
3 27
15 13
Ans
13
21 35 18
6 1 4 13 12 37
187 4 3 2
5 37 28 Ans
524
10 3 3 6 3 25
MOTION, OR CIRCLE MEASURE. |
^g,'> ' ''
sig.'> r
It
sig, « ' ''
(2)
2 7 32 16
(3) 5 10 46
38
(4) 45
5 27 24
11 37
18
1 9 18
1 6 17 13
1 47
12
14 21 34
7 38 24
18
2 8 13 54
4 5 42 19
2
52
4 7 12 19
1 15 12 23
11 57 '^Q
47 32
Ans
. 8 2 37 36
Ans. 8 10 20 37
Ans. 10 20 22
10
APPLICATION.
$ ds.
F. qr.
na.
B,p,qt,
fl)
375 45
(2) 57 2
(3) 2 2
142 371
1375 56|
29 3
2
3 3 5
45 1
3 1 1
32 3
38 2
1
2 4
Ans
18f}4 38^
38 2
Ans. 113 2
A, n
Ans. 242 1
3
F. qr, na.
P.
(4) 142 2
(5)
15 3
32 3
12
18 1 2
108 3
18
Ans.
25 3 2
Ans. 284 30
60
26 COMPOUND MULTIPLICATION.
M.fur, p. B. p, qt,
(6) 43 3 (7) 756 2
29 34 756 2
57 2 32 756 2
12 3 18 854 6
854 5
Ans. 142 2 4
Ans. 3977 3 2
COMPOUND MULTIPLICATION.
EXAMPLES.
FEDERAL MONEY.
$ ets. g cts. m. $ cLt.
(4) 26 18| (5) 100 40 4 (6) 66 18J
6 10 9
Ans. 157 12i Ans. 1004 04 Ans. 505 68J
$ da, m. $ ds.
(7) 26 37 5 (8) 665 62^
8 12"
Ans. 203 00 Ans. 6787 50 •
ENGLISH MONFV.
£, s. d, £ s, d.
(2) 14 6 OJ (3) 111 11 101
9 lO"'
Ans. 128 14 2} Ans. 1115 18 9
COMPOUND MULTIPLICATION. 271
£ 8. d. £ a, d,
(4) 37 6 91 (5) 66 ^8 7-J .
6" 9
Ans. 186 13 n\
Ans. 507 17 9| j
AVOIRDUPOIS WEIGHT.
T.cwt. qr, Ih, oz, dr. qr, lb, oz, dr,
(2) 6 14 2 7 5 2 (3) 3 16 7 8
4 10
Ans. 26 18 1 1 4 8
Ans. 35 24 11
CwL qr, lb.
(4) 12 6
10
Cwt. qr. lb.
(5) 4 3 17
Ana. 15 2 4
^. TROY \VI
U), oz.dwt.gr. lb.
(2) 43 8 10 (3) 113
4
Ans. 53 3 19
:IGHT.
oz.dwt.gr. lb. oz. dwt.
6 6 (4) 17 9 14
6 10
Ans. 172 1 13 16 Ans. 681
1 12 Ans. 178 1
lbs. oz.dvjt.gr.
(5) 41 6 18 2
lbs. oz. dwt. gr.
(6) 91 4 14 16
8
Ans. 291 6 14 Ans. 731 1 17 8
APOTHECARIES' WEIGHT.
Ik ^ 3 B gr. m ^ Z B gr.
(2) 63 10 2 12 (3) 17 5 6 1 4
9 12
Ans. 484 6 7 2 8
Ans. 209 9 4 2 8 1
-n .7--^ . . ^ r—T^, '!
28
(4)
Ans.
(2)
Ans.
(4)
An.
1
(2)
Ans.
(5)
Ai
J
(?) 1
COMPOtlSD MULTIPLICATION.
Ife339 m ^ Z B gr.
76 4 1 2 .. (5) 95 1 2 1 11
9 11
687 1 7
Ans. 1046 2 3 2 1 11
LONG MEASURE.
L, J\l.fur,p. M,fur,p,yd,ft. in,
4 2 2 29 (3) 18 3 20 1 2 10
7 5
33 1 3 3
Ans. 92 1 21 31 2 2
6 40 7
10
M.fur. p.
(5) 44 6 20
7
3. 66 48 6
Ans. 31^ 5 20
CLOTH IVIEASURE.
iJ.^. qr. na, E,Fl. qr, na, E,Fr, qr. na.
37 4 2 (3) 18 3 (4) 14 1 3
8 12 9
63 1 Ans.
217 4 Ans. 129 3
Yds. qr. na.
19 1 2
5
E. E. qr.
(6) 56 3
9
18. "96 3 2
Ans. 609 2
LAND ISIEASURE.
l.R.P. A.R.P. A.R.P. A.R.P.
9 3 20 (3) 10 33 ■ (4) 1 3 11 (5) 63 3 18
6 9 10 11
Ans. 119 1 00 Ans. 91. 3
17 Ans. 18 30 Ans. 702 1 38 1
-7^-r— r^ '}
COMPOUND MULTIPLICATION. 29
LIQUID MEASURE.
T, hhd, £^al. qt, pt. P. hhd. gal, qt, pt.
(2) 1 2 16 3 1 (3) 4 1 19 3 1
10 5
ins. 15
2
42 3
(4)
T.
3
h. gal. qt.
2 50 2
8
Ans.
29
2 26
Ans. 23 36 1 1
H. gal. qt. pt.
(5) 4 41 1
10
Ans. 46 33 1
DRY MEASURE.
Bu.pe. qt. pt. Bu. pe. qt. pt.
(2) 13 3 2 (3) 110 3 2
4 4
Ans
7
2
(4)
B.
A4.
^0
qt. pt.
1
7
Ans.
308
3 1
Ans. 443
4
(5)
P.
3
qt.
1
9
ns. Bush.
7
1
TIME.-
Y. m* w. d. k.min.sec. W. d. h.
(2) 17 8 2 6 4 40 18 (3) S 5 22
6 12
Ans. 106
1
2
4
1
48
(4)
F.
7
m.
w.
4
4
Ans.
63
10
1
1
Ans. 46
1
Y. m.
(5) 16 2
w.
d.
6
8
A.ns. 121 4
2
6
TT*"
30
(2) Multiply
Ans. 1
t
(4) 44
COMP(5UN]
£ S. d,
^ 37 10 6|
6X
a MULT]
RULE
EXAMPL
by 48
:8=48
56
=56
120
=120
Ai
4
.54
PLICATION.
2.
ES.
% Cts. 7/1.
(3) 66 37 5 by 36
6X6=36
225
'f
398 25^0
6
801
r
Ans.^2389 50
cts,
25
m.
3 by
7X8=
(5) 12 18J by 96
12K8=96
309
77
I
8
146 25
8
Ans. 2478
16
8
Ans. 1170 00
(6) 45
6
d.
9* by
12X10=
£ s. d.
(7) 96 12 3| by 144
12X12=144
544
1
6
10
1159 7 9
12
Ans. 5440
15
IS. 13912 13
A.
(8) 47
R,
3
P.
20 by 5
6X9=
(9) 48 7 25 by 88
11X8=88
538 3 35
8
287
1
9
Ans. 2585
1
Ans. 4307 7
COMPOUND MULTIPLICATION
31
I
lb.
0) 56
oz
9
.dr.
6 by fi
12X7=
4
84
681
9
7
\n^. 4772
3
RULE 3,
EXAMPLES.
(2) Multiply 7
Cts.
871
11x4+3-
(3]
47
28
cts.
68f
11x6+2=68
86
62^
4
■&5k
Ans.
(5)
Ans
315
56»
6
346
23
50
62|
1893
57
371
37|
Ans. 370
(4) 49
l^
cts.
75X3
12
1950
75
$
94
18JX1
10
597
00
941
'?
4179
149
00
25
2825
94
62i
18|
Ans. 4328
25
;. 2919
81J
32
(6)
Ans.
(8)
Ans.
(10)
Ai
COMPOUND MU
$ cts,
42 31J-X3
11
LTIPLICA
(7)
Ans.
(9)
Ans
(")
Ans.
noN.
£
28
*. d.
7 6iXl
4
465
43J
5
113 10 2
7
2327
126
18|
93J-
794 11 2
28 7 6J
2454
12^
822 18 81
34
s. d.
8 4|X1
11
Cwt.
7
(^r. lb.
3 22X1
10
378
12 A\
6
79
1 24
6
2271
34
14 li
8 4|
397
7
1 8
3 22
2306
2 6|
5. 405
1 2
lbs
12
. OS, dwts,
5 8X3
12
Jtf.
4
6 21X3
12
149
4 16
3
67
6 12
7
448
37
2 8
4 4
404
14
4 4
3 23
IS. 483
G 12
418
7 27
(2) Multiply
1
COMlhJUND MULTIPLICATION
RULE 4.
EXAMPLES,
1 56^X6 (3) 2
10
33
Ct8.
871X6
10
5 65X5
10
28
75X7
10
15
6 30
4
287
50
5
626 00
78 25
9 39
1437
201
17
50
25
25
AUB. 713 64
Ans. 1656
00
(4) 4
cts,
31^X9
10
(5) 18
Ci8.
93JX7
10
43
121X7
10
189
371X5
10^
431
25
6
1893
75
4
2587
301
38
50
86^
81|
. 7575
946
132
00
871
56|
Ans. 2928
18|
Ans. 8654
433
34
(6)
Ans.
(8)
Ans
25
CO^irOUND
cts.
43JX9
10
MULTIPLICATION. 1
$ Cts. 1
(7) 1JX6 II
II
254
371X7
10
171X6
10
2543
75
8
1
75X2
10
20350
1780
228
00
621
03|
17
35
3
1
Ans. 39
£
(9) 37
50
2
00
50
00
10^
65|
s. d.
18 6{X5
10
223'59
56J:
10
cU,
161X9
10
101
65X3
10
379
6 21X7
10
1016
50
9
87S2
12 !•
3
9140
304
91
50
95
481
^ 11377
2654
189
16 3
16 64
12 7|
. 9544
93J
'Ans. 14222
5 3J
£ s. d,
(10) 48 14 21x9
10"
COMPOUND MUIiTirLICATION.
36
487
2 IX
10
4871
10
4
19484
3896
438
3 4
16 8
7 101
Ans. 23819
7 101
(12)
£ 8. d,
58 9 6fX6
10
584 15 71x9
lo'
5847 16 3
3
17543 8 9
5263 71
350 17 41
Ans. 23157 6 9
£, s. d,
64 2 8X5
10
641 6
6X
10
6413 6
6
5
32066 13
3206 13
320 13
4
4
4
Ans. 35594
M, /. p.
(13) 25 3 18X5
10
254 2 20X6
lb
2543
1 0X2
10
25430 10
5086 2
1525 7
127 1 10
Ans. 32170 4 10
36
F.
(14) 48
COMPOUND MTJLTIPLICA
in.b.c. Yd. gr.n.
42x7 (15)2221X4
10 10
rioN.
Hhd.gal.qt.
(16) 4 37 2by 4250
10
45 60 0X5
10
483 10 2X8
10
225 2 2
10
4838 10 2X5
10
2256 10X2
10
459 33 0X2
10
48388 10 2
2
22562 2
3
4595 15
4
96777
24194
3871
338
91
51
1 1
82
, An
67687 2
4512 2
90 10
18380 GOO
919 3
229 48
s. 72290 1 Ans
. 19529 48
Ans.125182
02
APPLICATION.
gl.07 (3) $5
9
.62J (4) gl.l2l
12
(1) $12.50
(2)
Ans.
s. d,
2 2 by
7
Ans. 62.50
9.63 Ans. 67.47 6.75 [1
£
(5)
63 (6) 3
-X
Ans. 27.00
871 by G 1
8
15 2
9
31
00
8
Ans. 6 16 6
Ans. 248
00
$
(7)
1
COMrOUND MULTIPLICATIOrf,
C«*. £ S, d, $
15^X6 (8) 1 3 (9) 9
10 12
37
ds.
10X5
10
521
10"
15
11
91
0X6
10
15
25
911
Ans. 8
5
910
3
acre X 5
^
A
$
(11) 1
Ans. 10
161
2730
546
45
50
£
(10)
s. d.
9 6 per
10
n3.332i
50
ds.
18|X7
10
le cost.
4
15 0X2
10
11
871X1
10"
47
10
3
118
75
2
142
9
2
10
10 .
7 6
237
11
8
50
871
31J
Ans. 154
7 6
ins. 257
68| prin
IT
38 COMPOUND SUBTKACTIOI^.
Again: $\ 37^X7
10
13
75X1
10
137
50
2
275
13
9
00
75
621
g298
g257
g40
37» sold for.
681 prime cost.
68J gain.
COMPOUND SUBTRACTION.
EXAMPLES.
FEDERAL MONEY.
g ds.m, ^ cts, $ cts^,
(2) From 24 60 7 (3) 60b 62^ (4) 110 ISf
Take 19 30 : U^s' 99 10|
Ans. 5 30
7
(5)
$ ds, m.
960 10 2
9
Ins
. 960 09 3
Ans. 5
$
449
1
98 87^
(6)
ds.
621
06|
Ans.
448
55J
Ans. 11 81
$ ds.
(7) 1866 00
Ans. 1587 88|
COMPOUND SUBTRACTION.
$ ds. $ els, m.
(8) 104 06* (9) 4010 14 4 (1
9J 1011 12 5
0)
ns.
7
8
$
400
211
3d
cts,
00
121
Ans. 103 961 Ans. 2999
1 9 A
188
d,
6
H
871
ENGLISH MONEY.
£ s. d, £
(2) 47 6 7| (3) 419
28 5 101 227
Ans. 19 9J
Ans. 191
18
8f
£ s. d,
(4) 1000 11 113
200 9
£
(5) 1000
60
s,
2
7
d.
51
Ans. 800 2 11|
Ans. 939
14
n
AVOIRDUPOIS VVEIOHT.
T, cwt. qr, lb, oz, dr, cwt,
(2) 18 16 1 16 9 2 (3) 9
19 3 20 6
qr, lb. oz
3 20 2
2 23 5
Ans. 17 16 1 24 8 12
Ans. 9
24 13
T, cwt, qr, lb,
(4) 14 10 2 16
n ^g^^
Cwt
(5) 400
. qr
3
.lb.
14
Ans. 14 10 2 5^^^^
Ans. 397
14
TROY WEIGHT.
lb. oz, dwt.gr, lb. oz.
(2) 8 3 2 (3) 106
2 1 18 6 10 6
dwi
2
15
20
Ans. 6 1 1 20
Ans. 95 5
17
19
40 COMPOUND SUBTRACTION.
lb. oz.dwt,<^r. 11). oz.dwt.gr,
(4) 22 12 ^6 (3) 16
14 6 110 12 11 10 11
Ans. 7 6 16 Ans. 3 9 13
APOTHECARIES' WEIGHT.
Ife339^. fe53 ife33
(2) 48 9 6 1 4 (3) 59 1 2 (4) 69
1 10 2 8 63 7 5 14 9 1
Ans. 46 11 5 1 16 Ans. 5 5 5 Ans. 54 2 7
CLOTH IVIEASURE.
yd. qr.nci. yd.qr.na. E.E.qr.na. E.F.qr.
(2) 950 12 (3) 49 2 (4) 66 4 (5) 44 1
19 2 3 16 2 1 17 2 19 2
Ans. 930 2 3 Ans. 32 2 1 Ans. 49 3 2 Ans. 24 2
E.Fl. qr. Yd. qr. na. Yd. qr. na,
(6) 963 1 (7) Bought 17 2 (0) 75 3 1
174 2 Damarred 2 3 1 1
Ans. 788 2 Remains good 14 2 3 Ans. 75 3
LpNG MEASURE.
Dcs:;. m . fur. p. M.fur. p.
(2) 20 50 4 20 (3) Travels first day 43 5 20
11 56 30 second do"^. 32 4 00
Ans. 8 54 3 30 Ans. 11 1 20 more.
LAND MEASURE.
A. R. P. A. R. P.
(2) 502 2 10 (3) 69 1 ^3
111 3 9 17 3 2
Ans. 390 3 1 Ans. 51 2 1
m
COMPOUND SUBTRACTION.
^ LIQUID MEASURE.
T, khd. gaL qt. pL Hhd, gal,
100 -1 19 ^ 1 (3) 2
99 1 28 3 1 29
41
Ans.
3
Ans. 1 34
(4) From I pipe of wine, which is 126 ffals., subtract 93,
leaves 33 gals, of wine. Then from 4 nhds. of brandy,
subtract 29 gals., leaves 223 of brandy. Then from2 bbls.
of beer, subtract 1, leaves 1 barrel, which is 31i gals.
Answer, 33 gals, wine, 223 gals, brandy, 31^ gals. beer.
DRY MEASURE
J5. p. qLpt. B. p. qUpL B. p. qt.pt.
(2) 10 I (3) 695 3 1 (5) 600 2 7 1
9 2 6 1 589 3 5 146 3 2 1
Ans.
12 Ans. 105 3 3 1 Ans. 453 3 5
TIME.
H. min, sec.
(2) 16 29 33
7 36 44
Y. m. Wr
(3) 18 11 2
9 10 3
Ans. 8 52 49
F. m. IV. d,
(4) 900
111 6 2 6
(5)
Ans. 788 6 1 1
Ans. 9
3
y. m.
6
1 1
1
d. h.
1 1
s. 4 10
2
5 23
MOTION, OR CIRCLE MEASURE.
sig. ^ ' " sig. "^ ' " sig, ** ' "
(2) 9 7 40 8 (3) 10 10 16 12 (4) 11' 2 5 14
7 9 57 19 7 24 37 59 ; .907 20
Ans. 1 27 42 49 Ans. 2 15 38 13 Ans. 2 1 52 $A
T>%
APPLICATI(»r.
(1) 6 feet of chain at $2,75
per foot = $16 59
A gold ring for 4 50
Ear-rings 12 00
42
COMPOUND SITBTR ACTION.
g33 00 whole amount.
Ring 4 50 has been returned.
To receive $28 50
(2)
2 doz. pairs at 75 cts.
16 yds. at 87| —
28 do. at 22 —
5 pair at 31 J —
Amount
Note delivered
Must be returned
A, R, P.
(.3) 1 St tract contains 690 2 16
2d do. do. 400
3d do. do. 63 3 21
4th do. do. 63 3 24
$ cts.
:7= 18, 00
=r= 14 00
rrr 6 16
1
56J
39
50
72|
00
10
27J
£ s. d.
(4) 55 6 7
41 4 6
75
Collected 171 11 1
In the whole 1218 1 24 Lost 40 6
Sold 200 00
I have 131 5 1
Remains
1018 1 24
Bu,p.
(5) Bought 400 3 of wheat,
Sold 225 1 do.
Remaining 175 2
Bu. p. Bit. p.
160 Oof rye, 150 2 of oats,
37 2 do. 78 3 do.
122 2 71 3
COMPOUND DIVISION. 43
COMPOUND DIVISION.
EXAMPLES.
$ cls, $ ' cts, $ ch.
(3) 3)366 18 J (4) 6)384 S^ (5) 8)496 75
Ans. 64 141-f 2 Ans. 62 09|-f 4
tf cts* ^ cts* ^ cts,
(6) 9)587 68J (7) 11)976 43J (8) 12)1979 331
Ang. 65 293-f 4 Ans. 88 76^-f 9 Ans. 164 94-J-f 4
£ s. d. £ s, d.
(9) 3)560 9 7 (10) 5)475 19 •9J
Ans. 186 16 6J-f 1 Ans. 05 3 ll^J-fl
£ ,9. d, £ s. d,
(11) 8)596 15 61 (12) 12)756 4 llj
Ans. 74 11 ll|-f2
Cwt, qr, lb, , ' Cwf, qr, lb. Yds. qr. nn,
(13)5)45 3' 27 (14) 9)10 \b (13) 7)44 J 2 ■
Ans. 9 22+1 Ans. 1 14-f-l Ans. 6 1 l-f3
Yds, qr, na. M. fur, p, JSl. fur, p,
(16)11)56 3 3 (17) 12)105 5 22 (18) 6)45' 7 18
Ans. 5 2-f9 Ans. 8 6 18+6 Ans. 7 5 9+4
When the divisor exceeds 12, but is the exact product
of any two figures in the multiplication table.
$cts.m. $cts,m.
(19)6 )45 66 5 ;(20) 4)98 77 8
6l7]r0+5 ^^^ 11)5^+2 ^^^^
Ans. 126 8+2x0+5=17 Ans. 2 24 4+10x4+2=42
44 COMPOUND DIVISION.
^cis.m, $ cts,
(21)12)77 87 5 (22) 12)288 68|
8)6 48 9+7 9)24 05l-fl
Rem. Rem.
Ans. 81 l+lXl2+7=19An».2 67|-f lXl2-f 1=13
ds. m.
(23) 12)^6 37 5
11)41 36 4+7
Ans. 3 76 0+4x12+7=55 Rem.
£ s. d.
(24) 4)87 19 44
8)21 19 10+2
Ans. 2 14 11 + 6x4+2=2/ qrs.r=:J+2 Rem.
£ s. d. £ 8, d.
(25)3)55 4'7| (26)8)97 15 6}
7)18 8 21+1 7)12 4 5}+l
. 1 Rem. ; Rem.
Ans. 2 12 7+6x3+1=19 Ans. 1 14 11+1x8+1=9
H}id.gal. qt. JThi.gaX. qU
(27)7)44 28 2 (28) 12)150 47 3
9)622042 10)12351+11
Rem. Rem.
Ans. 0441 + 7X7+2=51 Ans. 1 160 + 5x12+11=71
COMPOUND DIVISION. 45
When the divisor exceeds 12, and is not the product
of any two figures in the multiplication table.
^ cts. ^ cts, m,
(31)78)196 75(2 52 2 An 3.
156
$ cts, $cts,m,
(32) 97)496 871(5 12 2
485
78)4075(52 cts.
3900
97)1187(12 cts.
97
175
217
156 '
194
78)190(2 mills.
156
23
10
Rem. 34
97)235(2 mills. ]
194
41 Rem.
g cts, $Ct9,
(38)123)376 811(3 06| An?
369
£ s, d,£ s. d.
.(34)87)44 7 6(0 10 2\ Ans.
20
123)781(6 cts.
738
87)887(10 shillings.
87
43
17
4
12
123)172(1
123
87)210(2 pence.
174
49 Rem.
36
4
S7)144(1 farthing.
87
57 Rem.
46
COMPOUND DIVISION.
£ », d,£ f. d.
(35)
148)156 15 8|(1 1 2J nearly, Ans.
148
8
20
148)175(1 shilling.
148
27
12
148)382(2 pence.
296
36
4
147
148
PRACTICAL EXAMPLEg,
$
ds.
«»• i! dt, t di.
(1) 6)47
87 5 • (2) 112)64 81}(o 57j Ans. ||
- 100
*P_
97
9+1
- 112)6481(57 ct«»
Ans. 1
99
4-f3x6-f.l=:l^Eem. 560
881
784
97
4
U2)389(S
336
43 Rem.
C03tP0Uril> DIVIBION.
47
(3) 72)56 25(0 78 1 An&.
100
$ cts.$ct8.m.
(4) 63)125 00(1 98 4 Ans.
63
72)5625(78
Ct8»
63)6200(98 cts.
504
567
685
530
576
504
9
26
10
10
72)90(1
mill.
63)260(4 miUs
72
252
18 Rem. 8 Rem.
£ s. d.
(5) 4)18 17 6
Ans. 4 14 4|
£ s. d, £ s. <?.
(7) 1000)576 18 9^(0 11 4| Ans
20
1000)11358(11 shillings.
1000
$ cts, g cts.
(6) 125)1875 81 1-(15 00^ Ans. 1358
125 1000
625
625
125)00081(00 cts.
4
125)325(2 qra. 305
250 4
358
12
1000)4305(4 pence.
4000
75 R6m. 1000)1222(1 farthing.
1000
222 Rem.
48
REDUCTION.
Gal.qt.pLG
(8) 89)150 2 1(1
89
,qtpL a I
2 1 Ans. (9) 19)9
4
jrJb.C.qr.lb.
I 25(0 1 27 Ans.
61
4
19)37(1
19
qr.
89)246(2 quarts.
178
18
28
68
149
o
38
89)137(
89
I pint.
19)529(27 lbs.
38
48:
aip.
149
133
16 Rem.
*»©®©M^
REDUCTION.
FEDERAL MONEY.
EXAMPLES.
0) fo
100
(2)
$
25
100
(3) 387
100
(4) 25
4
Ans. 1000
Ans.
2500
Ans. 38700
Ans. 100 fourths.
REDUCTION. 49
cts. CiSt ^
(5) 60 (6) 150 (7) 50
2 ,3 100
Ans.IOO halves, Ans. 45QthiTds» 5000
(8) 25 (9) 275
100 100
Ans/ 10000 halves.
2500 27500 (10) 10
.3 4 10
Ans> 7500thir(ls. Ans. 110000 qrs. Ans. 100 dimes.
(tl) 220
10
' 2200 dimes.
10
22000 cts.
10
Ans. 220000 mills.
JSTote. — When more than one denomination is given
to be reduced.
$ cts, $ cts, $ cts,
(1) 15 15 (2) 2 25 (3) 17 18f
100 100 100
Ans. 1515 cts. 225 cts. 1718 cts.
4 4
Ans. 900 4ths. Ans. 6875 4tlis.
50
REDUCTION.
$ cts.
(4) 13 27,J
100
% Ct8,
(5) 426 881
100
1327
3
42688
2
Ans. 3982 thifds.
Ans. 85377 halves.
ENGLISH MONEY.
£
364
20
70
12
(5) 12
4
(2) 364 (3) 20 (4)
20 12
Ans. 7280 s. Ans. 240 df. Ans. 840 d. Ans. 48 qrs.
d. £ s,d. £ s, d, £ 8. d.
(6) 26 (8) 18 12 7 (9) 105 13 91 (10) 36 19 7J
Ans. 104 qrs.
20
372
12
Ans. 4471 (/.
20
2113
12
25365
4
20
739
12
8875
4
Ans. 101462 Ans. 35503 qrs.
Cents to Pence.
(2)
cts,
36975
9
(3) 57697
9
10)332775
Ans. 332771 (f.
10)519273
Ans. 51927|-f£?.
EEDUCTION. 51
(2) 4590
10
Fence to Cent^,
d,
(3) 76975
^0
9)45900
9)769750
Ans. blOQds,
AVOl
Cwt,
(2) 260 (3)
4
Ans. 85527^5. 1 m,+l
RDUPOIS WEIGHT.
qr, lb, oz,
36 (4) 17 (5) 20
28 16 16
Aas. 1040 qrs.
Ans.
288 102 . 120
72 17 20
1008/6*. Ans. 272o5r. Ans.320rfr.
T, cwt, qr,
(6) 5 12 2
20
Qr. lb, oz,
(7) 2 25 10
28
112
4
21
6
Ans. 450 qrs.
81 lbs.
16
486
82
1306 ounces.
16
7836
1306
Ana. 20896 drams.
52
KEDXTCTION.
APOTHECARIES* WEIGHT.
3
(2) 72
8
ft f^ i 3 Bgr.
(3) 10 (4) 15 9 4 2 17
12 12
Ans. 576 drams. 120 ozs.
8
189 oz.
8
960 drs.
3
1516 drs.
3
2880 scru.
20
4550 scni.
20
Ans. 57600 grs. Ans.
91017 grs.
CLOTH MEASURE. |
Yds.
(2) 36
4
E.E.
(3) 20
5
E.Fl.
(4) 16
3
Ans. 144 qrs.
Ans. 100 qrs.
48 qrs.
4
Ans. 192 na.
E.FL qrs.
(5) 5 2
3
E.Fr. qr.
(6) 37 2
5
Yds. qrs. na.
(7) 19 2 1
4
Ans. 17 qrs.
Ans. 187 qrs.
78
4
Ans. 313 na.
KEDUCTION.
53
DRY MEASURE.
Pe.
Bu,
Bu.
m
32
8
(3)
7
4
(4) 12
4
Ans.
256 qts.
Ans.
28 pe.
48
8
384
2
Ans. 768 pts.
(5)
Bu, pe,
14
4
56
8
qt,
3
(6)
Bu* pe, qt, pt,
24 1 2 1
4
97
8
Ans. 451 qts.
778
2
Ans. 1551 pts.
LAND MEASURE.
A.
^. 12. P.
(2)
132
4
528
.(3)
54 3 23
4
219
Ans.
40
Ans.
40
8783
21120 p.
fe^-~
54
REDUCTION.
SQUARE MEASURE.
Sq, yds. Sq.yds. s,ft. s.in. I
(2)
120 (3) 29 2 102 1
9 9
1080 263
144 144
4320 1054
4320 1052
Ans
1080 264
. 155520 sq,in. Ans. 37^74 sq, in.
LIQUID ]VIEASURE.
Gals. Hhds Gals.
Tims.
(2)
28 (3) 5 (4) 110
(5) 6
4 63 4
4
Ans.
\\2qfs. Ans. 315^a7s. 440
24
^
63
Ans. 880 p/5.
72
144
Wids. gals. qts. Gals. qts.
(6)
7 41 2 (7) 47 2
1512
63 4
4
22 190
6048
46 2
2
482 Ans. 380^^5. Ans.
12096 |)f«
4
Ans. 1930 qts.
'
REDUCTION. 55
Hhs. gals. qts. Tvnskhds.gals. Tun.hhd.gal.qt.pt.
(8) 4 3 (9) 19 27 (10) 5 1 15 1 1
63 4 4
252
4
76 hhds. 21
63 63
1011
2
235 68
458 127
Us. 2022 pts.
4815 1338
4 4
Ans.
19260 (?f.9. 5353
2
Ans. 10707 ;?f*.
LONG MEASURE.
Yds,
(2) 48
3
(3)
Po. Fur. Miles*
27 (4) 18 (5) 34
b\ 40 8
Ans. 144/^
135 Ans. 720|>o. Ans.272/wr.
131 _
Ans.
1481 yds.
L. M. M.
(6) 108 ^ (7) 17 (8) 20
3 320 p.~l on. 1760 yds,=l m.
Ans. 324 vi. 340 Ans. 35200 yds.
— « 51
Ans. 5440^0.
56
BEDUCTION.
X.
FL in.
Yds. ft.
(9)
6
3
(10)
14 9
12
(11) 37 1
3
18
Ans.
177 m.
Ans. 112/jf.
8
Fur, po.
144
40
(12) 112 29
40
5760
^)4509
^
28800
22545
2880
2254^
Ans. 247991
yds.
31680
3
L, m.fur
(14) 2 1 3
.po. yds. ft. in.
16 3 2 10
95040
Ans.
12
n.
3
7
1140480 i
8
59
40
(13)
Ans.
M. fur,
450 6
8
po.
32
3606
40
1)2376
144212 po.
11883
1188
13071
^
3
39215
Ai
12
IS. 470590 in.
REDUCTION.
57
TROY WEIGHT
(2) 116
20
lb. oz. dwt.
(3) 25 (4) 29 16
12 20
lb.oz.dwt.gr.
(5) 19 11 14 21
12
Ans. 2320 dwt. 300 Ans. 596 dwt.
20
239
20
Ans.
6000
24
4794
'24
24000
12000
19177
9590
144000 g-^-. Ans.
115077 ^r.
TIME.
(1) 30
60
hrs.
60
yrs.
(3) 12
12
Ans. 1600
s. Ans. 720 w.
Ans. 144 m.
(4)
d. kr> min.
3 5 29
24
17
6
77
60
Ans. 4649 -min.
68 EEDUCTION.
MOTION, OR CIRCLE MEASURE.
(1) 24 (2) 4* (3) 11*12 (4)4 3 18 27
60 30 30 30
Ans. 1440 ' 120 Ans. 342 123
60 60
7200 7398
60 60
Ans. 432000 Ans. 443907"
PROMISCUOUS EXAMPLES.
^ Fur, Days. H.cls.
(1) 35 (2) 8)98 (3) 7)365 (4) 2)84
100 — —
Ans. 12 m. 2/i/r. Ans. 52 1/?. 1 d, Ans. 42 cts.
Ans. 3600 cts, — — —
TunscwU R, S, P.
(5) 8 15 (6) 63 (7) 2I0)15|7 (8) 4)175
20 40
, Ans. £7 17*. Ans. 43 6«. Sjjc.
Ans.l75ctt?f. Ans.2520 59. 2>cr. —
cts, Pts, Sec, Hhd.gcd,
(9) 100)76|42 (10)2)103 (11) 6|0)72|0 (12)733
Ans. J576 42 c^. Ans. 51 qts, Ipt, Ans. 12 mm. —
45
Ans. 474 gal.
REDUCTION. 69
Qrs. Dwis, S.
(13) 5)100 (14) 210)10|8 (15) 2|0)25|0
Ans. 20 E. E. Ans. 5 oz. 8 dwt Ans. £12 10*.
3 s,d. Days, Qrs,
(16) 7 (17) 8 8 (18) 7)203 (19) 16
3 12 4
— Ans. 29 w. —
Ans. 21 9 Ans. 104 d?. — ' Ans. 64 im,
drs, S, Thins,
(20) 16)74(4oz.l0<ir*. Ans. (21)13 (22)20
64 4 20
10 Ans. threepences 52 Ans. 400 cwt.
Qrs, Gal. qt, pL M,fur.
(23) 5)81 (24) 21 3 1 (25) 3 1
— 4 8
Ans. IftjE.Fr. l^r. — —
— 87 Ans. 25/wr.
2 —
Ans. XlSpts.
Cts, Days, Cts,
(26) 1|00)12135 (27) 3 (28) 121
24 4
Ans. $12 35 cts. —
72 Ans. 484 qrs.
60
Ans. 4320 m.
60
REDUCTION,
lbs, Qrs, Dwts,
(29) 13 (30) 3)154 (31) 210)246|1
16
— Ans. 51 E. FL 1 qr, 12)123+ 1 dwU
78 —
13
208
16
208
Ans. 3328 drs.
Yd, qr. na,
(32) 12 2 1
4
50
4
Ans. 201 na.
lbs, oz,
(34) 725 6
16
4356
725
Ans. 10 lb,3oz. Idiot
11606
16
G9636
11 606
Ans. 185696 drs.
Gals.
(33) 63)584621(4)9279
567
Ans. 2319 L Zhhds. Ug,
176
126
502
441
611
567
44 gals.
lbs. qrs»
(35) 28)27552(4)984
252
246 cwt. Ans.
235
224
112
112
SIN6L£ RULE OF THREE. 61
£ s. d. Days. £ s, d.
(36) 5 4 6} (37) 7)763 (38) 83 10 7
i^O 20
— Ans. 109 ly.
104 1710
12 12
1251 Ans. 20521 d.
4
Ans. 5017/i/r.
Ors, Q?.?.
(3y) ^10)122|0 (40) 5)27
3)61 Ans. 5E.E,2qrs,
Ans. 20 3 19
Pts, per.
(41) 2)1357 (42) 4|0)865|4
8)678+ 1 pL 4)216-1-1 4per.
4)84+6 qis. Ans. 54 a. r. lAp.
Ans. 21 6w. Op. 6 qts, 1 pL
SINGLE RULE OF THREE.
EXAIVIPLES.
lbs. lbs. cts. ds.
(3) State the question thus : As 2 : 8 : : 60 : 200 Ans.
For 50x8=400-^2=200 cts.
62 SINGLE RULE OP TUEE13.
/6. lbs. cts, cts»
(4) As 1 : 5 : : 12 : 60
For 12X 5=60-rl= 60 cU, Ans,
yds. yd, cts, cts.
(5) As 10 : 1 : : 650 : 55
For 650x1=550 which -M0=:56d^. Ans.
lbs, lbs. cts, ^ ct^,
(6) As 7 ; 122 : : 87-| : 15 25
For 87^X 122=10675 which -r-7=gl5 25 cts. Ans.
bu, bu, cts, § cts.
(7) As 1 : 209 : : 72 : 150 48
For 72X209=15048 which -M=gl50 48 cts. Ans,
lbs. lb. cts. cts,
(8) As 5 : 1 : : 55 : 11
For 55X1=55 which --5=11 cts. Ans.
yd. yds. $cts, $ cts,
(9) As 1 : 18 : : 4 25 : 76 50
For 425X 18=7650 which -hl=$76 50 cts, Ans.
lbs. lb, ^ cts. cts, '
(10) As 76 : 1 : : 24 32 : 32
For 2432 X 1=2432 which —76=32 ds. Ans.
bu, bu. ^ cts, cts. m.
(11) As 8,: 1 :: 3 94 : 49 2+4
For 394X 1=394 which —8=49 cts, 2 m.-f 4 Ans.
lb. lbs, cts, $ cts.
(12) As 1 : 57 : : 7| : 4 27|
For 7^X57=42n which*'~l=^4 27} ets, Ans.
bu, Ini, ds, ^ cts,
(13) As 1 : 243 : : 45 : 109 35
For 45X243=10935 which -f- 1=^109 35 ds. Ans.
lb, lbs. $ cti. $ cts.
(14) As 1 : 147 : : 1 12;i : 165 37^ Ans.
For 112^X147=165374^ wliich l-l=gl 65,37^ c/5.
lb. lbs. ds. jJ5 cfs.
(15) As 1 : 869 : : 4^ : 39 10^
For 4^X869=3910^ which" — 1=^39 10^ cts, Ans.
SINGLE EULB OF TKKEE, ()3
yds, yd, $ cis. f cU.
(16) As 24 : 1 : : 125 24 : /I 21-f 20 An&.
For 12524 X 1 — 12524 which -i-24=:g5 21 ct?.-f 20
C. /6. ^ 0^5. cts.m,
(17) As 1 : 1 :; 11 50 : 10 S-f-TO.
Zi5. lb. ^ c^*. C^'. J».
Or, as 112 : 1 :: 11 50 : 10 2-f 76 Ans.
For 1150x1—1150 which -M12:=cl0 cU, 2 m.-f 76
/?;. ^*. cU, ^ cf^.
(18) Aa 1 : 218 : : 7 : 15 26
For 7X218=cl526 which ~-f=gl5 26 <?^. Ans.
bu, btt, £, 8, 8. d»
(19) As 57 : 1 : : SO 10 : 10 8|-f S9
Or, as 57 : 1 : : 610 : 10 8|-f
For 610X 1=610 which -7-57=105. Sl-d.^Sd Ans.
oz. Ibs.oz. cts, § ci^,
(20) As 1 ; 3 5 : : 72 : 29 52
o^. oar, c^, ^ cdj?.
Or, as 1 : 41 : : 72 : 29 52
For 72X41=2952 which -r 1=^29 52 c^. Ans.
lb, lbs, cU, g ctt,
(21) As 1 : 135 : : 10 : 13 50
For lOx 135=1350 which --1=^13 60 cU. Ans,
C. T, C, £ s. d. £ 8. d,
(22) As 2 : 15 3 : : 7 12 C ; 1155 3 9
C, C, d. £ 8, d.
Or, as 2 : 303 : : 1830 : 1155 3 9
For 1830X303=554490 which ~2=277245f?.=
£1155 3^. 9d. Ans.
8, d, £ 8. d, gaL gals,
(23) As 4 10 : 54 7 6 : : 1 : 225
^. d, gal, gah.
Or, as 58 : 13050 : : 1 t 225
For 1 X 13050=13050 which -^58=225 gal^, Ans.
M. to. els, § cts,
{9-<) As 1 : 52 : : 250 : 130 00
For 250X52=13000 which -^1= ^130 00 rfg. Ans.
i]^ SINGLE IIULE OF THKEE.
J. A, R. P. $ ds. $ cts.
(25) As 1 ; 34 1 17 : : 4:2 ^25 : 1451 55-^25
P. P. ^ cis. $ cts.
Or, as 160 : 5497 : : 42 25 : 1451 55+25
For 4225 X54a7F=232 24825 which -T-160=gl451
55 cts. +25 Ms.
gals. gal. jj s. s.
(26) As 131 : 1 : : Qb 10 : 10
gals. s^al. s. s.
Or, as 131 :^1 :: 1310 : 10
For 1310X 1—1310 which -M31==105. Ans.
$ $ T. T.hhd.gaLqt.pt.
(27) As 754 : 1754 : : 1 : 2 I 19 1
For 1X1754=1754 wliich -r 754=2 21 M AW. 1 9
gal, qt. 1 pt. Ans.
s. d. £ 8. yds. yds.
(28) As 18 8 : 36 16 : : 7 : 276
d. d. yds. yds.
Or, as 224 : 8835> : : 7 : 276
For 8832 X 7=61824 which -^ 224=276 yds. Ans.
Ih. cwt. qrs. lbs. cts. ^ cts. m,
(29) As 1 : 5 2 17 ; : 91 : 60 13 5
lb. lbs. cts. § cts. in.
Or, as 1 : 633 : : 91 : 60 13 5
For9lX 633=6013^ which -Hl=^60 13c^5.57n. Ans.
its. jJ lb. Ibs.fiz. dr.
(30) As 114 : 354 : : 1 : 310 8 6+84
For 1X35400=35400 which -M 14=310/6*. 8 or.
6 Jr. + 84 Ans.
£, s. £, s. skeins, skcms.
(31) As 2 10 : 105 3 : : 100 : 4206
s. s. skeins, skeins.
Or, as 50 : 2103 : : 100 : 4206
For 100X2103=210300 which -r 50=4206 sk. Aus.
yds. yd. ' ^ cts. j^ cts. m.
(32) As 39 : 1 : : 350 38 : 8 08 4+ Ans.
For 35038 X 1=35038 which -r39=,^8 ^cts.Am.
SINGLE RULE OP THREE. 65
get Is, qts, gals. qt. pt. gals. qi8. pt.
(33) ei^gah.^Ql 2+62 1 1 = 123 3 1
pL gals, qts.pt. ds. ^ cts.
Then as 1 : 123 3 1 : : 37| : 371 62i
pt. pis. cts. ^ cfe.
Or, as 1 : 991 :: 37i : 371 62^
For37iX 991=^371621 which -rl^^3716?id*.Ans.
bu. bu. hu,
^34) 75+87=162
hu. hu. cts. fi cts.
Then as 1 : 162 : : 52 : B4 24
For 52X162=8424 which -r 1=^84 24 ds. Ans.
(35) 1 year equals 365 days.
day. days. cts. ^ cts.
Then as 1 : 365 : : 1871 : 684 37X
For 187^X365=384371 'which +1=^684 37| d*.
the sum he spends in a year ; his income yearly
is ^1022—^684 37| c^.=|337 621 ds. Ans.
cwt. cwt.qrs. lb. ^ cts. ^ cts.
(36) As 1 : 4 3 24 : : 2 10 : 10 42|
lbs. lbs. cts. ^ cts.
Or, as 112 ; 556 : : 210 : 10 421 price of stove.
For 210X556=110760 which ~n2=JlO 42^ cts.
price of stove.
Then 27 Ws. X 18j c/^.=g5 06 j- cts. amount of pipe,
and 50 c^A'.x2=gl.OO nrice of 2 elbowi5.
+ ^10 421 ctv, price of stove.
4-^ ^ 06}- cts. do. pipe-
-fg 1 00 c^. do. elbows,
$16 48 J Ans.
(37) 14 pair X 2=28 single shutters, which X 8^=243
whole number of sheets used.
sheet sheets, cts. $ cts.
Then as 1 : 243 : . Ill : 27 37
For 243X 11^=2737 which +1=^27 37 cts. Ans.
-—-/ [ ■ ■ ■ J I -J ■ I • !
6G SINGLE RULE OF THREE.
(38) If 45 men eat 1 lb. per day each, they will alto-
gether eat 45 lbs. in a day.
lbs, lbs» (1. w, d.
Then as 45 : 45G0 : : 1 : 14 2
For 1X4500=4500 which -^45=^100 d,^\ 4 ^veeJi's
2 days, Ans.
A.R, A.R,P, hu.pe, hu, pe,qts,pt.
(39) As 12 2 ; 37 3 5 : : 443 3 : 1341 7 1
P. P. pe, hu, jte. qlft, pL
Or, as 2000 : 6045 : : 1775 : 1341 7 1
For 1775x6045=10729875 which -^2000=1341 hu.
pc, 7 qts, 1 pt, Ans.
$ ds,
(40) Amount paid for the sugar 204 00
carriage 15 75
storage IB 31}
and would fjain 57 00
g295 00} the sum the
whole must sell for.
Cqrs, C, $ cts, $ cf.s,m.
Then as 27 2 : 1 : : 205 0G| : 10 72 9-fCO
qrs» qrs, cts. $ cts.vi.
Or, as 110 : 4 : : 29506} : 10 72 9-f 60
For 29506}X 4=118025 which —110=^10 '72 cis.
9 7«.-f60 Ans.
(41) To find how much per cent, he can ijay.
$ cts, $ cts, $ %
As 18284 40 : 9142 20 : : 100 : 50 per cent.
For 100x914220=91422000 which -M828440=
50 Ans. the first.
To find what the creditor is to receive.
$ cts. $ cts. $ $
As 18284 40 : 9142 20 : : 472 ': 236
For 472X914220=431511840 which —182^440=
p2e Ans.
SINGLE RULE OF THREE. iSJ
INXmSE PROPORTION.
m. VI. . d. d.
(42) As 12 : 6 :: 18 : 9
For I8x 6r=l08 wlxich -f- 12=9 days. Ans.
m. Tiu d, dk h,
(43) As 18 ; 12 :: 20 : 13 4
For 20 X 1 2=240 which -^18=13 days 4 hours. Ans.
d, d, m, m.
(44) As 4 : 24 : : 8 : 48
For 8 X 24= 1 92 which -r 8=48 men, Ans.
nu m. d. d.
(45) As 48 : 12 : : 24 : 6
For 24X 12=288 which —43=6 days. Ans.
h. h. d. (/. k.
(46) As 15 : 11 : : 5 : 3 8
For 5X 11=55 which -rl5=3 days 10 hmirs. Ans.
ft. in. ft. in. ft. yds. ft. in.
(47) As 2 3 : 30 6 : : 48 : 216 2 8
in. in. ft. yds. ft. in.
Or, as 27 : 366 : : 48 : 216 2 8
For 48X366=17568 which —27=650^4/^=216
yds. 2ft. 8 in. Ans.
d. d. > m. m.
(48) As 50 : 100 : : 14 : 28
For 14X100=1400 which -f-50=28 men. Ans.
PROMISCUOUS EXAMPLES.
Cwt. Cict. qrs. lbs. ^ ds.
(49) As 1 : 18 3 19 :: 11 371
Cict. qrs. lbs. lbs.
For 18 3 19=2119 which X 1137i=24l0362Jlthe
divisor; which —1 ctc^., that i3"'ll2 ;6^.=|215
21-5^ ds. Ans.
^ $■ $
(50) 730—22=708
yds. yd. $ $ds.m.
Then as 156 : 1 : : 708 : 4 53 8-f- Ans.
For 708X 1=708 which ~-156=g4 53 ds. 8 m.-f 72
GO Sl.^GtK RULE or THREE.
(51) To find the prime cost.
C, C. qrs. lbs. ^ ttx. ^ cts.m..
1 : 19 2 17 : : 9 31} : 183 00 7-f- '
lbs. lbs. ^ els. ^ cts. m.
Or, as 112 : 2201 : : 9 31| : 1B3 00 7+
For 93lAx2201=:20496Gl| which -M12=gl83
00 cts. 7 m. 4- Alls.
To find the sum it sold for.
lbs. lbs. g cts. % cls.m.
As 112 ; 2201 : : 10 65 : 209 29 1+
For 1065X2201=2344065 which ~112~:
C^*. 1 m. Ans.
To find the gain. It sold for ^209 29 cts. 1 »i.—
Jl83 00 cts. 7 m.rz:g26 28 cts. 4 m.
yds. yd. ^ cts. cts.m.
(52) As 47 : 1 : : 14 75 : 31 3-f
For 1475 X 1=1475 which -^47=31 cts. 3 m.+ Ans.
(53) 3 qrs. wide : 1| wide : : 3 J long : 61 long.
For 3|=15 ^r*. and ^\^=:b qrs. therefore 15X5=
75 which —3=25 ^rA'.=the quantity of hoUand
requisite for each suit, and this ib qrs.x'^^^
suits or men=8850 qrs. which —4=22121 yds,
Ans.
(54) First ^Sft. : 250 ft. : : 33^1;. 10 m. : 338/?. 4 in.
For 33 10X12=406 in. X250=101500 which -f-2c
=4060m.=338/if. 4in. the length of the shadow
of the tower. Then as the shadow is 1 Sft. 6 in.
longer than the width of the river, consequently
338/1?. 4 m.— 18/if. 6 m.=319^. 10 in. the width
of the river. Ans.
(55) First, 24 hrs, : 1 m. : : 360 deg. :17 m. 2 fur. 1st
Ans.
For 360X691X1=25020 and 24 Ar5.x60=1440;
therefore 25020-f-1440=17 m. 3 fur.
Again, 24 hrs. : 1 m. ; : 360 deg. :11m. 4/ttr.=
the velocity of the earth in lat. 40 deg.
For 360X46=16560-M 440=11 m. 4 fur.
Then, 1 7 m. 3/i^r.— 1 1 m. 4/wr.=5 m. Ifur. 2d Ans.
DOUBLE JlVhE OF THRKE. (j9
DOUBLE UUI.R OF THREE.
EXAMI'J.ES.
(2) Thus 3^. • ^8 ^.. ) ^^^^^ ^ l70A,2R.2GP,20yd8.+
For 8X24X32=61 14 the dividend.
And 3 X 1 2=36 the divisor.
Then 6144-7-36=170.3. 2 R, 26 P. 207jds,-\- Ans.
(3) Thus lOox. : 20ox, > ^ /, ^ ^
^ ^ 18./. .27.7. r' ' '
For 20X27X2=1080 the dividend.
And 18X10=180 the divisor.
Then 1080-7-180=6 .'I. Ans.
W^^^^%^;^-]:: 36/6.. : 48 /&..
. For 24X5X36=4320 the dividend.
' And 9 X 10=90 the divirior.
Then 4320-r90=48 lbs. Ans.
(5) Thus $100 : SJS335 ? . . ^g . ^30 15,^,
For 33r> X 18 X 6=361 80 the dividend.
And 100 X 12=1200 the divisor.
Then 36 180-M 200=^30 15 ds. Anc.
(6) Thus 20m. • 46m.K. ^.^ 3^,^^^^ ^ g^^g g, ^^^^
For 46X32X5631]=8289200 the dividend.
• And 20X5:;= 100 the diviBur.
Then 8289200^ 100=g828 92 cf*. Ans.
(7) Thus n-m. : 12?7i. > ...^ . r.A ' •
30./. : 90ri. l'-'' ^^20prm'..: 540;>air..
For 12X90X120=129600 the dividend.
And 8 X 30=240 the divisor.
Then 1 29600—240=540 paiW. Ang.
(8) Thus 12p. : 38/>. ) ^^„ ..^ „ ,-0
4//. : 16r/. \ ' * ^^^^^^- ' '^^^ ^^'' ^^^'''''
For 38X16X37=22406 the dividend.
And 1 2 X 4=48 t lie divisor.*
Then 22496-MJ;r^-. 168 lbs, lOJor. Ans.
70 DOUBLE RULE OP THREE.
(9) Thus8/fc. : 12/i. > .' . to Wo _l
For 12x7x5—420 the dividend.
And 8 X 4—32 the divisor.
Then 420-^32=134- Ans.#
(10) Thus liyds, : 247jds,2qrs. > : : gl7 37-J c^. : ,^132
3qrs. : Iqrs, \ 43 d*.-f
For 24i/ds. 2qrs.=9Sqrs. And '7^yds,=30qrs,
Then 98X7X17371== 11 91 925 the dividend.
And 30X 3=9p the'^divJBor.
Then 1191925-^-90=gl32 4Scts,+s Ans.
(11) Thus 20^. : 62h. ) : : Ubu, : 605w. 3pe. S^^^. 1;?^
22 J. : 3Gc/. 5 +86
For 62 X 38 X 12=26784 the dividend.
And 20 X 22=440 the divisor.
Then 26784-t-440=606w. 3pe. 2qts, IpL+^iie Alls.
For 563X 18X6=182412 the dividend.
And lOOx 12=1200 the divisor.
. Then 182412-^ 1200=1^152 Olct Ans.
(13) Thus 8/.. : -20/.. ) , ^ ^^^ , ^^^^ ^^^^^^ 3^^^^
7m. : 17771. ^ ^
For 20 X 17X6=2040 the dividend.
And 8 X 7=56 the divisor.
Then 2040~5G=3GT'. QcwL 2qrs. Sibs, Ans.
(14) Thus2y./.. : 50t/r/.. ) .^^j^ . ^^,^^
[yqrs. : 3qrs. ^
For 50X3X 1=150 the dividend.
And 2 X 5=10 the divisor.
Then 150-:- 10= 15/6*. Ans.
For 9QX 3X7=20 16^ the dividend.
And 21 X 32=672 th(* divisor.
Then 2016-^672=3. Ans.
DOUBLE liULE OF THREE. 7 1
(16)Thu^4m.: Um.K,^ giOO : §360
For 1 2 X 9 X 100=10800 the dividend.
And 4x7-^=30 the divisor.
Then 10800~30=$|60. Aiis.
(17) Inversely thus 40ft. ) : J 20ft, )
54ft. 5 : I i^4ft, > : : lOd. : Id, lO^krs.
127)1. : 21m. )
For 20X54X27X i 0=29 1600 the dividend.
And 40 X 54 X 72=155520 the divisor. ^
Then 29 1600^1 55520= Ic?. 10 J/tr5. Ans.
(18) Thus 305^.^ : lOj^^^l' j:: sp^ .. ll6J.-f254Q
For 1 056 x" 14X30=443520 the dividend.
And 305 X 121=38121 the divisor.
Then443520^3812l=116cZ. Ans.
(19) Thus $210 : g837 ) ^. 07 or ^r r
15w. : 4m. 5
For 24w. ^d.=llld. And 837X4X171=572500
the dividend.
And 210X 15=3150 the divisor.
Then 572508-h.31 50=1 81(i.=25wj. 6c?. +2358 Ans.
For 5X30X50=7500 the dividend.
And 2ix 15— 371 the divisor.
Then 7500—37^=^200. Ans.
(21) Thus 5m. : 34m. J . , g^^ ^^ ^^^^ , ^3^3^ ^^ ^^^^
For 34X90X2050=6273000 the dividend.
And 5 X 4=20 the divisor.
Then 6273000-^20=^3136 50 ds. Ans.
(22) Thus 24a..: ^760.. J ^, ^,3 . gj^g , ,,,,.+ , ,o
For 76X121X18=165528 the dividend.
And 24X45=1080 the divisor.
Then 165528^1080=^153 26 cf^. Ans.+
72 DOUBLE hULE br THREK.
(23) Thu.42.a, : 392^^^^^
For 392X7X6=10464 the dividend.
And 42X 14=:=588 the divisor.
Therefore 16464— 588=28^72. Ans.
(24) Thu« S^cut. : ^t.K,p,,as.:$m-!lilcU.i
For r>Ox 150 X 050=7126000 the dividend.
And 35X20=700 the divisor.
Then 7125000-^700=^101 78 J ds.-f Ans.
(25) Thusgll 15ch. : ^31 UVids. } :: gl25:g60356;
97n. : lyr. 6mo. ^ d^'.-f
For 3118j=12475(/r*.X 18m. X 125=28068750 the
dividend.
And $11 75d^.=4700^r*.X 9=42300 the divisor.
Then 28008750-f-42300=g663 56jds.-f Ans.
(26) Thus glOO : g275 } . . hj.. . ^7,
12m. : 56m. ^ ' ' »^ ' fc^^
For 275X56X6=92400 the dividend.
And lOOx 12=1200 the divisor.
Then 92400-r 1200=^77. An^.
(27)Thu8g56 :P ),,p,0:POO
For 6 X 20 X 560=67200 the dividend.
And 56X12=672 the divisor.
Then 67200-^-672=^100. Anjb'.
(28) Thus 12yds. : 75y^.. ), .^^^ . ^3^^,^ ^.^^^^
59)'*. : 3qrs. \
For 75X3X5=1125 the dividend.
And 12 X 5=60 the divisor.
Then 1125-r60=18/6. 12or. Ans.
PRACTICE.
PRACTICE.
EXAMPLES.
(3)
!at?-
148
74
CASE 1.
(4) |I|l|3268atl
Ans. ^16 34 cts.
Ans. $2 22 cts.
(^)
4260 at J
2130
1065
Ans. g31 95 d^.
(7) |2l||634 at 2 miZ/5.
Ans. $1 26 8
(6)
111115324 at 1
Ans. $13 31 cts.
73
(5)
352 at 4 mills,
70 4
70 4
Ans. gl 40 8
(9) |5m3456 at 5 miZZ5. (10)
Ans. $17 28
498 at 6 mills,
249
49 8
Ans. $2 98 8
74
(11)
I'KACTICE.
8462 at 8 mills.
4231
1692 4
846 2
(12)
1264 at 7 milk,
632
252 8
Ans. ^67 69 6
(13)
Ans. $n 84 8
4628 at 9 mills.
2314
923 6
925 6
Ans. $41 65 2
CASE 2.
cf5. d$.
(2) |6|| iVi3648 at 6J d*. (3) llO|yVp42 at 10 ds.
Ans. $228
Ans. $74 20
cf*.
d5.
(4) |20m8264 at 20 ds.
Ans. $1652 80
ds.
(6) |50|1|5876 at 50 ds. (7)
Ans. $2938
386 at 25 ds.
(5) |25p
Ans. $96 50
ds.
25
20
3542 at i:. c.'..
885 50
708 40
Ans. $1593 90
(8)
i'KACTICE.
ds.
50
25
5
r31925 at 80 c/5.
15962 50
7981 25
1596 25
Ans. ^25540 00
ci8.
(9) |12im4264at 121 d*.
Ans. g533
(10)
cts,
50
dL
^\ 18626 at55d*. (11)
9313
931 30
Ans. ^10244 30
(12)
cts,
10
528 at 16 els,
52 80
26 40
5 28
Ans. ^84 48
(13)
25
J 1724 at 371 cts,
1 431
215 50
Ans.
g646 50
cts,
50 j
^¥8
13854 at 56 J ds.
6927
865 87 5
Lns.
^7792 87 5
4858 at 29 cts.
Ans. gl408 82
(15)
cts,
50
2267 at 85 els.
1133 50
666 75
226 70
Ans. gl926 95
76
PRACTICE.
(16) |20J»|190at20cf5.
Ans. g38
(17)
cts,
6
3654 at 18f c<#.
456 75
228 37 5
Ans. $685 12 5
cts.
(18) 50 117638 at 70 c«5.
8819
1763 80
1763 80
Ans. gl2346 60
(2)
$ cts,
10 25
10
102 50
5 12 5
64
Ane. gl03 26 5
CASE 3.
(3)
cts.
4
15
7
29
05
2
07 5
1
03
7
51
8
14 8
3
7
Ans. $32 86 5
PRACTICE.
77
Cwt. qr. lb, ^ cts,
(4) 129 1 10 at 1 05
129
(6)
Ans. gl35 80 4
Cwt. qr, $
130 1 at 15
130
450
15
1950
3 75
Ans. gl953 75
qrs, lb, cts,
(8) 2 14 at 2710
(5)
Cwt.qr, g cts,
16 2 at 5 18
16
3108
518
82 88
2 59
Ans. g85 47
Cwt, qr, lb, cts.
(7) 25 1
9 at 175
25
ll
I- 875
4.
[350
4,
-43 75
43 7
I:
6 2-f
6 2+
1 5+
Ans. $44, 32 8
(9)
lb, oz. dwt, gr,
6 5 10 5 at
1355
338 7
Ans. gl6 93 7
g cts,
4 16
6
2496
138 6
34 6
17 3
3
Ans. g26 86 8
G2
78
PRACTICE
Ih. oz. dwi.gr, cis.
. lh,oz.
dwt.scr, cts.
(10) 27 10 4 18 at 2635 (11)
9 11 17 22 at 613
27
9
6
^ 18445
^ 5270
4^5517
1 ^ 306 5
10
5
2\
- 204 3
51
3
i711 45
1
1 13 17 5
: 25 6
4
]r 6 58 7
12 J 12 7
12
\ 2 19 5
6^ 5 1
6
V 43 9
- 5 4
2| 12
2^ 6
.
2 7
2
2
Ans. g733 92 7
Ans. }ei 24 -3
oz.
dwL gr, cts.
yd, qr. $cts.
(12) 816
13 12 at 12^ (13)
27 3 at 9 65
1 1
816
1
27
10
i 1632
816
408
2J
6756
1930
260 65
4 82 6
102 00
U
2
\ 6 2
2 41 2
j
\\ 12
J 6
3
II
12
Ans.
J267 78 7
A
ns.
gl02 08 3
=
PRACTICE.
79
yd, qr, cts,
(14) 860 1 at 84
860
(16)
5040
672
722 40
21
Ans. $122 61
gal, qt, cts
428 3 at 140
428
1120
280
560
599 20
70
35
Ans. $600 25
(15)
yd. qr, na, cts,
126 2 2 at 475
126
2850
950
475
598 50
2 37 5
59 3
Ans. 5^601 46 8
gcU, qt. pt, cts.
(17) 765 3 1 at 21 8 J
4
875
765
4375
5250
6125
6693 75
4 37
2 18
1 09
4)6701 39
Ans. $1675 34J
80
hhd, g'al.
(18) 5
PKACTICE.
$ Qts,
31| at 47 12
3H
^
5
233 60
23 56
AnB. g259 16
hhd, gaL qt. ^ ds,
(19) 17 15 3 at 64 75
17
(20)
bu, pe, cts.
120 2 at 35
120
700
35
Ans.
4200
17 5
42 17 5
hu. pe.qt.pt. cts,
(22) 1354 1 5 1 at 25
1354
100
125
75
25
338 60
6 2.1
3U
3i^
Ans. ^338 60 5}
453 25
647 5
1100 75
9 25
3 08 3
3 08 3
77 1
(21)
Ans. g llie 93 7
hu, pe. qt. ^ cts.
780 3 2 at 1 17
780
9360
819
912 60
58 5
29 2
7 3
^.
Ans. ^913 55
R, P,
(23) 35 2 18 at 54 35
35
16
27175
16305
1902 25
27 17 5
5 43 5
67 9
Ans. gl936 53 9
PRACTICK.
81
A.R,P. $ cLs,
(24) 146 3 10 at 35 10
146
A. R.P. $ ds.
(25) 750 1 4 at 12 25
750
21060
14040
3510
5124 60
17 65
8 77 5
2 19 3-f.
61250
8575
9187 50
3 06 24
30 6|
AnB. $9190 86 8|
Ans. $5153 11 8-f
APPLICATION.
Cwt.qr.lb, i cts,
(1) 84 2 14 at 10 60
84
CwLqr.lb, cts,
(2) 17 1 7 at 1212|
2
14
4200
8400
882 00
5 25
1 31 2-f
Ans. $888 66 2-f
2425 halves.
17
16975
2425
412 25
6 06 1^
1 51 5|
2)419 83 8 mills.
Ans. $209 91 9 mills.
82
T.cwLqr. $ ds.
(3) 15 10 3 at 80 15
15
PRACTICE.
yd. qr, pie, yd,
(4) 35 2X170=6035 at}
6035
10
40075
8015
1202 25
40 07 5
2 00 3J
1 00 U
4)6035 qrs,
Ans. p5 08
Ans. gl245 33 0|
A, R, P. $ ds,
(5) 175 3 12 at 52 15
175
26075
36505
5215
9126 25
26 07 5
13 03 7
3 25 9
65 1
Ans. $9169 27 2
(6) 1365 at ld,=$6 82|c^. Ans.
(7) 784 at 84 di.
784
336
672
588
Ans. g658 56
PRACTICE.
83
(4) [l[j|475at|
12)118f
STERLING MONEY.
CASE 1.
(5) mi[299atj
12)149|
Ans. 9*. lOfdf.
(6)
Ans. $l2s, 5|cf.
978 at I
489
244^
12)7331
210)6|1 1
Ans. £S Is. Ud.
(2) 1241978 at 2d,
2|0)16|3
Ans. £8 3^.
(4) [6j||792 at 6d.
2|0)39|6
Ans. £19 16^.
CASE 2.
(3)
499 at 5J.
166 4
41 7
(5)
2|0)20|7 11
Ans. £10 7*. Ud.
1
888 at 9d.
444
222
210)66|6
Ans. £33 Ss.
84
(6)
PRACTICE.
921 at lid.
460 6
230 3
153 6
2|0)8414 3
Ana. £42 4*. 3d,
CASE 3.
(2) |3|||487 at 15d.
I I |l21 9
2|0)60I8— 9
Ans. £30 8*. 9c?.
(3)
979 at 22J
489 6
244 9
81 7
20 4£-
2|0)181|5 2J
Ans. £90 15*. 2|cf.
(4)
532 at 23j<f.
266
177 4
44 4
22 2 4
n 1 J
2|0)105|2 11 J
Ans. £52 12*. ll|<f.
CASE 4.
(2) ,5|||489 at 5«.
Ans. £122 5*.
PKACTICE.
85!
(3)
937 at 11*.
468 10
46 17
Ans. £515 7*.
(4)
1286 at 15*.
643
321 10
Ans. £964 10*.
(5)
2798 at 19*.
1399
ft99 10
559 12
Ans. £2658 2*.
CASE 5.
(2)
10
£ *. d.
569 at 4 13 71
4
2276
284 10
56 18
28 9
14 4 6
2 7 5
1 3 81
(3)
Ans. £2663 12 7|
101
h-J
\\
6-
3-
3
T¥
£ *. df.
1967 at 5 16 9f
5
9835
983 10
491 15
98 7
49 3 6
24 11 9
6 2 \\\
Ans. £11488 10 2|.
H
86
ritACTICE, II
(4)
10^
1 :
? ^
^ 2975 at £7
195. llj(f. 1
20825
- 1487 10
743 15
. 595
99 3 4
24 15 10
12 7 11
6 3 11
3 1 11
Ans.
£23796 18^ OJ.
CASE 6. II
(2)
C. qr. lb.
9 2 17 a
. ! i
£ 5. ^. C.
14 7 6 (3) 11
9
1
/6.
16 a
£ ^ rf.
t5 6 71
11
21
2]
u
39 7 6
2 3 9
10 in
1 6J
1
14
2
T
58 12 101
1 6 7|
13 33
1 io|
An«. £42 4 fil ^"^- ^
60 14 8-H
(4)
7 3 22
1
It 1 18 4
7
"4
1 (5)27 1 19
1
at'
r
7
1
!
2 17 8>
3X9=27
2'
1^
14 J
7)
1 ^
-13 8 9
19 2
9 7
49
24
4
t
1
14
4
1
8 13 0|
9
7 17 6J
14 5-f
7 21
£» 1
Ans. .
ei5 5
i Ans.
£79 1 8? 1
1
TARE AjN'D tret. 87
TARE AND TRET.
CASE 1.
CwL qr, lb, Cwt. qr. lb. Cwt. qr. lb.
(2) 7 3 20 (3) 6 2 5 (4) 369 2 21
8 «— 1 11 —10 1 12
gross 63 1 20 Ans. 6 22 Ans. 359 1
—5 1 19
Ans. 58
CwLqr.lb. C.qr.lb. lb.
(5) 6 1 19^ (6) No. 1.3 2 19 tare 34
8 No. 2. 6 13 tare 57
No. 3. 4 3 5 tare 46
43 1 12 whole gross. — C.qr.lb.
—2 23 tare. 14 2 9w.t.l37==l 25
—1 25
Ans. 41 17 neat.
Ans. 13 1 12
CASE 2.'
C. qr. lb. qr. lbs.
(2) 4 2 24 2 18
7 7
33 gross. 4cwt. 2qrs. 14^6*. whole tare.
4 2 14 tare. ^
Ans. 28 1 14 neat.
TARE AND TRET.
(3)
C.
21
3
qr. 11
2 2
1
\
J at 5 50
Neat 18 2 t
-^
%
*.
i
4400
550
lb
1
1
2
9900
275
9 8+
4 9
Ans
. glOl 89 7
(4) 2
qr. Ib.^
1 25
9
lb.
30
9
C. 9r. lb
ross. 270=2 1 18
re.
$cts.
t 5 10
19
22
2
1 Ig]
1 18 ta
Neat 19
3 11 a
qrs.
^ i
4 ?
45 i
51 (
)0
)
)0
)5
11 5
M 8+
8 2-f-
96 i
2 £
1 S
1
Ans. $
101 22 5 value.
TARE A3SD TRET
89
CASE 3.
C. qr. lb.
(2) 7 3 14
4
lbs
31 2 gross.
4 2
1 14
5 2 14 tare.
Ans. 25 3 14 neat.
C. qr, lb,
(3) 5 1 13
10
lbs.
16
53 2 18 gross.
7 2 18+ tare.
Neat 46 at 8 75
46
5250
3500
Ans. ^402 50 value.
H,^
'90
TARE AND TRET.
(4) 4C. Iqr, 24/6.
26 3 4 gross.
Tare 4 l
Neat 22 1
8+
25+
Ibi.
27=2519 at 74
— 7j -
17633^
1259 5
Ans. $188 92 5 value.
CASE 4.
(2) 2C. Xqt, lOlb,
12
lbs.
28 8 gross.
4 2 1 tare.
7 suttle.
17 tret.
Neat 22 2 18 at 19 60
— — 22
lbs.
14
2
2
39 20
392
431 20
9 80
2 45
35
35
Ans. g444 15 value.
(3)
I"' ' =
TARE AND TRET.
C. qr, lb,
4 1 11
6
91
gr, lb,
1 5
6
iie 10 ^
13 2 tare.
cwt, 13 2 tare.
^)24 1 8 suttle.
"^ — 3 20 tret.
$ ds.
Neat 23 1- 16 at 6 75
^ 23
qrs.
1
20 25
135
155
25
1
68J
84;-
12
Ans. gl57 90 value.
APPLICATION.
C, qr, lb,
(1) 17 3 22 gross.
3 14 tare.
' — lbs, ds.
Neat 17 8=1912 at 23".
5736
3824
478
Ans. g444 54
92
(3)
(2)
5C
r
8"
K
Neat 7
C.qr.
6 3
7
5 3
8
TARE AND TRET.
\ 2qr. 19Z6.
3X5=15
i
2qr. 25/6.
3
No. 1.
No, 2.
No. 3.
No. 4.
7
1 2
5
19
5
3 5gl
3 3 11 ta
•OSS. C.IO
3 11 tare.
t g6 75d^.
74
le.
4 22 a
16^
2-
- 27 00
472 5
499 "50
r 96
z 24
12
/6.
18
10
26
3
A
grog
tare
atj
ns.
g500 82 vail
8
4
tV
i
28
1
s»
^3 75c<^.
2
1
Neat
3
25
1
lb.
1
rh
3 3
18 '
75 (
93 '
Ai
IS. ^
93 78 3 value.
(4)
TARE AND TRET.
IC. tqr, 23lb.
4X6=24
93
5 3
34 3 20 gross.
3 3 12 tare.
18^6.
24
72
^ C.qrAb,
432=3 3 12 tare.
Neat 31 8 at $5 l'7^cls.
2
1035 halves.
31
1035
3105
32085
73 9
2)32168 9
Ans.
79 4 value.
(5)
IC. l^r. 13Z&.
3X5=15
4
11
5
20 1 27 gross.
2 3 22 tare.
22/6.
15
110
J!«. C.qrJb.
320=2 3 22 tare.
Neat 17 2
5 at $9 64ctg.
— 17
2
1
2
67 48
lb.
96 4
163 88
4
A
4 82
1
5^
34 4
8 6
Ans. g
,169 13
94 inte:^est.
a qr, lb.
(6) 6 2 14
10
lbs.
66 1 gross.
9 1 24
1 20
10 2 16 tare.
55 2 12 suttle.
2 16 tret.
lbs.
cts.
Neat 53 1 25=5989 at lU
"i
65879
2994 5
Ans. ^688 73 5 value.
-MtoQeiM
INTEREST.
EXAMPLES IN CASE 1.
(2) 225
7
$ cts,
(3) 384 50
5
Ans. 5515 75
Ans. gl9 22 5 m.
INTEREST. 9&
£ 8, % cts.
(4) 580 10 (5) 1654 81
6 5
r- J6 *. eif. %cts.
£34 83 Ans.34 16 7 g82 74 05 Ans. 82 74
20
5.16 60
12
rf.7 20
^ j6 £ s. d»
(6) IllillSOO (7) 350 ^Ans. 18 7 6
Ans. $1 50
1750
87 10
£18 37 10
20
^.7 50
12
d,e 00
(8) |J|524 (9) 111842
2620 4210
131 421
Ans. g27 51 Ans. g46 31
96 XNTEKEST.
CASE 2.
$ £ s.d, £ 8, d.
(2) 540 (3) 124 5 6 4 19 5 Int for 1 year.
5 4 3
27|00 £4197 2 £14 18 3 Ans.
Ans. g54|00 «.19|42
12
rf.5|04 ;
(4) 482
6
g28f92 interest for 1 year.
7
Ans.
g202|44
CASE 3-
(2) 325
4
mo.
2 ,
^ 13|00 Int. for 1 yr.
4 ;
i
52 Int. for 4 yrs.
2|16|6 Int. for 2 mo.
Ans. $54 16 6 1
INTEEE8T.
97
(3)
840
4
33160 Inti for 1 yr.
6
168
8
00 Int. for 5 yr.
40 Int. for 3 mo.
Ans. gl76 40
(4)
mo.
4
840
7
58|80 Int. for 1 yr.
5
294|00 Int. for 5 yrs.
19|60 Int. for 4 mo.
Ans. $313 60
(6)
1200
5
Ans. g60 00 Int. for 1 yr. Then say, nslyr.: 15w.
^ $^^ '• $^'^ 30c<5. Ans.
(7)
240
960
120
60
Ans. gn 40 Int. for 1 yr. Then say, as lyr. : 61d.
gll 40: gl 90cfe. Ans.
98 INTEREST.
£
(8) 1000
7
£70 00 Int. for 1 yr. Then as lyr. : Umo. : : je70 :
£81 13*. Ad Ans.
(9) 450
51
2250
225
$U 75 Int. for 1 yr. Then as \yr. : 6mo. 20d. : ;
g24 ISds. : $13 15cts.+ Ans.
$ cts.
(10) 375 25
6
^22 51 50 Int. for 1 yr. Then as lyr. : Syrs. 2mo, 2w,
5rf. : : g22 Bids. 5m, : $72 85. Ans.
CASE 4.
(2) 854
30
6)25620
Ans. ^4 27
(3)
$
1100
48
8800
4400
6)52800
Ans.
$S 80
INTEREST.
09;
$
(4) 3459
75
$
(5) 1500
60
17295
24213
6)90000
jl 111 15000171. at
—2500
1
6 per cent.
6)259425
Ans. g43 23 7
Ans. gl2 50
CASE 5.
(2) 6 yrs.
4 dolls.
24 Int. of jSlOO for 6 yrs.
-flOO
£124 amount of £100 for 6 yrs.
Then as £124 ; £1240 : : £100 : 1000.
(3) 6 yrs.
6 dolls.
Ans.
30 Int. of glOO for 5 yrs.
100
gl30 amount of glOO for 5 yrs.
Thenasgl30
: $2470:: $100: $1900.
Alls.
(2)
CASE 6.
$
1476 amt.
1200 prin.
$276 Int.
And gl200 : $100 : ;
time.
Then as byrs. 9mo, :
$276 : $23 int. of $100 for the i
$23 : : lyr. : $4 per cent. Ans.
same
100 INTEREST.
$ cts.
(3) 927 82^ amt.
834 00" prin.
^93 8;21 int.
As g834 : §93 ^^cts777pQ^Q : gll 2octs.
And then, as 2yr*. 6mo. : §11 2bcts, : : iyr, : §4| per cent.
Ans.
CASE 7.
£ £
(2) 1600 2048
4 1600
£64 00 : Iyr. : : 448 : tyrs. Ans.
(3) 1000
41
40 00
5 00
§45 00 : Iyr. : : §281 25ctjf. : 6yri, 3f»o. Ans.
COMPOUND INTEREST.
§
(2) 760 prin. *
6 rate per cent.
45 60 int. 1st year.
805 60 amt. of let yr. and prin. for the 2d yr.
48 33 6 int. of 2d yr.
853 93 6 amt. of 2d yr. and prin. for the 3d yr.
51 23 6 int. of 3d yr.
905 17 2 amt. of 3d yi;.
760 00 1st prin.
Ans. §145 17 2 compound int.
INTEREST.
£, s. d, £ 8. d.
(3) 242 10 6 242 10 6
6 14 11 Oint. Istyr.
lOll
£14|55 3 257 1 6 amt.
20 15 8 5| int. 2d yr.
11|03 272 9 ll|amt.
16 7 int. 3d yr.
288 16 1 If amt.
17 6 7i int. 4th yr-
306 3 7 amt.
^242 10 6 1st. prin.
Ans. 63 13 1-f com. int.
(4) 1300
5
•65|00 int. 1st yr.
1300
1365 amt.
5
68|25 int. for 2d yr.
1365
1433|25 amt.
5
71 66|2 int. for 3d yr.
1433 25
Ans. gl504 91 2m. amt.
- u— ■—
102
$
(5) 3127
INTEREST.
t
3127
140 71 5 int. of , the 1st yr
12308
1563 5
3267 71 5 amt.
147 4 7 int. 2(1 yr.
gl40 71 5
3414 76 2 amt.
153 66 4 int. 3d yr.
1»R(
$ Cts.
(1) 620 25
3568 42 6 amt.
160 57 9 int. 4th yr.
Ans. g3729 00 5 amt.
JMISCU0U8 EXAMPLES.
(2) 420
7
3101 25
310 12
£29 40
20
nt. for 1 Jrr. *.8 00 Ans. je29 8*
$
1450
60
34 11 37 i
5
Ans. gl70 5B ^m
(3)
6)87000
14500 mills=gl4 hOds. Ans.
INTEREST.
103
£ s.
(4) 626 5
3131 5
156 11 3
£ s.
626 5
32 17
d,
6Jint. of the Istyr.
659 2
34 12
6| amt.
1 int. of 2d yr.
£32187 16 3
20
693 14
36 -8
7f amt.
5 int. of 3d yr.
«.17|56
12
rf.6|75
4
Ans
730 3
—626 5
OJ amt.
prin.
. £103 18
0|+ compound mt.
fr*.3|00
£
(5) 1659
4
r£66|36
20
Int for 1
yr..
«.7|2e
12
£^.2|40
4
5r.l|60
Then as 365 days :
Ans.
21 days : : £66 7^. S^rf. : £3 16*. 4j(f.+
104
INSURANCE, COMMISSION AND BROKAGE.
(6)
500
8
840 00 int. for 1 yr.
Then as g40 : gSOO : : lyr. : 12yrs, 6mo. Ans.
(7) Thus, Qyrs. and 6mo. at 2 per cent. =^13 interest
on glOO.
Then ^13+gl00=:gll3=amount of glOO. ^
And as gll3 : p50 : : glOO : g221 22ct8. 9m. Anfl.
£
(8) 450 amount.
300 principal.
£150 interest.
Then as £300 : £100 : : £150 : £50 which divided hy
the 5 years=10 per cent. Ans.
INSURANCE, COMMISSION AND
BROKAGE.
EXAMPLES.
£
(2) 1320
5
Ans. £66|00
(3) 3450
41.
m
13800
1725
$
1680
n
3360
840
420
Ans. $l55\25cts.
g46|20 commifl .
gl680— g46 20cfe.3=gl633[80cf5. Ans.
£
(5) 7G0
INSURANCE, COMMISSION AND BROKAGK.
$
(6) i ^ 5630
n
4560
380
£49140 Axis. £49 8*.
20
«.8|00
39410
2815
1407 5
Ans. g436|32|5m.
105'
17654
181
141232
17654
8827
4413
Ans. g3310|12.
(8) 2150
Ana. £43100
$ cU,
(9) J |||984 50
984 50
246 121
Ans. gl2|30|62l
(10) i iJllSsO 75
" U li
1650 75
825 37!
Ans. g24|76|12i
106
DISCOUNT.
DISCOUNT.
EXAMPLES.
(2)
Thus, 2mo.
at 6 per cent.
per an.=±gU int. of glOO
+ 100"'
1011 amt of do.
•■
Then as glOlJ : g850 :
Ans.
: glOO : g837 43cts. 8w.+
(3)
Thus, 9r/io.
at 6 per cent.
per an.=g4i int. of g 100
100
1041 amt. of 100
Then as ^
present
,1041 : g645
worth.
:: glOO : ^61 7 22cts. 4m.
645 00
Ans. $21 11 6
(4)
Yrs,
4
5
20 int. of
100
glOO for 4 yrs.
gl20 amt. of do.
en as ^120
$115 SOds.
: glOO : ^646 25ct8, Ans.
J/
Sino. at 6 per cent, per an.=^4 int. of ^100
100
gl04 amt. of do.
Then gl04 : ^580 : : g
100 : $551 69f^*.-f- Ans.
DISCOUNT.
107
Yrs.
12
ii
131 int. of 100
100"'
gllSiamt. of do.
Then as gll31 : g954 : : glOO : $U0 52cts.
8m. Ans.
(7) Thus, 15 mo. = l^yr, at 7 per cent.
num=g8| the discount of 100.
100
per an-
glOS^amt.
Then gl08| : g205
sent worth.
: : glOO : gl88 BOcts,
205 00
5m. pre-
Ans. ^16 49 5
(8)
mo,
6
I
2
5
3
i
s
3f discount of 100
100
gl033 amt.
Then as gl03f : g775 : : glOO : $146 9Scts.
7m. Ans.
108
(9)
mo» £
1
DISCOUNT.
mo. £
Again | 3 |JI6
H
15 7710.
5 dig. of lOafor lOmo. 71 dis. of 100 for
100 100
Jl05 amt.
1074
1005
—475
Rem. 530
Then as 105 : 475 : : 100 : 452 38. Ans. to first part.
Again 1071 : 530 : : 100 : 493 02 4
Ans. g945 40 4m,
(10)
2260
6
Again 6
5
135 60 int. fori yr.
5
678 00 int. for 5 yrs.
30 dis. of 100
100
|Jl30 amt.
Then gl30 : te60 : : glOO : gl738 46cts, Sim. pres. wr.
2260 00
521 63 8 discount.
678 00 interest.
Ans. ^156 46 2
EQUATION. 109
(12) 782 (13) 476 (14) 1335
4 3 6
£31|28 Ans. $U\2iicts, 33 10 dis.
20 1335 00
*»5|60 Ans. £31 5s. 7J. Ans. jJlSOl 90cts,
12
d.l\20
650
4-*
2600
325
29 1 25 discount.
650|00
Ans. g620|75
EQUATION.
EXAMPLES.
t
(2) 250X6=1500
250X8=2000
500 3500-^500=:7mo. Ans.
no
BARTEK.
(-3)
£
100x2=200
100X4=400
100X6=600
300 1200-f.300=4mo, Ans.
(4)
100X3= 300
200X5=1000
• 250X8=2000
550 3300-^550=6/na. Ans.
-^*^«^-
BARTER.
EXA:\irLES.
(1) Thus 2c
Then as
wl. 2qrs. 13/6*.=±.?93/6a. X 0c/*.=:2637c/*.
25cts, : 2637c/*. : : 1/6. . 105/6*. moz, Ans.
(2) Thus 2500/6«.X4^c/5.=^112 50d*.
Tiien as ^1 SOci^.l ^112 50d*. : : 1//^ : 86/6*. 802:.+
Ads.
(3) Thus 10a/5*.X5?1 25r/.9.=r^t35 OOc^*.
Then as U'icts, :'gl35 mcU, : : lib, ; 1542/6. 13o^.+
Ans.
(4) First, as \cwL : $3 75<?f^. : : 14nc«. Sqrs, 2Gibg. : ^56
186/*. 3m. the value of the rice.
Then as p Sl^ds. : $56 Ucfs. 3m. : : 1/6. : 29/6*.
150^.+' Ans."
(5) Jims 2cwL ^qrs, 17/6*. =32 5/6*. X 12-k/*.=g40 621c/*.
Then as 37c/*. : ^40 G'Zlds. : : lyd. : 109yds. 2qrs.
Ans.
(6) Thus 3576t«. X 0Ms.—p2^ 1 cL
Then 4Fycls. : g332 Olc/. : : l6tf. : 7376?/. 3/)«.H- Ans.
BARTEK. 1 1 I
(7) Thus UcwL Oqr. 21lhs.=:n01lhs,X20cls, =$341
AOcls.
Then ^9 50cts. : ^341 AOds, : : Icwt : 35cw/. 2qrs.
20lbs,-\- Ans.
(8) Th\\s95yds.X5pie.=z4'75yds.x22cts.=$\09 25cts,
And 32 sheep X 250= —80 00
SR29 25 rem.
Then as gl 50d^. : $29 25cts, : : Icwt. : 19cwt, 2qrg.
Ans.
1^9) Thus USeyds, at 43c/^. per ijd. = $552 9Hcts.
And 2c«j^. Iqr. 13lbs.=265lbs.Xl4cts.=z37 10—
Ans. $515 88
(10) Thus570/&*.X7cA9.=$39 90ds.
Then as ll|c^5. : $39 90c/^. :: lib. : SUIhs, l5oz.+
Ans.
(11) Thus U2cwt,X$5 0\ct8,=:$564 COds.
Then as UOSyds. : $564 GOds. : ; !?/(/. : 40ds. 7m.+
Ans.
(12) Tims 750^fe#.xgt 08^^*.— .$810 OOcf^.
Then Sr^.v. ; $810 OOd*. : : Mb, : I0\25lhs.=^90cwt.
Iqr, lUbs, Ans.
(^S) Thus2Mr/*.=126^a/5.X75rY,?,~$94 50cU, ^
Then 56yds. : $94 5()ds. :: 1?,'^/. : $1 68jc«#. Ans.
fi4) Thus 2108/6*. XlOd5.=$210 80cf^-.
And 3ldoz.XU\ds, ■= +3 56^
$214 361 amt. of the whole.
— 135 25*^
$79 111 rem.
Then as $1 58cf9. : $79 \\\ds. : : \hu. : 50har.+
Ans.
112 LOSS AND GAIN.
(13) Thus newt. X 4X 28=1904/6*. X 13lcts,=$25'7 04cU.
value of A.'s g^oods.
And 1200/?;*. ot the rate of gl4 per cwt.=150 00
balance of B.'s goods.
Ans. A. is to receive ^107 04
(16) Thus 25cts,
—20
5 gain on 20cf*.
Then a^ 5cts. : 20cts, : : 5cts. : 20ch. Ans.
(17) Thus CiOcis, : 50cis. :: 31 Jd*. . Sorts. Ans.
(18) Thus 105 tons at pO 03 per ton=^1053 IScts.
value, of the iron.
pays cash 650 00
250/7>s. at 20cfs. per lh.= 50 00
10 loads X 156?/. X 45cc^*.= 67 50
And fi5gah. at the rate of g75 per hhd.=lO\ 19
—868 69
1053 15
Rem. unpaid gl84 46
Then30d^. : ^184 4Cd*. :: lib. : 615Z6*. nearly.
Ans.
LOSS AND GAIN.
EXAMPLES.
(2) Thus lOds.
—a
2
Then 1/6. : 17G3/6.f. : : 2ds. : p5 2Gch. Ans.
LOSS AND GAIN. 113
(3) Thus g5 2^cts.
~5 00
25 gained per barrel.
Then Xhar, : 3636ar. : : 25cts. : $dO Ibcts. Ans.
(4) Thus g3 90c^^.
—3 75
15 gained per yard.
Then lye?. : \BQyds, :: 15c^5. : g22 50c/*. Ans.
(5)
First, IcwL : g7 SOr/^. : ; ISaof. 2^r*. : gl38 75d*.
the cost.
Then U^t, : %1 ISds. : : 18cw/. ^rs. : ^143 37icf*.
sold for.
Ans. gained ^4 62|
(6)
First, 210 rcam5X$2 621=^551 25d5. the cost.
And 210ream*x|2 87|=|603 75ds. sold for.
Ans. g52 50 gained.
(7) Thus, sold for $20 Ibds,
cost la 12j
gained g2 62| Ans.
(8) First, 50cf*.
—45
5
Then 16m. : 1506w. : : Bcis. : p 50cts. 1st Ans.
Again, BOcts, : 5cts. : : glOO : glO. 2d Ans.
K 2
114 LOSS AND GAi:^.
(9) First, 760/6*. X 90d.9.=g684 00 sold for.
810 00 cost.
Lost 126 00 1st Ans.
-J
ThcngOlO : $126 :: ^100 : gl5|. Ans.
(10) First, Slllds.
Then 31^cts. : B^cts. : : $100 : gl4| per Cent. Ans.
(11) Thus 15. : 2(1 : : £100 : £162 per cent. Ans.
(12) Thusgl3 75d.?. First cost of each piece.
3 12^ for dyeing.
gl6 J]7| whole cost.
ThenglOO : $112 :: $16 871d*. : $18 90ci*. Ans.
(13) Thus Iciof. : 1/6. :: $7+$3 : ^cts. 9m. Ans.
(14) Thus, paid 22cts, per lb.
Sold it for 19
Lost 4cts. per lb.
Then as 1/6. : 702/6*. : : 4cts. : $28 OMs. Ans.
(15) Thus S2 23c/*. : $2 75c/*. :: $110 : $135 65c/*.
And $135 65c/*.— $100=:$35 65c/*.=:35|- nearly.
Ans. '
(16) Thus $100 : $125 : : $2 lOcU. : $2 i62lc/*. what
1 hox sold for.
Then as $3 50c/*. price of Icwt. : $2 62^/*. price
of 1 box :: 112/6*. : 84/6*. Ans.
LOSS AND GAIN. 115
(17) First, lOpie. X gl4=g224 the prime cost.
And 5pie.X$ll=:$H5
6pie.X$i5=^pO
^175 received back again.
Then as ^100 : gll2 : : g^24 : ^250 SSds. price of
the whole with rate per cent, added. — 175 00
5)75 08 price of the
5 pieces.
Ans. gl5 17 G perpze.
(18) Thus ^500—^410=^90 gain on the whole.
Then as 31211)8, : lib. : : ^a0:24d*. Iw.-f Ans.
19) Thus $1 : glOO : : 5cts. : $5 00 the Ans.
(20) First, ^1 05r!.«f.X5l0— ^535 50d*. prime cost.
And ^1 30ci6\XiA0—^QC)3 OOcts. sold for.
mo,
3
6
1 50
100 00
glOl 50
Then glOT BOds. : glOO : : ^,663 : $^353 20cf*.+
Hence $653 20c^«. — ^535 50r^. = ^117 70^5.
Ans.
116
FELLOWSHIP.
FELLOWSHIP.
EXAMPLES.
CASE I.
(2) Thus D.'s stock ^500
E.'s 400-
F.'s , 300
Sum 1200
Then as t^OO : 500 : : 300
And 1200 : 400 : : 300
And 1200 : 300 : : 300
(3) ^ Thus A. ^1200
B. 600
C. 700
Then as 2400
as 2400
as 2400
Whole debt ^2400
1200
600
700
125=D.'s ]
100=:E.'S
75=F.'s ^
Ans.
1800
1800
1800
900
375
525
Ans
j^lSOO proof.
(4) Thus A. had 50 ca«/c.
B. 80
C. 70
Sum 200
cattle, cattle.
Then as 200 ; 60
as 200 : 80
as 200 : 70
$60 proof.
(5)
FELLOWSHIP.
$
Thus, to A. 120
B. 250 75
C. 300
D. 208 25
Sum 879 00
117
Then j
As j5879 : g650.
$
120 : 88 754-=A.'ssh.
250 75 : 185 42+ =:B.'s sh.
300 : 221 84+ =C.'8 sh.
208 25 : 153 99+ =D.'6 sh.
■ Ans.
(6) Thus A. is to have 1 portion.
B. 2
C. 6
9 sum of the portions.
Then as
900 : lOOrrrA.'s share.
900 : 200=B.'8 share.
900 : 600=C.'s share
ii
Ans.
(7) Thug, he owes to A. 250 50
B. 500 00
C. 349 50
Sum 1100 00
Then
As 1100 : 960
$ cis. f cts.m.
[250 50 : 213 61 8+ A.'s ;
500 00 : 436 36 3+ B.'s
[ 349 50 : 305 01 8+ C.'s '
Ans.
1 1^ FELLOWSiriP.
EXAMPLES
CASE 2.
%
(1) Thus 8«X3= 264
120X4— 480
300X6=1800
Sum of stocks and time 2544
% i i cts.m,
C 264 : ; 184 : 19 09 4=L.'s )
Then as ^2544 : \ 480 : •,. 184 ; 34 71 6=M.'s > Ans.
( 1800 : : 184 : 130 18 8=N.'s )
$ m. $ . $ m. ^
(2) 580X3=1^740 480x3=1458
+ 100 —300
680X9=6120 180X2=372
+500
A.'s product 78fJ0
686X3=2058
% m. $ —400
1000X9=9000
+ 200 286Xl=:286
+ 1000
1286X3:=3858
C.'s product 8032
%
A.'s 78<50
B.'s 12600
C.'s 8032 g ^ cU.m,
% (tx. C 7860 : 581 64 8+A ) .
28492 : 2108 44 ::} 12600 ; 932 41 4+B >'^^^*
.( 8032 : 594 37 7+C )
1200X3=3600
B.'s product 12600
EXCHANGE. 119
EXCHANGE.
DOMESTIC EXCHANGE.
(1) Thus, £63 Us, 6d.~152Ud~T2d. a dollar in Vir-
ginia=:^212 4lJc<*. Ane.
(2) Thus, £230 10^. 'rd.=5532'7d.~9Gd, a dollar' in
New York and N. Carolina=g576 S2cts, 2m. Ans.
(3) Thus, ^150
90^.=a doll. Penn. cur.
12)13500^.
2|0)112|r>
£56 5.9. Ans.
(4) Thus, ^377 40ds.
72c?. =a doll. Mass. cur.
754 80
26418
12)27172 80
2j0)225|i 4d,
£113 4;?. 4d. Ans.
(5) ^ Thus, g389 45cts'.
56<i.=a doll, in Georgia.
233670
194725
12)21 809J20
2|0)181j7 5
£90 17*. 5d, Ans.
120 EXOHAKGE,
FOREIGN EXCHANGE.
EXAMPLES.
(2) Thus £1 : je76 ;: $i 10cts,=^£l li'ish : ^311 60
cts. Ans.
(3) Thus gl 24cig. ~ 1 milrea : g532 Stids. : : Im. :
429m. 298recw.-f Aus.
(4) Thus eCcts. : gl869 : : Iru. : 283i^rw. Ans.
(5) Thus 1^, : ie5g, : : 39dJ. : g64 35c^*. Ans.
(6) Thus 33c<*. 5m.=lm. b, : §280 58cfe. 5wi. : : Im. 6.
: 837m. 6.-f- Ans.
(7) Thus 1/i : 562/i. : : 18d^. 5m.=l/j. : gl03 97ds.
Ans.
(8) Thus \0ct8.=zlriai plate : ^463 : : Irial : 4630ria/5.
Ans.
(9) Thus Ijfo. : 40cts, : : 591/o. 17*^ : §236 74ds.
Or 1«^ : 2d*. : : 591^0. 17*^ : §236 74f<5.
Then §100 : §160 :: §236 74d5. : §378 78^*.+
Ans.
(10) Thus as 100cr.+25 : 1005. : ; 2464m. 6. : 1971m. 6.
3sch. 2^pcn. Ans.
(1 1) Thus Icr. : 32-if/. : : 2000cr. : £270 16*. Sd. Ans.
(12) Thus as lpi.~Sri, ; 366?. ;; §1676 6ri.=:16766r/.
; £314 7*. a^. Ans.
(13) Thus lpez.=20sol. : 54d. : : ^MOpez, l5soL : £886
13*. 41(1, Ans.
(14) Thus \ru. : 4*. 3d : : 2586rw. : £549 10*. 6d. Ans.
(15) First £1 : £450 15*. : : 34*. 6rf. 1866104/?fnrp.
Or 20*. : 9015*. : : 414rf. : 1 866 lO^pencc Flemish,
or groots.
Then 50*^=100^. : ISeeiO^d. : : Iru. : 1866n/. 10-^
cop. Ans.
(16) Thus as £io8 6*. Hd, Irish : £100*<^. : : £813 3*
6d. : £750 12*. 6d. Sterhng:. Ans.
VULGAR FRACTIONS. 121
(17) First 20*. : 33*. Qd. ::5s,: Ss, 4U.
Then 5*. : 8*. 4|(/. : : 32i^. : 54^d. Flemish. Ans.
18) Thus 32ld. : 54^d. i : 5s, : Ss. 4ld.
Then as '5*. : 8*. 4^d, : : 20*. : 33**. 6c?. Ans.
*. *. d,
(ig) Thus |5|||33 6
8 4|=value of a crown at that rate.
Then 8*. 4lrf. : 6*. : ; 54fjC?. : 32|(/. Ans.
(20) Thus 32»ff. : 32c?. : : 36*. Gd, : 36*. 2|f f?. Ans.
(21) Thus 51c?. : 53c?. : : 42c/. : 4S}]d. Ans.
VULGAR FRACTIONS.
REDUCTION OF VULGAR FRACTIONS.
EXAMPLES.
C*ASE 1.
(2) Numer. 108)144(1
108
Common measure 36)108(3
108
Then 36)i^|=f . Ans.
(4) Numer. 126)234(1
126
108)126(1
108
Common measure 18)108(6
108
Then 18)lSf=f3. Ans.
122 VULGAR FRACTIONS.
CASE 2.
(2) 45X34-2=i|'7. Ans.
(3) Thus 1564X5-f3='7s^23, ^ns.
CASE 3.
(2) Thus 67-r-7=94. Ans.
(3) Thus 1 6)364(22 j|. Ans.
32
44
32
'' 12
CASE 4.
(2) Thus 6X8X11X13==6864 numer._^72_. . ^
And 7X9X12X17=12852 denom. '"*'
(3) ' Thus 7X15X8X6=5040 numer._^4oo ^^g
And 12 X 19 X 1 1 X 13=32604 denom. ^^^*
CASE 5.
(2) Thus 5)5 20 10 15 the denominators.
2)1 4 2 3
12 13
Then 5 x 2 x 1 X 2 x 1 X 3=60 common dcnom.
Then the com. denom. 60—5=12X4=48^
60-r 20=3 X 9=27 I „„^^^
60-4-10=6x7=42 f""""^^'
60—15=4X4=16]
That is fl iJ 41 U' Ans.
VULGAR FRACTIONS. 123
(3) Thus 2)10 2 9 the denom.
5 19
Then 2x 5 x 1 X 9=90 common denom.
90-r-10= 9X9=81)
90~- 2=45 X 1=45 > numer.
90-f- 9=10X5=50)
ThatisJJ^fJ. Ans.
CASE S.
^2) First lib. troy=240t?io«. therefore | of aiir=x2T?F=
;f^a. Ans.
(3) Thus 3xlXl_ 3 Anc?
And 8x4x4-~^^- ^'^•
(4) Thus lkhd,=:SO^ts, therefore | of shF^iwsJ''^^'
Ans.
(5) Thus 8/«r.=lm. therefore 9x1=9 the numer. and
16 X 8=128 the denom.=y|^. Ans.
CASE 7.
(2) Thus 2X112=224 the numer. and 252x1=252 the
denom.=f||=|/6. Ana.
(3) tIht of £l=Tifff^ of ^r ==l^ll=^^- Ans.
CASE 8
(2) Thus J of a Bhilling=5 of y=y =10|(/. Ans.
(3) Thus If of a day=|| of \^—%\^—^hrs. Ans.
(4) Thus fg. of an acre=TV of | of |-''=Vi" perches=
Ir. lOp. Ans.
CASE 9.
(2) Thus bs. 4^.=64J. and £l=240<^. therefore 4\=
y\£. Ans.
124 VULGAR Fractions.
(3) Thus Cmo. 2w.=26iv, and lyr.=52w. therefore ||
oriyr.=:|yr. Ans,
(4) Thus 2qrs. 3/i«.=llna. and lijd,=^16na, therefore
j}yd. is the Ans.
ADDITION OF VULGAR FRACTIONS.
EXAMPLES.
(2) Thus t\+A+A+tV=H=1- Ans.
(3) Thus 44-.iJ-f «=V=16. Ans.
(4) Thus 6)5 10
1 2=10 common denom.
And 10— 5X2=4)
10-10X5=5 P^"'^^-
Whence A+tV^A- Ans.
(5) Thus 3|=V, 8f=V% and 4x7x9==252 common
denom.
And 252—4X13= 819)
252—7x58=2088 >numer.
252-^-9 X 4= 112)
Whence fH+WI+Ht='¥7?l=ll|H- Ans.
(6) Thus i of |=H=A. andf of t^=^=/,.
Then 8)16 24
2 3=48 common denom.
And 48^16X5=15) „^^^
48-^24x7=14 r
Whence 4f+i|=o. Ans.
(7) Thus iof -fof Y=»|«=53'per.=Ir. 13Jp.
And ^ of V«=2f-«=28j[>.
Whence \R. 13j/>.
28
Ans. 2 U
VULGAR FRACTIONS. 125[
MULTIPLICATION OF VULGAR FRACTIONS.
EXAMPLES.
(2) ^ by 1 thus 2X 1=2__ ^
(3) Thus 6|=:26 by i=26xl^26_
4X7=28"
(4) 4f=V^ by f=19X2=38_
-=--y^. Ans.
4X3=12^^^=-^- ^"^-
SUBTRACTION OF VULGAR FRACTIONS.
EXAMPLES.
(2) Thus ^ of 1=0^ whence ^J— Jg.
4) 20 28
5 7=140 common denom.
140—20x10=133.
V numer.
19=133 >
1= 5[-
140-f-28X
wnence y^-jy — jaq — to — a?* -^"S*
(3) Thus 1X14=: 14 common denom.
And 14-^ 1X5=70)
14-14x8= 8 r"^"""'-
Whence 1^—^^=:Y^=4{^, Ans.
(4) Thus I of a league=| of 3 miles=2 miles.
And -^ of a mile= 7jf of 8 furlongs=:|^'==5-^ fur-
longs=:5 furlong's 24 poles.
Therefore 2m. — 5fur, 24/>o.=lm. S/wr. IGpo, i\ns.
(5) Thus 5|='^3 and 2|=| therefore 4x3=12 com. d.
And 12-f-4x 23=89)
12-f-3X 8=32 r'"'''^''
Whence f|— f|=ft=3^. Ans.
(6) Thus 2 of "^^=1-1 and | of |=|^.
And 4) 48 20
12 5=240 common denom.
And 240~.48X 14=70 )
240-20 X 3=36 P™^^*-
70 3 3 4 17 A ««
2Tff 2¥0 24^ T2 0* -^"S*
126 VULGAR FRACTIONS.
DIVISION OF VULGAR FRACTIONS.
EXAMPLES.
(2)|by?tIiusJ)f(5V Ans.
(3) 6|=^/-^lthusa)3J3(9/r=l9|. Ans.
(4) Thus f of 1=-^ and 1 of |=f.
Then T^-H| thus |)^tM='l- Ans.
(5)^byfthus4)i(TV=f. Ans.
(6)|ofi=iJand|of|=5V
Then 4J by J, thus |')J-KW=16f Ans.
(7) 1 of 17i=i of \'=^\'. -
Then =y5-^1thus-J)-V(V2=llj. Ans.
(8) Thus f of 91.p=.| of ^ry'^^f?!^-
And l^i'^'if thus i^i^'nV{\\m^=3i^Uif
Ans.
RULE OF THREE IN VULGAR FRACTIONS.
EXAMPLE.?.
(2) Thus 3l.yds.=\^ and 9j.9.=|-9 and ^7jds.=Y'
Then we have V = l"" = = '/ = l^*- 3</.
For 3,0 X V^=:lV5:~^\=|'iV=l 4.. 3^. Ans.
(3) Thus I : 20 . . 3 . 121/J.s'.
(4) Thus 273 x4/)e.=llly(Zs. ^nd 15§«.~16«. 8</.
Then say as in whole numbers, lyd, : lllyrf*. : : 15*.
ad, : £86 19 J.
For 13*. 8J.=:188c?.xllli/(Z5.=20868(f. which -7-12
-r20=£86 19*. Ans.
(5) Thus 55ci/?<.=V fi^nd £3m=»5»«.
Then we have =-V» : § : : »5-f« : £2 6*. 3||<i.
1 or 50 A y — jffjy ~5g — - BO^ff X. — **^ 0*. Jyfa.
Ans.
DECIMAL FRxVCTIOXS.
(6) First lf/6.=|.
Then J^/6. : |/6. : : ^oL : $2 '74^cts,
127
For^
$2 74^ds, Ans,
(7) Thus 20f(Z.=r:«2.
Then inversely thus 6m. : 10m. : : V^day, : S4Mays
For «^2 X Y = ^^-r-l=:^\%'—'^4±days. Ans.
(8) First ^ of 2lcv'f.=i of |=f of a cwt
Then this reduced to lbs", would be | of *l2_.56o^
Then we have 6llbs.= \p : s.^o . . 3 . ^q 76||^-;^.
For ^f^Xf^^ll^H-f^^l^f £^o/.=glO 7611^;?.
DECIMAL FRACTIONS
ADDITION OF DECIMAI.S.
EXAMPLES.
(5)
56.12
.7
1.314
6837.01
.15
Ans. 5895.294
(6)
361.04
.120
78.0006
101.54
8.943
.3
Ans. 549.9436
(2)
MULTIPLICATION OF DECIMALS.
EXAMPLES.
(3) 4560.
54.20
38.63
16260
32520
43360
16260
Ans. 2093.7460
.3720
91200
31920
13680
Ans. 1696.3200
li^
1^8 DECIMAL FRACTIOKS.
(4) .28043
;0005
Ans. .000140215
SUBTRACTION OF DECIMALS.
EXAMPLES.
(5) 13.16421 (6) 5960.
4.286 .3742
Ana. 6.87821 Ans. 5959.6258
DIVISION OF DECIMALS.
EXAMPLES.
(2) 4.20)148-63(35.304+ Ans.
1263
2233
2105
(4) 931.)2.00385(.0021523-f- Ans,
1280 1862
1263
1418
1700 931
1684
4875
16 rem. 4655
(3) 3.2).2142(.066-f Ans. 2200
192 1862
222 3380
192 2793
30 rem. 587 rem.
" ■ II I < l ■> I ■ m il
DECIHAL FRACTIONS. 129
REDUCTION OF DECIMALS.
CASE 1.
(2) 8)7.000
(3)
24)170(.70833+
168
.875 Ana.
200
192
80
•72
80
72
•—
8 rem.
(4) 2162.)3810(.1762+ Ans.
2162
(5)254)1160(.4566+ Ans.
1016
1440
16480
15134
1270
1700
13460
12972
1524
4880
1760
4324
1524
556 rem.
236 rem.
■■si. , .1 ■ ■■ ■■■Ja
130
DECIMAL FRACTIOIiS.
CASE 2.
(2)
Thus 2i2. 4P.=84P. lwi.=160P.
Then 160)840(.525 Ads.
800
400
320
800
800
(3)
2qr. 2na,=zlQm,
Then 16)100(.625
>96
40
32
80
80
And lyd.=zl6na,
Ans.
(4)
Ur.=:60wim. And
60)5.00(.08333-f Ans
480
(3) lo2r.=480^r*.
Then 480)1 000(.02083-l- Ans.
960
200
180
4000
200
3840
180
1600
200
1440
180
160 rem.
20 rem.
DECIMAL FRACTIONS. 131
(6) 2qts, \pl.—5pts,
lhhd,=::S04pts, Then 504)5000(.1to992-f Ans.
4o36
4640
4536
1040
1008
32 rem.
CASE 3.
£ Day. GaL
(2) .1361 (3) .235 (4) .42
20 24 4
«.2.7220 940 ^f.l.GS
12 470 2
qt,pt.
<Z.8.6640 7ir5.5.640 jp^.1.36 Ans. 1 1.36
4 s,d, 60
Ans. 2 84-
5r.2.6560 — ^mm.38.400
60
■ A»v. min* sec,
5ec.24.000 Ans. 5 38 24
s. Yd, Acre,
(5) .253 (6) .436 (7) .9
12 4 4
J.3.036Ans.3.036 ^r.1.744 r.3.6
4 40
qr. na, ' Jt, P.
wcf.2.976 Ans. 1 2 ;?.24.0 Ans. 3 24
132
POSITION.
RULE OF THREE IN DECIMALS.
EXAMPLES.
(2) Thus lAyd. : IS.yd, : : 13*. : £6 19s, 3d. l.Tljr.
For 13X15=195. the dividend.
Then 195.-t"1.4=£6 19*. 3^.719^ Ans.
(3) Thus \qr, : 1yd, : : p M.5cts. : p 2Qcte.
For 2. 34.5x4—^9 ^Sds, Ans.
(4) First sold it for pOS.SOds,
but paid for it 84.39.12—
gained on it g23.90.88
Then W.5cwL : Icwt, : : g23 90d*. 88m. : $2 21 ds,
7m. +
For 23 .90 88-r10.5=|j2 27d*. 7m. Ans.
(5) Thus ^20.8 : ^2.6 : : 2i0pie, : 145.38/we.+
For 240X12.6=3024.0 which —20.8=1 45.38pie.+
Ans.
(6) Thus S,Soz. •: 5.2o^. : : '74.6d*. : gl lOcfe. 8m.
For 5.2x74.6-^3.5=^1 lOds. 8m. Ans.
POSITION.
SINGLE POSITION. :
EXAMPLES.
i
(2) Suppose 162 in the box.
32.40=J
27.00=*;
20.25=J
13.50=jV
Result 93.15
Theng93 15ds. : gl62 :: |J690 : jjl200. Ans.
POSITIO?f.
133
(3) Suppose C.'s 40
+ 8
+ 16
64r=A.'s
48=B.'s
40=C.'s
152 result.
Then n2yrs.
yrs. yrs, yrs.
(64 :: 133 : 56r=A.'s )
. : J48 :: 133 : 42=:B.'s >Ang.
( 40 : : 133 : 35=C.'s )
133 proof.
(4) Suppose No. 3 cost 20
3
60=No. 2.
120= No. 1.
60
20
Result 200
Then 200 :
350 : 2lO=No. 1.
350 : 105=No
350 : 35= No,
Ans.
M
134 POSITION
Yrs,
(5) Suppose 60
2
120
3
5)360
3)72
24 result.
Then 242/r5. : GOyrs, : : 14yr$. : 35yrs, Ans.
£
(6) Thus suppose 40
200
20
10
T * r 1 20
Int. for 1 yr. <
[«.6|00
Then as £10 14*. 8rf. : £201 5*. : : £40 : £750. Ans.
£ s.
And \l\2 6
4 years.
Int. in 4 yrs. 9 4
3
7 8
Int. for 8 mo. \ pj^ ^
Whole int. 10 14 8
•^ <
(7) Thus, suppose the cistern to hold 100 gallons. i
Then 100-^ 45min.=2^^aL=ihe quantity which the'
first cock discharges in a minute.
And W0-^55min.=^l^jgal, the quantity which the
second cock discharges in Imin.
Then 100-^30mm.=3^^a/.=the quantity which the
discharging cock discharges in Imin. Consequent-
ly, 2^gaL^l-fjgaL=4^^gaL the quantity which
the cistern receives by both the first and second
cocks in a minute. Then as 2igals, run out in the
same time, ^r^gctl. — S^a/.^jfg-aZ. that the cistern
gains in Iwim.
Then l^gaL : lOOgaL : : 1mm. : 2^^^, 21nii7i. 25 f see.
Ans.
DOUBLE POSITIO.V.
(2) First suppose they received 276
3)552
184=:what A. spoiU.
-i-250
434=:what B. spent.
—276
1 58 B. w^as in debt every
7 year.
1106=7 years' debt.
—350
756 error too much.
136 POSITION.
Again suppose the salary was 300
2
3)600
200=A. spent.
J- 250
450 B. spent.
•—300
B. was every year 1 50 in debt.
7
And in 7 years he was 1 050 in debt.
--350
700 error too much.
Then 756 X 300=226800
700X276=193200
Difference of errors 56)33600(^600 the salary, f
336 of which=400
A.'s share, then
00 400+250=650
B.'s share. Ans.
(3) First suppose 30 working days.
§30
— 10 that he forfeits.
Tlcceivcs 20
27 50
7 50 error too little.
137
Again suppose 20 worldng days.
Forfeits 15
Receives 5
27 50
22 50 error too little.
Then 2250x30=67500
750X20=15000
Difference of errors 1500)52500(35 workino- days.
4500
7500
7500
Therefore 50 — 35=15 idle days. Aiis.
$
(4) First suppose 10 cow6=160
And 10 oxen=240
40 calves=240
The whole 640
—320
320 error too much.
Again suppose 8 cows==12S
And 8 oxen=:192
And32calves=192
The whole 512
320
192 error too much.
138 rosiTio:N'.
Then 320x8=2560
192X10=1920
DiiFerence of errors 12S)640{5cows boxen & ^Ocaltes.
640 Ans.
(5) First suppose Again suppose
Ft, Ft,
No. 2=20 No. 2=30
10=1 i5=i
15 15
25=No. 3. 30=No. 3.
4-15 +15
40 45=No. 2.
—20 —30
20 error too much. 15 error too mucli.
Tiicn 20x30=000
15X20=300
Difference of errors 5)300
60=No. 2, then 60—15=45=
— No. 3.
And then we have No. 1=15, No. 2=60, and No.
3=35, which added together= 120/1. the length of
tht; pole. Ans.
rosiTiox. 139
(6) Thus first suppose the whole property to have been
worth jS £
396 Again suppose 432
198=1
216=;
—40
—40
158= A. 's share.
176=A.'8
132=^
144=1
+ 12
+ 12
144=B.'s share.
156=B.'3
—80
—80
60=C.'s share.
76=C.'s
144
156
^58
176
366 sum.
408 sura.
396
432
30 error of defect. 24 error of defect.
Then 432X30=12960
396X24= 9504
Difference of errors 6)3456
£576 Ans.
£
Then 576-^2—40=248 A.'s share.
204-r-3-f 12=204 B.'s do.
204—80=124 C.'s do.
£576 proof.
140 POSITION.
(7) First supDOse each boy received 3
2
6 = share of each
3 woman.
18= share of each
— man.
And 19X3= 67
11X6= 66
7X18=126
249
172 19 4J^ 1
76
7 J- error of excess. j
£
Again suppose each boy received 1
2
2 share of each woman.
3
6 share of each man.
£
And 19X1=19
11X2=22
7X6=42
83
172 19 4J 1
09 19
4J. error of defect. 1
, , ^ J|
INVOLUTION AKJ) EVOLUTION . 141
£, S. d.
Now 89 19 4|X3=2G9 18 0]
76 7JXl= 76 7J
345 18 8i
Which -—166 sum of errors=:=jG2 1*. 8c?. -|- =each
boy's ehare, which X2=:JC4 35. 4|(/.4- =each
woman's share, which X3=jei2 10^. OJd!.-f =
each man's share. Ans.
INVOLUTION, OR THE RAISING OF
POWERS.
EXAMPLES.
(2) 14X14X14=:2744. Ans.
(3) 2.8X2.8X2.8X2.8X2.8X2.8=:4S1. 890304. Ans.
(4) .263X.263X.263=.013191447. Ans.
(5) }XiXiX|XiXjXiXi=^7i^^. Ans.
(6) 401x401x401x401—25850961601. Ans
EVOLUTION, OR THE EXTRACT-
ING OF ROOTS.
SQUARE ROOT.
EXAMPLES.
(2) 39375655(6275 Ans. (3) 14C6.179010(38.5o. Ans.
36 9
122)337 68)586
244 644
1247)9356 765)4217
8729 3825
12545)62755 7705)39290
62725 38525
Rem. 30 Rem. 76510
142 SQUARE ROOT. 1
(4) ^6385163(9817 Ans
81
(^)
.0001 324960(.01 151 Ans.
1
188)1538
1504
21)32
21
1961)3451
1961
225)1149
1125
19627)149063
137389
2301)2460
2301
Rem. 11674
Rem. 159
1
(6) 18.362147(4.
16
285 Ans.
82)236
164
848)7221
6784
8565)43747
42825
Rem. i :
(^) 15^5=,!' •"- ^' a^iarc root is J. Ans.
(8) 36)1?-=- whose
square
root is ^. Ans.
SQUARE ROOT. 143
(9) 500)3200(v^64(.8 Ans. (10) 50x64-f 49=:3|4 9,
3000 64
-; Then 3249(V=7J. Ans.
2000 25
2000
107).749
749
And \/. 6 4f. 8 denominator.
64
(11) 30x100+25=30.23 (12) 1296(36 Ans.
3X3=9
Then 30.25(5.5=5-,%. Ans.
25 66)396
396
105)525
525
(.13) 169(13 Ans. (14) 3097600(1760ydf^.=lmi/€.
1 1 Ans.
23)69 27)209
69 189
346)2076
2076
00
b
144 SQUARE ROOT.
(15) Thus 15X15=225
24X24=576
V^801(28.3ft.An«.
4
48)401
284
563)1700
1689
Rem. 11
(16) 212X212=44944/^.
And 202/<?*.=6OX60= 2600/1,
41344(203.332/?. Ana.
2X2=4
403)1344
1209
4003)13500
12189
40663)131100
121989
406662)911100
813324
Rem. 97776
CUBE ROOT. 145
CUBE ROOT.
EXAMPLES.
(2) 7532641(196.1)2 Ans.
1
{ Defec. div. and squ. of 9=381 6532
^+270=:com. divisor =651 6859
5 Def. div. and squ. of 6=108336 673641
^ +3420=com. div. =111756 670536
Defective divisor 115248 3105000
;Def. di. «fe sq. of .02=1152480004)3105000000
I 4- 11760 = com. div. =1152491764)2304983528
Rem. 800016472
(3) 12.113847500(2.296 Ans.
2X2X2=3
; Def. div. and sq. of 2=1204)4113
» +120 = com. divisor = 1324)2648
5 Def. div. & sq. of 9=145281)1465847
(+5940 = com. di. = 151221)1360989
5 Def. di. & sq. of 6=15732336)104858500
( + 61830 = c. di. = 15773556) 94641336
Rem. 10217164
146 CUBE ROOT.
(4) 5382674(175.2 Ans.
1
5 Defec. div. & square of 7=349)4382
( -f 210=complete divisor =559)3913
J Defec. div. «& square of 5=86725)469674
I -f 2550=:completc divisor=89275)446375
J Defec. div. & squ. of 2=9187504^23299000
I -f 10500 = com. divisor =9198004)18396008
>Rein. 4902992
(5) .378621 350(.723. Ans.
7X7X7=343
J Defec. div. & sq. of 2=14704)35621
^4-420 = com. divisor =15124)30248
J Defec. div. & sq. of 3=1555209)5373350
( -f 6480=com. divisor =1561689)4685067
Rem. 688283
(6) 46.295363543(3.590 Ans.
3X3X3=27
J Def. div. & sq. of 5=2725)19295
I 4-450=com. divisor=3 175) 15875
J Def. div. & sq. of 9=367581)3420363
J +9450 = com. di. t=377031)3396279
Defective divisor 1 2888 1 )24084543
ALLIGATION.
147
(7) Thus4)X«|5=
.2007722
J Defec. divis. & S(
( -f 200=complete
5 Defec. div. and sq
14-8700 = com. di
(8) Thus
=23%> which reduced to a decii
Then .200772200(.585
125
[nal=
Ans.
Ans.
ju. of 8=7564)75772
divisor = 8764)701 12
.of 5=1009225)5660200
visor= 1017925)5089625
570575 Rem
;j/36.|«=V36.8666664-(3.32
3X3X3=27
5 Defec.
I 4-270=
div. & sqi
=complete
1. of 3=2709)9866
divi. =2979)8937
5 Defec.
14-198:
div. & sq.
= com. div
of 2=32i?704)929666
isor =328684)657368
Rem. 272298
^9®9^
ALLIGATION.
CASE 1.
(2)
Cwt,
2 a
4
7
13
$ cts. $ ds.
t 25 =50 00
20 50 = 82 00
18 621=130 37^
g262 371
Then as
Ans.
newt. :
UwL :•, $262 ^71^^. : $20
I8jd*.
148
ALLIGATION'.
(2)
Mean rate 50
CASE 2.
=36 at 34 cts. ^
=60 at 42 cts. I .
= 16 at 86 cts. f^^^'
= 8 at 110 cts. J
CASE 3.
(2)
Mean rate 92
Then
86 cts.
94 cts
18 at 105 cts
'^
Ans.
CASE 4.
(2)
Mean rate 145
Then as 80 : 50
80 : 15
80 : 15
32
32
32
80 sum. of difter.
20 at 130 cts,
6 at 160 cts
6 at 180 cts
i:|
Ans.
ARITHMETICAL PROGRESSION. 149
AFJTHMETICAL PROGRESSION.
CASE 1.
EXAMPLES.
(2) Thus 40—1=39 (3) 10—1=9
2 com. dif. 4 com. dif.
78 36
2= 1st term. +10=^lst term.
80 1st Ans. 46 last term.
2= let term. -flO
82 sum. 56
40 10
2)3280 2)560
gl6.40 Ans. 280 2d Ans.
(4) 75—1=74
2 common difference.
148
-f 6= 1st term. ^
^1.54 for the last* Ist Ans.
6= 1st term.
160 sum.
75
800
1120
2)12000
00 in the whole. Ane.
^ 2
150 ARITHMETICAL PKOGRESSION.
CASE 2.
(2) Thus 175
—21
8—1=7)154 .
jj22 common difference.
And 175+21=196 sum of extremes.
8 number of terms*
2)1568
784 whole sum.
Lastly 21-1-22= 43=2d payment.
43+22= 65=3d
65+22= 87=4th
87+22=109=5th
09+22=131=6th
131 + 22=153=7th
153+22=175=8th
763
21= 1st payment.
$784 proof.
(3) Thus 49 Then 49+4=53 sum of extremes.
-—4 10 number of terms.
10— .1=9)45 2)530
5com. dif. Received $2.65 Ans.
GEOMETRICAL TROGRESSION. 151
GEOMETRICAL PROGRESSION.
EXAMPLES.
(2) Thus power 12 3 4
Ratio 3 9 27 81
27 3d power
"567
162
2187=7th power.
5= 1st term.
l6t Ans. 10935=:last term.
3 ratio.
32805
— 5= 1st term.
Ratio less 1=2)32800
jei6400 Ans. 2nd
(3) Thus power 1234567 8 9
Ratio 2 4 8 16 32 64 128 256 512
512
1024
512
* 2560
262 144= 18th p.
4=2d do.
1048576=20th p.
1 1st term.
1048576=lastt.
2 ratio.
2097152
l = lstt.
Ratio less 1= 1)2097151
Ans. g20971.51c <r
152 COMPOUND INTEREST BY DECI]>LA.LS.
COMPOUND INTEREST BY
DECIMALS.
EXAMPLES.
(2) Thus, tabular number 1.2155062
750
607753100
85085434
911.6296500
Amourtt of £1 for 6mo. 1.024695 from table first.
45581482500
82046668500
5469777^000
36465186000
18232593000
91162965000
je934. 1423442067500
20
«.2.8468841350000
12
rf. 10. 1626096200000
£ 8, d.
Amount 934 2 10-}-
Principal 750
Interest 184 2 10+ Ans.
ANNUITIES AT COMPOUND INTEREST. 1 53
CASE 2.
(1) Thus £695 13*. 9d.=:695.6875£.
Then from tab. II. 1.2762815)695.68750(545je. 1*.
9rf.-f Ans.
(2) ThusjeseO 5«. 3<i.=260.2625je which-rby 1.191016
from table II.=£218 10*. 5d,+ Ans.
ANNUITIES AT COMPOUND
INTEREST.
CASE 1.
(2) The number from table III.=5.637093
200=annuity.
Amount for yearly payments=l 127.4186 which X
1.014781 proper number for ^ yearly payment from
table V.=^l 144 08 2m.-{- Ans.
CASE 2.
(2) Thus, the num. from tab. IV,=4.21236
£70 annuity.
^294 86 52 Ans. for y.
payments.
Then jj!294.8652 X 1.014781 from table V. =
$299, 22.2-{- mills. Ans. for i yearly payments.
And 294.8652X1.022257 for quarterly payments
from the same table=^301.42.8-f mi//#. Ans. for
quarterly payments.
1 54 , COMBINATION.
ANNUITIES IN REVERSION,
(2) Th^ 9+4=13yo.=9^.98565 table IV.
4 do.=3.62989— .
6.35576
120
1271152
635576
62.69.1.2m. Ans.
e@»44.~
PERPETUITIES AT COMPOUND
INTEREST.
(2) Thus, ratio— 1=1.06— 1=.06)260.00
g4333.33.3m.-f Ane.
COMBINATION.
EXAMPLES.
(2) Thus 20X19X18X17X16X15X14X13X12X1==
1X2X3X4X5X6X7X8X9X10=
670442572800
. = 184756 Ans.
3G28800
DUODECIMALS.
165
PERMUTATION.
EXAMPLES.
(2) Thus
1X2X3X4X5X6X7X8X9X1C
479001600 number of c
15 seconds.
X 11X12=
tianges.
2395008000
479001600
6|0)718502400|0 sec
6|0)11975040|0 min.
365AcZ.=8766 hrs.)l 995840(227 yrs. 248 days. 6 hrs.
Ans.
»mCQ9«»>».
DUODECIMALS.
ADDITION OF DUODECIMALS.
EXAMPLES.
Ft,
(1) 10
15
18
12
in. " '" "" Ft, in, "
5 6 11 6 (2) 37 8 10
9 5 2 10 43 11 2
4 17 9 19 7 5
8 6 5 7 18 4 1
/// ffff
6 9
4 7
3 8
7 2
Ans. 57
3 8 3 8 Ans. 119 7 7
10 2
1
156 DUODECIMALS.
Ft. in. "
(3) 16 8
14 6
17 9 2
Ans. 48 11 2
SUBTRACTION OF DUODECIMALS.
EXAMPLES.
Ft, in. " '" "" Ft. in. " '" ""
(1) From 38 8 4 7 5 (2) From 720 3 8 1 6
Take 15 11 6 9 3 Take 13 9 4 7 10
Ans. 22 8 10 2 2 Ans. 706 6 3 5 8
Ft. in. " '" ""
(3) From 475 7 2
Take 81 2 5 10 6
(2)
Ans.
394
4 8 16
MULTIPLICATION OF DUODECIMALS.
CASE 1.
EXAMPLES.
Ft. in.
64 10
5 7
Ft. in. "
(3) 6 9 3
3 5
31 11 10
274 2
2 9 10 3
20 3 9
306 1 JO
Ans. 23 1 7 3
(2)
(3)
sq.
6
1 -
4"-
1
DUODECIMALS. 167
CASE 2.
Ft, in, "
\ 81 10 4
7X2=14
573 4
2-
1146 8
J 40 11 2
L 6 9 10 4
» 2 3 3 5 4
6 9 10 4
1)1196 7 9 7 8
is,l22 8 7 9 7 8 Ans.
in,
4
1
3"
6//'
1
1
I
7
^t. in. " '" .
2 5 7 2
} 9 10 4 8
2 5 7 2
7 4 9 6
12 9 7
9 10 4 8
2 5 7 2
ft. 1
110 8 5 4 11 10 contents of Ish.
10X10X10=1000
10 10 7 6 1 10 4
10
108 9 10 5 1 6 7 4
10
1088 2 8 3 3 6 14 Ans.
158 PROMISCUOUS EXAMPLES.
PROMISCUOUS EXAMPLES.
(1) Thus A.'s 25 years.
+ 15
B.'s 40 years.
+ 12
C.*s 52 years. Ans.
% Cl8, % Cts,
(2) Thus 220 50-f-5=44 10 A.'s own share.
220 50+6=36 75 B.'s do.
80 85 sura.
220 60
139 65=C.'s own share.
^ ds. j5 ds.m.
Then 36 75+2=18 37 5=^ B.'s share.
44 10
62 47 5=A.'s last share.
^ els, m.
And 18 37 5
139 65
Ans. 158 02 5=C.'s last share.
PROMISCUOUS EXAMPLES. 159
(3) glcrO— g7l : poo : : p6 25cts, : g60 Slds. 5m.
-1-25.
For 5625X100=562500 the dividend.
And 100—71=921 the divisor.
Then 562500— 92i=g60 Slots. 5?n.-f 25. Ans.
(4) Thus B. gains 2 miles per hour.
Then as 2m. : 50m. : : Ihr, : 25hrs. 1st Ans.
Now as B. went at the rate of 10 miles per hour for
25 hours, 10x25=250 miles, the 2d Ans.
(5) Thus^=J)750
187 50 whole price of the damaged.
100 loss.
87 50 what it sold for.
Then $1 25cts, : g87 50c^^. : : 1yd, : lOyds.zzzqmn-
tity damaged.
And 70 X 4=2S0yds, the whole quantity.
70
210 undamaged.
And ^750 OOd*. cost.
87 50 received for the damaged.
2l0yds, : $662 50 : : 1 : g3 I5lcts.+ Ans.
160 PKOMISCUOUSf EXAMPLES..
(6) Thus lOGO— 1=:=999 number of terras— 1. ♦
1 ft. common dilTerence.
999
2 ft., first term.
1001 last term.
2
1003 sum of the terms.
1000
2)1003000
3)501500 ft.
220)167166+2 ft.
0)759+186 yds.
94+7/wy. UQyds. 2ft. Ans.
(7) Thus admit the wall to contain 3600 feet.
Then 20)3600(180 feet raised in a day by A. B. & C.
24)3600(150 * B. C. &D.
30)3600(120 C. D.& A.
36)3600(100 A. B. & D.
3)550
1 83i feet per day by altogether.
Then 183 J- And 183.}
B. C..& D. 150 C. D. & A. 120
A. 33}
PROMISCUOUS EXAMPLES.
161
And 183
A. B. &D. 100
C. "83^
^ And 183 J
A. B. & C. 180'
D.
days.
Then, feet per day by A. 33J)3600(108 for A. to do it in.
do. by B. 63fj3600(56|J B. do.
do. by C. 831)3600(43]. C. do.
do. byD. 31)3600(1080 D. do.
And 1831)3600(19^ days all working together.
Ans.
d, d,
(8) Thus 4 crowns at 146 each=584
3 dolls.
2 ducats
108
136
1180c;. sum.
And £1055 155.=253380cif.
Then
1180 : 253380
d.
584
324
272
d, d.
125402-rl46=:858f|cr.
69572 "
58406
2-rl46=:858f|cr. )
2-T-108=644^5^g. \
6-M36=429||<£wc. ^
Ans.
(9) Thus 9wi. : 21m. : : g332 50c<5. : $775 83jc«5. Ans.
For 33250X21=698250 the dividend.
And 9=the divisor.
Then 698250^9=^775 ^^Ids.
O %
162 PROMISCUOUS EXAMPLES.
(10) Thus 12
4
16yrs.=10.n3'711 Table IV.
Time of reversion 12 = 8.86325 do.
1.97462 difference.
720.25 annuity.
987260
394904
3949040
1382164
gl422. 1480300
Or ^1422 14cls,' 8m.+ Ans.
(11) 3150 gigs —
2250
X Sets,
igs~7X 5=^ g cts,
) wagons wh. > 135 00 for the wagons.
cts.= 3
3150 gigs -f- 3 X 5=^
5250 footmen wh. > 52 50 for footmen.
X let.— )
6250 footmen -r- 6 X 4 ^
= 3500 horsemen > 70 00 for horsemen,
which X 2ds*= y
3150 gjs at 4cts. per ) j^g ^^ ^^^ ^j^^
Amount of, toll 383 60 Ans.
(12) Thus 15^a/5. in 3min.~5gals. per min. that nm in.
And 20-7-5= l/.:flf7*. that run out in a min. Con-
sequently, the gain is 5 — 4=^gaL per min. which
is OOgnh. per hour.
Then nO-'60=50^<»vTA?. yet to nm in.
Then Sgals, : SOgals, : : Imwi. : 107nm. Ans.
PROMISCUOUS EXAMPLES.
163
(13)
Thus 264
6
6
3
1
15 84 Int. for 1 year.
7 92
3 96
1 1 88 Int. for 9 months.
264 00
30 00 profit.
g305 88 for the whole.
lbs ^ cts Wl
Then 28cw?*.=3136)30588(0 9 7+ Ans.
28224
23640
21952
Rem. 1688
(14) Thus, the proportions are A. 4 B. 5 C. 3=12.
Then 12 : 780
' 4 : 260 A.'s share of profit
5 : 325 B.'s do.
' 3 : 195 C.'s , do.
1st
Ans.
pSO proof.
$ mo.
Then 260x5=1300
325X7=2275
195X9=1755
5330
164 PROMISCUOUS EXAMPLES.
r 1300 : 1405 36 A. 's stock.
Again 5330 ; 5762 : : \ 2275 : 2459 39 B.'s
( 1755 : 1897 25 C's
g5762 00 proof.
Now 2459 39
2087 00 B. received.
372 39 B.'s loss of stock.
And 325 00 do. of gain.
Ans. '^697 39 A. & C. would gain.
(15) 1004-51=105 75. $ cts.m.
Then 105 75 : 100 : : 1000 : 945 62 6 cost C.
20 75 less.
$924 87 6 cost B.
Again 100
—5 50
94 50 : 100 : : g924 Slds, 6m, : g978 llOcts.
4m. that the whole cost A. which ~20AM^.=g48
93c^*. 5m. -f Tperhhd. Ans.
(16) 10X11=110 sold for.
10 X 7= 70 worth.
$40 gain of A.
$ ds, m. $ ctt.
And 110-r3= 36 66 6+ paid cash. 5 25
110 00 4 50
$73 33 3 to pay in paper. $0 75 B. gains.
1 Then 450 : 75 : : 73 33 3 : $12 22ds. 2m. gain of
1 B. $40— $12.22.2=r$^27.77.8. Ans.
PROMISCUOUS EXAMPLES. 165
(17) Thus 21—14=7 years to be of age.
Then gl 300
6
' 7800 int. first year.
1300
1273 amount— 100.
6
7668 int. second year.
1278
125468 amount— 100.
•6
752808 intnhird year.
125468
12299608 amount— 100.
6
73797648 int. fourth year.
12299608
12037584 amount— 100.
6
72225504 int. fifth year.
12037584
11759839 amount— 100.
6
70559034 int. sixth year.
11759839
11465429 amount— 100.
6
68792574 int. seventh year.
11465429
^ i 1 15.33.54m. amount— 100. Ans.
IGG PROMISCUOUS EXAMPLES.
Another solution :
First, 1.067=1.5036302. See table II. Arithmetic.
And 1.5036302X1300=1954.719. Amount at . Com-
pound Interest.
Also, 8.393837X100=839.383. Amount of glOO An-
nuity for 7 years, table III.
Hence S5l954.719—g839.383==glll5 23cts. 5m. Ans.
(18)
E B F
64
^K
^'^""— — ^
14
D
50
C 76~^
L Statue, L
Thus, referring to the above figure.
A B is a perpendicular line erected on the centre of the
statue's base, which forms the side A C of the right
angle A C D ; and the other two sides, A D 86 and C D
76 are given to find the length of the side A C.
Now 76^=5776 & 862=7396
—5776
x/1620diff. (40.2-L = AC
PROMISCUOUS EXAMPLES. 167
Then 40.2-|-14 the difference between the columns
=54.2 the whole length of A B. Then 54.22=
2937.64 & 972=
that is A E=9409
—2937.64
V6471.36=(80.44-f for E B.
+ 76 that is BF
14=DF 156.44=EBF
14 156.44
56 62676
14 62576
93864
196 78220
15644
24473.4736
196
2^/^24669.4736=157 ft. Ans.
Note. — ^This solution snpposes the statue to be lower than the
columns : admitting it to be higher, the operation will, of course,
be different; but may readily be performed from the one here
given.
(19) Isec. : 47*ec. : : 1150/?. : 54050/?. Ans.
(20) 15m. 7/5/^=83820/?.
Then 1150/?. : 8382t)/?. :: Iscc, : Im. I2{^pec,
Ans.
168 PROMISCUOUS EXAMPLES.
(21) First suppose J of 8.2245 in. to be gold.
4.1 1225=^ 4. 1 1225 in. of sil.
10.36 5.85
2467350
1233675
4112250
2056125
3289800
2056125
42.6029100oz.g. 24.0566 625o5r. sil.
24.0566625
66.6595725
63
3.6595725 error of excess.
Again suppose | of 8.2245 in. to be gold, the rest silver.
2.7415=^-
10.36
5.4830=silver.
6.85
164490
82245
274150
28.401 940o2r.
32.075550
60.477490
63.
274150
438640
274150
32.075550oar. sil.
2. 5225 1 error of defect.
[Seefolloiping page<
PROMISCUOUS 1&XAMPX.ES.
169
in o
o Tt
o «>
00 1—
GO 1.^
O GO
d d
to LO
vn
^
l> 1— '
o
^ 5
(^
lo X
UO
c^*
1?^ o
CD
r- ^
<->
to UO
(M
05 G^
CO
O G^
CO in
CO
GO ©<
II
fl
lO
.Q^T3
(^
^ !=!
t-
o o
O
O O
o o
o
O 10
LO O
LO CO
Oi
LO O
LO G^
G>^ GO
C5 CO
<?^
Gv) O
G^ 00
'^ GO
O CO
rf
CO CO
O O
Oi CO
r-4 lO
LO
lO >o
O CO
^ G-f
^ G^
05 ""^
-rf
s^^ t-
LO CO
CO CO
O t-
G^ Oi
GO
<3^ 'f
O UO
O ^
>0 Tf
CO ©^
GO ■^
a> CO
GO 5<
CO CO
O 05
Oi "^
LO "<*
Lf5 LO
CO CO
r-i r-*
0)
^
•M
ns
C
KJ
m
<
Cf^
o
M
r/:
a>
O)
>
o
-73
s-j
(C
C3
o
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170 PROMISCUOUS EXAMPLES.
Another solution :
oz. oz. oz.
First 63-^8.2245=7.66 weight of a cubic incli of the
mixture.
Til "7 ftA 5 10.36s^r=1.81 proportional hulk of gold,
inen 7.t)t) ^ 5,85^=2.7 proportional huJk of silver.
Also 1.81X10.36±=18.7516 proportional trei^^,« of gold.
And 2.7 X 6.85=15.795 proportional lOCTg*^ of silver.
34.5466 sum.
oz.
Hence 34.5466 : 18.7516 : : 63 : 34.19587 gold ) >
And 34.5466 : 15.795 : : 63 : 28.80356 silver. ^ "
Proof 62.99943
(22) Thus llhs, beef at 5jcf5.=40}cfe.
5 bread at 6 =30
Then AO\cts, : g34 50cts. : : 30cf^. : $25 lids. 4wi.+
Ans.
(23) Thus^oflof JJf=^V
Then l^/^«^=fif||. Ans,
(24) 1000
6
60|00 int. for 1 year.
8
int. for 8 years.
PROMISCUOUS EXAMPLES. 171
Then 8 years.
6 per cent.
48
100
148 amt. of JJlOO for 8 yrs. at 5 per cent
$ $ $ $ c«*-"»-
Then 148 : 100 : ; 1000 ; 675 67 5 the present worth.
1000 00
g324 32 5 discount.
480 00 interest.
Ans. gi55 67 5 difference.
(25) V32=p5.656-|-
v^24=4.9
10.556 sum.
V67 =4.06+
Ans. 6.496 difference.
(26) Thus glOO : ^105| : : $24.30 : ^2587 20cf*.
Ans.
(27) Thus the amount of gsOO lods, for 9 months at 6
per cent.=::g533 2nds. 4m.
172 PROMISCUOUS EXAMPLES.
cts, ^ CU.
And 5064x21=126 60 price of the boards.
140X13= 10 20 do. tallow.
144 80 amt.
623 28 4
§378 48 4 to receive in flayseed.
Then as ^Z\cts.: §378 48c«#. 4m. : : Ihu, : 409j|J6w.
Ans.
(28) 9 yrs.=36 qrs. the sum of terms.
—1
35
3 common difference.
105
-f 6=lst term.
Ill last term.
6= let term.
117 sum.
X 36 number of termi.
702
351
2)4212
g21.06cf*. duehim. Ans.
PKOMISCUOUS EXAMPLES. 173
(29) Thus Syrs, — 2\yrs.:=^2lyrs,
Then 1.06x1.06x1.045=1.174162 divisor.
And 2363.3875 — 1.174162 = ^2012 ^2cts, ^m,
Ans.
(30) Thus, from January 14th, 1802, till July 5th,
1807, inclusive=5 years 173 days. And the
amount of jjl 854.69 for that time at 5 per cent
per annum =
^2362.3161
285. paid off.
2077.3161 second bond.
4|
83092644
10386580
5193290
98.67.2514 int. of the 2d bond for 1 yr.
Then 98672514 : 365 : : 52.65 : 194 days the
time of the second bond.
Now 2077.3161
52.65 interest.
2129.9661 amount.
102.43 paid off.
2027.5361 3d bond.
!>£>
174 PROMISCUOUS EXAMrLES.
Which was out from J«nnary 12, 1808, till Octo-
ber 26th, 1813, whiuh L^ 5.789 years.
$9Aj7.0M3 last amount.
20'27.5361 last bond.
469.4962 gained on the last bond,
'' — which was out 5.789.
years, and this bond
inclusive to the time
= 11737.4064829.
Then 11737.4064829 : 469.4962 ; : 100 : 4 per
cent. Ans.
(31) First suppose 10 horses at 50=500
20 cows 20=400
60 sheep 4=240
51110 sum.
45
684 error of excess.
3 $
Agam suppose 8 horses at 50=400
16 cows 20=320 '
48- sheep 4= 1 92
g912 sura.
456
456 error of excess.
PROmSCUOUS EXAMPLES. 175
Then 684 x 8=:5472
456X10=^4560
Difference of errors=228)9 12(4 horses.
912
$ $
For 4 horses at 50—200 )
Scows 20=160 >Ans.
24 sheep 4= 96 )
55456 proof.
Another solution:
$
First 50 price of each horse.
20x2=40 price of cows for each horse.
4x 6=24 price of sheep for each hbrse
114)456(4 numher of horses. .
456
$ $
Then 4 horses at 50=200
4X2= Scows 20=160
And 8x3=24 sheep 4= 96
456 proof.
176 PEOMISCUOUS EXAMPLES.
(32) Thus r 16--V = 6
Mean rate 19 ? 17>, ) = 5
3+2=5
oz, oz,
mi r in ^5 : 10 of 17 carats fine. ) .^^
Then as 5 : 10 : : J 5 ^ ^0 ^^ 24 carats fine. \ ^''^'
(33) £100 : jei20 : : £230 5*. : £276 6*. the amount
in sterling.
Then as £l : £276 65. : : J4 44c««. 4m. : gl227
filets. 7wi.4- Ans.
(34) Thus f^'ff+J=l4|, and ||| subtracted from 1=
^|^=the 27 feet.
Then if| : nft. : : 1 : 113/55. 4m. Ans.
(35) $1 : 56jc?5. : : $400 : $32 14fd5. AnS.
(36)
Thus 30
+96
126 sum.
25 number of terms.
630
252
2)3150
$15.75
Ans.
BOMISCUOUS EXAMPLES. 177|
(37) Thus 4 : 9 t : 47 : 105.75 the greater number.
47
152.75 sum.
58.75 differ ence.
76375
106925
122200
76375
Product 8974.0625 Ans.
TBS CND.
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