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SERIES OF J^^ATIO^TAL SCHOOL BOOKS
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FOR
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;*:.-^.--,v' , .n. .. 1^ - • . •, ,-
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REVISED EDITION, ADAPTED TO THE NEW DECIICAL
!;r; CDRREXCY OF CANADA.
•^ v'^"."'-'^ -v^'^.f^ ;''v ■■<•'■ vi" •'
■■'.-: r*>^
• Ty r-^ - ' •*
■ ^f :ft'v;:l-/ ;-^ t r n t 6';;^ v 'vy^;:;:^^'"
Published by robert Mcphail
•National School Book Depot, 66, King-St., Eaw.
^^c'wSt;^'-:'
I860
Entered, according to the Act of Uio ProviDciHl Parliumeut, in the year
one thousaod eight hundred and Hixty, by RonRRT McPhah., in 1I)«
Office of the Registrar of the Province of Canada.
in4
a)
/ ^/
PREFACE.
TN adapting this well known Treatise to the Deci-
mal Currency, neither expense nor pains have
been spared to make it worthy of universjil patroo-
«ge. The assistance of a gcntleniaa has been
«ccnred, who brings to the work, besides the qualifi^
cation of a Trnctical Accountant, a long expcrieucf
as a successful Teacher. As much as possible of tii^
•Id Book has been retained entire, bnt all the Com-
mercial Rules have been considerably enlarged, and
geveral important ones have been added. The
arrangement,^ also, is more methodical, and as a
whole, the book, a^; now presented, is perhaps one of
the most complete elementary Treatises ever published
oa this Coutinent.
THE PUBLISHER.
CONTENTS.
ARITHMETICAL TABLES.
V\QK.
Afl'ViUon Tablo 1
Miiltiplicafioii Tubit'.... 2
Pence Tablo H
Signs used ill Arithmetic. 4
Honey Tuble 4
Wciftbts and Measures.,
Nunn-nvtion Table
Uoniaii Notation
Table of Aliquot Parte.
ft
8
8
70
AIllTIIMETlO.
Ntimeratlon 8
Notation 9
Simple Addition 10
Subtraction 11
Mixed Qut'Htiona 18
Simple Multiplication... T.>
Division 23
Fkactio.vs — dofinitioua. . 27
Decimal Fractions 28
Addition 28
Subtraction 21)
Multiplication... 29
Division 30
. Rediictloa 31
Decimal Currency 33
Vulgar Fnictiiins 35
■ Prime Numb<*ra. . 35
Common Mea."ure. .3(>
Common Multiple 37
Canctdlation 38
«- R«'duclion 40
Addition 43
Subtraction 43
Multiplication... 44
Division 45
Reduction cont'd 45
Promiscuous Exer 49
Addition oC Money 50
Subtraction of Money. ... 61
Multiplication of Money. 52
Diviaioii oi" Money 54
Rednciion of Money 67
of Halifax Cy. to
$ and c-<'nts. . . . , 69
W.iorjits and Measures., . 6i
Praciice 70
Tare jind Tret 72
Hills (»f Parcels 76
8impl<,' Proportioh 76
Compound Proportion... 81
Partitive Proportion, or
Fellowship 89
Compound i'artitive Pro-
portion 68
Medial Proportion, orAl-
li};ation S9
CoiiJ<»ined Proportion. ... 93
Perc(Mitage, or Profit and
Loss... 95
Simple Interest 98
Commission. Brokerage,
Insurnnc<'. Stocks, &C..100
Componnd Interest 102
Dii^count 103
Barter 106
Involution 107
Evolution 107
Square I'oot 107
Cube Hoot 108
Dnodeeimal Mnltiplicat'n 110
Mental Arithmetic 113
Answers to the QuestioBsllJ
2
2
3 -
3 -
3 -
3 —
3 —
3 —
3 —
3 —
5 ~
3 —
ARITHMETICAL TABLES.
ADDITION TAnr.E.
FaOE.
^res... I
.... 8
.... 8
'arts. . 70
.... 67
Py- to
.... 69
ires. . . 6t
.... 70
.... 72
.... 76
.... 76
on. . . 81
)n, or
89
e Pro-
88
orAl-
8«
n 93
it and
95
98
erago,
Ac 100
102
, 103
106
107
107
107
108
cat'nllO
113
StiOQ£ll7
and
1 are 3
— 2—4
— 3 — 5
— 4 — f,
— 5 — 7
— 6 — 8
— 7—9
— 8—10
— 9—11
— 10— 12
— n— 111
and
and
6 and
6 —
6 —
6 —
12 —
1 arc
2 —
3 —
4 —
5 —
G~
7 —
8 —
9 —
lo-
ll—
12 —
1 are
o
3 —
4 —
6 —
6 ~
7 —
8 —
9 —
lo-
ll—
12 —
1 are
2 —
3 —
4 —
14
4
5
(I
7
8
9
10
11
12
13
14
15
5
G
7
8
9
10
11
12
13
14
15
1()
(i
7
8
9
5 II I id
5
5
5
5
5
5 arc
(i —
7 —
8 —
9 —
lo-
ll —
12 —
1
2
are
l> Ulltl
(i —
(I —
(I ~
() —
(» —
(; —
G —
G —
G —
G —
(; —
7 nrul
7 —
7 — 4 —
7 — 5 -
G —
7 —
8 —
9 —
10 —
n -
1-;
1 ure
2 —
3 —
4 —
5 —
•>
—
4 __
5 —
(i —
7 —
8 —
9 —
lo-
ll -
12 -
1 arc
2 —
3~
t —
7 —
7 --
7 —
7 —
7 —
7 —
8 and
8 —
8 —
8 —
8 —
8 —
8 —
8 —
G
7
8
10
11
12
13
14
15
IG
17
I
8
9
10
11
12
13
14
15
IG
17
18
8
9
10
11
12
13
14
15
IG
17
IS
19
9
10
11
12
13
14
15
16
8 and
8 —
8 —
8 —
!> and
9 —
9 —
9 —
9 —
9 —
9 —
9 —
9 —
and
9
!)
1
1 —
1 —
1 —
1 —
1 —
1 —
1 —
1 —
1 —
1 —
1 —
2 and
2
2 —
2
2 —
2 —
2 —
'>
2 —
2 —
2
9
9 are
lo-
ll —
12 —
1 are
2 —
3 —
4 —
5 —
6 —
r»
1
8 —
9 —
lo-
ll —
12—
are
—
4 —
5 —
6 —
7 —
8 —
9 —
lo-
ll—
12 —
1 are
2 —
3 —
4 —
5 —
G —
7 —
8 —
9— .
lo-
ll —
12 —
17
18
19
20
10
11
12
13
14
15
16
17
18
19
20
21
12
13
14
l!i
16
17
18
19
20
21
22
23
13
14
15
16
17
18
19
20
21
22
23
24
I*
iRiTlIMKTICAl. TABLKS.
MULT11»LICATI0N TAP.LK.
Tw'icd
3 times
4 tinv'S
5 timcH
tiraca
7 i\mc9
1 are 2
1 arii I)
1 :
iro 4
1 art
• 5
1
are
1 arc 7
2—4
2 -- i;
•>
8
K)
2
12
2 — 14
3 f)
3 — 1)
3
— 12
o
15
:{
— 18
3 21
4 - 8
4 — 12
4
Hi
1 _-.
20
4
— 21
4 - 28
n — 10
5 — i:.
.')
- 20
5 —
25
5
- - 30
5 — 35
a — 12
- 18
i)
- 21
(5 , -
30
- - 30
42
; r ~ 14
7 — 21
7
— 28
7 •
35
7
^.. 12
7 - 49
1 n ~ 16
8 — 24
8
32
8 -
40
8
— 48
8 - 5U
1 ^ 18 !) 27
9
30
9 —
45
9
— 54
9 — 03
10 - 20 JO y)
10
- 40
10
0!?
10
- 00
10 — 70
n — 22 11 :v.i
11
44
11 —
55
11
— (u;
11 77
Vi 24 J2 - :ju
12
- 48
12 -
00 i
12
■- 72
12 - 81
«
•
1 8 times
1 aro 8
J) time
s
10 times
$
11 times
12 times
1 are
9
1 -
- 10
1
11
1 n
j 2 - Ki
2 ~
18
2 -
- 20
2
22
2 24
3 — 24
3 —
27
3 -
. 30
3
—
33
3 — 3fr
4 — 32
4 —
3(1
4 -
- 40
4
44
4 — 4t
5 40
C) —
45
5 ~
- 50
5
—
55
5 CO
— 48
r, ~
54
() -
- 00
—
00
G 72
7 — 5(i
7 -
()3
7 -
- 70
7
—
77
7 84
« — (;4
8 —
72
8 -~
- 80
8
—
88
8 - 96
•) — 72
9 —
81
9 -
- 90
9
—
99
9 108
iO — 80
10
90
10 -
100
10
110
10 — 120
U 88
11 —
90
11 ~
■ 110
11
121
11 — 132
12 - 9(;
12 1
08
12 —
■ 120
12
132
12 — 144
EXTENDED MULTIPLICATION TABLE.
io.vB 26
39
62
65
78
01
14 tiinps
*2 ar« 28
— 104 i 8 —
4'2
f)6
70
84
98
112
15 tiiiu'9
'2 nre 30
3
4
5
6
7
8
45
flO
75
■(M>
105
12<»
16 times I 17 times
'2 iire [il '2 are 34
. , il7 9 — 1-26 9 -- I
><?
- 48
- f,4
- 80
- 06
- 11'2
-- 128
- 144
61
68
85
10-2
119
1J3
IS tinier
ID tiinm
2 are 3f.
2 are S*
y — 54
'.\ — 5T
4 — 7-2
4 — 7ft
5 — m
5—95
R — 108
6 — 114
7 ~ 1'26
7 — 13*
8 — 144
8 ~ 161
I
4.
12
13
14
15
16
17
18
19
20
21
22
■>o
24
25
26
27
28
29
30
ai
32 -^
13
14
♦«.
149
iiOO
i40
«(»<»
400
480
oOO
hOO
700
:'2o
800
fiOO
«60
1006
1100
12M
9 — 1C2 . 9
171
ARITHMETIC AI, TABLB8.
FENCE TABLE.
time*
are 7
-- li
— 21
— 2«
- as
— 42
— 41)
- 5U
— (i3
— 70
— 77
— 81
times
- 1*
— 24
- 3©
- 48
- CO
- 72
- 84
- 9()
- 108
- 120
- 132
- Ui
— 57
- 7«
95
114
13.1
15Q
171
4.
S.
d.
d.
s. d.
d. 8. d.
d.
«. d.
12 Hre
1
35 aro
2 11 57 ai'o 4 9
79
ar« 4 7
»:{ —
1
1
3(1 -■
3 58 — 4 10
80
— 6 t
14 —
1
2
37 —
3 1 59 — 4 11
81
— 6 t
15 —
1
3
38 —
3 2 00 — 5
82
- 6 If
16 ^-
1
4
3(» —
3 3 61 — 5 1
83
— 6 11
17 —
1
5
40 —
3 4 02 5 2
84
— 7 f
18 —
1
«
11 —
3 5 (:3 — 6 3
85
— 7 1
10 —
1
7
12 —
3 (1 04 6 4
80
— 7 2
I'O —
I
8
13 —
3 7 ' 05 5 6
87
— 7 3
21 ~
1
!i
44 —
3 8 00 — 5 6
88
— 7 4
22 —
1
10
45 —
3 9 07 5 7
89
— 7 6
2?: —
1
11
40 -
3 10
08 6 8
90
— 7 fi
H —
2
47 —
3 11
09 — 5 9
91
— 7 7
25 —
1
48 --
4
70 5 10
92
— 7 8
26
2
2
40 —
4 1
71 — 6 11
93
~ 7 »
27
2
3 ! 50 -
4 2
72
94
— 7 10
28
2
4 51 —
4 3
73 - a 1
95
— 7 11
29 —
2
5 52 —
4 4 1 74 — 2
90
— 80
30 —
2
G 53 -
4 5 75 3
97
8 1
ai —
2
7 54 ~
4 6 1 70 ~ 6 4
98
8 2
32
2
8 55 ~
4 7 i 77 - 6 5
99
— 88
S3 —
2
56
4 8 i 78 6
100
— 8 4
Si
2
10'
1
•
EXTENDED PENCE TABLt
it
£.
*. d. d.
£ n. d.
d £ s. d.
d.
£. ».d.
\49 arc
11 8 nnoaro
5 8 4
2500 arc 1 8 4
3700 aro 1 5 8 4
iiOO —
Iti 8 1400 —
5 10 S
•jr>0(> _ 10 IR 8
3S00
- 15 10 8
i40 —
1
1140 —
6
•j(UO — 11
oH iO
— 16 8
U0(» ~
1
5 lf)00 —
6 .'.
2700 — 11 6
a.Hio
— 16 6
400 —
1
13 4 H'OO —
6 !3 4
2800 — 11 13 4
4000
— 16 13 4
480 -.
2
lr.S(» --
7
V8S0 -- 12
4080
— 17
600 —
2
1 8 1700 —
7 1 8
-2000 — 12 18
4200
— 17 10
*iOO —
2
10 U 1800 —
7 10
aofiO -- 12 10
4300
— 17 18 4
700 —
2
IS 4 1900 —
7 18 4
a 100 — 12 18 4
4320
— 18
T'^O —
3
19-20 --
8
3120 — 13
4400
— 18 6 8
SOO ~
3
6 H 'i'lOO —
8 C 8
3J00 — 13 6 8
1500
— 18 16
900 —
3
15 ViOO —
8 l.i
3300 — 13 If)
4560
— 19
«I60 —
4
2ir,o —
9
;^3fiO — 14
4700
— 19 11 8
1006 —
4
3 4 2-200 —
9 3 4
a400 _ 14 3 4
4800
~ 20
IWO —
4
11 8 -2300 —
11 8
3f,00 — 14 11 8
4900
— 20 8 4
1200 —
6
. 2100 — ;
10
3C00 — 15
5000
— 20 10 8
%■ IRITnUETICAL TAUrEfl.
SIGNS USED IN ArwITIIMKTlC.
4- namfid plus, pi^uifioa Addition, as 4 f-*J equal 6.
— named minus, sijjnilics Stihtruction. as 5—2 equal 8.
X multipliod by, Hiji;iiili('a Miillipiiculiun, as 1x2 equal S.
4- divided by. sigiiilics Division, us 10-i-2 cquul 5.
s= equal to, sigiiilios Kcjuiiiity, uh 2-f-l=().
' • so JH i signith's Proportitni iix 1 : 2 : : H : fi.
• to I '^^^^^' l^K^'i''-''* '^''^' ^''*i'* >'^'ad, as 1 is to 2 so Is 3 ♦>« i
%/ marks the Squan? root, as s/ I =2.
^ maiks the Cube- root, as ^ b =:2,
I
MOXKY.
i farthings = 1 pr^nny
I'J piMico = 1 I'liilling
20 shillings = 1 pound
21 Khillings = 1 guini'a
£ denote? pounds, .>. shillings, and (/. pcnco.
^ one fiu'lhing. or oni' quarter of any thing.
^ a halfpenny, or a half of any thing.
I three farlhiags, or three quarters of any thinf
AYOiKuuroia wkkiht.
16 drams (dr) = 1 ounce
10 ounces = 1 pound
28 pound;^ = 1 quart" r
4 quarters or 112 lb. = 1 hundred weight
20 hundred weight --^ 1 ton
marked
oz.
lb.
qr.
cwL
T.
14 pounds make one Rtone, and 8 Ntono 1 hundrerl weight.
Tlitji weipT t 1*3 nfpd f«»r br«»n<l. moat. jrrnp«»ry, for goods in gCBCi^
Mid fov all the mctal.s except gu\\\ aud Bilver.
*
ARITHMETICAL TABLES.
al8.
tqual S.
TUOY WKKHIT.
14 pralna (i^r.) == I prMUiywcighl;,
20 ptMjijyweiijljtH == 1 ouiic«s
12 ouiicua = 1 putitid,
dttt.
OM.
Wih weight in uhed for guld, Hilvcr, JewelH, haA Hquorji.
AroTiu:CAuiKii wkigut.
is 3 f« i
20 fijraitis
3 scniplcfl
8 drains
12 ounces
= 1 scruple
= 1 drain
=^ 1 oiinco
= 1 pound
.Vpothec&riiH u^e t)ii!« w('i;^'ht in inixiiig their modidnoi ; kat Uinj
lVj>«f ftod Rcil bj Avuu(Jup(ii.s vieij^cht.
marked.
icr.
dr.
ox.
lb.
1.0X0 MKASUUK.
J tbinf
iark«4
oz.
lb.
qr.
cwL
T.
lit.
12 liiirs
12 iiichc:*
H fi'C't
iO p(,'rcli(s
8
3
Rifirked.
in.
A
yd.
per.
= 1 inch.
=s 1 loot,
= 1 yard,
=:= 1 p('r(!h,
= 1 CurloDg, fur.
= 1 mil**, m/.
= 1 IcP.gllC, l<r.
^0 Oe<)Kraphioal .nilcs, o:- ) ^ ^
t59i Hritisli miU'S ) o > ^
3()0 dogr' cs = thu earth's circumference.
lurlongH
An Inch i^; fluppost-a to h« P(\w\\ to tin en bailcy-rnrnH in Icnf(th
v'flreu y.\rt!« Irisli tqii.vl ca\c j;«-i('Ii, Klovrn miles Irish are equal to
:'nurt»«Q milt's English. 4 inches m.Lt- ouc baad, lueil in motiswAng
CLOTil MKASURK.
24 inches = 1 nail,
4 naiU = i quarter,
4 quarters = 1 yiud,
marked.
n/.
qr,
yd.
The Flemish ell is three-qnarterfl of a yard, the English eS it ftw
fv'Murkrd of a yard, aud the I'roach ell aix-quarteru of a yar4.
ARITHilETICAL TABLES.
SQUARE OR LAKD MEASURE.
144 square inches
9 Rquare feet
304 square yards
40 eqnare perches
4 roods
640 acres
= 1 square foot
= 1 square yard,
= 1 square perch,
= 1 rood,
= 1 acre,
sq. ft.
tq.'ifd.
tq per,
rd.
ae,
sq. mile.
= 1 square mile,
In Ireland 49 square yards make 1 squ.re pole or perch. The nqtiart
«f »nv number is obtaineil by multiply in;j it bv itdtlf, 12 multiplksi b/
12 — IM, the square of \L
CURIC, OR FOLID MKASVllE.
1728 cubic inches
27 cubic feet
40 cubic feet of rough timber, or
50 cubic feet of bcwii timber
42 cubic feet
r= 1 cubic foot
= 1 cubic yard
= 1 ton, or load
r=: 1 toUOfshippiRf
A cube is a solid figiiro, .•••••milnr lo <li,'^»». and ha?, six oqiial sides. Tkl
(Hibe of any nijmber is fibtniued bv uiulliiljing it twice by Jtrcir—
ttu8, 12 X li y l:: --- 17-2S, {he cub?" of 1-'.
MKASuuii or CArAcny
4 gills
2 pints
4 quarts
2 gallons
4 pecks
8 bushels
5 quarters
= 1 pint,
= 1 quart,
= 1 gallon,
= I p(;ck,
= 1 bushel,
=•• 1 quarter,
uiHrked.
pt.
qt.
gal.
pk.
bush,
qr.
Id.
= 1 load,
By this xneafiure botli liquiils nnd tlry good;^ nre meHsured. Th« ^pl^
Eivlnt. quart, gallon, are iiseil for liciniils. The peck, bushel, quarter,
oad, are uj'ci for dry pxnls. Tlic jjallon contains 277/274 cubic incheii.
The measure formerly called hoaptd iiaoasure irf now, by Act of i'ar-
Bftment, declared illegal.
Ale, wine, and beer were formerly measured by diflerect
measures. In some places a barrel ol' be^r contains 32,
in some 34, and in others 36 gallons. A hogshtp.d of alt
was computed to contain 64 gallons, a hogshead of wiue i»fi
gOllODB.
2 hogsheads make 1 pipe, or bu
2 pipes, or butts make 1 tun.
AKITJIMI'TICAL TABI.E.3.
^I
WOOL WEIGUT.
m
q.ft.
q:yd,
q per,
d,
tc.
q. mile.
The flqtiart
lultipliod b/
c foot
ic yard
or load
)fshlpi)iR|
I sides. 7ki
I by itrflf--
marked.
7
2
pounds = 1 clove
cloves = 1 Btoue
el.
St.
2
stones = 1 tod
td.
1*
2
tods = 1 wey
weys = I Rack
sacks =K 1 last
wy.
ik,
la.
TIHK>
marked.
60 seconds {ate.)
=r 1 mlnate
min.
CO ralnutes '
' — 1 hour
hr.
24 hours
== 1 day
da.
7 days
= 1 week
wk.
12 inonthP, or 1
•
52 weeks and 1 day, or >
= 1 year
yr.
8G5 days )
./▼e-j fourth Tt'?.r contains SGC u.-va, aud i.s called leap year.
DAYS IX EACH MONTH.
Thirty days liatli September,
April, Juno, and Noviiinbor ;
All the re.st have thirty-one
February twenty-eight alone,
But in Leap Year twenty-nine.
DITIJ^IOXS OF TUB CII?.CLK.
1. The g^
lel. quari«r,
:ubic incheji.
Act of rar-
Y differed
n tains 32,
I ad of alt
3f wine iA
viHrlce^.
<0 seconds" — 1 minute
min. or
80 minutes = I degree
deg. or •
80 degrees 1 sign
S.
12 signs = I circle of the zodiac
c.
QUANTITIKS.
znaiheiji
12 articles = I dozen
dox,
20 articles = 1
Bcore
sc.
144 articles = 1
grof?s
gr-
24 fiheels pap^^v = 1
quire
qr.
20 quiies = 1
ream
rm
ARITHMETICAL TABLES &C.
i:
I,
I
NUMERATION TABLE.
1 Units.
21 Trns.
,321 Hundreds.
4 , 321 Thoiisaiida.
54 , 321 X. of TlioiisandR.
654 , 321 C. of Tliousauds.
7 . (>54 , 321 Millions.
87 . (154 , 321 X. of Millions.
9S7 , (154 . 321 C. of Millions.
1 , ().S7 . (;5l . 321 M. of Millions.
21 , 9H7 . (151 . ;;-:l X. M. of Millions
321 . 9.S7 . (^54 , 321 C. M. of Millioiis
4. 321 , Db7 . {)54 , 321 Billion^.
M.
1000
rvOMA.\ NOTATION'.
I). C. h. X.
600 lUO 50 10
V.
5
i
■^
ii
t-.:
.1
EXERCISKS IN NU M F. I L\1 ION.
R.'ad, or write down in words the nuftiotrs si[:,AlJ'.€<i ^
ihf fo/ioiving Jii;nrrs :
1. 1. 2, 3, 4, 5, (>. 7, 8, 9, 0.
10. 11, 14, 1(). 19. 20. '12, 18, 17.
200, 420, 007. 98(1. 473. 217. 3-;4.
2.
H.
4.
0.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
IC.
17.
18.
912, 874, 78;{. (150. 202, (KH,
40(>0.
1010.
2700.
7o:>o.
<Su01,
4i;oo.
703(1.
9111.
210).
•tOTd.
510.
10(10.
5870.
2(1012. 70101. 42100. 30100, 90201.
700000, 701020, 92(1427. 10I2(!G.
9000000, 97(142(18. 8202100. 502:'>0r.7,
2M000(10, 4101010. 2001000, 110214*?.
40000000, 29002(187, 50020017. 1070020.
941208707. 207002007, 401107080.
290020870, 710020010, 270(iO:)0.5().
1402300740, 3400700010. 4023001497.
7042003714, 5079007900, 1704070000.
81402,300012, 40007087081. 9408042 13fi0.
14023041201. 20800002001, 40002000202.
Sl070G020ti204, 24002G10U201, 5yoyU012t"020.
EXERCISES IN NOTATION.
i
i
fV^J,fd V^
)20.
Express in Figures the following JVumhert.
\. Six, — seven, — nine. — citilit. — fivo. — ten, — twelve,—
fourteen, — sixteen. — eightetu. — twenty, — nineteen.
2. Seventy-fonr, — twenty-six. — thirty-one. — forty-nine,—
ftfty-ciglit. — sixty-two. — seventy-six. — sev< nty-seven, — nine-
ty-sevenf — eighty-tour. — tirty-Ii\e. — nini'ty-nine.
3. One hundred. — one linndred and four. — two hundred
and forty-four. — six hundred and ninety-one, — seven hun-
dred and fifty. — nine hundit-d and nine, — nine hundred and
ninety-nine, — eight liundrcd and two.
4. Four ihousand.^ — tour thousand two hundred, — five
thousand three htmdred and li!ty-t'A0. — six tlitjusand Reveu
hundred and five, — seven thou ;u;<i lUid lilly. — nine thousand
•ii^d two. — eiglit thousand and t;i^hty, — i-ix thou&and sevtn
hundred and seven.
'5. Ten thousand, — (iftten tlu '.'and five hundred and
pjxty, — nineteen thousand and nii, tt ••n. — twenty-six thou-
sand five hundred and nimty li\t. — ',liirtv-<ieiit thousand
nnd thirty-eight. — forty tliousand s-.nd forty. — fifty-six tbou-
FP.iid five hundred and two. — seveiilv lhuui^;and sevcu hundred
and seventy-seven.
(5. Four hundred thousand. — U\\\? lumdred thousand and
forty, — six hundred thousand S(V( ii Inintired and seven, —
nine hundred and eighty thou and. — two hundred and fifty-
Fix thoui-aiid nine hundred and .seven ty-livc — seven hundred
thousand seven luiiulred and seven. — nine hundred and
»lxty-four thousand two hundred and fifty-nine.
7. Six millions, — five juillions four hundred and ninety-
three thousand. — eight miilions forty thoin-and four hun-
dred and two. — seven millions four hundred and ninety-three
thou.^'and fH'v<'n hundred and sixty live. — te!» niillioue ten
tliousand and ten. — twenty millions two hundnd and forty
thousand six hundred and six. — fifty-three millions fifty-
three tliousand and fifty-three. — eight hundred and fifty-
three millions niiu? hundred iind forty-eight thousand
huiulred and fifty thne. — two hundred and three mill
four hundi'Ml and six thousand five hundred and eight, — r
hundred and ninety-three iniilious.
i&
10
SIMPLE ADDITION.
Addition is the method of finding one numbcf
equal to two or more numbers.
AM together 423, 134, 267
Rule with Exampi.!:. — Write th(» nurnVrii
under each other, so tliat units may stand uiulor
423
i:u
207
824
itatts, tens uudt-r tens, hundreds under hundreds,
rkc. Draw a line undi^r theni Add the ligures
tn the rijiht hand column together, thus 7 and
4 make 11. 11 and 3 make 14. Put down the
figure 4 of the number 14. Take the one of the 14, and udU
it to the next cohimii ; thus, 1 and 6 make 7, 7 and 3 make
10, 10 and 2 make 12. Put down the n<,nire 2 of the 12.
Add the figun- 1 of the 12 to the next column ; thus, 1 and
2 make 3, 3 and 1 make 4. 1 and 4 make 8. Put down tin' ^
The number 824 is called the Sum.
EXE
UCISES.
I
2
2
3
1
4
3
9
2
3
1
1
2
4
S
4
4
2
4
6
5
6
9
8
8
8
9
XI
12
2
4
6
3
4
5
3
4
1
2
4
4
3
4
7
6
3
3
2
5
r>
7
8
9
12
21
23
14
21
4t
11
12
24
35
34
23
23
24
35
43
75
97
H
57
82
92
130
1G2
4\
84
2G
37
42
28
24
24
42
25
56
1^9
JS6
63
59
74
85
Al
BIUTLE
Mimjiojx,
VI
P
(2)
(3)
(^
412
243
623
854 ;
ic numbcf
346
427
325
678
146
67«
236
675
423 i
t5)
(6)
(7')
(8)
lu 1
2fi4
450
647
856
207
3fi8
407 ,
653
479
752
679
865
627
824
8G5
636
276
'894
1 4, and udcj
■■' ■
aud 3 make
of the 12.
tlius, 1 and
m
(10)
(11)
(12) .
down tin* ^
246
457
47
8 .
78
60S
602
70
*
604
92
68
926
40
400
720
47
6
4
7
78
79
^
^
12
(13)
(14)
(15)
' (16)
5129
4268
3687
2407
4
7142
2426
4215
798
ft
9687
4276
708
46
9
4312
8507
9362
7083
8687
2390
9G
679
^«
•
«r
23
97
(17)
(18)
(19
(20)
5126
2427
5036
780
162
1472
768
784
5708
6826
9412
6070
1070
28
9687
893
85
687
^9
2764
4026
7507
5368
Al
4279
475
687
759 I
• •■•
i2
SIMPLE ADDITION.
1
!i
m
\\
(21)
(22)
(2n)
(24)
42«74
24786
4s7(;s
4G537
3412(1
fif.Sia
8(;270
64263
687(>8
2(5879
4(187
43986
28(142
4:1(153
578
6079
657(;8
(58754
4n()(;o
81
74387
50287
187()<J
641
9G728
()5423
70471
08076
25. How many do 7 i\nil 4 and S and 24 and G2 make ?
2G. How many aro 42 and «M and 40 and (18 and 79?
27. How many do G7 and 79 and 1)3 and 104 and 05 make?
28. How many do 420 and 07 and 240 and 742 make?
29. Add togelhor 0470 and 81(i and 70 and 507 and 742"?.
50. Add 7424-04 -f-S-f-:i4 1 -}-S0 ! -f-tiO-j-C. l2-|-70O-f-80G.
31. Add 7200-f 1404-f 84y0-{-21 i:!-f l(;-f- tTSCf 3326.
32. Add 41204-27304-f-20J;7-f42n-{-870840-f74(:807.
S3. Add 70870+204 (i-fS00S74-f 087087 l-f-1208-H27G.
34. Add 307C08'-|-0470^-f Ot 0.s7-j-OS70f 24 8!)-}-204.
35. What is the amount oT f'onr hnndr<'<l luul f<ix^y-l.hrf^e,
-live tiioiiHand and sixly-i'our, -kcVv ntj tliovj.vaud and
ttlnety-eight, — and iilly ?
30. Add together s(!ven linn<Ired and ninety six. — five ihoa-
laod four hundred and forty. — nine liundr<d and eight. —
five tlionsand four hundred an<l nine, two iiiiiidrcd and
two thousand and lilty, -ninely-rtix thuuiaud and nine,-—
four hundred and on<'.
37. How much do the ftvllowing snmp of lorrAvy amount
to, when added together, $, !J(;G.~-$H01,— Siii.- ' $2048,-—
$40897 ?
38. — I saw four large buckets full of apple s ; in one of
the baskets th' re were four iiuiuh'e<l and ninety four apples,
in another tliree hundred and .sixly-elj;itt. in uiiOther ninf>^
hundndand eighty, an«l in amdh' r foiir iiuiuirid and four,
how many apples were there in tlie four l»asket>^ ?
39. I gave John 12 apple.y. .lames 15. I'atrick 20, and 1
bad Btill 25 remaining ; bow many apples bad 1 ;U liist ?
I
I
i
r
SIMPLE ADniTION.
13
(24>
54263
431)86
6079
81
641
D8076
nake?
70?
G5 make?
lake ?
nd 742(5.
-BOG.
826.
807.
-4276.
k.
x^y-l.h^f^e,
aud and
five Ihoa-
eit^hi. —
drcd and
nine,—
r nmonnt
$2048,--
n ono of
\i\d iuur,
10, una 1
40. In ft school wh'vM T visitod lately, thore were six
classes ; In tlu livM \',\ '.rn \v»m(.» 2:> l>ovs, in tliu st^cond 18, in
the third '^2. iti tiic fourth 27. in tlif tilth 56, and in the
gixth 48 ; can you tell me how many boys there were ia the
school ?
41. A man walkcid 2'^ mllfs on Mondiy. iM on Tuesday, 46
on Wednesday, 'M on Thursday, on Friday being unable to
walk, he procured a liorsc. and ro«b* 41 miles, and com-
pleted his jonrn(;y on Saturday, having trav<dl"il that day
67 miles j how many miles did b^i travel during the
week ?
42. A gentleman planted on his property 478 oaks, 748
beeches, 64027 lirs. -10) apple trees, 1761 pear trees, 878
eherry trees, and 87 peach trees ; how many trees did he
plant in all ?
43. If Jamos has 74 marbles. John 213. Tom 185, Henry
809, William 831, and Patrick 648 ; how many have they in
till?
44. A farmer laid out on ox-n $P>18, on horses $487, on
fiheep $964, on cows $I8!>. on laboring utensils $209 ; how
much did he lay out altogether?
45. In a house there were nine windows in front, and each
window had twelve panes of glass. In the n-ar there were
iix windows, and each of these windows had nine panel
of glass ; how many panes of glass were there in all the
windows ?
46. A fruitoror bought six chests of oranges. Tn the firai
ehest there wer.- 468 oranges ; in the second 679 ; in the
third 804 ; in the fourth 979 ; in the tillli 1042 ; In the
lixth 1709 ; how many oranges were lli'Te in all the chests?
47. A linen draper sold 4(5 yards of clotli on Monday; 78
on Tuesday ; 65 on Wednesday ; Jhe same quantity on Thurs-
day ; 64 on Friday ; and 97 on Saturday ; how many yards
of cloth did he sell during the week?
48. A grocer received for goods sold on Monday $4 ; oa
Tuesday $6; on Wednesday $10; on Thursday $9; on
Friday $13 ; and on Saturday as much as he ha<l received
all the former days of the week ; how much did he receivil
during the week lor goods?
1
14
SIMPLE SUBTRACTION.
Subtraction is the method of finding the difference
between two numbers.
From 6237 take 4895.
.ii
111
''1
(1237
4896
RcLK WTTH Kx.vMPLK. — Place the less nnmbor
undor the grout mf. so that units may stand uiuler
unit?, tens undt-r tens, »fec. Draw a line under
them. B»';j;in at the units place, that is at the 5. joj^j
Take 5 from 7 and 2 remain. Put down the 2
under the 6. Go on to the next figure, which is 9 Take
9 from 3 ; this cannot be done ; whon this is the case,
atld 10 to the upper figure, whicli will make it 13. Take
9 from 13 and 4 remain. Put down the 4. Whenever 10
has been add«'d. as it was to the 3, one is to be added Ur
the next figure Thus, add 1 to 8 which makes 9. Take
9* from 2. it car) not be done ; then as before, add 10 to the
2. Now take 9 from 12 and 3 remain. Put down the 3.
Add 1 to four, it will make 5. Take 5 from H and I remains.
I^ut down the 1. The sum 1342 is called the Remainder,
ibe D'.ffereiiec or the Excess. The number from which
the subtraction is made, viz , (5237, is called the Minuentf.
1*he number which is subtracted, viz., 4895, is called th«
tittJ)treih€7id.
I\i
w
I
i
EXERCISES.
426
647
754
827
968
214
423
621
403
412
212
224
133
424
656
643
498
783
869
548
411
132
172
217
2-13
423
742
sm
646
«4S
279
489
478
298
1^9
144
253
356
248
47i
SIMPLK SUETIl ACTION'.
1»
582
715
9:it
CM
640
49G
2(18
748
2M
70
8G
447
186
347
4G4
(1)
402
(2)
023
821
(4)
G02
(6)
714
278
147
479
14G
178
(6)
643
(7)
741
(R)
610
(9)
100
(10)
101
268
278
79
4
11
fll)
42(154
(12)
3G871
(13)
7:{2(;8
(14)
08G43
2G47.9
17928
4729G
27896
(15)
74G03
(IG)
910.^0
(17)
41021
(18)
4(»000
37G84
12G47
7G8
1001
(19)
42G81
(20)
4l:h;)0
(21)
81000
(22)
4r>801
19G97
27(101
(24)
110201
2GU
«>
20009
(2?,)
741()'>()>^81
61
(2;"))
148120718
2781)01896
17
syOG8l
1
74198648
(2(;)
8612G4981
(27)
921 0024 C
(2ft)
181-01041
248000989
198007049
89890122
16
SIMPLK SUBTRACTION.
il
I ,1
'I
2J). 7 liR'if; 121741-
30. 8llii!)sl7K]l2
81. hliOl lOOlOlH
32. 4-5170! iCMi-H:-
?ui. <;i42i4(.^<7i;4s-
34. 41UUU0JUU()M-
427084(142814
7148!H;412<i4
107!KS78(;-M4l
7ii^(;i4i'{;,s7
•11)(;412741);M)
■ 212()10170(;
35. From s^von liundnd and nino tliousfiiid four hnn-
dred and tvv(nty-S'V«M. (!(k<* two Ijuiidiud and iilty-ooe
thuii3iind eight hundred iiiid seventy-two.
30. From two iniHioiis two huiidicd utid two thon?and and
two, take nine hiindnd aii\l ninety-six thousiind tind seven.
37. What is the dill'i'Mine httweeii sixty-five hundred
thousand and lour, and twenty-nine hundred iIioui«and Kcven
hundred and sixty ?
38. TIow nineh does sixty-fonr fhonsjand two hundred anj
four, exceed six thousand two-hundred and rorly-nine?
30. John lent Jiniies $!)071. of this Piini lie has received
back $[)\)0 ; ln)W' ur.ich has Janiea yet to pay ?
40. On a chcrry-treo tir re were 204(1 cherries, of tbcsi
1875 were gathered ; how many remained ?
41. Columbus discover" d America in the year 1402; how
many years is it from that time to 183() ?
42. In a certain school there are 430 boys, of these onlj
204 can write ; how many are unable to write?
43. In one of the Natioinjl Schools there are 427 boys
in another tiiere are 210 ; how many more are there iu ll|
t)ue than in the other ?
44. John hud 202 nuts in his pocket, but thorn Wnng a
hole iu it, he lost 0(5 nuts ; how many had he remaining?
4.'>. On an apple tvov there were 1(15 apples, the wind
blew olf two dozen aiul a half : how many were left ?
40. A draper bought 4780 yards of cloth, and sold 3987
yards ; how many yards has he unsold ?
47. What sum added to sixty-five thousand seven hun-
dred and ninety-six. will make one million four hundred
and fifty-two thousand three hundred arid thirteen?
48. 1 was born iu the year 1828 ; how old shall I be in
the year 1830 ?
i
SIMPLK SUBTRACTIOJi.
It
fulir hnn-
id lilty-ODC
ion?aiKl axul
Liid seven,
le liunflred
ui-aiid seven
hundred anJ
-nine ?
bas received
les, of thcs<
r H92 ; hovi
f these onlj
e '127 boys
there in tU
horn Ix'ing a
nainlng?
es. tlie wind
left ?
hd sold 3987
seven hun-
01 J r hundred
en ?
shall I be in
i
40. Ireland is about 300 miles in l-'^npfth. and 170 mi^
in breadth ; how much greater is the length than tno
fcreadth?
fiO. r?en Nevis, in Scotland, the hif?)! 'st monntain in the
British IsliindM, is 4:550 f ct above tlic level of the sea ; the
lumrnit of MairiU'ouddy's Flceks. tin,' hifrhest point in Ireland,
is 3(110; what is the ditfeninco in height between these two
mountains?
51 . Th" Shannon, the larpfost river in the British Isles, has
ft cours<; ol'aliont 170 rnili*»s. The Ania/on in Sonth America,
has a course of uimut 3000 miles. What is the difFereuce in
length of* their conrse?
62. The d'ameter of the Sun is about 88:52 K) miles; thai
of the Earth atjont 7012 ; what is tiio dilference in the diame-
ter of tlie Sun and Earth?
63 The surface of tht* «'arth is nearly 200 millionR of
fiqiiare miles, of this it is protnit)!*' tliat )iO millions are land;
how many rnor*' sfpiare miles of water tlian of land are there
in the eartli's surface?
54. The population of Lomlon in 18^1. was 1,770.506. The
popnhition of l>ul)lin is about 20:).(i.")2 ; how many more
people are there in London than in Dubliu ?
55. Mont Blanc, in Switzerland, is the higho.'?t mountain io
Europe, beiiig l^.tiBO feet almve the level of the sea. Chim-
borazo. the highest mountain in America, is ab«)nt 21,000
feet in height. W'hat is the ditiereuce in height betvveea
these two mountains?
5(). Coals were discovered at Newcastle. A. D. 1234 ; hoit
long is it from that time till the year 1830?
57. Since convicts were first sent to Botany Bay, it is now,
?iz.. 1830, about 42 years; in what year were convicts first
•cut?
58. Sir Isaac Newton was born A. D. 1G42. and died 1727 j
bow old was he when h(; died ?
5f). Petersl)urgh was founded by P' ter the Groat, A. D,
1703 ; how bmg is it from that tinje till the year 1836?
do. The art of printing was tru>covered about the yeai
H49 ; how long is it from that time to the year 183G?
i
19
II
SIMPLE ADDITION AND SUBTRACTION.
MlXi:n QUESTION^?.
1. Tom had *J'"I mail)!' s ; 1h» pivr ••! lo Jiimcs, 75 to Wil-
liam, and 42 to John ; how many Imd he Iclt?
2. A mprohani had I'iiiH yardu ofcUUh. on Monday he w>W
IIG yardP. on Tuesday 97. on \Vrdn«Hh»y liJJi. on tlnirHdajr
108, on Fritlay .'U!4, on Saturday 1!)7 ; how uiuch cloth had
^«! reinauiing?
8. Three rcp-'inontM wont to ImttK* ; In tjio flrst there wore
908 BoUlicr?'. In the second 7<;0. and ir Ihe thii<i 817. There
wepc 218 mou killed in the first rc^jlnnjni, M«»H in Ihe 8«'Cond,
Mid when the n'lriinents |-. turned Iht'ie Nvve only !,i6 aieu iu
4bc third ; how nniny nturncd from the buttle .
4. A miui had a journey of '2!>8 miles to irnke ; th« first
ilay he walked 12 miles, the seeond !<'• mii' h. i,e third ol
alics, the lonrlh 27 miles ; how nuich '. r ht \\Mi ho to go?
5 Three vessrl« sailed to Am'MJea wiih em!jr'*J»r ts ; in the
•rr.t vessel there were 12i) in n. W wcuncn. ami 41^ children ;
io tbc fiecond vessel there W( re 08 men. !^7 wonun, and 2tf
•bil^rcn ; In tlie third vosjsel there were 4'{ men. 2/ women,
and 8 chiPre'i. Iti the first vessel three persons Oied ; ia
I^Q second tvo were wa-hed overht)ard ; the Ihird vtEscl wat
wrecked rnd uM on board pvji.shed ; how uuiuy got taSe if
Aincrlea?
6. A little l^;(T.»nt to iho Zoolo/rleal Gardens to 80« th«
ftuimalp ; he la'o lu ^ hat on the ^n'onnd. which coniwne4
2()4 nuts ; while h\r- .'itent'on was en^mired. the nnukoy
•tole 27 of his lans ; w'sle he was pursniuji: the monkey,
a squirrel made orf *ruU 't> more ; how many had be .'«-
naJDiug?
7. The popnlalion of (JorJ- N nlont 108.000 : of Belfast,
65.000; of Liverpool. bJd.dOO; of Glasgow, 203.000; by
kow much does the population M London «'xneed all thcBd
eitie.s, the population d' it beiuit, ^,7« '»e'>^><» 'n the year 183H
8. Received on 'T. »u' "'. 17^ ^ "^ aw if (« Tuesday
$19(> ; received on '' (..n'stijiy $l?t!)' j^ai ' rv, t """^ Thura*
^ay $402; ree- ived on Friday $(I87 . p.'it' av>i^ oiv Satur-
day $398 ; what money hud 1 still remuuiiuR ?
1*
'J!
<iy:
M
10
1. 75 to WIl-
1(1 ay he boW
II 'rhnnfday
) clutb bad
t there wore
S17. TlK-re
ih(» srcond,
\Mi Mieo iu
^(! ; th« first
,0 third 31
I ho to go ?
[»r tfl ; in lh«
SIMPLK MULTIPLICATION.
Multiplication toaclios us to find what a number
vill amuuiit to, wlien it is repeated a number of times.
Cask I. — IVhen the MuUlpinr dots not exceed 12.
Multiply 53 by 7.
Rirr.E WITH E AMPLK." Place the numlier by which »j»
you are to multiply under tht' numbi'r to he inuUlplifd ; -
thoii say 7 tiinos 3 muko 21. Tut down (he 1 under
tho 7. Thon 7 times 5 make 35. n id the 2 of the o»,
21 make 37. Put down the 37. The 53 is culled the ^'^
Mulliplicand ; the 7 isoalled the Multiplier ; un«l the 371 in
called th(i Proditr.t. 'V\w multiplicuiid and the multiplier
taken together are called the Factors ; thus 53 and 7 .r«
fuctora.
EXERCISES.
nun, and 2<i
t. '14 women,
»iis Oied ; in
d vte«cl wai
659
2
1318
427
2
854
642
2
1284
718
2
149G
396
2
792
i got f afe t«
■ns to »o« tb€
486
6
9«8
3
C87
4
983
4
758
ch coniwnei
tho moL-kcy
the monVcT. ]
y had he .'•-
896
5
793
G
378
7
596
8
974
9
4480
4758
264G
4768
8766
: of Belfast.
203.000; by
eed all thcsa
e year 1831 ?
742
10
856
597
12
903
6
009
8
c« Tuesday
T ^-^ Thur».
'%\ Oiv Sat^^
0)
4270
4
(2)
67287
2
(SI
8G4."
»3
5
(4)
752G8
;i
:| 20
SmrLE MULTiriJCATIOX.
i||l (5)
1 . 0468
(fi)
84076
(7)
43256
(8)
74879
1 ' 7
-3/
: ^ 45G87
8
9
10
(10)
9G854
(11)
63875
(12)
47389
11
12
9
12
1 13. Multiply
^ 14.
87546 by 4
— 7
22. Multiply
23.
98327 by 2
— 7
fi 15.
— 9
24.
— 4
1: 1 16.
— 6
25.
— 8
I:t^ 17.
— 3
2().
— 6
J 18.
— 5
27.
— 6
i 19.
— 10
28.
9
1 20.
— 11
29.
— 12
m 21.
— 12
30.
— 11
■1
Case. II. — When the Multiplier is a Composite number.*
Multiply 436 by 32.
Rule with Examflk. — The mnUiplIor, viz. 32, is 436
formed by the two factor? 4 and 8 : therefore instead 4
of multiplying by 32. you may multiply by 4, and 1744
obtain the product 1741. Multiply this product by g
the other factor. 8. and vou obtain 13952, the product
•f the 43G multiplied by 32. 13052
31.
426478 X 16
37.
368745 X 64
32.
74M(i87 X 18
38.
24(1876 X 56
33.
9i;8748 X 24
39.
784078 X 72
34.
6748(17 X 27
40.
201074 X 108
35.
6430(i7 X 3()
41.
43687 6 X 1-^2
36.
426456 X 49
42.
496876 X 144
• A composite number is the prorUicl of two fncfors ; tliup. 16 in •
composite number, because formed of the factors 2 aiiii 8, r-r 4 and 4:
31 is formed of 3 and 7 ; '.^7 of 3 aad 9 ; 30 ol 4 aud 0, or 6 aad 6, or 3
Mdl2.
SIMPLE MULTirLTCATIOJT.
O.
4879
10
(12)
17389
12
by
2
7
_-
4
.—
8
—
6
^_
6
— — ■
9
__
12
—
11
number.*
, is
436
^ad
4
ind
1744
by
8
uct
13052
51
56
72
08
:r2
11
llUP.
16 in*
f'T 4 1
(ind 4 ;
aud 6, or J
3426
342
Ci^iK 11. — When the Multiplier contains several figures
Multiply 3421) by 312.
RiTLK wiTrf Ex:.\Mrf.K. — Place the multiplier
under the multiplinand, uuits under units, &c.
Multiply by the unit figme of the multiplii r,
viz. 2. Then multiply by the next figure of tlie
inulliplier, viz. 4; tuns, 4 times (> make 24, but
♦ :ike notice that you are to place the 4 of the
21 din.'ctly undi.r that figure of the multiplier
by which you are multiplying. Proceed in the
pamv manner with the (igiire 3 of the multiplier,
logether the products obtained.
13704
0852
570^
10278
inim
Then add
Multiply
G1S7 by2:;0.
2:;0
194{;iO
52974
1192010
43.
Mult.
98176
by
042
44.
758
45.
—
205
4().
—
49(5
47.
857
48.
—
43(J8
49.
___
7.S9G
50.
—
3 Go 4
Multiply 6487 by 203.
203
51.
52.
53.
5t.
55.
5().
57.
58.
19 in I
129740
131G8()1
Mult. 65839 by 058
— 627
— 3<)S
— 426
— . 701
— 8743
— 6007
— 9864
59. Multiply r-xty-four thousand eight hundred and fifty
two, by nine hundred and eighty-seveu.
60. Multiply four hundrtui and fifty-eight thousand six
hundred and ninety -four, by eight thousand and seventy-six.
61. Multiply nine hundred and eig!ity-six thousand seven
hundred and forty, by four hundred and nine.
62. There are 8766 hours in the year ; hov/ many hours
are there in 20 years?
63. A grocer sells goods to tho amount of $56 per week ;
liow much does he sell during the vear?
64. In a flock oi 643 .dieep ; hov; many feet were there!
f
I
I
&L
22
SIMPLE MULTIPLICATION.
65. Suppose the ^age of a book to contain 49 lines, and
each line 47 letters ; bow many letters does the whole page
contain?
66. In 264 dozen of wine, how many hottlea are there?
67. A gentleman dying gave orders in his will that his fcr-
tune shnnld be equally (livided among his five children} eikcSi
received §648; how much money did he leave?
68. Suppose that there were in the parish 896 houses, and
that eacli house in the parish contained live persons ; what
would be the population of that parish ?
60. A father has live children, their food and clothing costs
him two pence each per day ; how many pence does the
fcupport of the children come to in the y< ar ?
70. There Mere in a garden eight trees, and upon each tree
there were 268 apples, how many apples were there upon all
the trees?
71. There were 4768 geese plucked, and 17 quills got from
each goose ; how many quills were got from all ?
72. There were 27 desks to be made for the school, and
each desk required 29 nails ; how many nails were required
for all the desks?
73. In a school, there were six windows in the boys' room,
and four in the girls' room ; in each window there were eight
panes of glass ; how many panes of glass were there in all?
74. I knew two boys, one of them was lazy and lay in bed
lill nine, the other was an active little fellow who rose every
iMorning at six. how many hours did the active boy gain in a
year that the other lost ?
75. How often does a clock strike in a year at the rate of
156 times a day ?
76. How many pins may a boy point in 6 days who works
8 hours a day, and points 16.000 pins in an hour?
77. A gentleman bought an estate containing 6,968 acres,
at the rate of $26 per acre ; how much did he pay for the
estate ?
78. How many miles will a person travel in 34 years, sup-
posing he travels 9 miles per day, and there are 365 dti/d iA
the year?
#
23
I lines, and
vbole page
there?
that his f^r-
Idren ] e^cli
houses, and
sous ; what
3th inj^ costs
ce does the ^1
3n each tree J
le upon all ^^
lis got from
school, and .^
ire required |
boys' room, /I
[} were eight |
here in all? |
d lay in bed -l
rose every t
loy gain in a \
1 the rate of
s who works
; 6,908 acres,
pay for tho
4 years, sup
! 3ii5 ^uyd lA
SIMPT.K DIVISION.
Division is tlie method of finding how often ona
uufnber is contained in another.
Cask I. — When the Divisor does not exceed 12.
Divide 252 by <;.
Rtri.K WITH ExAMFLK. — Put tho nnmbf^rs down n>,nr^
iiccordiujjj to the aniu'Xf'd exatnplo. Find how often *
the fip:ur«' by wliich you are (o divid \ viz. ♦> is T^
coiitain(Ml iu the first, or first and second (ij^urt'S ;
thus, i] in 2. th* re are none, tlien (> in 25 : th<r.' are 4 sixca
iii 25 and 1 over. Put down the 4 under tlif 5. Suppose
llie 1 placed before the 2. which wouhi uiiikc it 12 Say 6 in
12. There are 2 sixes in 12. Put the 2 under the 2. The
number (J is called the Divisor ; 252 the Dividend ; and 42
the Quotient.
2)4n28
EXi:
2)()824
PtCI
flO)
20 SI
SES.
S)(;0:)9
4)8408
2:^14
2)47(158
3412
3)70389
2013
4)85730
2102
C)7n590
238:i9
(1)
4)27 r.45
25463
(2)
5)0871)4
21434
6)79087
12703
(4)
7)81)020
(5)
8)7(;42G
(fi)
9)28076
(7)
10^64208
(8)
11)40267
I2)7t;42(;872
8)4
•042
(11)
7)9O!O2087
u
SIMPLE DIVISION.
' I
ill
(12)
9)642(187 oO
(15)
f.)7C0020'il
18. Divide 5G472G89 by 2
19. — ^
20. .
21.
22.
'IS.
Z4.
25.
26.
27.
28.
(^n)
:2)4i;87fc376
(in)
9)4302601
2
20.
3
30.
4
31.
5
82.
C
3a.
7
34.
8
35.
3(5.
10
37.
11
■58.
12
39.
(14)
8)46876400
(17'
7)412G0(;02
Dividfs 74068028 hy
i
It*
(>
t
10
u
u
n it:
n
m
Case. II. — When the Divhor i> a Composile number.
Divide G7S9 by 28.
two
4)(;78D
7)1 (-"1)7 remniiis 1
212 remains .M
RuLK WITH Example. — The
factors that produce 23. are 4 and 7 ; 28
divide then by 4 and by 7 as in the
example. The quotient foinid is 242,
but with two rcnniinders. viz.. 3 ;ind
1. To obtain the complete remainder,
multiply the tirsf divisor, viz. 4. by the last remainder, viz. 3,
and to the product add the first remainder, viz. 1 ; — thiu--,
4X3-f-l=I3 the true remainder.
54
72
1 08
\:vi
Hi
40.
426'! 78
41.
743(187
42.
96S718
43.
6748(17
44.
^43007
46.
426156
16
46.
368745
18
47.
246876
24
48.
784978
27
49.
20-l()76
36
50.
43H876
49
61.
49G876
TO
54.
snirLF. mvisii^.v.
^
(14)
687G400
or
12G0()02
68023 by 5
It*
r)
— 0.
«)
• - 10
— II
— u
e nnnihei-.
89
1)7 re in III 119 \
2 remains ."i
C^iJts III. — W'Acn /?//e Divisor contains several JiQUreJi,
Divido4317C9 by 528.
528)i:U7,C9(S17quoUenl.
J 22 4
528
40S9
ofi'JG
oDS rt-maliider.
IvOLK WITH EXAMPI.K.* — Put
(?i»\va the Slim in this lonn. Con-
sider whether ih^ divisor, viz.
n2S, ia contaiiicd in th«; lirst three
ti;iitres of the dividend, viz. 431 ;
v»Hi Fee ^t once tluit, it is not;
iiiark oft' then four liffiires, viz.
4.517. Yon are now to find iiow often
;V.\S IP. contiiiiifd in 4:517 ; for this
{.lirpose lind liow often the tirst
ti>(>ire of the divisor, viz. 5, i.^ con-
tained in the tir^t two (ignre:- of tht' u'vu]«Mid. viz. 43. It is
ivMUitrtined 8 times : put the 8 on the oppusiif .-"mIp of the divi-
lilcnd from the <livi8or. Mnlliply 528 by 8, and pnt the pro*
[duct under the 4317 ; subtract, arid thi^e remains i)3 ; bring
ki this the next fijiur*' of the dividend, viz. 0. "^'oii are now
If) lind how often the di\ isor. 52S. is contained in your dc\«
dividend, 93{) ; lind. as yon did before, how often the first fig*
jtjro of the divisor, 5, is contained in the lirst li^nre of the divi-
dend, 9. It is contained once; put the one beside the 8 ;
hiiiiltiply 528 by 1. and place the product under the 98G ; sub-
jtriict and you obtain 408 ; bring to this the next figure of the
|divid«nd. 9. Fiml. as before, how often 528 is contained in
h083. Kecause 5 is contained 8 times in 40. von will be in-
^liined to try 8. Do it and you will lind that you obtain tho
%)roduct 4224, but this is ^rreater than the 4089 from which
|;«ou have to subtract it ; wIkmi tliis is the case you must try a
fiinialler figure, in this case take 7.
tinder, viz. :),
/. 1 ; — tliiu-,
-f- 54
'- t)f>
- 72
'- 1 ()9>
!_ 1 32
•- \U
yL Divide 7423G by 42
43
44
45
,>3.
54.
.>5.
5(). Divide 7423G by 46
67. 689
58. 799
59. 410
* TltiM is r.allier a difliciilt R»ile to understarnV and I think jout
feRclu'C coiil''. explain it to von, by iti«>ans of a black board and a bli
Jt-S' cbiilk niiicli better than 1 C!»n liojio to do by jtny wiilton e'S|,1iinft
?if.n ; y«t„ if jcu pa/ atientiou, I (shall do my letit to niiikc you tudtr
i
I
m
§
I
I
I
26
SllirLK DIVISION.
Sijt
ml
E "t
T,l
Divule 8710:i by
(111
7(1.
8I278(^
,,*,
7«
:;i2
;);i;s-i:f
„ *,
;)4«)
:.K I
78.
4..0i07ii
„ *,
4:;b
7i)H
7!).
(Mli;S7!)
*
()1K
2i(;
Hi).
iiK(;ii»7()
1 * 1
bO«
;5r)7
M.
2^7<i'10/"
_^
1107
I'.'S
S2.
DU'jSCU)
M81
:.o2
S:{.
})>o;'H7
Go7(!
r.IH
.Sk
4i)7::s;)-IS
«! .,
4L'78
7;;{;
S").
71i;>'(ill
— i—
2. SCI
•MS
.sd.
8<ill:'0J
— ^—
M07
ii;i
S7.
*2IN()70S
'um
>.-.7
vSS.
7s(!n'^(i
—1—
7110
ri-ji
^\).
.3()i»2(;(i2
8(»au
•KKl
!)().
402i*2(il
9 MOO
<iSl
1)1.
9Gb7t;0U
~r"
4o00
60.
61.
(>2.
63.
(M.
()r>.
C().
67.
68.
69.
70.
71.
72.
73.
74,
75.
92. Divido six millions P(>von hniwlrod aiHl ninety-four
Ihoiisanfl. by lour liumlied and eighty thoaTaad six huudred
and nine.
93. Divide £79ni8 mnonjif 271 porsons.
94. What is the ninth ol' ,C(;t);^7 ?
95. A sliip sailed in I'onr weeks 12(;2 miles ; how much is
that per day ?
96. If a ve^^pel contains (IIS rrallons of water, how long
will it take to discharge it all, at the rate of 18 gallons au
hour ?
97. The popnlaiion of Irchind is about eiiiht millions, and
Ihere are ubout ;il)0.(() sipiare miles of huri'aee ; liow many
persons to each iiiilc '.'
OS. The fiittn is iilioiit '.)'.) millions of miles distant from th«?
enn ; how manv days would a liorso i;ji<(> jn y aciiing tlio sun,
supposing he went at the rate of la miles per day ?
99. The r;iys of li;;!)! eome IVom the sun to the earlh in ^
minutes, or 1!'") seennds ; at what rale does light move per
eecond, the distance IVom the sun to the earth being 9517.0000
miles ?
100. Th(» cireu!iir<"*(>noe of th(* earth is a>)or(t 2.'0(^0 miles :
Ijow long would a man take to v.':ilk round it at the rate of 27
miles per day ?
sont
oth(
thir
T
tlie
liiiis
llUlll
T
into
BJIOU
by t
apph
cqiia
A
ratoi
A
meru
A
and
or J
A
tioii
A
writi
6 ma
10 tl
by n
(lenoi
by tl
27
78
4 lib
1107
ln07
7410
DOOO
4o00
linety-four
IX liuudred
>w mucb is
how long
gLiUons an
ill ion?, and
liow many
lit from the
ins the sun,
- V
r •
carlh in ^^^
t move per
;1.»5 178000
"000 miles :
10 rate of 27
I
FRACTIONS.
A FuACTTOx is a part of anytliing, and is reprc-
sonteil l)V two iininhtTS, one above the line and tlio
otl)er below it : thus, |, J, |, — read cue-half, two-
thirds, threc*foiirths.
The fijrure above the line is called the rrdmerator y
the tiji^iire below the line is called the denombuitor ^
thus, ill the fraction J, rend four-fifths ; the 4 is the
numerator and tlie 5 is the denominator.
The denominator marks the number of equal parts
into wliich the wh^olo is divided ; the numerator
kIiows the number of those intended to be expressed
by the fraction : thus, if I say that I have f of an
apple, 1 mean that the apple was divided into three
equal })arts, and that I have two of these parts.
A Proper Fraction is that which has its nume-
rator less than its denominator, as ^, |, 4-
Ax Improper Fraction is that which has its wm-
nQV'Aiov greater than its denominator, as J, J, |.
A CoMPOuxD Fraction is a fraction of a fraction,
and is expressed by two or more fractions, as f of |,
or \ of f of f .
A Mixed Nump,er Is a whole number with a frac-
tion annexed, as 2|-, 4|, ICJ.
Any whole number may be made a fraction of by
writiui^ a 1 under it for a denominator : for example,
6 nniy be made a fi'action of by writinj^ it thus |-, or
10 thus »j-*. The vjdue of a fraction is not altered
by multiplying^ or dividinjj: both the numerator and
(lenomiuator, provided botli be multiplied or divided
by the same number.
1
w
;t;
'I
:i
M
2S
DECIMAL FRACI'IOXS.
A Decimal Fraction is a frattlon whose de-
nominator is 10, 100, 1000, tVc, or a unit with as
many ciphers annexed to it as thrio arc figures in the
numerator. Thus, j^, Z/^,-, f'jVc, ^''^' decimal frac-
tions, nnd are usually written in this manner : .5,
.25, .325, the denominators being omitted ; biit a
point is })laced on the h^ft liand to distinguish Acm
from integers. In reading them the first is called
5-tenths, the second 25-hundredths, and tlic thircj
o25-thousaudths.
When tliere are not so many figures in the numO"
rator as tliere are ciphers in the denominator, ai
many ci|.)hers as arc necessary must be prefixed :
thus' rs =-03 and j^^o -^.OO'S.
Ciphers on the left hand of a decimal decreast
iis value ten-fold : thus, 5 is 5-tentlis ; .05 is 5-huii-
dredtlis, and .005 is 5-thousandths. Ciphers on tho
right do not alter the value, for .5, .50, .500 are the
same as y\. j^^\, fVA. ^^^^ these are of equal value.
bo
ADDITION.
Rule. — Place the nnnibrrs to be added r-o that the decimal
points be directly under eacli other, and add a? in Simple Ad-
dition. Insert the point in the answer directly under the othei
points.
Add together the following numl.'crs : —
(1) (2) (3)
2.13 48.27 820.71
.426 9.042 2.006
21.2 712.417 84.213
7.03 41.007 217.072
C40.072 .9G2 9.341
It
ihp
plio
Are
of t
DECIMAL FRACTIONS.
29
4. Add 4 231, 72.G2, 920.7i. .0;J74, 37C.05.
5. 723.812, 91.0006, 2.0251, 3724.7, .00007.
6. 37.214, .73(1. 7213.01, 123.47t), 21.0743.
7. 800.273, 498.0009, .290, .0071, 42»l0.008.
f. 320.492, .23U87, 970.00C 9.08G, 41.7(i2.
SUBTRACTION.
Rui.K. — Place Ihe numbers us in Addition ; subtract as in
Simple Nun)b(M'?>. and insert the point undor the other points
1. From 72.378 take 4.8G1
2. 9.007 .902
3. 41.217 7.0i)(;8
4. 29S.012 .9999
i. K-IO.OOl 170.98
Ck From 279.71 2 take 97.0076
7. 72.0070 1.973
8. 900.005 89.1171
!). 243.21 .9G4213
0. 4ti2.00()8 134.791
MULTII'LICATION.
Rum:.— A5"r;in<,'e the I'actors, and multiply a.", in Wliolt*
t^nmbcrs. Iteckun the nnnjbcr of decimals in both factors,
«n;l point o!l' as many from the li.^ht of ihe product. When
the nnnibor of fit^nreB in th(! proilnct »?! not so many as (he
Bnml)er of deciniah in both factors, as many ciph(;r3 as may
be n('ces.^ary to make up thu d-.'nci' nc-y must be placed at th«
left of the product.
Multiply 7.4 by M'i.
7.4
.35
370
Multiply .045 by .03
.045
.03
.00135
lu the above example there
-^Jy'jQ are five dcclraal plac«!8 in the
I factors, and only three figures
In the above example there ! in the product ; thf.'refore two
•ro three decimal places in | ciphers are placed at the left
the multiplicand and mnlti- of the product to make the
plier ; therefore three fijjnres
are pointed off from the right
of thL' product.
number of decimal places in
the product equal to those in
th'j factors.
k.
W
W
m
f
30
1
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iti
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}
DECIMAL FK.VCTIOXa.
1. UuU;
.27
by
.27
7.
Mult.
2300.7
2.
4.21
3.11
8.
704.23
S.
97.04
80.03
!).
.780
4.
.4102
.1004
10.
4.802
6.
.700
.800
11.
200 03
6/
.871)
10
12.
.00070
•
DIVISION.
by
18.003 i
.0007
100
.75
.002
1000
tllKlC!
' n.'i III
;; riphi
RuLR. — Dlvido as in Whole Niimbcrs. Poini off as niaiiy
decimal places in the quotient, as the dividend has nioro
Hum the divisor : if necessary place ciphers to the left of the
quotient.
If (he divipor has more fijjiires than the dividend, i\Cn\
ciphers to the right of the dividend.
When there is a n'mainder the quotient may be carried
to any degree of exactness, Oy annexing ciphtrs to th*
ren:iainder.
4
Divide 4.7614 by 3.8.
3.8)4.7014(1.253
la this case the decimals in
the dividend exccvM' those in
ttie divisor by three ; three fig-
ares are therefore marked oil'
in the quotient.
1. Divide 0.74 by 2.34
2. .490 .278
JV 7.6 .734
4. 7.23 4.00
5. .024 .001
6.t 29.0 10
Divide .7041 by 4?..
42).704'1(.0182
In this case die decimal!^ in
the dividend exceed those Id
the divisor by four ; a cipher
is therefore prefixed in the quo-
tient to make four diciuial
places.
7. Divide 721.1 by 38.07
8. 82.03 9.000J
9. 7.(i24 2.001
10. .6213 24121
11. 31 .1210S9
12. 3408.9 lOOO
i
If
nre
h'>gi
each
«hft
• Tn order to mnlliply a dccimn! hy 10, rtrnove the point one figur*
to the right; if by 100 remove it two.plllC(^^, and so on.
f To divide by 10. 100, &c., reitiove the decimal place of tlie dtvidead
•s maoy plttced to llie Irft as there ace ciphers.
Id
i
1
rile
I I
:RCIMAL Fll CTli'NS.
91
)0.7 by 18.003;
1.23
.0007
U>
100
!r,2
.75
► 03
.002
07 G
1000
nt off Jis many
h-nd liaa nioro
I (ho left of the
dividend, add
may be carried
liphtrs to Ui«
;ii by
42.
(.018U
lIig decimals in
xci'cd
tho?<e iu
four ;
a cipher
ixcd in
tlu'qiK)-
four
dt elm III
M by
J58.07
.03
O.OOOii
i2-t
2.001
^13
24121
31
.121(i8i)
8.9
lOOO
point one Qgura
e of Ute divtdead
REDUGTIOy
7\> reduce nvmlwrs of a fotvcr (hnomiiiatiun to
the decimal of a hiij;hir.
jluLK. — Write thr {jjivon numbors. if more tlian one. direcLlf
niidcT <'ach olhvT, bc-^iiiriinjjf with tlic b)\vcsl. and divide by
«fl many of tin- lowur as nialcu ont; of th(3 higher, aauexiug
!r.iphoi's if ni'ccs,-;ary.
Rodiico 12.V. 'U. to Ihe dcci- R(duco ICv. «./? to the d»-
ii<al of a pound.
12) 3.00
20)12^2^
.ijVl'iAns.
lion? Ih'^ sliillinpis and ponco
nrc placed under each othcrj
cimal of a pound.
^1) 3.00
12) (;r7)00^
20/ i(;/iTi2.-i6
Ifrro the farlhin.frs, ponce,
I lt';ihcr.
o
b"f)f!!jnin{}: wilh thf lower; and and sliilliM,!,^-', arc placed under
each divided liy as nuiny of each other. b>^j:innin<x with the
tho lower as nuilve ouo of the; lowest ; eacli i.s then divided
by as niiiny of the lower aa
make one of lli'j hi<^hor.
1. Reduce lO.v bhi. to tlio decimal of a ponnd.
2. Reduce ir).v. 9,J^. to the decimal of a pound.
.^. Reduce \'os. id. to the decimal of a pound.
\. Reduce i)c/. to ihe decimal of a pound.
5. Reduce 3 cwt. 2 qrs. 8 lbs. to tho d<>cima1 of a cwt;
6'. Reduce 4 feet 3 inches, to tlie decnnal of a yard.
7. Reduce 2t) min. 31 sec. to the decimal of a week.
8. Reduce 5 furlongs 3 pol(>s, to the ueclinal of a mile,
\). Reduce Aid. to the decimal of a guinea.
10. Reduce .') dwt. 12 grs. to the decimal of an ounco.
11. Reduce 2 roods 12 perches, to the decimal of an acre,
12. Reduce 17 yards., 1 foot, G inche.?, to the decimal of a
r.ile.
t
19
I>rXiMAT. KKA^.TlONdl.
i I
In
m
To find the vuliit of a tfccimai.
JliTt.K. — ^Fiiltiply tli(» (lt!clmul l»y iva niuny of tlin nnxl \owf.i
dcnoininiUioii us inako one of the f^lvop dniuiuiiiutiou. Point
off, from tlio product, us many (h'cimiii phlc^^s i\h are in the
ProciMMl tlnis t(]
the Iclt of tho poini
«iven decimal. Proci!
The fi^urcH on
dccima!.
H( Iow(!rtt tlonomination.
itH uro thu vuluu of iht
What is the value of .427 of
Ik pouud ?
.427
20
8.0 4«
*6.4«0
4
What is the value ot 243 cf
a day ?
.243
.24
6.832
(0
i'XVi'lO
(iO
^liifi. i hn<. 4'J iii'n. 6/5 ».ri.
1. What is the value of .7C:U/.?
2. What Ib (ho value of ..'IlliV.?
5. What h the value of .007(!/.?
4. WHiat is the value of .701 cwt.?
6. What is the value of .l»;)(t Ihs. avolrdupoIiiT
6. "What is the value of .007 ton?
7. What is the value of .7:J2 shillinj^?
8. What is the value of ,071) crown ?
9. What is the value of .0218 day?
10. What is the value of .40() yard ?
11. What is the value of .079(1 mile?
12. What is the value of .7.32 lb. troy?
13. What is the value of .9^^7 oz. avoirdupois?
14 What is the value of .087 oz. troy?
10 What ifi the value of .779 llw. avoirdupoia?
I
'! ■]
i
pi.
83
DECIMAL CUllUENCY.
The coins now circulating In CauuJii, are :
100 cents = 1
fiO cc'HtH = A
25 cents =: J
20 ctMits =3 1
ID c<'iits = 1
6 cunts =r IJ
3 coiUh = 1^ ptMlliV.
1 cunt =r= ^ piMMiy,
dollar.
(lollur.
dollar.
Hirtllin^. ITalifLix Currcncj.
BixHt'ii'jo,
P'.'llC'^
It
nearly,
uoarlj.
The Units of the United St rites monry im* :
Mills. C: iitn. IJ'i:i"S. 7WA/r.T. and Kagh^
10 mill:} rt:: 1 OtMlt.
10 Of'iii.s = 1 tli.'nc.
JO (linicp or 100 centH, = 1 dolliu'.
10 <h)li;U*i r^ 1 OUgl''.
Tho char;if!t<'r $ is used both in Can-idiv iind the United
Slates to rt'prcsent doilivr?, thn? $0 i.s >i.\ duilarn.
The dononiinations commonly ir-iod in bnsiness are dollan
and cents, thns (54 (•afj:lrs. 5 dollars, W dinu's. 7 o<'nts. 5 nilllf^
are more hiinplv written and read a,■^ (I lo dollars. Ii7^ cent?.
The Rui.K for workin;:^ in the D"cimal Cnrrency is th<»
same as in Decimul Fractions. \\\ Addition and Subtractiojt
he careliil to arran^(! the deeimal points niuh-r »'Heh other,
then add or subtract, as the case may be. as in the Binipl*
Rules.
In MuKiplicalion and Division work as in the simple Ru]r««^
point oil" the (h'cimals ; then. wIkmi the rrholf sum is com-
pleted, throw away all the decimals hut the two on the right
iftnd of the point ; the fii^nn'S on the left side of the poiat
will be dollars, and the two on the right will be cents.
EXERCISES.
1. Find the Pum of $100.72.\. $2").0'>. and $110.49.
2. What sum should be paid for a hat at $5.87^, a y**H
»t $3,181, and a pair of shoe:? at $2 (.2] ?
I
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i
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i
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k
I
u
DECIMAL CUKRENCY.
3. Find tho sum to be paiil for a lot of grocfrios at $13.37^,
a qiuirtur of buef iit $7, a barrel of llcur at SLiiO^, aad a
lot of butter at $2 Oiij.
4. How iniieii sliould be paid for a quire of pnpcr at 25 cents,
% bottle of ink at 12^ centi'. a dozt-n of books at $1,184, J^nd
a bunch of quills at 374 coats.
5. Sold a barrel of su<?ar for $15, a sack of colTec for
^13.0'). a keg of rice for 65.1L''j, aud a box of candles
for $9.08.
G. A merchant's bill was as follows : what is the amount!
Mr. Johnson,
3^ yards of Clolh,
3 pairs of Stockinpffl,
1 do/'ju skeias of Silk.
Bov.^!-ht of Thomas Smith,
. $21.00
1.87,}
. . . .to
7. Of $325 how much rrniaini.; after paying $03.0G| ?
S. A lot of goods coist $579, and .sold for ;t(i;30.87.], what
*a3 galiird ?
9. Find tlie loss on Flour bougkt for $372.1.21, and gold
h'V $321. 5n|.
10. Multiply $:'.0(;.\ by 7.
11. What hliould Jje paid for 9 huudrcdweigiit of lobacct
It $10.37.^- pta- hundredweight?
12. How tnuch should bu paid for 8 yard« of cloth at
$'J.5(iLand 12 vards at 87.\ ceiit.-, per vara 't
13. What should be paid for liead of cattle at $13.18|
f LT head, and 7 nniles at S80.50 per head ?
li. Divide $12.76 successively by 4, 5, G and 7.
15. Divide $12.75 by 3.\.
10. Divide $21.20 l)y 5|".
17. If 4,^ cords of wood cost $9, what is the pi'Ice of a cord*
18. Wliat is the price of wheat per bushel when 25^ bushel*
f<d! for $37.f!8n
19. What is the price of butter per pound when 13J pound!
i^-ll for $1.(32?
the amount !
35
VULGAR FRACTIONS.
Vulgar or Common Fractions are those in wUich
iiie denominator and numerator are both expressed.
PRIME NUMBERS.
A Prime Number is one which is not the product
of two factors; thus 7, II, 13, ttc, ^vi^, 'prime because
tiioy are not divisible by any number irreater than 1,
without a remainder. A Composite Numl^er is the
product of two factors, thus 6 is composite because
]^ U the product of 2 and 3.
To Resolve a Composite JVuniher into its Prime Factors.
fvULE— 1. Divide the given niiniber by any prime number
j;;(;atcr than unity, that vvill divide it without k^mainder.
2. Divide the quotient in the same way coiitin*ially till U
Hecomes a prime number. Then the hist quotieut and thi
it'veral divisors will be the prime factors r* quired ; thus
KxAHPLK. — Rusolve 3780 into its Prime Factors.
9)3780
4)420
5)105
3)21
1
tjlvlng 0, 4, 5, 8, and 7 as the prime frtctors of 0780.
Find iiiL Prime Factors of the fallowing fuimberH :—
(1) 735 (2) 3;}0
(3) 510 , (i) S90
(^) 550 (6) 930
(7) 1330 (8) lOlO
[d) 4350 (10) C020
•tr. I
If;
I
S
ae
MJLGAR FRACTIONS.
COMMON MEASURE.
-S
A Common Measure is a prime factor common to
two numbers; tlnis 3 is a common measure of 12 and
18, 9 is a common measure of 18 and 81.
To Jifid the Common Measure of two or more numbers.
Rule. — Resolve each number to its prime factors, ant! soloci
those which are common to a/f the numbers. Any one, or
thii product of any two or mor;* will be a common measur*'.
and the product of all the common measures will be th^;
Greatest Common Measure ; thus
Example. — Find tho Common Measuren and the GrcrAa^t
Common Measure o^ ^>oO, 510 and 090.
Bv resolvinpr each iuto its prime factors bv the last rnle. W
we fisid
');n'
330
— -
2X3X5
X
11
510
—
2X3X5
X
17
390
=
2X3X5
X
13
rbe Factors common to the three ^iven numbers are 2, 3.
and 5. The product of 2 and 3, 2 and 5. and 3 and 2 are
also common measures, and 2x3x5 = 30 is the groate«t
tommon measure.
1. Find tlie greatest comraon measure of 252, 180, 28^
2. " " " 120, 141, ](;??
3. « " " 210, 3.3(5, 432
1 " •• ** 392, 604, oCO
604, 5(i7, (130
33(), 688, 756
288, 480, 672
4C0, 1035, 1150
620, 1116, 1488
42, 210. 12<i
8.
10.
a
ti
u
$*
u
n
u
it
u
u
ft
41
M
ii
i.
m
VULVAR FR.ACTION'3.
3t
? numbers.
he GrcrUffit
Mi last rnle.
COMMON MULTIPLE.
A Multiple is a number wliich contains anotlicr a
niimbor of times without a nMuainder ; thus, 10 is a
niiiltiple of 5. A Common Multiple of two or moro
liiunhcr.s, is any number that contains each of them a
Miuuber of times without a romaitplcr ; thus, 30 is a
i.i'inj^ion multiple of 10 and G. Ttio least Comniou
Mulfi|)le of two or more numbers is the smallest num-
')i>r that contains each of them a number of times ;
;';:i^), 13 Ls the. least common multiple of 3 auiJ 5.
Tc find the Least Common Multiple.
• it LK. -Set the numbers in a line, find divide two or more
<*'{ tiiem by any common measure. Set the quotients and the
lithiioidid numbers in a lino and divide as bcfon;. uJitil no
i.vo numbers in the lo'.vost line can be divideci. Multiply the
iliv-fiorii and tlie nnmt>ers in th" lowest line toijether, for tht
least common multiple of the pjiven numbers.
ExAMeLK. — Find the least Coiomon iMultiple of 7, 13, 2%
\Z, 2i\. 18 and G.
Thus,
7)7
.10.
"n
13"
28
.42
2f).
18
6
C)l
13)1
4
4
f)
~1
2()
2B
18
3
6
1
2)1
1
4
1
2
3
1
1
1
2
1
1
3
1
■^L'jri 7X^>Xl"X2XiX3=!i5r)2 the least common multiple)
dial is. fj5o2 is the smallest number that ia divisible by all
fiiV given numbers.
i. Find the loost common raaUiplo of 4, 7, 9 and 2\
3, 9, 12 and la
4, G, 8 and 10
6, 4, 12 and 20
8, 7. 10 and 14
6, (), 10 and 24
6, 10, 13 and 24
2, 7, 13 aud 15
fi, 7, 2 and 17
11, 4, 5 and n
1.
10.
(<
((
a
II
(t
(I
4t
n
»t
((
({
(v
(1
U
u
u
u
t*
u
a
ti
<<
41
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M
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{"■!
«
VtTLGAR FRACTIONS.
ON CANCELLATION.
CancolIaMon is a method of shortcnini]^ ArillimtjtlcAl
operations by omittiii!^ or (laiicelling common factors,
and arises out of two priiic![)Ie8:
First. — Tho cancelling of a factor ia any number is equi-
Talent to dividing by that factor.
Second. — If the dividend and divisor b<? both divided by
the same ntunber, the quotient will not be changed.
ExAMPT-K. — Divide '.Mi by 18. Place the
divisor under the divid'-nd. thus
Reduce eacii number <o its factors, thus ,'>(>=
4X0 and I8::=2x0, thi'U arrange the factors
of 18 under those of .')(», thus
ftfter canc'lling the common factor 9, it will
only remain to divide 4 by 2.
30
2'X^
ExAMPr.E.— Divide G0xl"X'2CX'>G by 13Xl28x3JXoO
Arrange them thus —
<^0 X J/7
X ^^
7
X $^
7
xt X xn
8
X U
x^
X 30
8
Proceed thus — 1?> will divide 20 twice, cancel both, and plat?*
th(» 2 over the 2<>. This 2 will divide .'VI seventeen timejt.
cancel both, and plac' the 17 under the 81. This 17 will
cancel the 17 in the dividend. 20 will divide (50 twice, cancel
both and place the 2 ovrr the (iO. This 2 will divide 128
sixty-four times, cancel both, arid plact; tho ('A urider the 12vS.
Then (54 and r)(5 are each divisibh? by 8 ; 5t5-~8=7, cancel
6(5 and place 7 over it ; and (Sl-j-8=8, cancel G4, uud place
the 8 under it. There are now only 7 left in the dividend
and 8 in the divisor ; therefore 3 is the answer.
It will be generally found convenient to arrange the dividend
oa the right side of a vortical line, and the divisor on the left.
VULGAR FRACTION'S.
30
tlimotic'fti
I factors,
cr is eqiii-
flivided hy
1.
18
2 X^
8
. and pltw«»
,een timen.
lis 17 will
ice. caned
divide 128
cr the 12v«.
=7, cancel
, uud plac»?
e dividen<l
iG dividnnd
on the left.
Ex\Mr].R. What is Ihn quotient of 4 X 8 X 13 X 7 X 16
divided by 2ii X U X 8 ?
8 beinp^ a coninioM fiictor is cancelled.
lo '.vill divide 2:J twice; cancel bolh,
and plac»' the '2 io th.- li'l't of the 2(1.
Tlii.s 2 will divi;!.' the 1 () ei,<i;'ht times;
cancel b-jlh ui\'\ place 8 to Lilt' ri«,^!)t of
1(5. 7 will dividfj II twice; cancel
both, and ph-tOi' 2 lo the b,'rt of 1 k
T'iis2will tiivid-: H four tinieh'; cancel
bolh, an<l plac" 4 to the ri^rht of 8.
Tiie divisor is thii:; entirely cancelled,
and it only rein;uns to n;nUiply llie
^ U
4
X
X
X
^ XA\X$
X I X
$\ t
X
/0 4
uncancelled factors, 1 X 1 = i^>> the required answer.
Note." .V careful explanation of the process of cancellation
by the teach'T. at this 8i,a;;e, will save much future trouble,
and greatly int<'i--'st lh(j pupil. The followinu: examples ap-
pear mort! <li!iieult to the eye than they are in rt';ility ; they
Vvill serve also as rx.erci!<!'s in the iix • of si/jjus. !']ach question
(Should be lirst worked in full, and then by the Rule.
1. What is the quotient of 42x.'iX25x 12, divided by
28X1X15X0?
2. What is the quotient of 125x00x21X12, divided by
2-3xl20Xo!;x5?
.'5, Wh:it is the quotient of 4tXl8x2(;xM, divided by
llX3yx7X2?
1. What is th'^ quotient of 8 tini ^r 210 multiplied by 5 times
111, divided by 21 times 57 multii 'led by (J times 1-5?
f). What !^ rho value of [224-8-^-1 "i x [184-104-21] divided
by [94-:)+7]X[154-^]?
6. Find the value of [140-f8G^^31]X[107-|-I9] divided
by [237— U I] X [174-20 -If,] ?
7.Divid.'[[12x:>]-[2X9]]X[l2f30]by[5X8]X[2X9]
X [104-17].
n. Find the quotient of 210x141X10 divided by 175X
66X27.
I
^i f
ii^t;
I!
.ii'li'
I
ll
tim ;
P I
if '
I'j
'V > 1
M
id
VULGAi; i'RAOriO.VS.
REDUCTION.
G\i<N f. — To change an ifuprcpo' ft action into a whole •r
iniutd nninbtr,
KuLbJ. — Divi<lo tho num<'r;itor by the dciuwuinator. and if
Urto b<; liuy nMiiiiiuder wnto the (Icuomiualur iiadcr it iii the
toriu ol' u IVtiotioii..
6)1367
27o| Am,
Kx^MrLK. — lledtice the impnipor IVj":.-
•ion, ' V'» ^^ '^ whole Of mixod iHnnl)or.
1. Reduce "^Y" ^" ^^"^ cqulvtileiit whole or mixed number.
2. Keduoo "f^-^ to itH equivulcuit whole or inix-^d number.
3. Reduce ^\Y to its equivalent whole or mixed numbe/.
4. Find the value of ^lli"^ in wlioie or mixed numbers.
5. Find the value of 'j!j ' in whole or mixed numbers.
Ueduce the following rruetion.s to whole or mixed number :
0742 »! 08 1'?
J. ,J^, 1-.
*^^'- 2 J r ft
114 2 1 11
^^* 4810O0 ■*^^-
Cask ll.-— To reduce a mixed number to an improper fraclioi^
Rule. — Multiply the whole numbiT by the denominator o4
tbe fraciion ; add the numerator, and under the product plaib^
the deuoniinator.
ExAMiM.K. — Reduce the mixed uura- 40^
V>er -iG j to au iniprn^)er fraction. 6
2;i0x3=:3^,''
Rofluofe the following mixed uumber.T to their equivalew
iwiproper fractions :
'*• 4 J
7 TOB 2
8 3H4:i
7 :j <^ 2 t
T> 4 3 10
8 7 ♦•) 3 4 f
4 06 8
15. 7i
IG. 8}
17. 174
18. IDJ
19. 27^
20. C47,^^
21. 3(i0|;
22. 9703,5
%\. H42ij
24. 084} 5
25. 976,2^
20. 843 jVr
27. G87^Vf
28. 709,'.J»
29. 807^1}.
Ill
TUI-GAR FRACTIONS — REDUCTION.
41
I
Cask III.— Ta reduce a compound fraction to a simplt
fraction.
RuLK. — Mnlti])1y to*oiher all the nnmorators for a numera^
tor, and nil tlio denominators for a denoiuinator.
ExAMPLK.— Roduco the compound 2xOX.'5
3X"7X1
fraction § of Jj of 5 to a simple frac- -^j^ZlZ T~'ri ^^*^'
tiou.
Rednco tho following compound fractions to their eqniTa
lent simple ones : —
35. ^l of 5 of ^ of 13
30.
3 n^ 2
of ?
31.
7 3
'6 ' • f i
S
• • in
32.
5 17
1 ft
•21
33.
4 !)
tf • • IT
1 1
' • 12
34.
7 «_
i T • ■ i li
.. 7
36.
1 2
1
7 • •
1 8
53
. . 19;
^7
t 1
17
135
..24
O 1 ,
2 1 • •
3 6 • •
^l
38.
If • •
2!)
^8
.. 32
30.
7
T5 • •
1 3
21
3 1
. . 27|
Case IV. — To reduce a fraction to its lowest term.n,
Rni.E. — Divide the numerator and d^'nominator by any nnnv-
hor that will measure them ; that is. that will divide them
without a remainder. Do the same with the quotients as lonjf
rf« any number can be found to divide them.
Reduce JfJ to it3 lowest terms.
Divide the fractions and
\be quotients by the fig-
ures placed above them.
(2) (2) (.3) (2) (2)
14 4 7 3 ;if. ^2 fi _
2 4 5 — r '2 6 3^ 2 i 5 "
Ans.
Or,
If a nnrabor be wished for that may brinff the fraction t»
its lowest terms at once, divide the greater term by the lej??,
and the divisor by the remainder; and so on. dividing each
divisor by the last remainder till nothing n^niains. The last
livisor is the numb<'r by which, if the numerator and deno-
minator of the fraction be divided, the lowest terra will h$
obtained.
m
ilr
i.
u
f.
43
VULGAR FILVCTIONS— RKDUCTIOX.
iiii. J
!5 '
Reduce ^4^ to its lowest ternH.
The denoniinai^or of the fraction heiiip^ 14i)2'J0«l
•h;; 114(1
!)6
jrreattM*. it is (li\ itl <l by llu' niiiiu'rator.
The foniier <livis()j'. 1 H. is now to '>e
divided \>y Ihc icinaiinlci'. 9(1 ; the re-
niaindiT. 4S. is now to divide the foinuT
divipoi'. '.)(». Thi' Iuki divisor. 48. is the
iMiinlK-r by which, if tlie innncrator and
dononiinator biMlivid'd. the lowest term
will be oblaiu'.Ml : thus, 'iy).;^;^, ■^= l> as in former exnmplo.
48)00(2
Reduce the following' numbers to the lowest terms :
40.
41.
42.
43.
4iL
2 1 -2
4»i
I Iff
1 in
1 60
44.
45.
40.
47.
74
af.is
48.
7C.4
41).
f)4 4
1 1 ''1 6
50.
82 5
VO2O
51.
t :.'4A
2 "? »
' :<4 4
"> .". '.} S
> 4 ti :t
1 offi"
Case Y.- To reduce fractions to a rommou (ituomlnator
Rule. — Multiply each numerator by all the denom'npiton
except its aim. for a new nuini-rator ; ami multiply all th
denominators to<?<'lher fur a new denominator.
]!t
\n ,
Reduce §, ^, and ^. to a common denominator.
moratoi*
Here tlie first nurricrafor. 2. is 2X5^-7=^: 70 )
mulfiplit-d by .'> and 7 tlis' deno- 8X-^X7= fi8 a nu
minators ol' the other fractions. 4x;>X;")= CO )
Mark, that it is m.t multiplied JO<"ox v=T05 com. denom
by its own denominator. 3. The
same is done to the other numerators. The answer then U
7 V »! :<
79 5' Tos-
co
'«r.
Reduce the following fractious to others having a common
leuominutor.
52.
53.
54.
55.
2
3
41
5 7
^■> 8'
^_ JL
TP 13'
J 3 I !
18' ?3'
and
and
and
and 11;.
1 T
e;A 17 in 15 n-nA 13
• 2l" 26' 4 2' ""^ TV
4'i „„fl 27
and
57.
58
21 1 a
4 1' srr
: I _;? !' 4 10
BT' 26 i'r ^o i '
nq Kis 7J0 7»''J .^,1
<^^' 45 i' 5^2f'0^ j' *"^
■BfTr
H.I
i -■
YULGAR FRACTIONS.
43
lamina for
ADDITION.
RirLF!. — Reduce compoiunl fractions to simple fractions,
and mixed numbers to improper fnictions. Tlavinjrdone (his,
\)T\iv/ ttu'm to a common «lin<»tuinator. Add ull the numera-
lorH tojjethcr. imO , luce, undtT tl)e result, the common de-
nominator. If tlie answer be an improper fraction, bring it
to a mixed number.
Add together the followin;:; fractions, -3, j, and 4^.
Ht'vo the mixed number 41 is 2x'^X-=
first brouglit to the improper ;'>x'!X-=
Invctlou !|, and then all ili" frac- Ox'^X-''^^
lions an* brought to a comtnon
nuraeratorf
denominator.
Therefore H -f i^ -f
4.
0.
'^X''X2= :iO com. denoni
y^P =5J^j; sum required.
Add togetlier the following fractions and mixed numbers.
7. f of ';-i-A-\-^ of 3
8.
2 I r? I 4
5T-5 I >»
4 11 111 8
7 11 ;iii4 I ?r»
IT I i 1 1^ I 1^ 1 2 I
_B _L.li_i_ I 1 4
1 3 i^ '2 ;< "^ i "J 1^ :'. ^
2 1_1_4 1171 i-''3
%2 T^5:j i^eo I 2 3
^+Aof {?+^of5|
0. Yl of 7i|of ^+^'of H
10. q+ilof2^-f-;|ofG|
11. {;of^;;ofi7i-h*ofi2
12. l^H>f^^+^iof8;}
fS
lumeratop
SUBTRACTION.
a common
RuLW. — Reduce the fractions to common denominatorj?, as
in Addition. Find the ditfrrence of the numeratois, under
which write the common denomiiuitor.
From {% take *.
Here the fractions are first 12 X
brought to a common denomina-
tor, tiien the (lO taken from 84,
and the common denominator
K-ritten under tl)e difference.
numeratom
7= 84
4 X\r>=z 60
l5X 7 105 com. denom.
Therefore ^^^
6
1 u5
_ S4
the answer.
W '
i
44
VXM.OAll FRACTIOXS.
a.
•' ?''i
*•
"What is the diff"onMico lietut'on Mif rollowln"; fractions?
i.
o
3.
4.
4
I i
7
3
i
3
I 7, I 3
.'J. fl
I It I 7
5.
U -
- ,°«
0.
07
-51
7.
-'8 -
8.
0^-
_ \
10.
9
1 f
I I
if
11. 1(5:) ~ ir^
12. 70; - J of r.)
MULTIPLICATION.
RcLB. — Reduco tho mlxo<l numbers to improprr fi'actioai,
and coinpouiul fractions to simple ones ; after tlii.s has bees
done multiply all the numerators tofijetlier for the numeratoi
of the product, and all the douomiaators together for its d«
nominator.
Multiply G;; by § of J.
Here the mixed number n? so „n/l a ^F "J ■:— «<
I 18 converted into Iho , o„^ i4 _o;jo_. o.u j^,
improper fraction y. and 3 '^ 24 12 12
the compiiund fraction j of ^ into the simple fraction l\-
The numerators and denominators beinji multiplied, pro
duco the improper fraction %^r^, which being reduced tf j
a mixed number gives 'di^ the answer.
Multiply together the following fractions.
1.
3
A
X S
5.
»? X A
9.
8| X f of 3
2.
7
X ,'v
6.
7 X A
10.
16 X i of V,
3.
1 1
^ 1 2
7.
5^ Xllj
11.
17| X IJof 7J
4.
4
ill
X f^
8.
3.? X 4i
12.
24.'jX|lof9j
VULCAU FKACTI0N3.
45
Vac lions?
—
A^'f
!
.-— ,
i
._
i of 1
^1
>or fi'jictiom,
tills has been
e numeratoi
er lor its d«
DIVISION.
RuT.K. — Proparo tim fructiona as in miilU plication ; thor
iavcrt the diviaur ixiid prococd as in multiplication.
Divide ^ by J. 'ij-r-S inverted tlius
4x5=20
7x3=21
I. Divide
2.
3.
4.
5.
C.
V by
1 !
i i
21
80
tV
U
J
ii
3
iff
\2
4f
1 B
56 1
4
9 1
7.
8.
9.
10.
n.
12.
Divide ii^ by
^4 8
5
T
11
iof7
11(),V iof5}
§ of ^ by i of g
RF.DlJCTrON, CoNTLVUKD.
CVsK Y[. — y*? reduce fnictiont from one dcnom'mation
to aiiOiker.
3 rtf 7 .:_ !4
S '-'^ * — '24
•=3!|f Tim
fraction tJ*-
tiplif^d, pro
; reduced if!
ons.
X f of -3
X i of y«^
X 15 of 1\
rX liofOj
R[;i,n. — If from a lo'.vor namr" to a liiijlior, multiply the
dcnotainator, as in rtsluctioti of wholo numbers. If from
a liio:!ior natnc! to a lower, multiply the 'numerator as ia
rciiuotion of whole numbers.
Reduce | of a farthing to the fraction of a pound.
Here the denoniiriator is multi- o 2
nlie.l, as it is to be brought to a ~^,^.^^o(\ ^«^
higher name. 3XiXl2X20==28bO
Reduce f of a pound to tlie fraction of a penny.
Hero the numerator is multiplied, as ^X20X 1L=72Q
it is to be brought to a lower name. 6 6
i;^
i
16
VCI,GAR F^.ACTI()^^S - nKIU'CTION*.
1. Rod HOC
2. IloJuoo
3. K 01 luce
4. lloduco
5. R«uiiicc
0. Jioduco
7. Kuduce
8. Reduce
9. Reduce
10. Reduce
i) of a r.utliinj]; to lli»^ rimtion of a pound,
* of a |»')und to llu^ fi'aiMiou of ii penny.
I of a sliiiiln^ to I ill' fraction of a jjjuinea.
^ of a rtliillin;^ to tijc fraction of a farthing'
I of a fartliinij: to the fnu^tion of a crown
,^„ of a day to I lie fraclioji (tf a week.
I of a week to llio fraction of an liour.
^ of a nail to the fraction of a yard.
I of a cwt. to the fiaction of a dram.
I of a yard to the I'raction of a niilo.
in'
Case Yir. — 7\; cxprfisfi nnif f:^ivf'n fffntnli'ti/ a.t n /taction uf\
another quantUf/, coufiidc/cd as an integer.
Rcr<K. — Reduce both qnunlitio:^ to one di'Moniination ; thfiii
•nakc the reduced inl.ey^er the deiioiuiuator, and the ollivrl
qu.vntity Die numerator.
^Miat part of ]/. is lls\ Ad.t
Hero hoth qnantitiori. tlic 1/. iiiul
(he l.'J.s. Ad., are reducid to ]>('i)c<' ;
the pence in the iiilcger. 210, is
made the drnoniinator, and the
pence in Uic oiher quaatily is made
the numerator : the fraction.
I (I u
of
/.
•JO
n
L'lO
a pou
nd. ip. when l>rou"rht to its then
ino.
2 4 (1 '
13
12
itid
Ans.
lowest terms, equal to 3 of a pound.
11. Reduce 145. M, to the fraction of a pound.
12. R'duce 17s. \d. to the fiactioii of a pound.
13. Reduce 5.9. ^\d. to the fraction of a pound.
14. lieduce 17."?. 9t/. to the fraction of a penny.
15. Reduce O.v. 74^. to the fraction of a farthing.
16. Reduce 7 hours 21 minutes to the fraction of a day.
(I pctuinl,
jtouny.
a j2;uinoa.
II larlhin;;
a crown
week.
liour.
anl.
Irani,
[iiilo.
VULfl.VU rUACTIONS.— RKnUCTIO.V. 4t
17. HotliiCL' 7 11h. .") (Iranw to t!»o fraction of a cut.
IM. Il'.'iliico 8 c'.vt. 2 qr.s. 1 1 Ihri. to tlio fraction of Xj Oanoe.
ID. Ilctliicfj .'» lbs. 1) u/. to (lio fraction of a .Ivvt.
ji). iVifluoo 1<) iioui's l;j miiuit'.'S to the fraetloi. A '■, il".y.
C.vn VIII. ~7\) find Ute vJuc of a fra'Uii.n.
l!i i,K.— Ro<liHfMlie nunicraior to tho next iii'Vrior namr,
1,1 ii .llvul.' 1>T tiiti (li'MorniiMtor : nMl;ic(» Hk? riMiiaiiu'.'M', if uuy,
It ) ih-' ir:xt loT,'(.'r naino, and divide aj^aia, and iio on tr) tlw
jlo'A'i'JiL naiiu!.
What is tho valuo (^f \ of a j.<)ui)d siteillng ?
Hto tli'» nnnKTiitor. 7, is rniill;])lird l\v 20, 7
//•a(,'^/*»N <>/ Hto liiinii: it to liic ih'.\t, iidV-ri.)!' iiaia •, I lOv. 1:0
|Tli'' 1 IOn. art; (lis idt'd l»y S.\\iii(!l! ;riv<'.-; I7.v. and 8)1 !(•
4 wf a PMiiaiiul r : the I is in;illip!it'd hy I'J, -^j
t'l hriD'j: it to tli" ii".\t iiiCcrior nam!'. '18,'/. ; it "
•^vr.
lation ; tbfiii
id tho olbtT
s.
rf.
13
4
12
1 i'i^
-I Ans.
I.
1.
J.
1 of a day.
t llicn <livid»'d liy .;. u Iim'!) gives C \\ illionl auy __*
ivMuiiinior. 'Clif an.r.vt'r llieii U 17v. (la', which ^'Jfi
i^ I'.j'! y of a pound. "jj
21. Wliat is liio \;il'i'' of !f of a pfmnd ]
22. Wiiat is tlio value of I of a .shillin-^' ?
2:^. What ilio value of '] of a crown?
24. WUut 18 ih.e vahK) of |'', uf a vlay?
25. What is tlio value of K' of a {guinea?
2G. What is the value of fy of a yard, 1 )ng measure !
27. What is the vahie of j|j of a lb. troy ^
28. Wiiat Is the value of |,y of a lb. avoirdupois ?
20. What 13 the value of :]'.| of a cwt. \
0. What is the value of ?, ; of a mile ?
I
n
S
IM
48
VULGAR FRACTIONS.
Cask IX. — Tt) Reduce a Vulgar Fraction to a Decimal,
Ui'Li:. — Divide the niiniorator liy tho denominator: an*
nexin<5 as jnany ci[»hf3rs to tho niiiiioi:it(>r ;is may be neces-
sary. Point oii* as many dreimal }ilaces in tlie quotient
as there were ciphers ann(!xed to the numerator.
Reduce \ to a Dcclmnl.
2)10
.5 the answer.
1, Reduce Mo a decimal.
2.
3.
4.
5.
5.
\
7
"8
X
a
5
V
I
Reduce 'l to a dccitnal.
4);;oo
o
.75 the answer.
7. Ik'duce ,"g- to a decimal I
8.
9.
10.
11.
12.
I
1 rt
1 1
3 » 4 2
1
Ca.sf. X. — To Reduce a Deciiuul to a Vuh^ar I'Vaction.
Rui.K. — Arnke the given deciin;vl ihe numerator, and
place und.'i- it. for a diMioiniiiator. a unit with as manj
tjiphors as there are li.i^ures in the decimal.
Reduce .5 to a mil g(U' fraction
'^^ the answer.
1. Reduce .25 to a vulgar fr.
2. — .025 —
5. _ .375 —
4. — .005 —
5. — .01 —
Reduce .078 to a vulgar frao^
yJHy the answer.
G. Reduce .001 to a vulgar f i
7. — .41 —
8. — .021 --
0. _ .007 —
10. — .019 —
12.
13.
14.
15.
v:>.
17.
\ of a
18.
19, 1
'2~, 1
3.; I'y
VULGAR FRACTIOXS.
49
I Decimal
PROMISCUOUS EXERCISES.
If the fi'acLioMs are of (linVront donoininutlans. it will tx»
necessary to hv\n>/^ t.h mu to ihc Hiuno iiuine befaic ihvy are
ntlded or KubtracLid.
a decimitI>B mixed nunjber
r Fraction.
1. What arc the facloys of 39, GG. 72, 84. GP., 18. 35,
nd48'?
2. Find the frrcatcd common nipasuro of 84 and 5G.
o. Give the lead coinm;)n r:iulti[ile of 0, 8. 15, and 21.
4. What is the qant-LM.l of lGxl8x24x42, divided bv
:x8x3Gx48?
). Ch;in<,!,o ih'i impr.jpcr fraclions *"''^", ^|
4 ;' -7
into
0. Chan<i;e tho niisod numbers 18. .^, D^, 45S, into iin
g'
[irupcr fractions.
7. Reduce the compound fraction /jsk f->^li t>f '/ of 30
8. Reduce ?n, ."'i and I!'i:! to their lowest terms.
4 .1 •> ;. I
C:?!)"
Ij. Reduce
4' 1 ■>.'
WW
1 ;? t
o a common ucnominator.
10. Add i of a ton to /'., of a cvvt
11. F
rom 7' o
)f 2 t;
ike I o
12. i\Iultiply 2', of :; by 70.
13. Divide | of
14. Reduce i of
i 1 ./
C)
to a vulgar f.
a owt. to a frat'tion of a dram.
15. Reduce 8 houro oO minutes to tiie fnietion of a da,y
IG. What is the Y.iliie of 1' of a pound avoirdupois?
17. What is the dirt'orcnce between ^ (4' a lejg>ie. ajvd
I of a mile ?
18. Mow much is 8 times ]l of a yard ?
19. Find tlHMv.ult of [104-4]— [r)-f3]x[17-3]x[Gx
7 ] di \ ided by 8 X <*' X 7 X 28.
i of ' of •! of I of
20. Reduce the C!)m[)ound fraction
3i;
by C
iincc
Ihiti
on.
21, How much is 8 times !| of a pound avoirdnpoi»'
11
■I
„■!?>
I .3
50
COMPOUND ADDITION.
IvULE WFTir KXAMI'LK. — PlaCO pounds Ulltlt;!' pOUllJn, bllil-
Ung.s under shillings, and poiict^ undor ponce.
Add {.ha larthin;j;s, and di\ ide by i ; ibf quolicut £ .v. d,
in ponc(N the remainder is f';irllnnjj;s and must, bo (iJ 12 fjj
put under farthings. A(hl the pence with tlio 8(i 15 C.J
la.-sl quotient, and divid(^ by 12 ; the quotient is 14 1(5 f).!
sliillin^.s, the remainder i.s pence, and mu.-t be 'M 17 !'4
'o-^)
put under pence. A<ld th.e sliiiling-,s with tlie hi?t
quoLioutand divide by 20; the qnutientis pounds, 201 2 2]
tlio remainder is shilling-s. and must be put under
t;h.i!ling-s. A'id t!ie pounds with the hist quotient, as
ui
tuiple Addition.
KXERCISES.
£ s. d. £ s. d.
(1» VI 14 (1.1 (2) 04 12 7
£
d.
2(1 VI d.V
4 10 7
>0 IS 4,
>7 11
Zkt
i:
C:^
Vl
42 11 lO.V
(1)
£
.s.
43
10
05
13
84
12
!)2
11
41
10
d.
4
>> 1
(■>)
.£
Of)
72
i:j
10
72
s.
12
17
8
14
12
4
7i
^1
(3) 12 10 4^
10 4 oi
04 17 2^
43 12 tJ
('j;
£
s.
d.
30
13
4i
12
8
Oj
11
19
lol
17
14
^;f
28
12
Oi-
7. I boii.Tht o"o<)ds r<)r wiiich 1 piiid £!!)>> 10,s. 0*/. ; I paid for
pr*eking O.v. 8f/,. for case hi.v. (i<7., lor cordage \s. Of/.. for portei'
ago 4.V., fur IVoight £1 1 1,-?. ()^/., for waggon carriage 13,9., for
booking 9(/. What was the entire cost (d' the goods?
8. The expi'U'-es of building a liOU'H> was: architect £108,
bricklayer £t7t!2, mason £2111 1 0.s. OJ., carjx'nter £27(18
Ms, \)d.. plumber £h')';) 1 I.s.. painter a!id glazier £l;UO lo.>i. H^f/.,
jKipcr-liangcr £213 18.v. Id. Wiiat did the house cost?
•J. A housekeeper paid fur lea £2 \us. 7t/..conee £2 75. S.^t/.,
sugar £3 14s. ()./.. beef £2 Us. ikl.. nuilton £1 17.<f., ham 9.*.
75/i., and on various other articles £3 IJ*. 1\. How much
uioney did bhe lay out?
51
ids, bhil-
£ s. d.
U VI fi
8(i V> (*'>,
14 IB (A
:i4 17 H
:oi 2 ^\
!ut, as i«
.<. d.
1(> 4^
4 ()i
17 2^
12 7i
5.
d.
i:j
\h
8
n-
19
10.^
14
^;i
12
(5i-
; I paid for
.for portoi'
go lu."?., I'ur
:)ds ?
litcct £108,
ntcr £-i7(;8
UO ITjA-aiJ.,
cost '.'
£,'l's.^d.,
7.S., bam 9.'«.
How inucb
COMPOUND SUBTRACTION.
From £VA Vis. O.]//. take £27 18s. 8^.7.
Ul'LR wttii ExAMi'i.K.-- Place the smaller
ftiiinlKT under the greater as in Simple Sub-
t-acLioii. Then, IJ larthinos from 2 fartbings,
laiHiot; add 4 iartbinfj^H (= 1 penny,) to the
2. and 3 farthings from (!, there remain 3,
I'lace the '\ under the farthings. Add 1 to
ilie 8 : then i) pence from (1 [)ence, cannot, add 12 pence
i=_; 1 shilling) to the (], then l> from 18. there remain 9, put
[he 9 pence, under the pence. Add 1 to the 18, then V)
shillings from 12 cannot; add 20 shillings (= 1 pound) to
th<' 12. thcPi 19 from 32, there remain 13, place the 13 under
llio hlilliing-s. Curry 1 to the 7 and proceed as in Simple Sub-
iirfCllun.
EXERCISES.
■
*
n
*
£
s.
iJ.
-> f
()4
12
t>^
t
27
18
sf
36 13 0^
M
£
.<?.
d.
19
17
4h
17
14
n
32 3 2]
(1)
14
^
2U
17
H
(4)
i;s
13
7
28
10
10]
G)
88
18
«.l
(
19
H
(10
)
.M)
12
0^
17
]2
04^
£ s. d.
Ci4 8 3^
27 KJ 7^
36 1 1 V}
(2)
47 It; 8.\
28 17 (i|
94
24 17 9^
17 (-.7
19 U\
(11)
24 19 8?,-
7 12 9"
£
s.
d.
73
10
5A
48
18
n
21
11
^
SQ
17
4
27
19
04^
((')
83
17
0]
47
n
(0)
20
11
m
1
17
iiX
(12)
48
12
8
17
19
^
ml
l^
53
COMPOUND MULTIPLICATION.
f
CAiJK l.~TV/icn the J\lult/'plier does not exceed 12,
Multiply £G 12s. -nd. by 7.
Rule with Exami'lk. — B.'-^'m iniilti]>lyin<:j Iho fiirtlilngs by
7 ; tlni.'*, 7 times \ are o}i, .set down }, iviid carry
.> to th(? p(Mice. 7 tiiiU'S 4d. are 2.^. •'//.. and '.kl.
curried are 2,v. Id. ; set down 7 undi r the pence
iiLul carry 2. 7 times 12 are 81. and 2 OiPTi(>d
iro 8()S., v.'hich is equal to £1 (Is. ; bet 'loAii the
(J under the s]iillin,L?H, atid c:irry -i. 7 limes G
are 42 and 4 carried make £i'6. riace it under the pounds
£ ."c. d. £ .<?. d. £ !i. d. £ s. d.
(1) G4 7 4\ (2)43 12 G."i (:5) 57 IG 8} (4)79 18 4j
2 ;r 4 /i
£ s.
G 12
1'
4G G
7^
Case II. — ]Vhc7i the Miiliip/ier exceeds 12.
ip/
Multiply XI C5. 3c/. by '123.
RuLF, iviTii ExAM!M,K. — Wiieu llic multi-
plier, 423. is a hundred or above it. multiply
Ihe multiplicand. '"I G.?. 3-/.. twice by 10. and
£ s. d.
4 G 3X'i
10
.s,. by the number of hun-
1:
{be product. Jl '31 )
drcds. 4; Iben miliip'y tl:e prodtu.'l of the
ir?.t 10.
ci. i-'t
Cut.. ])V Uie number of tens. 2
and place it under ihe prcduci of the 4. £1725
(?.5. M. iMuliiply novv- 'ii;;'. lirst line. £ { G.s. 3(/.
by the nuinbrr of unit^■,. 3; pat the product
obtained irnder Ih*' product of the t< ns. atid
add the ])roducts of the huniirrds. (h(> lens, a.nd
the units lou,-cther for tlie required answer.
For thousands muUi]*ly by 3 tens, and pro-
ceed in the Kame manuLr.
43
2 cxa
10
431"'
5
4
172.)
8G
5
12
18 9
£ f. d.
5. Mult. (14 K; 7^ by <
8G J 3 -1.1
('9 1
G
8. _ (M8 H; 7'
^>(
7 li
1.
10.
G58 13 7
GS
241)
478
11. Mult 4(>7
1;
14.
IG.
G75
r)G3
807
!)8
42
1824 a
9
.1. d.
15 8| 1
!y G47
4^
GOS
12 O^i
78.-»
14 ^
ficMJ
13 8 J
87
16 7i
45
J
.5. d.
i
G 3X^
10
J
2 0X2
10
1'
5
\
.)
U
G
5
2
18 9
?I
COiirOUND MULTIPLICATIOJ^. b%
Cash III. — To Midtljily hy parts.
Multiply 45. Shd. by 4^.
If Uio part 1)0 4. take a quarter of the multlplicaiKl. If the
ri\rt 1)0 h. take a lialf of tlio nr.jUiplicaiid. If the part by |,
itikc half aiiil a quarter of the niultiplicaiHl,
or divide the multiplicaud by the under
fiijr.rt^of the fraction, and multiply the pro-
duct by the upi)i'r n!-!:uro. Add the quotie-it
fJuis oblaliU'd to tiie jM'od;:;;t obtained by 18 10
4 8k
4
iTiultiplyin;^' the iniilliplicai'.d by the whole
iiuiiibfr iti tlie Muilliplior. Thlb latter v.'ay
ai..!>lioB to aiiv fraelionai part.
^
half of
lop
Uue
1 1 2V
£
d.
!7. MulL 4 2 (•»
18. — 7 1'
7.^
l.i. ~ 28 V.) 8
0.
87 1
9.
21. — 87 t 12 in
f.>
■ i'i'i
1
c
9.
12
11,
£
23. Mult. 7 8 0,1 h
21. — 4 10 3i
25. — 48 17 Ci
— 50 14 11
— 70(1 i;i 4k
— 80 I 10 0[
y
»')(
»"!',>
^^).
87}
94^
20. What do 7;; I'o- of tea come to at bs. o.jfi. per lb.?
"0. What do 4 lbs. of butter come to at Is. \d. per lb.?
4. Patrlcd: earu.s \s. Vkl. per day, what does that come* to
hi
») da
c'J
:!2. IjouQ:ht llr" toiis o!" h-.iy at £3 IT.s-. C^d. per ton ; how
much did they coaie to?
X). A gctitlernan i^'perid 9 £1 7.v. GJ. pf^r day •, how much
(I'X'ri he .'^pvuid in a year?
oL A f;i;-mer paid iu r'^nt £it() IC.s. G(/. every year; how
much did he pay the laudh.ird iu the course of 2j3 y^iirs?
;>5. A carpenter received lis. Qd. per week ; v/hat did his
uMXOs auiouut to in a year?
8G. V.'iuit is th.» value of 5G8^- ounces of gold, ,'alucd ai
I £3 105. (Id. per ounce ?
H7. Sold 8 oxen, and gained upon each £2 llr. 7^d. ; Low
I much did I gain?
ij
■SX
.1
54
COMrOUXD DIVISION.
Case I. — When the Diin.'ior dots not exceed 12.
Divide £8 12.v. 7.]/M)y G.
Rdlk ^yrTlI Example. — Procoed lliiiv, in
6)8 12 7^
8 once and 2 o\er, sot down tin? 1 I'.inlcr tho
8, and carry 40.v. for the 2/. to tlie 12; Ukmi (5
in 52, 8 times and 4 over, set down I lie 8 and
carry A^d. for the •!*'. to ilie 7 ; then (I in 55,
9 times and 1 over set down the \) and carry 1 farthinp;? tg
ibo farLbing, 1 a;^ -o <», in (i uuce ; f-ct down \.
1 8 9J
2) 71 16 8:
\) 70 12 2|
£'S1 8
4
1
£
.<?.
</.
1.
DIvido (iS
17
9.1
bv 2
12.
2.
42
12
^'l
;]
i:i
3.
r;9
18
7f
1
II
4.
7 •18
15
o.\
5
15.
5.
17()
19
lOj
r.
III.
6.
407
M
2.^
»»
(
17
7.
8G47
17
11]
8
18.
8.
7508
V\
*:>,
9
19
0.
50(;o
7l-
10
20
JO.
8(;87
18
1 1 \
11
21.
11.
4711
11
7'.
VI
12. DlvMo
£25 10 8^-2
.C .«?. d.
98 11 7:V liy ;
47 i;j CV 8
(17 1!)
8(J4 1
71
■I
587 M 10.}
;{ii 7 11}
..'000 v^
8i;8i 11
7010 18 0}
:;(i7l 2 lU
87<;2 17 o![
V,
r
• I
23. A tradesman ]i;ul ia the siwinj^c'' "bank 9(7. IC.s. fiJ ;
tbis sum bo bad saved iii 5 vear.s ; bow much did he tiuve on
an average each year ?
21. Ten men rented u Iiousl at ?''/. 11^. 8'/. ; bow iniifhls
bad each to pay ?
25. A faiher left 42o/. ICv. CJ. to b- divhled cnjially wiaoriii
liis ei^ht children : bow mneb <li(l e;.eh jjjet? »*
20. Twelve persona subscribed 28/. 15.s, ijd. per annum, ioi
the Fupport of a Fcbool ; bow much did each subscribe?
27. A pi(!ce of cloth conlainin/jf niiu; yards was bought fot
Al. 10*. 8(/. ; how much was that i»cr yard?
SI.
32.
S4.
^o.
'Ml
3".
.iS.
0<>Ml-i.U.\D lil VISION.
55
• '
2''. noii;;lit nino «lo/v'ti boiUtB of wliic, for 'aIiIoIi 1 pu'ul
1:'/. Ms. \)d. ; wlial did I pay per dozcii?
2f). Nino vessds Irnpoiicd goods, valued at 79G87/. IO5. ;
what was the avcriigo value of each cargo ?
Cask II. — IVhcn the Divisor exceeds 12.
Dlvid'^ £0i 75. 8^ri. by 47.
RuT.E iTiTii Example. — Divide the
pounds as in pimple long division. Mul-
tiply the rtntainder, 17. by 20, adding
to it the shihii.gs, 7. l)i\ide again as in
simple divit^ion. Multiply the reniaiiidcT,
IS, by 12, adding to it the pence, 8. 1)1-
Tide aguht as in simp!" division ; iriuUiply
the rvraaiiider, ?A], by j, adding to it the
farthings and divide as bcfcro. Tiio qno-
li'nt tin-n is 1/. l.s. \'\iL with
niainder.
5 of
a ve-
£ s.
A1)U 7
47
17
20
d.
47}o47(7
329
"T8
12
47)224(4
1_88
4
47^14(i(i5
141
it (■
o remain
'. ; how inuf'hi
nuallv aiRoniL
81.
32.
37.
:i8.
Divide
47
78
487
798
080
0^27
70G3
4317
s.
Hi
lo
10
17
t
14
1(5
4).
Hi
8'l
hy
28
37
14(1
31;;")
478
042
80(5
718
30.
40.
41.
42.
4 a.
44.
4-).
4<j.
Divide (10
97
(547
870
093
708(^
9103
7l'08
s.
It)
13
14
19
8
17
n
Oh
by
4
76
lOfl
264
489
785
908
759
*"
56
COMPOUND DIVISION.
I
CAdK. III. — JV/ie)i iJit Divisor contains a fraction.
Divide £24 As. qu. hy 2^,.
TvUIE V/ITTT KXAMI'T-K.— Multiple l)(!;!l lllO £ ». d.
flivld'Jiul :\!id the divisor by tlic ur.dcf lijc- ?i)21 4 Cj^
lire of Ih'j rr:'.clion. 2. audiiiii- in tl
iipi
i;'i L
figure \ to the pioiluct ot llif divl>(ir ; iiud r ^(^ <j ^
divide l.y iihovt oi' long ui\ itiuii na iLu cu^o -
Biay require,
u i;; n\
,1.
£
o.
47. i;
48. -
4y. -
50. -
iviuo
\^ AO
2 14 (
04 1
\}- ],Y :]}. ' 5;i
( (
O'
97 18
847 112
018 17 (•
51. —
62. — 403 l'>i
0] , n4.
7:; j n.'».
'•17.'', ;''(').
M)4 I ;>/
' ' > ) i re
^i,^^^ (;{ 17 (u hyv.
1 "" ' •
•> I i -x *^
0;i
CM
^:
780 0^ 78!
[^07 10 10 J 841
l'7y 17 Gi[ DOi
5'). A fanvcr niii. a r::rm ai T;;:/. K'^- Ctl. per annnn!
lit) wishes to l:iy j,
rent : hov»" inucl; nv.i^L ':■■ ;;;.\c culi wc k
li ''\' ly u(<k ny may pay th
('0. A moreliant i,;iinMl ]!t;7/. i:: Ij v. nr:? ; \\liat wjy
itit: uverii::'; ji;iii!i p( r v^; i ?
01. In a i.^>rgo town ilicre v.-i r ' 4": ' c}i!!dr(Mi edttrutcr
by T/O tcaeberfa ; bow !!!;i!iy inij'i'- 0:1 un avorj|i,-:; to t'Ui.>
toacher ^
02. A inrni'.ifr.c'uv. r y';'.'!
1 in \\\
•sh \^vi\ ?ACL Vs.
receive ?
were .;i.! wvrS.tiui;
L.llcl
1 (I : \.i
U,]i !1
fil
Go. Tiiere. are about r'i<:lit hundred liiiiiior.:- of people
the world, und it !.•< tl-oii^ht that as n.aiiy die i:i o2 yean
Uiw many .ti<.
*)t. If ."^0 m;
J on an av'.')'at;-e in a \''ar
■ (li<' in a year. I.. '.v D.anv d!o in aii Lour,
there being 87'J5 lioiir.^ in a yar?
('.". A ])r!ze of 7l';"7/. r;,v. Or/, is to he divided equal')
among 500 fr^ailorn ; v.hal. is ee.eli n);in"s ."-liare?
00. A frentleman hv<} an optnic of ']j{;8 acrep. for Avhich
her'. c»'ived pvr a!.num ^'7U/. IC.v. 8c/.: how much v.- as it let
for p;r acre ?
57
■j r
llEDTJCTIOX.
Reduction is tlio brin'/inp; of one (.Icnomination U
AuytLicr wiUiout altering its viilue.
O.-JL
-4
5 51
V4
Si
> 0^
7c^!.
1 10.V
811
%'i
icr nnuuni , K
Cask I. — ^o bring from a h(,s:,her to a lower*
Rui.K WITH ExAMiT.K. — Miiltinlv l)y as £3
limit V of tlio Ic^s us nrakf oir' of I lie p:vt';il(-r. 20
TliU3 to brinpf li/. to sln!liiin;s. miililply 2 by
20, l'-:causo there nre 20a'. i;i a pound. iOs
Case II. — To Z^r/..'^ a lotccr to a higher.
IluLK WITH Ex\MPi,i':.- -Div:'!*' ny as many
»T tiio leps us niukc one ol" the gr'Mlei-, Tims
(o briiij^ 40 shiiiin.u'-' to ixiuiids. (ii; idc by 20,
l)ccAU5;'j there are 20 Hhilliii'.;,^* in u ^^oir.id.
Bring £1 9s. fJ.V/. to iliriLIng?,
Multiply the 4 by 20. and add (!) > H.v. ir) the
proJuc', thJBwill givi! tlie nninb"!' ; !' -I 'MingH,
H''9. Multiply then l)y 12 .\d(lin;>- pence,
tills will give tlie number of ptuce ; 107i</.
Multiply by 4, and add the. t'o jartiiing:-; to
t!;e product ; this v/ill give the :)UJub,.r o' I'ar-
luiai?,!, iu 4.1. i^s. {),\d.
2,0)1,0
£2
£ 5. d.
4 9 6i
20
89'
12
1074
4
4201
i
it
in an Lour.
!dcd equal') t^
Bring 4208 farthiugs to pounds.
Divide the farthings l)y 4. tiisAvill gi ve 1074 ^ ,42 '5
pence and 2 farihings. Divii.le thi.M by 1 2, and ;/.fi[)74_J
^ J uliiUlngs and sixpttnce is o'naioed. l)ivid« ^- . . ■ ^. ;
i V 20, and the quotient is 4 poundd y bhiiluigs J^.-I—^.
h\ all 4/. 95. G.^^. ^^ 9 H
.'ft*
Ml
s:
REDU,
."S.
I. IIoA' in.iny larlliings are ther<> in 12/. 7*. Ctld.'!
1. In 2ul/. [)s. KW. how many pence?
:;. Reduco 3(11/. H.v. 9l<{. lu I'luUiingH.
4. In 217/. ]2s. ny, hovv many IralCpcnco?
5. Uow many ptuco are tlioro in 2iG gaincas?
0. In 2'.i8 crown;'. l:ov»' nuuiy farthing? ?
7. Ri'dnce r-}(i48 j^ixponccs to rarUiinga.
8. In 42708 farlhin.:;^,; Iiow many pence?
9. How many ])Ounils ar.; tlicrc in (;7S00 fhiillng*;?
10. In 'liO.STiJ liu'ihijms. liow manv ponnihs?
11. lIow many (]i;ni:'.<.'a^ are JherL' in 3->789 shillings?
12. In CSV94 nr;:iM\ lio',
manv crown?*
13. IIow ma;\v fonvp; net:; ar<j llu'rc in 37'J80 shillings?
M. In 2i70/. hnw inawV crov.n.-?
15. lIow many ponn(i.s in Gl'OTtl lialfcrownri?
lis. In 2l)C8o hvoiv'Uf.-s. hi)W many shiilinj^s?
17. In 43l'87 crowns, how nia:iv (hrccp'-'iiccs ?
18. IIow many fivrponc-'.s arj there in •4700 crowns ■
Id. h\ 7uij71 ha!!'penco, h.ow many fonrpenccs?
20. In 70S302 pouiuln, how many fcixpcMicos?
21. IIow many crowns uro ihorf) I:i 7l)^!S guineas?
22. In 79201 half gninoas. h<jw mvv.y f\?vcn sliilling pieces
23. Ifow many fivcponccs are Ihero in 7G4 ponmls?
24. In 73027 fai'lhinjijs, how niaiiy cighlpenccs ?
25. IIow many IralC-^ov'. reigns aix- them in 7<J42 gnlr.tufl? |_
2C. Rcdnce 7(;32/. 17.s. 0;,o'. to farthings.
27. Rednce 5010/. ll.v. 8/7. to farthings.
23. In 7324 gninrn?. how ma.ny !iinepences?
29. How often ia three fartlr.r.gs contained in 742/. l7^'*.0^W.t
30. la 7C0O fonrpences?; how ma-ny Gvepenccs?
14
KKDI'CIION.
60
!'
To Reduce Iliil'fax Currcnct/ to Dtcimal
Currency.
KrLE — Multiply tho ponnda by 400. MoUiply iho ^hll
liti'Tfs by 20. I'l'dnco \\w. ponco and rai't.i*:iji;s to f;vrlhirij;3
Multiply by Jivo. siiid divido by 12. Add all tlio rcsull.a to-
i;(Hher, and cut oil" two figures to the rig'.it luuid for cents ;
tbuL' :
R<»dnco £12 Ws. ^^\J. to Decimal Currency.
£
F,
d.
42
n
^
400
20
4
1G800
280
26
280
6
10
12^100
5170.90
10
\s
owns •
«>
as?
Uing p'
eccc*
inds?
9
•
i2 gull
>vnfl ?
Reduce the following amounts to their equivalents in Peel-
mal Currency.
81.
£4
7.9.
8Ar/.
41.
£3
t;5.
hU
32.
G
5
42
42.
4
7
8
33.
7
8
p;^
43.
2
G
34
31.
6
4
21
44.
5
8
ii^
35.
3
7
H
45.
4
7
^
36.
6
4
H
4G.
3
7
n
37.
o
6
4^
47.
6
3
n
38.
5
7
8
48.
3
7
84
39.
3
G
44
49.
8
9
Ci
40.
4
7
a
60.
3
C
H
ii-
Ht;
W' ml
60
WEIGHTS ANT) MKASUUCS.
EXERCIS
ES.
AVOIUDUrOIS WEIGHT.
ADDITION
•
twt.
4
2
6
S
qrs.
2
3
1
2
lbs.
VI
14
7
24
(1)
avt. qrs.
7 3
8 1
4 2
8 1
lbs.
10
11)
27
13
qrs.
I
2
3
•>
(2)
/.';.^
It
24
13
17
oe.
12
1')
7
13
17
2
1
SUUTRACTIOX.
etvt.
IG
12
qrs.
2
3
lbs.
12
24
LVt. qrs.
17 1
10 2
lbs.
10
27
qrr.
1)
11
A'-.
22
20
0*.
12
li
'A
2
10
tV)t.
4
qrs.
IG
4
MT^TirtJCATlOX.
G 2 IS
7
qrs.
2
23
09.
12
9
19
2
8
(twt.
3
lbs.
8
DIVIHfOX
(7)
act. qrs.
G)14 2
•
Ihn.
17
qrs.
l))IS)
lbs.
n
Mr.
6
2
12
9. A tobacronis'-- r«ir»oivo(l K» ewt. 2 qrR. 2r> lbs. of lohr-rcv
nd sold 12 ewt. 3 t£is. 20 loa. ; how much luw lie uuisyld ?
'P'
WniGIITS AND MKASUKES.
61
10. A brewor boni^ht Ilvo l>a<^? of hops ; No. 1, wcif^boil I
cwt. 2 qrs. 14 lb. ; No 2, wci.^'linl 1 cwt. ;i q^^^. 21 lb. ; No. 3,
wti^Iit'tl 1 cwt. 1 (jr. 27 II). ; No. -I, wci^-Vii'-d 1 cwt. .'5 qi'H. 2'j
1 I.; No. f), woigbud 2 cwt. 2 qrs. 25 lb. ; what wna tho weight
of i\w whole?
11. A p:roc."r sol J l,ho first year ho \\\i^ In l)iisia''.s3, Hi cwt.
T (jr.s. 2() lb. 14 oz. of.«n<^ar; th'j thud year ho wa.s in liu.siiirss,
li" sold 8 tiiiioi3 as much ; how muc.'i il;d hu s-dl iii the third
)''i\r?
12. 7']lr?!it ho?:^:h"ads contained 108 cwt. 3 qrs. 20 lb. of
^iij^ar ; how much did each contain ?
Ill A plantation prodnctMl the first year PJG cwt. !!^ qr«.
1*1 lbs. of .sugar ; Lh'j second y<'ar 4715 cwt. 1 qr. 9 lbs. 1.5 oz. ;
flic third year <iOH cwt. 14 llr-). 12 oz.; t';;u Iburlh year r)tJh>
cwt. 3 qr."?. 13 oz. ; tli'j lirtli year 737 cwt. 2 (jrs. 13 Ib.s. 10 oz,
13 drama ; how much .sugar was produced on the piantution
in Ihcao five years?
14. A grocer bon.jyht 3 Idids. of funfar. each containlr ^; i
C'.vt. I qr. 13 Ib.-^. Tliu lirst month lie sold 2 cwt. 3 qrs. It lb.
13 oz.; the second month lie sold 2 cwt. 2 cjrs. 14 c .. lOdrams;
tlio third month he Fold 3 cwt. 1 qr. 11 lbs. 15 iraris; how
much has he on hand ?
15. What is tlio we!p;ht of 8(1 hhds. of tobacco, each hhd.
Weighing 5 cwt. 3 qrs. 14 lbs. 13 oz.?
in. Eleven pieces of iron weighed 4 tons, IG cwt. 3 qra. ;
how much did each piece weigh?
17. Ten packs of potatoes weighed 10 cvt. 3 qrs. 13 lbs.
11 oz. ; what was the v.'eight of "ucii .«ack?
18. How many parci'ls, each containing 4.^ lbs. can be madt?
out of 2 cwt. 2 qrs. 23 lbs.?
10. If 3G bagr] of cotton weighed 41) c ^t. 3 qrs. 13 lbs., bow
much did one weigh?
20. How many hogsheads of. sup;ir, each containing 13 cwt.
2 qrs. 14 lbs,, may be put on 1»oard a ship of 324 tons bur-
den?
21. St. Paul's bell in London weighs 5 tons, 2 cwt. 1 qr. 22
lbs.; by how mucli does t!ie great bell of xMoscow exceed it,
which weighs 198 tons, 2 cwt. 1 qr. ?
'1-' - f-
if!'..
At' i
:, J
1- •;
'i 1
";i
^
,1*!
J
f3
WEIGHTS AND MEASURES.
TROY WEIGUT.
ML'LTl PLICATION.
(22)
(2o;
lbs.
oz.
diet.
Ihs.
yx.
dwt.
oz.
£/t<>^
/^v.V.
18
G
lA
4
2t
a
12
8
43
5
M
9
71
lbs.
;)17
•)
I
lli
dwt.
U
17
DIVISION.
(24)
/Z'.'?. oz. dtl t HZ.
1)G7 8 17 7)13
(25)
dwt.
Ill
22
'*%«
2(5. A silvcrsmltb madn tlireo dozen spoons, •«'t'igli!n<;- 5 lb.
oz. 8 dwt. ; a tea-pot, \Yei;j,hing ;» Hi. 2 oz. 1(1 dwt. KJ grs. ;
two puir Sjilvcr candh'.-tieks, wci^hii!;; i lb. oz. 17 dwt. ; a
dozen silver forks. \\oip;hi:ig 1 ll>. 8 oz. 10 dwt. 22 grs. ; what
was the weight of all ihci arlicks?
27. Three dozen silver table spooiirs wcliilied 5 lb. 9 oz. !
dwt.,>\hile three dozen silver tvMSjiootis weighed only 1 lb. J
uz. IG dwt. ]H gr.s. ; what vras the dilL-rencc in weight?
28. Sold eight silver tt-a-poL-;. each weighing 3 lb. 9 oz. ]S
dwt. 13
o ^v^. ;
how nuich did
liivy a!! weigh V
29. A silversmith received 3t'. lb. 8 cz. 11 dwt. IG gr.?. of
Bilver to make 12 tankards; what would the weight of each
tankard be ?
30. What is the weight of 3G ingots of silver, each ingot
wt'igbing 2 lb. 10 oz. 15 dwt.?
31. 2 lb. 4 oz. 9 dwt. of gol<l cost 59/. IG5. Qd. ; what did i!
cost per dwt. ?
32. What is the w^eight of 3 dozen spoons, t'acb weighing
2 oz. 3 dwt. 19 grs.?
WEIGHTS AND ilEASURHS.
LONG MEASURE.
G.^.
.1 i^
tk
Dt. gr.i.
5 n
1)
ADDITION'.
(.3)
(3t)
ttiL
fur.
per.
fur
. /xr.
yd.
per.
yc/.
/^
•t
(i
20
7
it
LG
8
1)
5
i:}
G
22
4
17
4
1
4
9
It)
3
24
5
7
12
(J
11
f)
23
2
2
25
11
5)
22
SrBTJ5ACTr()\.
liin^^' 5 lb.
^.10 grs. ;
7 (iwt. ; u
jrs. ; ^vbat
b. 9 oz. !
ily 1 lb. J
>. 9 oz. 1?
1 <; ji^rs. of
t of CUCh
ach Lugot
rhat did il
weighing
.
ml.
fur.
per.
fur.
(3'>^
pi r.
y^/.
per.
(36)
/^
4
6
20
10
1
IG
2
1
1
7
6
,M5
25
2
10
4
12
4
2
2
37. A mnn rode 35 miles. 2 fiirlon^-s;. 31 ptM'cbos; v/alknd
5} miles, G rin'lori;:^s. 25 perches. 2 yuids; tli'Mi rode agtiin 42
miles, 7 rurloiigs. 4 yards ; llieii walked ;!_i;-ain 15 mile?, 4
iuiloiigp, 38 perches, 3 yards; uhat wus the leiigth of hi:?
j'juruoy ?
1)S. A traveller walkcil on Moiiilay .'>2 tnlles, 5 riirlon;j:s ; on
Tmrday he walked 27 liiihs. 7 lurloiiU'^. 3") perches 5 how
Uiiich did ui;3 journey of .Moiuiay exceed that of Tuesday?
TiO. A mail e-nieh travelled at the I'e.to of 7 miles, 5 furlonf^s.
2-< \) rehe.s. p v honv ; how fur would it g'o in twelve hoLir.'i?
40 A surveyor who had 10 miles. 7 roods. 30 perches, of
r-'ae. to keep in repair, appointed 12 m n to the work ; Avhut
leiiu'lli of road had each to attend to?
•11. A man travell-d in nine days 150 miles, {furlong,
IS perches, ',\ yards ; how much did he tiavel per day on uu
hvci'a<re ?
|i
A -'^'.
64
WEIGHTS AND MKASURES.
CLOTH MEASURE.
MULTIPLICATIOX.
yds.
24
qrs.
2
nh.
3
4
yU.
IG
(42^
qrs.
■6
nls.
2
7
98
o
(43)
7/^/.«. 5'»-5. ///5.
■ > / *
3
9
yds.
4')25
qrs.
PIVIFION.
(44)
f/'/.s. (^r.f. 7j/."f.
yd^.
li)3()
(ir>)
qrs.
3
1
6
1
8J
40. A Ifiilor 1)oi.!;;lit four pieces of cloth ; In the first lhrr<i
wero 27 yds. 2 qi"^. !> mIs. ; in th,- Rccond. Wd yih. 2 qrs. 1 n!.
in the third, o2 vd,-;. ;! (jrs. 3 al^. ; iii the lourth, 47 yals. 3 qrs
2 nls. ; how much hi vAl ?
47. A tiiilor. f.-nm n piece of clot!; oonlairi'ii.^ 37 yds. .'> qrs
2 Ills., cut oil' 13 yds. ;.) qrs. 2 nls. ; h;.«>v much remained?
43. A dozen wcavrs wove, cacli. of) yds. 3 qrs. 3 nls. of
cloth; ho'A' much was woven by the whole?
40. In nine pi^cf'? of cloth ci' cqnol l(M!.!::[th, there -were 1^7
yds. 2 qrs. 3 nl<. ; how much in each piece ?
50. A piece ofclolli at 7.9. (>/. per yard, cost 17/. 12.?. CJ. ;
low many yarda v. ere there in it?
51. What is tlie difl'crenoe in len<j;lh of one web of clolh
inoa^uring 30 yd;-. " qis. 3 nls. ; and two webs, each mc:u>-
urlng 23 yds. 2 qrs. 2 nls.?
52. How many Puits of clothes can bo made from a plocf>
containing 31* yds. 2 qrs. 3 nls, ; each suit requiring 3 yds. 1
qr. 2 nls. ?
WEIGHTS AND MEASURES.
65
! I
SQUARE AND LAND MEASURE.
i3)
►-5.
2
h/9.
3
9
ADDITIOX.
(5:v)
etc.
rd.
per.
ac.
/•//. p/^r
32
•6
Hi
46
3 27
16
2
21
12
2 10
7G
1
13
61
34
24
2
27
46
3 17
(54)
ai\
rd.
per.
37
2
12
^l
3
21
C2
1
17
47
2
34
liO
37
'»
SUBTP. ACTION.
rs. li!s.
3
first th"r«
qvs. 1 III.
y<jls. 3 qrs
y(]s. 3 qrs
aiued?
5. 3 nlis. of
were 1^7
h of cloth
ach incjw-
m a piecf^
g 3 yds. 1
(5-.)
ar..
rd.
per.
ac.
rd.
/?<";•
42
1
10
36
20
16
2
25
13
2
30
25
2
25
(56)
ac.
rd.
^er
42
1
25
17
2
35
57. I bouglit four fields; in llio first thcro were 6 acres,
r> roods, 12 porclufs ; in the second 7 acres. 2 roods ; in tho
iJiird 9 acres and 13 perches : in tho foarLh 5 acres, 2 roods,
Iv) perches. How much in all ?
58. A (armer sowed with whrnt. a flidd containing IS acres,
2 roodn, 25 perches ; and another with oats, containing 19
aores, 3 roods, 34 perches. How liuich larger was cue field
than the other?
59. Eight men cut down a field of hay ; cacli man cut 3
acres, 2 rood:?, 27 perches. How much was mown?
60. Twelve men ploughed a field containing 16 acres, 3
roods, 35 perche'S. IIow much did each plough ?
61. In a field containing 211 acres, 3 roods. IG perches;
170 acres, 2 rooiis, 23 perches wen> sown with wheat; the re-
mainder of (he field was sown wiih barley ; how much was
town wiih barley ?
62. llonght !)() acres, 3 roo(l<. 17 p Tches of land, for which
I pay 1701/. ; what did I pay lor it per perch ?
66
WEIGHTS AND MEASURES.
MEASUIIK OF CAPACITY.
WUCni'MCATfOX
(<!:•.)
(G-i)
qrs.
bus/t. pk.
ij?r.s\ biish. j)k.
qys.
lush.
7? A
7
G 2
■a 7 a
49
5
2
•>
7
8
23
3
2
qrs. huf^h. pk.
2^9 7 2
()7. Sold to oi:o
DIVISION.
(05)
O-r.;-. biisli. pk.
r/;,-?. bush. jih.
iU;\ll 1::^
ii".^. G bus!
pcCu?
to O.IlOlluM
5S qr?. 4 bu>Ii<'ls. 2 p 'cks ; to aiHiLlHT tO qrs. G bash{>ls ; arid
to aiiothcr i)8
ki all ?
burl)-.
o \K
ckj^ : liow much did 1 Bell
(18. Lent a pt^rsoii -10 qr?.. 2 biuhcls. 1 prck. I have re-
how much docf
1 . •>
1 o , O
peci
coivod from hiiti Wl qr^. I> bushc
be still owo inoV
CO. John has 21 qrs. 3 1)nsh('ls. 2 pecks; but Tom has I^
lini'. p as much ; how nniih has ho ?
70. I received 218 qr.s. G bushels. 3 pecks, and gave away
a sixth part of it ; how much did 1 <.';ive away?
71. What quantity of beer v ill bo c
onf-uni
ed in a year, at
Hie rate of 2 gallouH, 3 quarts, 1 pint p( r day
72. One cafdv contained T.\ gallons, 3 quarts, 1 pint [ another
37 [gallons, 2 quarts, 3 gills ; how much more did the one coi>-
tain than the other ?
73. Nine fitdds produc d each on an average 2i loads, 4
quarters, 7 bushels, 3 p cks ; how much was the produc(3 of the
uiuo iields?
74. In 27 '/arrels th.ere was on an avorag * la each, 20 gal-
tons, 3 quarts, 1 pint ; hovr much in all V
fs/i. ph.
5 2
8
7 2
to o.notlHM
did 1 sell
I liavc re-
much docf
Dm lias H
a year, at
f • another
ie one coii-
21- loiids, 4
■ducy of the
c-V, 20 gal-
i
WEIGHTS AND MEASURES.
TIME.
M
ADDITIOX.
(75)
(7G)
>/;•*.
U'/i-."?.
dt/f:.
7/rs.
whs.
dys.
dys.
Iirs.
mi7t
21
fi
3
27
110
4
'd')
17
c
12
Ifi
5
4:\
12
4
24
18
14
41
24
4
7t
43
(1
52
12
5
32
la
G
27
18
.')
C4
13
110
SUIITKACTIOX.
(77)
(78)
t/r.s'.
irhs.
Jt,'S.
V^-'. tvhs.
dys.
di/s.
hrs.
m/«
43
4
2
:i2 3
4
47
12
10
24
«
5
IG 7
6
17
20
40
18 49
4
70, The bricklayers wore enj;a,ired about a house 23 weeks,
4 days, and S hours ; the ciirpentcrs, 14 weeks, G "days, and
II hours ; Ihe p;iir.toi'3. 12 wook?. 5 days, 7 hours, and 34
minutes ; the upholsterer. 5 weeks. 10 hours, and 42 minutes ;
how lonjT were those dilfereat workmen en,'>:a(ired about the
'.10 use ?
SO. Two vci-sels sailed for America ; one of them was 9
weeks, G days, aiid 11 hours on the voyage ; the other got to
America in 7 wee!;s, 5 days, and 10 hours ; how much les8
!':ne did the cue go in than the other?
PI. I can go to !'„ certain town by the railvvuy in 9 hours,
2.") minutes, and 30 s^ccosids ; it wouKl take me, at least, five
times as long to go by the st:vge coach ; how long would the
coach take ?
ft2. There are 805 days. 5 hours, 48 nvnutes, 57 seconds.
ill a Kolar year ; how much is there in a twelfth of it?
83. Row many seconds has a )>oy lived, who is 11 years
old?
H
+'> If
ts
WEICniS AND MKASURES.
it
REDUCTION.
AVOIRDUPOIS WKICIIT.
1. In 7 cwt. 2 qr:'. 14 lbs. ; how nuiiiy pdunflH?
2. Ill 3 qrs 13 lbs. 12 oz. ; how luuiiy ounces?
3. How many pou-uls are !hcio in M'J7 (./..?
4. Bought 24 bagp of hops, <\}ch w<ij',}nng - c^^•t. 2 qrs. 13
lbs. j how many pound:; in th.- '.. iiolo ?
5. In 3 cwt. 2 qrs. 11 lbs. of su^/nr : ho\, many parceli?aro
there, cacii coDtaiuiog hd'A' a pouiid ?
TKOY WF.KiUT.
6. In 24 lb.„ of gold ; how many penny wcif^hts?
7. In 2.1<J<:> gTaii;^ of gold dust; how r.iuny ounces
8. In a silver siiuff-box weif»hin;' 10 oz. lH dwt. ; how
grams
many
0, How many silver tablo spoons, oacM wApJunn; 4 oz. 16
dwt., can b« mud*.! out oi' 2 Iba. 8 oz. 13 dwt, ol" silver?
la
xdvo
What quantity of gold will it r(Hjuir(» to make
gold ornaments, each weighing i oz. IS dwt. 12 gr. ?
II. A gentleman sent a silver tanl^tinl (o a Hilversmith,
and ordered him to makfi it into spoons, caeh to weigh 2 oz.
12 dwt. ; how many spoons did he made, the tankard weigh-
ing 4 lbs. 7 oz. ?
12. In 4 lbs.
ArOTnECARIKS WKIGIIT.
8 OZ. 4 drams, 2 scr. ; liow many grains?
13. In 2487 grains, how many ounces?
14. In 7 ounces, 5 drams, 3 scruples ; how innny Rcmplrs?
15. A patient is required to take daily ' "lams, 2 scruples
of bark : how long will 7 lbs. of b»ark i;
'lu?
t. 2 qrs. 13
9
cea?
how many
\rf 4 oz. 16
.ver?
[iko twelvo
K ?
ilvrrpmitli,
•('i«;h 2 oz.
lid weigh-
•iiins?
2 ecruplcs
WEIGHTS AN'D MEASURES. — REDUCTION.
69
1,0X0 MlOASrUK.
1(). Ill 7G miles, (i fiirlong-i ; how rn;iny perches?
17. In '179(>8 iucbes ; how miiiiy yards?
18. From Dublin to Livorpo'jl is about 38 leagues ; how
;;i,nv vurds is it?
10. From Diiblta to Cork is aboii^. 130 miles; how ol'lon
iT I 's a co.ieh-wli'U'l turn ^^)Ui!d b(;i,wetMi the two places, tlic
■ ';\3iiiuferoiice of tli ; wheel bSuv^ 12 feet?
L'O. Frorii Diihliii to Belfast is iil)0!it 90 miles ; how often
■<()•:« a coach -whe^'l invn round between the two places, tbo
ij.caaifereuce of the wheel being 12 feet?
CLOTH MKASUIi;].
2!. In 'lib yar;].-!, liow m-iny nails?
2.''. In ■178*] nails, how manv yards?
2:5 From a ]);ec.: of !i;i;;!i co:it;^in;ng 2 ! En.alish ells, hovf
.'ijiiy Tshirls can be mile. e,ich nii} lirin,^ 3,] yariKi ?
'il. Hiiw many .^nits m\j be male from 2(5 yds. 2 qrs. each
»,i'( roaUining .3,] y.irils?
Mia.-riJK or ("M, i'Acrrv.
2'). It;. 24 gallons, 2 fin.ii-L--, 1 pint : iiow many pints?
2'!. In 4;»;-7 pints; how nuuiy f!:t{!!)ns?
27. In 2t lo;i(l-i, G bn.^hcls, ;> j^ecks ; how many pecks?
2i How many bushels are tliere in 179G pecks?
2!), In a lK;]j!'/".id of wine contaiuliig 'j3 gallon-!, bow many
jiilc. are tiiere ?
TIME.
30. In (i weeks, 3 d'lys, 11 hodrs ; how many hours are
^acre ?
31. Jn 74G07 minuses: how many days?
;»2. Hi- nanr \ni!;utes h.is a boy lived, who is 10 ycar.s
And C \ L-ks old?
3V A clock otrikes I5;i time?, during the day j how often
iior* It htr '.ke ill G years ?
I,
-T' ^.:«..
..:m^M^
'*
10
niACTlCE.
PracJlce, is an easy mothocl of app]yin<]f the rule^
f>f Arithmetic to que^jtious which occur ia trade ami
business.
All Aliquot Part of a miinl)er is an e^iad part ;
lu'uce, if a niiniljcr ))0 divincii by an aliquot part, tho
CiMutient will be an integral nuiuber.
TABI.K OF ALIQUOT PARTS.
l'artriot'lirl:Part8ori:ii Parts of [Parts of liPartsof u
Year.
CTS.
GO =r
I'M I
t>^>j == 3
25 = h
20 = -»
it
lOl i
l^V == 8
^i — 1 8
s. il. I Shil]in<;.l V'^^' Month
7} 10 ;= ^ pence. j (> = ^ jf^«//'S.
I
•2 ()'
15 -
5
i .»
.1
4 0=3 i I 3
p, 4 1 I o
2 0=^
18='
1 '.>
1,2 = i 7.} = \
•f^.!
mn. I 3 =
— VI
KxAMPT.E. — What is the cost of 37G yards of cloth at $1.75
=1| dollars pnr yard?
At 1 dollar per yard it won'd oost .... S^JO 00
at 50 ecu's. ~ $.\ per yard, it womM Cf)?t . . 188 00
at 25 cents, = $,^ per yard, it would cofit . . 94 O'.i
Total cost . . . $C58 00
ITenco at $1.75, = $U dollars, :)7(; yards will cost $058,
1. What is tho cost of lOG yards of cotton at 9 pence, =
i| Bldlling, per yard?
2. What is tho cost of 425 yards of tape at Hd. (=^.<f.)
per yard?
3. What is the cost of 475 yards of tape at 1]^/. p?r yard?
4. V/kit is the cost of 35 i yards of cord at l\iL per yard*
the rule?}
trade and
ad part ;
part, tUo
i r
Parts of
u
Month
.
days.
15 ^
I
10 ==
i
7-} =
\
6 =
1
s
5 =
B
o ___
1
>th at $ I
.75
$?JC>
00
188
0(1
94
oa
$G58
00
cost $f
.58.
9 pence
1 — '
PRACTICE,
71
pir yn.rd?
. per yard*
r>. At 12,] cnnt;-?, = $g per yard, what will be the cost of
47')G vai'ds of Ij1(?<ic!um1 shh"tin>jj?
C. All a,<;ricultnrist sold VJilnvf. of hemp at $7.50 per
liundrc'dncight. Wliat did it coiiio to?
7. At 2.S'. <v/. = Xj per p;ui\ whut will ho the cost of 375-4
\u\\vs of gloves?
8. If wheat is selling at os. Gt/. per bu'^hcl, what will be tho
•jost of 5321) bui-hels?
W If bro.idcloih cootr. XI 75. a yard, what will be the cost
of 135 yards?
10. A fjiniier bourjht ][lo aci'os of land at $10.87;^ per
n^*:'i' ; what did it cj.^L hiirj ?
11. What will b'j th<i cost of 10 poiuid^ of so;\p, if 1 pound
costs Gij cents?
12. If a yard of twisted coi->l co:^ts 2| cent.s, what will be
(lie cost of 140 yards ?
i;;. If one bushel of apples costa ('^'2\ cents, what wdll bo
the cost of 870 bushels?
11. How much wh'Mt would a field containing 17^ acrob
produce, allowing each ajr.j to [n'odiice '.'MOi/ Aj>.?
15. If one yard of oxIra-superJiae ' l>th costs $9.50, wuat
Vv'ili b>.» the co^t of <SJ.\ yards?
K;. Wli.'.t will bo (he cost of ISIS yards of Ihien carabrio
ai 87 A cents a yard '■
i7. If one yard of broadcloth co t $ I.ST.^r. = $1^, what
will be the cost of G'JG vards?
18. If the price of one yard of cloth Is 81.75, what will
1)0 the cost of 28.] yards?
19. If one quart of oil costs 14\ cents, what will be the
cost of l/i//c/. 2,if<//. 3y/s. ?
20. What will bn the cost of 3'jO bushels of potatoes at
:;..•. {\il. = iJ.Us. per bushel ?
21. What will bo the cost of 1000 quills, If eyery 5 quilla
cn;-t ].', cents?
2:i. If lin'^-> cost.s 25. Qd. - 2.V?. ayanl, what will be tha
CO 4 of l)CO • .ds?
<»
i
if.''
\l ^
72
tv
I
VXWE AND TUET.
Giu)33 Wi;i(;nr iin-aiis llie \v(Mi;'lit botli of .'i;oo.(H
nnd i)iickai4X', whcllier these packuges be biirrc^ls.
(joxes, or .^ack .
Tare is a!i fiilowancc maJc to piircliasers fur iki-
weight ot the })ai'kage.
TiiCT is nil aUowancc of 4 lbs. on every 104 llv^
of gouJs, for waste, or Vr i of the whole.
Ci.OFF is an allowance of 2 Ib;^?. on every '^ ewf.
m-ulo to tho.se who retail gooils for tiirnii)g- the .sealoK.
r^urriJ'": Is what remalus after part of the a]h)ua.neo
UJ taken from the i>Toss.
Case I. - Whc.i -iv. aflowancr h m'file for the Tare
per barrt'l , box. or sack.
Wliat is Ihn not w-i;';l)t of •! libds. of siicct^.r. cneli •vvoighiiu;
locwt. ',:>qyr>. 1 libs. ; tli(j turo bciiig Iqr. lOlbs. pu ■ hog^ht'iid '
Rule with Kkamti^k. — Multiply tlio weight of each Ii0[;s-
hotul by 4. to liml t!it> ijji-o^'s \vci;;hL
of tlu3 \vh()b\ fi-'icwl. 2qr3. ; then ctrf. cpr,. Ihs. (jr. //;,v.
rrniltiply llii' lure oa each hopj:-lit"a;l, IJJ J li 1 JO
]qr. 101 bs. by tlio niimbor of iilids. 4, 4 ■]
find yon fiml lli'? i:».rc lipon lliu 1
lilids. to bt! If.'wt. i(u-. 12!l)s. : plnco 55 2 1 1 U
tliia under llio <ir()..8 of th(> J hiuls., 1 1 12
55c\vt. 2 qis- . t'.nd sul>lract. Tbc
rcmaindor. 51cut. Oqr. l-lbs., is the 51 IG
net weight.
1. What ip the net weight of 9 chests of lea, each wcighin;;{
5cwt. 2qrs. lOlbs. ; tare 'Slbo. per cheHt?
2. What is the net v it o'' (! chests of tea, each weighin.';
Icwt. 3qrs. 91!>s. : tare iH\Uyi. j. r clu'st?
3. What is the net weifclit of 7 hhds. of sugar, \v( 'ghir g
6cwt. 3qrs. lilb.s. gro.s? : tare 121b^ per hhd.T?
I' . p
1m' I lie
I ' I
7 W
1 • .. I. ,)•
1.
TAr.E AM» lUKT.
CaS3 II.— ^r/«.',7 the tare . au iniic'i jtcr Cwt.
The gross vvoij^hl of a lo! of Miiriir is ITHcn-t. [-?qr8. ITlbs. ;
tiuo IGlbs. per cwt. What is Ihc net \voi{j;lit?
Rl'LK with EMAMPr.K. -Divide lb.
cwt. qrs. Ib.i,
the Ai'O.'- w«'i(;lit, 17;!c\vt. '.)riv>. 17 IK™;.) 173 3 17
Dm., l>y llio aliquot part of ;i (Mvt
■:•■' V .....J. .v.. 1 ... », X..,..., ,j ,
itiiis. 1 llbfj. is Iho ,'j of a cwt. ; dividu " i' 21 2
8 >
U'Miii 21 bs. i» the i of Mlbn.
(l;vido by 1 ; add tlio two quotients
tu.'vlhor. and 2^(^wt. '.Uiv. UUh. ai\)
ol)!.iiined ; lot thi^^ bo taken from the
(t
26
11
1 3 9
IJi) 8
;^ri)SH weight. 17;M'iivt. Ilqrrn 17 lbs..
;id liOcwt. Oqr. (Jib;-, aro obfainod,
V. iiiuh i.s tho M' t W(;i,::;lit. Tho reni.i!n(i( rs have not been
ijtirndod to in this quostion. as they arc not ;i.:ci.'.s.sary in Ox'do/
10 understand it.
1. Wliat is tbo nnt w(Mj:^lit of S hhd.s. of tol;at:eo. each 3cwt
'2'|i>. gross; tare 18!b3. per cwt.
;'i. The g•^o.^s weight of GO kerrr, of butter is 202cwt. 2qra
Ii^Hh. ; tare lolbs. per cwt. What is the net weight?
Casi: III. — When mi aUuii'nuce is made both fur
Tare a/ul Tret.
V/hat is the net weight of Icwl. 2qrs. lilbc- gross; tare li
I' '. [» M* cwt ; tret as allowed?
ilvi.r. wii'ir Ex.\MPM<;.— Find tho tare
I he last.
and subiract it from tho
cwt. qrff. lbs.
4 2 14 gro33
2 8 tare
s called, by 2ii (2i» being tho fourth of 2())I~ (i.suttla
•s: divide ih<! remainder, or suitle. as
101) for the Iret ; this, when subtracted
ti'iiu (Ij'j suLtle, leaves the net weight
>[iMre(
1.
t>
17 tret
17 net
;h weighing | r.. What is the net weight of Ohhds. of tonacco, wclghln'g
."> ;. 2qrs. 12lbs. each ; tare di'Abi. pir hhd. ; tret as usual?
7, \Vh it is the net weight of (5 chests of tea. each w(Mghing
r.- 1, ."(jrs. ;>lbs, ; tare 18lbs. per chedt; tret as allowed?
vr, wc'ghui; | H. 2t barrels of ric 5 weigh f)7cwt. 2r)rs. KSlbs. gross; tar*
{'• 121!>5. per barrel ; tret as usual. Wliat is the net woigUtt
, I
vt.
n
X'1
•ii. i
u
TAUE ANH TUr.T.
Cask IV. — ll'/un Tit re, Tr/t,anil Cloff art i^i-ovul.
What is fhf n "t '.vo;;;!it f)f '1 cwt. 2 nv. 11 Dm. i;ro.^f«, li»r«
llUw. pel' ova. ; Lii't iij^ .iliiiwil ; cloll' us allowfil?
i.xvv and tlic lr< I Iro-n tin* ;,'r(if<s us
bi'ToH! : (livitlf ih'i r.'maindfM' or
ButMo by liMSiIti'"* l)<'in;j: t!i" li.ilf
of II cut. oi- :; ;i; \<)s.) lliis Ixdn;^
Fubtraclcd, 1'M\' s tli - !"'l \V( ijiiit.
Th'! clod' :u.;y •.'.'••o '>..' (il>l;ii!M'«l !»/
multiplyiu.u" '!'" ^"^ I by Hkj hit
fiulllo bv L'. uiid -liNid- l;v ;{. re-
coiviiiii; l!)'; mioiititt pounds: —
li h tine
2'i) 1 «i
IV livt
h;t<);i ;i iTNuitic
12 <don'
:j m i"> iwt
0. VriiiTl I-^ tlr' p. d W(M;rht of S blid;-', ofsiii^ar, cwch woljjh-
ing (i cwt. 8 qi'rf. 1 { lb;s. ; tare J2 Ib^i. per cwl. ; tret and cb)l(
tui usual ?
10. Wliat i-; Ihe net W(;.i>;ht of 8 lihdH. of tabaooo, (<j\(di
8 owt. 2 (jrs. gross ; tare 18 lbs. j)er cwt. ; Irct and cloU' ius
aUowcd 'i
11. 'i\w Ljro-'s w« i,u;ht of 50 casks of iciMcr is 202c\sl. 'j
qr.=?. 12 lb-!. : \-m\' ].> li).*. per cwt. ; trel and ebtll' as uHowcd.
What is file ncl weight?
12. What is \\i<) net Weight of 21 lii)d.s. Wrli^liin^i", ^rosM,
il cwt. 2 qrs. IS lb.-'-. ; tare 2 qrs. 18 lbs. per idul. ; Irel a,>i
ii.^ual ?
13. What is the not wei;rht of \9 chesLs of [>'i\. em. !i
weigbinj,^ 2 evt. Id lbs.; tare 11 I.)-'-, per cli«ui,; Iril .ib
allowed?
U. Wiiit i^ \h" value of the n^t wei-ht of :; hhds, rd' \.n.
bacco. each weii^lsbig 4 cwt. 2 <|rs. 12 lbs., gros.^, at JCl lOt.
Cd. per cwt.. alle\'. in,!*- 7 lbs. per cwt. for tare ; tret a.s u.-ual.
and clotl' 2 ibs. per hhd. ?
1'). What is M.]..' net v,'Mj:^h+ of 9 hhds. of .«n;.';ar, rach wiMg))-
fug 7 nwt. 2 r^ri. !3 lbs. ; tare 12 lb.-, per cwt. ; trot and clulf
ftb usual ;
A n
work p(
(Iclivert
r.ecal Sil
r doz. Fl
;i doz. Til
1 <loz. M(
lionnycas
Mrs. W
'» lbs. c.xf
VI ibs. bri
.'• 11 »s. Mo
1 barrel <
k ll)s. liic
U*,\i. Jo I
1 Dre.':
1 blac
(! Nccl
1 Hat
('> pair;
1' pair.^
75
f
■I liuc
i
: clolV
") not
11(1 Cl'itf
O. ('l\cll
c.w I . '1
loWt'il,
!rrt as
£7 lOv.
lul clulf
BILL OF PAnnaA
A r»Ill is ii wi'ilttMi Mcconur of (ro()(1s' piirclinsod or
\\i)vk p('i-iurin(.-(l A r>ill of I'nn.Tls is that which is
(hilivci'od with the '^*)oiU at the time of i)iinjhnsc.
IJOOKSKM.FIi's niiJ,.
Toronto, rcbruary 21st, ISOO.
f.ocul Superititondont of Schoo]":;,
Jhiught of Tl(i!;KUT MoPiiAir-,
!■ <lo/. First Aritluiietics. at 87,]r. per doz. - $1 .IT.jr
:> iloz. Third Hook of L('r'SoaH,'ut ijl.i'O per doz. - i AO"
1 <lo/. Mo)-s<!'s (Joosrnphy f) 87»]
]invl, IV llij.>h School Aril'liinotic - . - - 1 12,t
ilwai))casllc'"8 Alii'thra, ;j vols. • - - -a o7^
GROCEUS BJIJ,.
Hamilton-, March U't, IPCO.
Mr«. AVji.liambox,
BOVJ^IU of Sm1T]{ & JONKH.
Ti lb<i. cxtru-fino Youn,'; Hyson at G2^r. per lb.
VI Hts. bri^lit Muscovado Suf,^iu*, at lUc*. -
U lbs. Nfocha CoH't'C at 'l~)c. - - - -
1 harrol cxtra-^nfMiline laniily Flour
k Hks. Rico, at 12.U. per lb. '- - - -
CLOTTTIKr's lUIJ,.
London, C. W., March 3rd, 1800.
U'.M. Johnson. E«q.,
Bongh! (f Thoi'.nton &, Son.
1 Dress Coat $12 r)0
1 black s;\tin V^'st 3 To
(5 Neck-Ties ut 75c. cuch - - - - 4 .50
1 Hat 5 00
(! pairs woolen Socks, at OO^*. - - - 3 00
1' pairs Gloves, at 87^c. - - - - 1 75
f
I
ti
$3 ]?.^
1 20
M
1 t>r>
,''{
7 .S7.i
h
1 00
76
SIMPI.i: PROFOUTION.
When we have three iinin'Dors given, this rula
teaches how to find a fburlli iiunihrr, which niav
have the same proportion to the third iiuiiil^er, thii^
the second has to tlio first.
I'm
Thus, if the thrco given nrmbcrt^f be 1. 2, 'A. it is rcqiiin^d
lo lind a fourth nunibcr \\iiich will have tiie Hiinic proporlion
tt> 8 that the ^ has to 1 : now. Mie 2 is douhle the 1 ; there-
love, the required iiunilier must be double of the o, ihut h
('). To express ])roportiou iho numbers are put down thus,
I : 2 : : S : G, and are read thus. 1 in to 2 as U is to 0.
Cape I. — To find out a fourth proporlional to three given
jntnibers.
Find a fourth proportional to the numbers 4, 8, G.
RuLK wiTJL KxAMi'rK.— I'laco them thus. 4:8 : : G
ni'.d multiply "fae secoiul and thii'd numbers G
!of,'etlier. and divide by llie lir.-t ; the quotient ^j 4^
i.^ 12. which bears the same proportion to G
'Ju\t 8 doe? to 4.-
To 3, G, 12. find a fourlh proport'oual.
To (). 8. 3, find a fourth proportional
12
. 24.
.4.
To 8. 0, 8, find a fourth ptopoiiional IG.
To G. 12. 4. find a fourtli proDortional 8.
To 10. 150. G8, find a fourth proportional. . . 1020.
. 10.
. (18,
Find a fourth p'roportional to 1020. (JS, loO,
Find a fourth pr(iporiionul to loO, 10. 1020,
Find a fourth proportional to G8, 1020, 10 l.OO.
Find a fourth proportional to tlie following numbers :
.'ins.
To 2 tons. 17 tons, and 25/ 212/. 10.?.
To 10 lb.. ir>0 lb., and '>s 75.v.
To 9 yds., 3G yds . and 18.v 72.9.
To 5 lb., 1 lb.', and lo.v :U.
To 4 yds., 18 yds., and 25 95.
To 1 cwt., 215 cwt., and 50.s 10750.<j,
'10 5 toup, 50 tuns, and 27/ 270/.
].
iv'res
')
I.ii' OU
*> T
}''.tds
.1,
enght
r>. I
I?. v./.
•l
»1
PijrrLF. rno PORTION.
i 1
s rulo
I may
r, i\vdt
)pi)i'lioP
; there-
, that b
\\i\ thus,
CC EiVCil
G.
G
24.
4.
16.
8.
020.
10.
(;8,
150.
bera :
10.-f.
75.-.
72.9.
:'>.s.
1)5.
)7r)0.'!.
270/.
RuLK. — 1. Talce from the question that torm which is of
tVr pame nature as the an^.-wer will be, and inaice it th(3 third
lerm of the proportional.
2. If from th(* nature of the qiier.tion the answer will be
greater than this third term, select the greatei' of tlie two
remaining terms for the second lerm of the proportional —
itherwisc, take the less; and the remaining term will lu-
'ho first.
0. Rcdnco the first and srcond terms to the aamc denomi-
1; ilion if necessary.
1. Find a fourth proportional by muliiplying the second
>nd third terms together and dividing by the first. Thy
^Diswer will tlu'U be in t!ie name name as the third term.
ExAMPi-H. — If 6 men can perform a work in 80 days, in
v.liat time ought i;> men to p'.rrurm the same work?
The question has n Terence to thne, select therefore th"
t'nm term from the qne;-tion for the third in the proportiena).
Then consider whether J:» men will require more or less tim<i
lo do the work {\v\\\ (> men. Of course the more iiifu, tht;
',',<<? time ; tlien^fore as the answer will be less than the third
: rm. phice thti (i in the secoiid phice and the remaining term
1.'-! in the fir^t.
The stalement will bo l:} : n : : 30. and the operation
t\ill be I'.O X -:- i:j ~ ^\)\y dnys, tlie answer.
KXEUOISKS.
1. If acres of land sell for $2C0.G2.i, what should 5
tvn'cs bring at the same rale ?
2. If 1,5 tons be hauled 40 miles for a given sum, how
lar ouij-ht 3 tons to be hauled for the same sum?
\). How much cloth may be bou;2,ht for $73.75, when 4.25
v.'uds of the same kind cost $12.75 ?
•1. If 7 masons can build a house in 28 davs, in what time
ought 17 masons to build the house?
5. If .') yards of silk cost $0.25. what should be paid for
1? ijd. 3 .7/-, of silk, at the same rate ?
78
SIMI'LE I'KOrORTION.
6. AUov/ing 4 horsrs to con?ume lobii. Zpk. of outs in a
week, bow much would 9 hoiacs require for a week?
7. If tlic trn.nsportution of lOrwY. 100 miles cost $2/),
wl-.at would bo paid for the conveyauce of oZcwt. 2qr. tlio
suDie
aiice
8. If 7 men can do a certain work iti § of a dny, u\
what time ou|;bt 9 men to do the same work ?
\K If a person, by travelling 10 hours a day, perform a
journey iu ol days ; iu how many days ought he to per-
lorni iho same journey, if he travel Ki hours a day ?
1 0, If 10 head of eatrle require 20.'?. 2Z?. of papfure ground
for a summer, how many acres ought 25 head to have, for <h«
liaine timo V
tl. A cistern is filled with water, by 2 piprs, in 3//. 'li^m. ,
ia what time would it be hlkd by 5 pipes of like size ?
1'2. A sum of money having been equally divided Hmop*;
Tv) men. each man n'celved $'};}. If the number of men hiid
boeu oO, what v.'ould have been tlie share of each?
13. Allowing ^:,A. ?.^P. to prodsice iO^lbn. 'Ink. of wheat,
bow many bushels would be raised from a tield containing 4\)
acr<-'S, at the same rate ?
14. If 25 packs, each measuring Mit., wili conbiin ;< givrn
qt:a!itity of corn ; hovr many !^acki', each muaiiuring ulbu.
will contain the same quanlitv?
15. A post, standing in a siream. has I of its length in
the earth, | in the water, iuid 5 feet above the water ;
what is thL' length of the post?
Analysis. \ -\- §
Is; and 1
J 3
n
The post has therefore ^-. of its length above the surface
«f tlie water; ^\ of its length is then 5 feet ; -j'_^ of it is \
5 feet, and the whole length ia
2t.
' ->■ to
AvaI
1 5
'i of 5 feet = y =. 37^ feet.
The proportio7i in the qu.'^stion is, the part f-^ above tho
water is to a unity as tlie length 5 //. of the part above
lt;e water is to tho entire Icn^ih.
2">.
uav.s.
SIMPLE rr.oroKTiojT,
T9
outs ill a
'I
jost $25,
a dny, irt
perform a
le to per-
r?
re p;ronn(i
,vo, for Oi«
size ?
led uniop*
■)f men iu-'l
:. of wheat,
utaiiiing .Mi
lain a ci^'f'*
ts lengtli in
= 15'
■ tbe surfiicft
V of it i? ^
1 ;>
_2j above the
e part above
It?, A farm'^r pold V of li*s bind to A, i of it to B, and the
li'.maindiT, which was 100 acres, to C. llow much laud did
the farmer oxra ?
17. In a cortalu scliool, 4 of the pupils ^tndy Arithmetic,
I of them study Lanj^'uixgcs, and tho remaiuiuf^ 3G are em-
|t!'\ved on various other subjects. Required the number ia
ihe scliool.
18. A ppr?-on failini( in bu?incP3 ov/cs $5000. and is able
t> pay but $-000. ILow much can be pay per dollar to bid
[or.s
ID. A traveller bavino: rff^ne
'>ib.-> m:>-
on tii.^ journey,
ii'nis lh.it [i of it r:'main?s to Ire travelled. What was tho
1 ■:)(,' Hi of his journey?
•Jl'>. A gt-ntloman who ov.-ned ^ of a manj.i factory, sold 4 of
i his wbave for $3000. Whai was ihe ei-iUmated value of tba
iiohj establlshnieiit
••>!
How ma^y miles mr.st a person w^alk in 5.] days, to
lyconii^lii-h a iourn'-'V
vlav
f r,n;
/.-> \n\U
at
^uniQ rate, in 15
'I'l. A bankrupt owe.'*) ST)?. 19, TT). a-i'l Iiup propr-rty amount-
in;; to $2;>00. la an equitable (ll.'^i;-ii)ution. of his property,
much will a creditor r
..- <^ . i. t K.,
w!iu;-e elaiui U $100
2-b A borrowed of B S500. v,i;;cb he kept 3.} years. On a
Fulisequcnt occasion A leii'ln H '.?;]75 ; hf»vv io!!;: o!ir;-ljt B to
'■»■ CO tills latt'jr sum iu return I'or the acuoinmjdatiun be had
.tVi.rded A?
2t. Ailowinj^: a man to do a certain work in 3 days, and a
) -v to do it in 5 days ; iti \vhat time onf;lit the two to,a:et.her
,u lio the v.'ork ?
AvALYSis, — Tiie man could du }, and i!;e boy |, of th^j
r.iik in 1 dey ; then both tou-'tie-i' could i]o '.--!-l~-^,. of the
njrk in 1 day; bene il)i'y eoiikl do
the fntire icork iu V <^f ^J- dav.
1 ,5
1 ,j
of u day, and
2'. A can dip; a ditcli in 5 dnvs, B in (1 d;ivs. and C in S
days, Jn wliat time could tbe three togetlur dig the ditch?
2''). Tf AT. Iflrv/'/. of iron 1)0 conveyed 50 miles for $30,
L v.' far could OT. bcwt. Zqr. be conveyed for Ibo same Bum?
U!
SIMI'LE Pi;orORTION\
27. Two ma^nns to;yot,licr build a wall in 10 (lny3. Oiw (T
them could liave Imilt tlio wall liiinbolf ill 15 duvB ; ia what
timo could the otl'er have done it?
28. A iTn-rchaiit bought throe piocos of clolh, each con-
taining '2'n/(l. "Iqr., for S500 ; and Bo!d bQyd. of it at cost.
What did the 50 yards amount to?
2!). If I of + of an acre of land ^.'A\ for $18.18|, whal
would a lot containing iJi. 2R. 13P. bring at that rate ?
30. How many yards of linen which is h yd. wide will W
equivalent to 30^f/. of another kind v.hich is | of u v.ird
wide?
31. ITow many yards of carprting which is j of a yard
wide, will bo ro(j:iired to co\cr a floor that meiusurcs 2f) f •. < l
In length, and 2U feet in brcadlh?
32. A farmer has a ndd 100 poles in length, and 45.2'j
poles in width. He wishes to lay off another Held to con-
tain the same ({uri'iiily of ground, and be 80 pules in li.Miglh :
rhat nuist be iis brea'Ith?
33. The governor of a besieged place ];as provision for 51
^ays, at the ra'.e of lllb. of bread to eacli man ptr day, b-il
(s desirous to prolong the siege to 80 days, in expect ai ion
of succour ; in that cas^, v.hat must the ration (.if bread b<-?
34. A pole (I f(»et liigh throv.s a shadow of 5 feet 8 ineh<s ;
v.hat is f'e height of a spire which throws a shadow of 15(.;
foot?
35. If 51 men can build a house in 00 days; hov\ many
men would it require tu do it in 12 days?
30. A person reaches a crlain place in 18 days ].y walk-
ing 8 hours a day ; what number of days would ho havti
taken had he walked 12 hours a day?
37. If 14 men could make a ditch in 18 days : in v,lii^l
time would 31 ni'-n do it?
88. A pliip was provisioned for a crow of ^10 for 3 months :
how long would these provisions last, if the crew were r<-
duced to 32 men ?
39. If 8 horses can subsist on a certain quantity of 'any
for 2 monlhs ; how long v.ould 12 horses subsist on the ►^am**
quantity?
; in what
2ac1) con-
t at cos!.
18^, Avlial
rate ?
]q will ]»o
3f a yiinl
•cs 25 r. ( I
and 4o.'2'j
(I to con-
u )(Murll! :
ion for 5>1
r dav, It'll
:p(,'Ctaiion
k-cad hr ?
8 iiiclif f-- ;
)\v of i5(.>
10 v\ manv
r"
Itj walk-
he havt-
; in whA
; in on tils' :
were !'<■
y of hr.y
the >^air^
81
COMPOUND PllOPOllTION.
Wbcn in order to find a fourth proportional, sov
cral clrcuiiistaiices require to be considered, it is
called Compound Pruporiion,
If li horses cat 5fi bnsliel.s oi" oats iti IG days 5 how raany
b;ish<ds will l>c required for 20 h<)]y,-:i ]"or 2i days?
Rb'LKwrTir ExA\fiM,K. -Write li^rses 14
flown for thi' tiiird t(!rni that {\.\\< 10
22^
lyt
20
2t
bush.
5(J ;
nuniber whicii i:i of liie .'-ani »
ku.d with the an.-w^'r r. qi,;rod —
[)() 'HLhels. Tin ii take Uvo niun-
Ifirsof thesaine kind --I 1 hornes
and 20 horse:-" — ■^■■'r^ Cv)i.-id"r, ar,
ill Simple Proj):)ri;o;i, v.helin.'r
ii'om the nam re of Ih*} qu'.'S-
'ion, the greater or less is to )-,3
put in the lirsi, or seeond tei-ni.
If 're it isobvions tii.ii the gi eat-
'•r must b' in the see'^nd te-. m. as
liO horses will eut neu'e tliaii 1 t
horses. T;tk') the otlu'-- two ri'sas a. id proceed in the sam^
manner. After all th ; terms i;ave h ' n put down, multiply
the two (irst terms. It and Iti. tojreth'T ; do the same witb
t!je two S(.'Cond terra?, 20 aiul 21. and proceed as iu Simple
I'roportion.
CoN'TKACTioN'. — Let tlie question be the same as In the la^^i
"xample.
4bO
28.S0
2 100
22 n2i;sb(}a20 bus.
221
418
o
After the terras have been properly ar-
r;iaf?;ed. the opi.'ratlon may often be j^rratly in
shortened by using the following method : ^^^ ^ ^4^^ :*tk
Draw a line, and place the lirst~" t*"rms, 14 ^^ X ^^^^ f v
;uid 1(), under it. and the second and third jJi x /0
terms, 20. 24. and 50. above it ; then divide fh ti
any number aljove the lino and any below
hy ?ny number which will divide both without leaving a
82
co.MroL'XD rKorouTiox.
I
>M
r?m;u)iaor. It v. ill ho vsoon tl^at in all qnof-iioiis in Compound
Trf. portion tivro i» oiio term th:U is lil.i! iIk ri'ijitin.-d iui^\\(-r,
ninl tiiisi must bo put in the third piaco. Tin'iitill Mit.'<Hiv.M'l(M'in3
iu'\' ii,rr;jM<4('f! in paii's. iind it, is Iii^^iily l!i:|MM't:int toi^h.-crvr tlmt
cdi'.f'i pair i.< to be eonsiui'red ;\.s e:;t;rely iiudpc/n/rui of cncry
oLher. a-iiil tin rel'ore the uumbi-r of circum.-^luiiees lo bo (?ou.
hidereddoe;-: nut injieaso the dUiicuUy of stating the qneslicMi.
K^;\^f^L^. — If 5 coi-npo^itors In 16 doyp, v.orhin/jj M liour^
n (lav, cati conmose 20 sheets of '?A pai^es eacdi, aO lines to -,\
page, aivJt JO letters to a lin;'; — in how many iU\y^, workinjj
7 bourn a day, can 10 couip'!:.MJ.or> co;r.p()-e Jt) fduM-s of lo
\)d\^c6 in a slieet, GO lined in a pa,j,e, and .'>0 lotlers ia a line?
Here ti'O question refers to dajf ; releet that trnn for tho
'/n7-ii place' ; th.-n compare the f<everal p^'lvs for th<j lirc-t and
3<'C0ud ieruis, thus -10 ui .ai v/ill require /.':.••.)'
t' ihaa 5, therefore 10 ;.- to 5 as in niarir'n 10 : Fi : : Vi
T hoars a df.y will te.ko i'lorc time Vr.xw 1!. 7:11-
10 clieciswill ref|'iire a ^•, '7 /;'."/' I'm-' !lia;i 20, LO : •JO
I;; pages will require less time than :'.\ paj^e:-, 21. : 10
fiO lines will t^>!ve a ^rcaftr ilii\-i thaa eO line;-, 50 : CO
i)\J letLer.t. will take more tiiue thau 10 letter;-. -10 : 50
Ilavinp' plated the qurrtion. iTMiliiply nil the srrii7hl t'Tu'i
fttid the third to.i-t^thi r. and divide by ii-.e pro.luet o!' u\\ tju?
first teriu'^, accordiu;;': to llio l;-'M1' ral rule ; iIk; woi'k M'ill
flaud tin!?, and is eai^ilv pei'.ori.ieil i'V (.■a;ie<dlatiou : -
J 6 X_5 X 14 X -10 X :iJ X CO X "O
" 10'">r7"x'20 X 2 4 X GO X 10
"- IJ2 day;?.
NoTi:. — If any of the pair;? are uut ia Ihe -am" nanu lliey
ma.;t be reJaced.
The teacher is rocou";mcnd''d to make' the pupil siniply .s/a/f*
several of the (Vdlowiap; questions on t!ie sletr or black-board,
b";'ore troabliui; him v. it!j the operation of tlie inechiinlcai
p'.iri of the work ; and all (he nn(!stions should tirbt b'J uorkcd
o;tt in fuU and then Ijv Canallation.
oniponnd
(I Ulli\\(T,
ivM'ti'i'iim
M'i'vc timt
' of v.svvy
o 1)0 cou-
qiu'sticiu.
II lu):iv3
iiics in !\
I'lS of It)
a u liiK'?
m for tlic
Iii>,t and
5 : : KJ
: U
: 10
: 10
: CO
: 50
)7nl \.'
■ni"i
)!' till
(hfl
wci'k
\vill
(t:.iy:?.
lain J tlicy
mply .s/'a/P
;ick-boiir«l,
nt'chiiniciil
COMPOUND rROrOIlTION.
S3
1. If 15 moil bnilil 37 roods of wall in 27 days, how many
luodK will 74 men build in (k> days?
2. If 8 mon for 5 days' work get $10 ; bow nmcli ought 32
uu:u to get for 25 days' work ?
:i. If 4 men can mov/ 20 acres of graM in 7 davf^ ; how
iiiiUiy acrc« can 12 men mow in 28 days?
I. If 6 tailors can make 10 puil.s of clutheR In 4 days ; liow
tr-my suits can 20 make in 7 days?
r>. A wall, 2vS foot in hei,nht. was built in If) dayn by C8
!);• n ; bow many mea workinr;^ at the i^amo ruLe could build d
v,a!i 32 I'eet liii^h in 8 davK?
i.'k If 12 herpes in 5 davs dra'.V il ions of f- tones from a
ii'Miry : how mauv horses wuuld it require to draw 13;i tons
i;, 18 davs?
T, A g-arrison of L'OO men h.as provisions for 12 we^ks, at
I'.i- rate o!" 20 0111100? per day to each ii'.an ; liow masiy men
w ili tlie same provlsio'.u-; maintalij. ivv 20 week^-, uHowiug each
,■;;;;;: only 8 OLinces per day?
•••v If 50 mon can do a p'^ ci of woik in 100 day??, w(»rkin£»
^ liours per day ; in '.vhat lime -.vill 120 meji do ii, working (i
l.wurs pur day t
;•. What is (lie intorcHt of $!:>22, for 2^1 yearn, at U poi
c •'.•'{. pir annum?
!i). If $;;00 iii^dA $]?0 la IS ii^nnth;^ ; how mncli will $103
:,' wa 'n\ 12 month i?
11. !{' two men can di;^ 125 rods of dIi.oh in 75 days, in ho.NT
•I sny days can 18 dig 213 rods?
12. If 400 soldier:-? cousnmo 5 b^Tels of flonr in 12 davs,
].^'^' n/any soldiers will Gonoume 15 barrels in 2 dayt;?
13. If a person can travel 120 miles in 12 days of 8 honra,
' M'h, how far will ho be able to tra\el in J5 davs of 10
l;''.ivB each?
11. If a pa^'tnre of 10 acres will ford (5 horsos for 4 months
i. -^s many acres will li.cd 12 horsey for 9 mcntliB?
>i.
m
•i
Ii
84
COMPOUND nioroRTioy.
15. If GO l)iisli('ls of oats will feed 21 borscB 40 days, how
long will 'JiO bushels lecd '18 horses?
16. If 82 men built a wall :JG feet lon^, 8 feet hi}?h, and 4
feet tliick, in 1 days, in what liino will 48 men build a wnll
Biii leet long, G loot high, and 3 IVot wide ?
17. If the freight of 80 tierces of Kugar, each weighing ?,),
hundred weight, lor l.lO miles, cost S«l. what must bo paiil
for the freight of oO hogsheads of sugar, each weighing J J
hundred weight, I'or 50 miles '•
18. A family consisting of G persons ur-nally drink lo.i;
gallons of beer in a week ; how nineli will they drink in J'2..'
weeks, if the number be increas'.d to D ?
10. If 12 tailors in 7 days can linish 14 suits of cloth'-.
hew many tailors in 10 days can finish the clothos of a re,c;i
ment of 41)4 men ?
20. If a garrison of 'M'SO vvn\ eat a certain quantity of
bread in j.*) days, at 24 ounces per daj' to eacli num. lion
many men, at the rate of 14 ounces per day, will eat twice a:>
much in 45 days ?
21. A company of 100 men drank $80 wortli of wine v\
50cts. per bottle ; how many men, at the same rati', will $'if^
worth supply, when wine is worth lir)Cts. per bottle'.'
22. W the wages of IM men for 7 A days, be $110.7C, '.\h:.t
will bo the wages of 20 men for 15-j days?
23. If .1, fool nan travel 204 miles in (i^ day.^ of 12,] houri-
each, in how many days of 10;j hours each will he travel 121'j
miles?
24. 120 men. in '] day? of 12 hours each, can dig a treic- ',
of 30 yards long. 2 leet broad, and 4 feet deep, how m:niy
men would be required to dig a tre.nch 50 yards long, G I'-m j
deep, and U yards broad, in 9 days of 15 hours each ?
25. If 40 men can perform a piece; of work iu 12 days. Low
many men will perform another piece of work three times nt«
largo, iu oue-iil th part of the time ?
26. A person having a journey of 500 miles to perform,
walks 200 miles iu 8 days, walking 12 hours a day ; in how
"f 7 i\
ile"p ;
JHMlIld
•> i
• 11.
V.'iHt'
KH) ill
.1,1
• >u.
\iliat !■
i ■*///.
'.:-r 2
i.;u-r;s(
'^mm
coil roL'N \) rrioi'OUTio n ,
85
s7
lay??, how
<?h, and 4
ild a wull
ighing nj
<t bo paiil
ighing IJ
rliik lo.r.
ik in ]2.:)
if rlolh. *•.
ol" a rogt
lantity of
mail, Ihvs
a I tuic(! a>
I'. \\\\\ $'^^
' i2.\ lKm!>
[ravel 12l*i
if^ a ti'ou'-!.
ilOW TTI'-lliy
onji, (j !'•■< J
acli ?
I dayt=, boNv
eo tiuu'S '.!*>
Lo peiTornr
\j ; in bo>v
Ti' 'My diiy^, walkiuir 10 Iinnr.s a day, will ho couiploto tha
iMiaindcr of tlio Jouriu y ?
:17. If ]()0') moil, b<'si(';;('d in a town, willi prrA'islons for 28
i\\\-^, ill tin; raU; of JS outics a day I'or cai'h man, bo roin-
'oriu'd by (iOO tiicn. 'low niiiny iwici's a day inu.''L (;ac!i maa
if\*; tliat llic nr'.)vi,-!on uw.y hi-' ihcai I'ur 'i'J djiy.s ?
::^. JC a. bar of iron ;'>/'/. lon,i:-. 2.U"//. wide, and li]m. (.hick,
v.: i;;h -I.'; lb.-.; how liiuch will a bar ol" ihc h.uue Qictal weigh
''i;.i !;- l/t. \oi]<;. :):n. widv'. .md 2.]///. thick?
::'). Fifty thousand bricks are to bo romovod a given dis-
'•c'C- in 10 i\;\yA. Twelvo hors;'s can reniovc i ■ jOO in (J days ;
i''\ inw.y hors;;;; can rcniovo the rLMnaludor in I days?
:'0. If " nion, w()rl*in;2: 10 hour8 a d y, . \n plant a fu Id loO
' 'vl.-* bv 210 rod- in ••dass, liuw many men. ^s-orkiiii( 12 liourH
,1 duv. car. idaa .\ litld measuring- lUli rod., by uOO ruda, io
Ulay^?
:*,!. If 2 IS niop, in 5.5 days of 11 hours each, di}^ a trench
"! 7 dotj^rcios of hardness. 2H2i yards loiig;, '6$ wide, and 2^
•l<.'"p ; in liow many days of 9 hours lonj^^ will 21 men di^ a
tr'iich of 1 d(!grccrf of hardneii.s, o37^ yard^j long, f>i| widu.
;tud ;Jr} deep ".
;i2. If 1 men eat i}\ pound:- of bread in 2 weeks, how many
j.^'uads will It) men eat in 7 weeks?
:'.;;. If 5 o.\en reqnlro an aero of p:raJ=a *'<>r 9 days, hov*
le.any acris will 20 oxtn rociniro for ilOh day :
:'!. If a man travid !()■) miles in ?> days 1 1' li) lionrs each.
i.'cv far miglit ho travel in i'^ days of 1J,\ honr.s each?
:;.",, If tlie eonveyanco of '20nrt. 4Q miles, co?t $ir>.87,|,
\\\::\t Hiionld bo charged lor the eonveyanco of iJOcwt. 'o</r.
iOU mites?
;;i5. if 2 yards of cloth, which Is ]}.i/tl. \\'..\\ coFt $10.25,
\iiiat should bo paid for 13 yards of liko quality, which is
1 '1/(1. wide ?
•■^7. If n000//;,s. of broad will supply a garr' an of TOO men
'or 2 monthri, how long v.ill I'.OOO/i'.v. 8npp!y throe such
(5; u-risouii ?
80
?3V
\t
V A M T I T 1 \ K V n r II T I N ,
0^; rAiiT>;ERSiiip.
Kx vMi'i.K.— Div'ulo $l.")i> tunr'ng ilir-j'j per?ous, A. 1) unci (\
iu ilie pruporLioii ul' 2, ai!<.l o.
ri'opoitional Terms ,* .'i
) ^
Sum of the Tltids.
10
10
.10
AniouTif.
: ir.O :
: l')0 :
: loO ;
2 to A'p nliaro.
'.] to l>"s sliare.
o to U's feliiire.
then l.'O -^ 10=r^ ! ■ h- M 1.- X i^ = A'd bliarc ; 15 X 3 = T/i
share : and ];"> X -"' "- C'b t-iiur.'\
1. A. B, niul (?I. ciit.r into po.rtnor;^hip wiHi a capital <vf
$7500, of wliich A }ui! ii) irlZnuo. 13 put ;:i ^^:!U00. ami C put
in the r('niaiii(h.'r : at tho (r.il of !hy yrar their gain ua?
$oOOO ; what was each oueV; t-hare ?
2. Divide $'_>{() h(nv.(yn three por.=ons in sneli a manner
that their .shar<'s >hiiU be a.s ihe nuinlsers i"^, 4 and J.
8, A and P. };ave a joint ptoek of $1200. of which A o\\ ns
SoCOO, anil h SCOO : th<'y gain in one year $2000 : what i.s
each one'n t-hare of the pi'oli's?
4. A genllenian divided $10000 between In's Fon and
danghter in the prcportiou of IJ to 2. What are their re.-pec-
tive tjharew?
5. A, B. C, and D, have $10000 in trade, each an eqi^al
share ; at the end of a yenr tJieir prolitn amount to Sh'OOO :
>',
llisidiii::
!i sli:iil
I of {hit
\d /enns.
CDUOlllit
is to ii.-
n unci (\
lire.
.irc.
K \) = \V\
capital of
uiiii C put
gain ua?
a manner
:h A o\s \\%
I son nnd
tiir roHpcc-
an '^qral
rARTITlVK PUorOllTlOX, oil PAUTNTRRSIIIP.
87
wliat I*' oacli one's Fharo, nllowlnc^ A to rocoivo $50, iirul I)
$;)0, out of (ho prolitM, lor extra sorviccH ?
»1. A top!.i(()i' lnNjiiradv^l SlTiO'lO to lii.s widow, (lau.t^litfr,
a!<il Fon, in the ])roporlion of ii, o, and 7. What were Lh-jir
r«,-pcctlvi; f.liarc's?
7 Five p' r-ons 1) ivo to s'lare b twoon (iinm an estate of
^jOilOO : A is i.) hiiv' on'j-roniLh, ]> on''M'i^r:iiij. C onn-sixtli.
It o:i"-.,' .■■liiii, and i'] wlial i.> lul't. What ■ 'iU bo llio share of
ui'h?
A FiKTchaiil iMn[)lov. ,] ilirco cl -rlr;-: at tlii aau
o
tvin;^^
uuliy
of SLiUO, $100. and .i^MtO. Atthooiil of t!t.
1) IS)!!!'" Itaidvi'npt. !i>! lias but $(J50 to b • divided |
;iin,»ag them. WliuL will be the portion of cacli .'
0. Tlireo nv;M\^lianl;H loaded a vos^:' 1 wlili llonr : A loadol
r')0 barrels, li 700 barrels, and \j 1000 l)arrel.s . in a storm at
s a it becatn" n(>e!'ssary to throw overboard liO barrel.s.
What was eaeli one's s^iiare of the loss?
10. An insolvent dr^btor owe.s lo A ?1'2')0, to B $100, and to
C .;v]00. lb' is al)K; lo pay :;pl-0 ; what bhuiild each of the
three creditors receive?
11. A man b>qneath(>d liis osfato toliis four pons in the fol-
iowinf^ manner, vi/.: to his fii-.'t S.3U0O, to his !^i'e()iid S b'lOO,
b) Ills third S blOO. to his fwnrlh SIOOO. Bat on seitlinp^ th«
estate, it was Ibaad that after payin<^ the delils and expent-''-:*,
only $12000 remained to be divided: hovr nmeii sliould oaeb
receive ?
12. It is required to divide i^lie number ISO into three parts
ttiiich shall be to one anoiher as \, j, and '\.
13. A widovN' and her two sons rrcelvt; a leoacy of SloOO,
of which th(! widow is to have half, and th' two sons each a
Tjiiarier. But the <ddest son dyin^', the whole is to be divided
in the same proportion between the mother and youngesL .^on.
What will each receive?
14. A person propos(>d to divide $1000 ])etwoon his two
Rons in th(? proportion of i to .',. pi-ovided eitlier of tlvin could
ascertain the amount otlered to him. What would be their
respective shares?
♦ ■
t ,:
.. i
IMAGE EVALUATION
TEST TARGET (MT-3)
//
"^
1.0
I.I
- Ki III
2.2
1^ IIIIIIO
11.25 ■ 1.4
11=
1.6
- 6"
m
^l
7
Hiotographic
Sciences
Corporation
1% WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 872-4503
88
COxMPOUNl) PAIITITIYE PHOPORTION.
When Pai'tnerH in business {.livklc their profits iu
proportion both to the amount of capital employed,
and the thm it in continued iu the business, it ia
called Compound Parlilive Projporlion, or Fellow-
ship with Time,
lluLK. — >rnUip1y each term l)y its time, and tuko the pro'
ducts for tlio pro)\oi'tlonai terms, then work as bofore.
Il\AMPi.K.— A puts $200 into a business for 7 m»nlhs, and
H $300 for monthg. Tiiey gain $100; what is the share
of uach ?
A's amount $200X7 mouths=l 400
B'a amount $;iOOX9 months=2700
Gain.
Sura of the products 4100 : 100 : : 1400=A'8shar»i
And as 4100 : 100 : : 2700=B'a shaiY.
1. Three persona rent a pasture for $20. A puts in 20
«heep for 4 inontlis ; B 30 sheep for 3 montlis ; and C 4'!
•heep for 2 months. How much of the rent should accord-
ingly bo paid by each?
2. Three men hh'O a pasture for $70.20 : A put in 7 horsoa
for 3 months* ; U U horses for 6 months ; and 4 liorscs for
6 months. What part of the rent should each pay?
3. A, B, and 0, contracted to make a road for $5000. A
furnished 30 laborers for 45 days, B 42 laborers for 34 days,
and C 60 hilKircrs for 30 days. What are their respective
Ehares of the $5000 ?
4. A commenced business witli a capital of $10000 ; four
montlis afterwards B entered into partnership with him, and
put in 1600 Imrreli^ of (lour. At the close of the year tlioir
profits were $5100, of wliich B was entitled to $2100. What
was the value of the flour per barrel ?
5. A, B, and (J, In partnership, have made $400. AVhat
are their respc^otivo ^harea of profit, supposing A's capital iu
the businoHH lo liave been $500 for 10 mouths, B's ;i>U00 for
1 year and 3 montha, and C's $000 for 2 years?
89
noN.
arofits iu
L
mployed,
ess, it ia
Fellow-
the pro-
ore.
itnths, and
the share
=A'8 shara
=Jj-a 8hiu>i.
pats in 20
and C 45
lid accord-
in 7 horses
horses for
B5000. A
jr 34 dtiya,
respective
1000 ; four
,h him, and
your their
ILOO. What
00. What
capital iu
"s ;j>yOO lor
MEDIAL PROPORTION, or ALLIGATION,
Medial Proportion is proportion applied to mixing
two or more in^j^rcdients of diflfereut values for a
compound of a given mean value.
Case I. — For Two Ingredients.
Rule. — Take the quantities inversely as the difference*
between their respective rates of value, and the given mean
rate.
Example. — In wliat proportion shall Rye at 37 cents per
bushel be mixed with Oats at 25 cents per bushel, to make a
compound worth 30 cents per bushel ?
The difference between the Rj'^e at 37cts. and 30 =- 7
.". " Oats at 25cts. and 30 = 5
Take these numbers iywersely for the answer — thus, 5 bushela
of Rye, and 7 bushels of Oats.
1. In what proportion must Corn at 40 cents a bushel, and
Oats at 25 cents a bushel, be taken to form a mixture which
Bhall be worth 33 cents a bushel?
2. In what proportion must one kind of Tea at 75 cents a
pound, and another at 90 centb a pound, be taken for a mix-
ture which shall be worth 83 cents a pound ?
3. In what proportion must one kind r.f Coffee, at cent*
a pound, and another at 13 cents a pound, be taken to form a
mixture which shall be worth 12.^ cents per pound?
4. In what proportion must one kind of Wine, at 90 cents
a gallon, and another at 75 cents a gallon, be taken for a
mixture which shall be worth 872 cents per gallon ?
5. A farmer wishps to purchase two different qualities of
land at $20 and $35 per acre. In such proportion that tho
average rate shall l)e $27.50 per acre. In what proportion
must the two kinds be purchased?
C. In what proportion should Hay, at $25 per ton, and
Straw at $12 per ton, be taken to form a mixture which Rball
be worth $17 a tou?
II
mM
to
MEDIAL PROl'ORTIOX, OR ALLIGATION.
I
i i Case II. — For Three or more Ingredients. . ^ <
Rule. — The ratos of tlio several injxredlonts are set one
untler another, witli the mean rate on the left. Link together
each rate wliieh is less than the mean rate witli one tkat is
greater. The dili'erence between cnrJi rate and the 7ncan
rate h set opposite the rate or rates with which it is
connected.
NoTK. — As the combinations are varions, most qiieetions
will he snsceptible of several answers according as the terms
are linked.
Example. — A grocer mixes four kinds of sugar, at 5 centa,
8 cents, 13 cents, and 14 cents, to make a mixture worth 10
cents per lb. What is the proportion of each ? < > --^*-
[lOc]
^V(;. 1.
5->, 4 lbs. at octs.
3 lbs. at Sets.
2 lbs. at 13ct3.
5 lbs. at 14cts.
13^
U
[lOc]
jVo. 2.
5 ] 3 lbs. at Sets.
8 M 4 lbs. at Sets.
5 Urn. at 18c Is.
2 lbs. at Mcts
13 J
14
Ao. 3.
[lOc]
5
8
13
J
[lOo.]
14--^
5— I— I
13lJ
14 •
4 4- 3 = 7 at
4 c
5 cents
^ cents.
3 cents.
7 at 14 cents
5...
54-2
J\o. 4.
4 -f- 3 = 7 at 5 cents.
3 at 8 cents.
6 4- 2 = 7 at 13 cents.
5 at 14 cents.
The work may be proved — thus, take the answers of No. 1.
4 pounde at 5 cents = 20 cents.
< 3 pounds at 8 cents =s 24 cents.
'■■'■ • 2 pounds at 13 cents = 26 cents.
5 pounds at 14 cents = 70 cents. ! :
' 14 pounds
of 10 cents per pound.
for
140 cents is at the rate
5.
MEDIAL rROFORTIOX, OR ALI.TGATION.
91
m
Us, :<
ire set one
i)k togetlu'r
one tkat ih
the mean
vhich it is
t queetions
3 the terms
, at 5 cents,
worth 10
bs. at 5c ts.
bs. at Sets.
I)s. at 18c Is.
D&. at licta
9 of No. 1.
at the rate
1. What proportions of coffee, at 8 eta., 10 cts., and 14 cts,
per pound, must bo mixed together, so that the compound
thai I be worth 12 cents per pound?
2. In what proportion must rye at 37 cents, oats at 23 cents,
inid corn at 32 cents n bushel, be taken for a compound which
thull be worth 31 cents a bushel ?
3. A merchant has teas worth 40 cents, 65 cents, and 75
ct.'its a pound, from which he wishes to make a mixture worth
(;0 cents a pound : what is the smallest quantity of each that
he can take and express the parts by \ hole numbers?
^, A wine merchant mixed brandy 1 1 30 cents pe; gallon,
and wine at $1 a gallon, with water, an I found the compound
to be worth 50 cents per gallon. In whit proportion were the
boverttl ingredients taken, the water being rated at ?
5. A farmer sold a number of colts at $50 each, oxen at
$40, cows at $25, calves at $10, and realized an average
price of $30 per head. What was the smallest number he
could sell of each?
0. A merchan* wishes to mix three kinds of tea, at 90 eta.,
$1, and $1.50 per poutul, so that the mixture shall be worth
$1.25 cents per pound. In what proportion must the diflfereut
kiuds be taken*? ,
7. Wimt is the smallest quantity of water that must be
mixed with wino worth $2.80 and $3 per gallon, to form a
mixture worth $2.()0 a gallon, wheu all the parts are express-
ed by whole numbers ?
8. A farmer has one tract of land worth $15 an acre,
another worth $22 an acre, and another worth $25 an acre.
Ill what proportion must he sell from the several tracts, that
the average price shall be $20 an acre ?
9. A produce merchant wishes to mix rye at 30 cents, oats
at 26 cents, and barley at 60 cents, so as to make a mixture
worth 30 cents per bushel. What quantity of each must he
take?
10. A grocer wishes to mix three kinds of coffee, at 18 cts.,
20 cents, and 25 cents, to form a m'xture worth 22 cents per
pouLd. How much must he take cf each ?
M
M
m
MEDIAL r:^OPOi;TIO\, OR AI.T.TOATION.
Cask III. — ir/yr/? the qvaiitity nf vue of thf
Simp/fs ift ghm,
RcLK. — Fin(] Iho prnportionivl qniinlillcs ns IkTofo, tlK.'n r.j
[heanioiiMt ol' the iiit^rcd'n'iit LIhih roiiiKl is to llic gi\cMj amoiim
of the sjimo ingrodit'iit, ^^o is tho amount of uiiy olbrr ingre-
dient to its required quantity.
ExAMPLK.— What quantity of Ftigar at 12 ctp., 10 rts.. am!
<l els., must bo mixed with 1{) IbiB. at 1 clr-., to make the mix-
ture worth 8 cl8. a pound ?
''■ " 12^• 2
4 — J 2 lbs. at 4 cuiitf, but t]>e given quantity is 2*
pounds, therefore as 2 : 20 : : any other proportional to it*
quantity.
1. A farmer mixes 10 bushels of wheat at 70 cts. per bushel
with rye at 48 cts., corn at oli cts., aiul barley at 30 cis., so thai
a bushel of the composition may be bold for 38 cts. What
quantity of each must he tako ?
2. What quantity of teas at 12j9., lO.v., and Gs., must b«
mixed with 20 pounds, at !.«. u pound, to make the mixtur*
worth 8s. a pound ?
3. How much water must bo mixed with 100 gallons of
rum worth $1.50 per gallon, to reduce its value to $1.25
per gallon?
4. How many poundRof Fugarat 7 cIp. and 11 cts. a pound,
must be mixed with 76 pounds, at 12 cents a pound, bo that
the mixture may be worth 10 cts. a pound ?
6. A farmer mixes 20 buFhelc of rye at 65 cts , with barh-y
at 51 cts., and oats at 30 cts. ; how mucii barley and oats mu'jt
bo mixed with the 20 bunhcds of rye, that tho provender mjy
be worth 41 cts. per bufchel?
6. With 95 gallons of rum at R.*.. T mixed other rum at
Cs. 8fi. per gallon, aiul some water ; then 1 found it stood m«'
in (is. 4t/. per gallon. I demand how much rum and ho^v
much wjiter 1 took ?
oa
',i'
ihf
ire, lh;;n ns
I en a moil n I
ilbtT ingiv-
10 dp., and
ko tln! mix-
untify is 2<
ioiial to iw
per bushel
cts., so thai
cts. Whal
s., must hi
he mixtuK
gallons of
le to $L2u
Is. a pound,
iiid, BO that
wlili barh'V
(1 oalsmuil
,'t'iKkr nijy
er mm tA
it stood m<»
n and ho^v
CONJOTXED PROPOTITIOX.
Conjoiiiod Proportion U a kind of Comp'umtl Pro-
portion in w.iicii llio ratio of one <»f llic anruce-
dents to its consuquont is innl(3 to depend upon
tqaiva/enccs among the terms of Proportion.
Uui.K.— Si't frfn'vtlfnt t<?nns on the left atid ri^bt of tht
8i^M = aiid so rhiil. MriiHol' the kuiii ■ kiiul shall biMin opiiosito
gidcs ill thi: dill'itroul «-Npivss o is ; also s^t the odd tfiin oa
til ' sdt* which is opptisjc tii"? oih -r terms of the sanv Iviud*
Multiply the l«'i'ins o i |.h« (somplett'd side tojfelh'r lui* ml
divid tid, and thone uu the incoinpleie side for a divisor.
Ex.vMiM.K.— If 'A (ju U'ters of cl<dh b^ worth 4 galloiiH of
wine, and i gallons ui wnic be worth 6 lbs. »i t<*a. hnw inauj .
qiiartHrs of cloth will be fipial in value to 12 lbs. of tea?
Arrange the terms thus; cloth '^ qrs. = 4 frafs. wine.
wine 2 ^u/s. = 5 tt^s. tea
t tea llibs. == ihe aikiwer required '
3
Then 3 X 2 X -r?J 18 .^, ^ ^ , .
4 X ii 5 *
KxAMiMiK. — IC 10 lbs. at T^oiidon arc vova ^n f) lb* at
Ain'<tj'rdani. and 4A lbs. at Ainsterdaui ^.o -'»' ''is. at Hni^refl^
and f^S lii-i. at nni;f«'s to 11(5 Hh. at Ij'.'iAh^i how mati^
pounds at Daniziu are equal to 112 \Uf <. /.ondon?
Slated thus— Lotnlon 10 = ^ at Atnst(»rdanii. i
Atn^terdam 15 = ^rt at Hmjifcs. *«»
i;ru;jr<'M 1)8 = lli> at D.i itzic.
I)antzic ••• =• 112 at Ijondo.i.
Then 9 X 4!» x ll»» X 112
10 X 45 X m
12!> 9- 11*3. at Dantzic
1. ir 7 buslieN of* wh<*at be worth as much as H cord.s
of wo<hI. and !) cnrds of wond as uMc'i as 2 tons tif hay;
linvv inafiv bushels uf wheat should be exuhut.ged fur 5
tuna of iiay ?
It
li
M
I!
H
COXJOI>fKD PROPORTION.
2. If .'J barrelw of corn be jfivpn forr 7 biixhfrlfl of whoat. arvj
4 bii.xlu'lM ;)t whoiit lui* 18 of ry»?. jiimI I j of rye for "iO of oais ;
how riiiiij iiiislieb uf oaia would bo an (.'(^uivalent fur 10
barrels of com? " ^ .
. 8. If A can do as much work in ^ve days a^ B can do in
8 days. hihI li as iiiiioti in 4 «lays us C can do in II daysi
in iioA many days could A do the samu that U could do iv
20 dav8 '.'
4. If 10} yards of silTc cost ^loJ."). and $♦! vill pnrchaso
1 yard of bi-oiidcloth, and 4^ yards of tin* cloth hf bancriMl
for 2 ) yanirt of Irisli tin n ; Im)w many yards of iho silk would
b"6 uii iqiiivaknit for 4l> yardn of ihc linen?
6. Allowinjj that in a c Ttaiii factory d g'rla do as much
work in a d;ty as 4 boys, and 8 boys :is much its (i men ;
bo.v niaiy moa would be required to do a:i much work a-<
20 girls'.'
6 Supposing A to oarn as much monoy in 4 months as B
tfarns iii (> months, and li as much in 5 numths a.s C7 in 7
months, and aH much in 10 nionihs as l> in '^ months;
ill wihit iimt* could [) earn the name that A could earu iu 12
muath.s?
7. If ]'l pounds in Cana'la l>e equal to 10 ponnds at Am*
rterdutn. and 100 pounds at Anist rdani be equal to 120 lbs.
at r.u'iis ; hoiV many pounds al Tarib arc equal to 1J>0 pounds
in CaniMla ? k
8. If 1('» horses can draw as much in one day a<» 12 mnto*,
and 42 mules can draw as much as .jo oxen ; now many oxeu
would b required to do the work of 144 horses?
9. If .'jO bu.^htds of wh at b<* f'xchan«^(Ml for 80} bnshtds of
rye. aiid .> bushtds of rye for 4} bushtds «>f c«n*n. and btiT-hela
of corn for 12 bushels H p cks of oifs. and ;{i bushels of outs
be worth $1 ; what is the valu*.> of 100 bushvds of wheat?
1(>. If l^<r.7.» in llamhiirgf m dd^ \etl in Holland, and lefh
In *I "llaiid make 4 in Fraiic<\ and 7 in Franoe mak«' 5 yardi
in Kn4i.«:'d : how many yards lii England arc equivakuti ta
58ar</* ill licimburg? ....
(►5
;/'•
' wlioat. arvj
' 20 of (laiH ;
Uunt I'oi' lU
D can do in
iti II dtiys;
ill pnrcliaso
til Ik wuuld
do asi much
its U limn ;
ich wovk u«
monifis as B
s as in 7
:^ niontliH ;
(i euru iu 12
Hiids at Am-
I tu 110 lbs.
100 puuudd
k
\<* 12 mnlc!*,
maiiy oxeu
', buslK'ls of
il ba>h«d9
tliclK of uats
wUeat?
d. and lr!h
iak»' 5 yardi
|uivaleufr to
PERCENTAGE. Oil PROFIT AND LOSS.
Perccntnsie is :in jillowuncc, at a (TitHin rate, for
every liuiniriMl. P^r Ct'iii. is a (•(MitiJHMjon of the
Jjutin per cenhtm, i\\u\ means by Uie /iimd/ed. The
ratio of Pi'rffrjtii«rf is tin; ratio ol ihi* liih- jmt cent
to 100 ; thus the rjjtio of per CMiiiiine for jk-i* cent
is YoTii ^*'' -^^ whicli is the rale lor eneh iiuit of the
quantity on \vhi(,*j) j)ercenlage is to l)e caUmhited.
NoTK. — To rxprcss tin? ratio of p'Tccntnp' d« cifnally.-dividt
the rut.<* |H'r cviil. hy 100. thus tJM' ratio lor 2ii p»r cent, is
2.5 -J- 100 = 0-5 ; t li.- rate lor 4 {mt ctwil la 4 4- lOU = ^4 ;,
tbo rate lor h por ci.-nl. is .05 — h/0 = .OUo.
Cask I. — To Jitul the Pncvntafse on a oivcu number.
ExAMi'i.K.- (.'lofji which eo<t ^.")0 Ta sold i\t :i prolit of 33f
j^er cent. ; \vhi«t jtmount of profit was niadc ? j
,y f"0 75 X .:5:J] =$l(i.!)H. tin- answer. ' • ''
It if evident ihat this liule Ih notliiiiji: but Sinipl<^ Proportion
for the (pifstioM nray Uv stattHJ thus. If SluU gaui $15*.)^
what »vi!l S-'iOT.") ;::iiu? Hence tin* tb'.lowinjj:
Ylvi.K. — Miiliii)ly the given niiuiher by thi' "itfo of per
etntagc.
l.'A grrocr Uivuijht a hoirsle ad of pujrur for $r>r)*75. and
fold it at a prtriit ol' 1-.^ p r cent. What anu)ui»t of profit
did he uuik«- 'i
2. A nine! suit pnrclinprd a quantify of etoth at |fi.30
p*>r yjUMl. At what pr.ce niUNt he sell the cloth to gaiu U34
Jmt cent, f ■. , • - , . ;. , ,,
3. What would b*» thf annuat freiuium of i»?8»irance onti
mannfaetory. valufd ai $*J >.UtM. at U p« r ctui ?
4. A f»nM«M' lw)nj»!d buid at $4-t,7rj p» r nerc. At what
price nuj*!t h«' m'11 tln' lam! i«» niako a profit <»! 2'> p«'r enuf.!
o. A inercluuit bought silk for $ir0. wlreh on aeeonnt of
daniaj?*' nc»'j\«'d he sold at a lo^s of oA percent. Wbal
was the entire losa f
■^J
'.i
f
06
PFUCKNTAGR.
Cask ll.—To Jintl what ptr Cttif out A umber in ofamVtfr.
Exwin K.--(hi Hit inv4stninit of $S.7'>(i. a piTsoii piiiuU
$Ki7}>.hi^ ; wluit wuH tli«' gtiiii jht ciiit,.? 'I'ltiK Kiik ul^o
dt^pciuJs uii SinipU' rifpoiiioii. hihI iiuiy Ik* sIuKmI liiit^ —
If $8-7:>0 pitii $l;«»7.1«;|. what w.ll $loo }?aiii ? lii'iico the
Rn.K. — hividf Ihi* aniit ov loss liy lh»' luiinlM r t'xpff'HPing
the cuiistf III ihi.' >x\.u\ }<uiti or losx. >iii<I mull plv hy lou ; thua
$l;!l»7 H>^ -i- $8-7.")() X I0«»= l.lltt porcfut.
7. A pi'ixm pii (I >i tux of $*>:'. S'S] on properly valued at
$352r).rM) ; nt. what fati' pt r c*'nt. was lh«* tax a>M'hM'd ?
8. Th»' prop, rty of a villa^'v amounls to $1(K)(MM). and into
bi^ ta\«(l to til*- niiionnt of :r2'zoO. tor pnlilic iiupiuveuicuts.
At what p< ictiiniin \\\\\>\ iIm- tax ix* laid ?
9. If silk \v« n- pmrhast'd at $l.a(> per yard, and sold at
$2 per yard. v\liai would l» ihr gain per (:< ut. ?
10. A f>«rm«*r puirhaH'd Ian<l at $:i7.r)(t p r acre, and boM
the Haniv at $t2.1^^ p( r acre. \\ hal was thu pcrcenlutu of
prutit uiiidi* t
11. A MM'rrhant lionyht hooks at $2..')0 p<T doz'n. and sold
thcin at |;:i.7.*) ptr do/.cu. What wa.shis naiii per cent.?
12. A in'M'chani 'joughl (lou»' Ht *.'>.7.'> pi r harn-l. and pold
it ut ^7. \6'\ p K )>urrel. Ilow uiugh d.d he gaiu per cent, t
Capw ]If. — To fiml 'I J\*intthtr to which Pfrcnitnfre being
at/ttnf at 'i ^iveu liatf. will tniminil to o cettuin Sum.
KxAMi'j.K. — A tlro\«'r >ohl w h t %A entih* for $ JKM). wh'ch
f/as ai a proHi of ". '.» p'-r cent. Wlmt dd he pay lor them?
This nih' IK also l)a.<itd on >iiriplf Proportion : for example,
FUppose the cattle eost ^\{)() it is <videni the selling pr>ce ttt
the gi\eu proth would he :^liM» -f 2o = !.!<). therefore
SujfX'Ked S»>i^ /Vir«. Titif St-r,, i'ticf. !iuj'i>«> "<! f^xt.
iSI-O : *IH'0 :: ^h>0 to the tpie coPt
Now if tiie Mrst term. l.(». Iw d vhled l*y the third, 100, we
obtain 1.2(»: henee the foUowiujr
; liLLK.— Divide the }ii\ (Ml sum hy I /'/iM the r«/io.
Thus OUO -^ 1-1- .10 ~ $75'}.
Ca,
y
.4
PKUCKN'T.UIK.
07
Kiile uUo
iliiiif. —
•ncc tlie
lOU ; thufl
lit.
valued at
•I'd t
I. and is to
uveincuts.
id suld at
». and gold
eiiiuiu of
and Bold
!unt. ?
and pold
cuiit. ?
r/;j? being
It Sutii.
00. \\hTh
or tliem?
fxaniple,
)i piicu at
ore
•le coft
J, 100, we
rv A prncfM' prll« siipir at I*J.', p«?.t« per 11>. and 'm undoing
mokoH li protit ol' 'i*» p<'i- coitt. oti i!u' cusi. Wliai did tU6
t>kijzar cusl him pel pniiiiil .' ^
14. An u)r»'Mt nrt'lvis a n'niitfanct' nf $rjOO to pMrH»af>e
cloth, and ix to rfiaiii l< p<r edit on tlie purchase. What
aiiuuint of pmvhasr can lie make?
IT). A inochjini haviny Hi>ld a h)t ol' silk?* for $1012.05,
finds that his pKitit is ui \[\v rule of CO per cont. U'hal wufl
the cost ol" till? s iks?
1(5. A shociaaUiT sold a lot of hootM for $ 100. which was
Z'.)\ p'r c<>nt advaM(*«> on thir cosd ul' making ihein. What
wa8 tilt' coi<t of the Ixiot.s?
Cask TV — Titfiml n uuniUet jmm >rh'rh Pf*'ernta?e bring
subtracttd at u ^ivtn ratf, will leave a fx'ven remainder;
Ex.4MPi K.-— What amonnt of Tank Ptock can Ik- hoiijrht for
$475. at 5 p.r c nt <liM'oni»l ? Tins is has.jl on Sin>ple Pro-
portion: for «'.\iini]>lH - at *> p'>r c*'Mt discount $100 liuak
Stock can he pnichasid lor $100 — 5 = $'.».">. thcrelorc ^
Supposed y^lliny p'itt.
475 : :
101) io th«' truo cost.
Now. if the first term h" divided hy the third we hivve 1)5 H-
100 = '.♦o ; heiKM* th«- follow insx
Rui.K. — l>ivide the ^liv n snni hy 1 tninns the ratio.
Thtia §475 -J- .!).> = .'-';"/C0. the 8l«K!k which can Iw bought
with $47.*>.
NoTK — fr will be ppr'n that the only dilference lietwpnn
Ca.se y/Aaiul ('use 71". is that in the loine-r tlif rate is added
to loO for lh«' lirsl tertn. and iti the latter it is siibrract«'d.
17. A milh'r }»old a lot of dafnsiufcd flour at $.''..75 por
barrel, which wa*' at a loss of \ *\ p«'r cent on tie- I'xt of it.
What did the flour cost pi r l>arr« 1 ?
18. Wlwn rail-roswl slock sells at a discount of'7i per cent,
what amount of st<»ck can he purchas«'4l for $2775?
1J>. What Hmonnt ol stock in tin* capital oT » mi ninjr com-
pany, at 3.] p.r cciil diacuuut, may be purchu:iod for $IUUO?
t'-'
iff
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m
• "I
? SIMPLE IXTKIIKST.
Inteufst is the moin^y paid for the loan of money.
; The PrincJiud is the sum of nioiiry h'lit
The li'Uc is the rutio of the priueipal to the inter
CJ^t for I vt'iir, th«H 7 per cent sigiiilics that $100
will j^aia $7 in 1 year.
The Atnijant. is t,h« interest n<Me(l to tlie prhicipal.
Thu.^ $l.)» iIk' rrinciiKvl.
$ 7 tliu lit t rust.
$107 iUi' Amount.
Ilonee thrrf* arc four tliinjjfH lo b<' co^iHidcrt'tl ia this Rule, —
Uie Frinci/hiL Interest. Time, ami Rate.
ExAMiM.K.— Wlitit is th'^ intf-P'st of $:ii'i for \l moiitlw. at
S p«M' c nt "* It is fvid !iit tliiit iliis Itiilf is h\**'*\ o:i i\w prin-
jlple of Sinnil • Prnpurtioa, thus— If $100 prodiw^i $3, wli«4
will $325 pnxitic**?
Sl;it.«?m«'nt, 100 : 32.') : : 5
Mvidinj]^ tho th'nl It-rtii at onc^ by ino tli* llrst t«*rrn. we hara
r«»r the I'tiMd .'T) ; tiieti the priucipiil 32> X .0.3 = the later'
est. Hence th ;
Rru.K. — Multiply the fnt(«rf*st by the r itio *»vpr«>ssi»(l in
iocini;Us, Ww tli • iiiftTost of ! y»*:u*. If th»* (|ii('stioii ooiitaini
yean, nn»'iths. nnd iliiys. iMiiltip!y th(* iiit<'r"St for I yytwv by
the mumiIht of y<>:irs. atiil talcu the aliqsiot partri for inonihf
Atid iavs, as follows: —
V tAMJM.K. — \Vh If. is th«* iMtf-n'^t of $1752.96 at C per cent,
for L years. 4 inoitlhs, ajU 21) days?
, Mlb'lM
.U't thf* ratio
12" I0ri7r7 7<> int . for I y. I0").177nx2 y. = $21 n.:r)V2 for 2 y»
SUiHTytil'^nTt. for I m. 8 7<; 18X 4 m. = :i') U")JI2 for 4 m.
~ltii 1 iilut.'fi »r I a. 292 KJ X 2:» <1. =x »<.472<itV)r 2^ iL
• Tuial InttTi^t . . . $2.>;i.ii870
noivcy.
lO intor
t $100
Rule, -
oiitlhs. at
lite prill-
$3, wli«i4
w(» have
<>sso(l in
Icoiitaini
y»Mir l>y
iiioulUi
)er cent,
for 2 y>
tor 4 m.
tor 2D d.
^'v-
SIMPI.K lyrKUEST.
9<^
1. What W tlu; iiitonHt of %i\'i^ for I yeftr, at (i\ p'>r ooni!
2. What Ih ilie itUcriKt of $871.26, fur 1 your, at 7
per cvni?
a. Whiit If) tlie iiiUrcst of $r>35.50, for 7 yearn, at 6 per
cent p«'r luinuni ? *
4. WImt is the interest of $1125.883, for 4 years, at 8
ficr cvnt?
6. Wlint is the interest of $119.48, for 2 ypai'P G months,
«t 7 pi-r cent ?
6. Wliut is the inten-ftt of $2.i0.C0, for 1 year nior.tua,
it (J per cent ?
7. Wluil is the interest of $9JG, for 5 years ami 4 months,
at 9 per cent? . :> ."iV
R Wliiit is tlie intTPst of $ar)8.r>0, for 1 year 8 months aD4
i (l:iy». JU 7 per ctiit ? , >
9. What is the intere!»t of $1401.75, for 4 years 9 monthi
»n<I 15 'lavs, at (> p r cent ?
10. What is th»' inter.'st of $1230, for 2 years 4 niouthl
%n(l 12 days, at 1^ \wy cent ?
1 1. Whut is the interest of $1500, for 9 months and 20
iays, at 5 per cent ?
12. What is the interest of $15^6.25, for 10 nioiuhs aad
18 «lavs. at 8 per cent ?
i:i Whut is the interest of $(140, for 3 years 2 montlw
and '.♦ rhivs. at (>.] per c»Mit ? ,
It. What is the iut^re«t of $'J7G.50, for 11 moiilhs and
21 days, at 10 p«'r cent? ,j ^
l'>. Whi\t is the amount of $378. -12, for 1 year 5 monthi
Arid 1} ilavs. at 7 p«*r cent ?
* f
lil. Wiiat is th«' amount of $1250, for 7 months and %\
Uays. t«t lOA per cfiit?
17. Whnt i."* tile interest, of $0500, for 2 months and 10 days,
at \)ii p-r cent ?
18. Wliat is the intere.«?t of $70.50. for 10 years and 10
months, at 5| pir c nt ?
lU. VVhal will $bi50 amount to in (U) days, at 10 per ceii^t
v^<fl
f )
100
COMMISSION, BKOKERAOE. IXSUKAXCR
liUYlNG AND SKLIJXC. STOCKS.
Cowmissim is an 5jI1()\vjuu'C fiivcn to an agent or
tdctor, tor l)nyin<r or st'lling goods or i>roperty,
ue«j:otiaiiii«r ImIIs, 4^c.
• BnUrnfre is an allowance to a lirokcr for procur
f«g sali's, iransfers of proju'rty, kv.
Ivsurfnicf is an allowance ('ailed prewmm, frivon
to pci>;nn«« wlio cnjiage to make good I lie loss o(
'ilii|)s, nicrrluindisv', houses, &c., that may be lost oi
tianiaged l)y storms, lire, &f.
St(d' is I lie debt owing by government, or the
t?opii!d of railroad, banking, or oJlier companies.
KoTK.- TJ!?' following exercises are all ptn'rorni'cl by th#
Uuh* ot Simple Inlen'i't.
ExAMPi,K.~A eoniin'ssion m'Tcliant foh\ a lot of gon(]s fot
Tliich he !«'(• ivrd $7r)40 : he cliar^cd '21 \n'V cvi\i couinihulvn
What wa." tli<' iitnount ot h s roiii-
miHsiitn. .'okI how much mast he jmy $<.')'10
.on
ovrr? \N ♦• (itnl tin* conmiission us
in sinipU' |M'ic«'nt}Vii<'. l»y nmltipl viiijr SlJSh.50 cammisnon
Uy th*' <1» Mjiil which "vrM'»"'>cs iIm' t:T h\
rate. The princ |ml, «liminii-lM «l l>y ,^^ -^
^be commiss o)i. givcss tbo uniouat — '- — —
U) \ni psiid over. S • •>»> i • ^'0 arnt. pd. over.
EXERCISES.
1. A cominisnion mcn'haiit rrc«'ivrs ^IMOn.TT to he Invest-
*d in groceries : he i> to receiv*' 'A per cent. conint!s.'*ion on
'be anioitiit ol the purchu.^e. What uaioitnt is luiU out in
ijrocesio ?
2. An auctioneer sohl h house (or ^MliTi. and the furniture
for ^lo. 0. Wliaf was his coimnissioa al ^ per cent ?
3. A colhctor of taxes leceiven i} per c«'iif tor collect'np: a
tnx ot $.504.25. W bui wati the amuuut uf bin ])erceulage 7
npon
iXC]
ijront or
roper ty,
' procur
7, jrivoB
loss vl
! lost 01
, or the
'd by thf
good? foi
mmisfion
. pd. over.
l)e inrest-
jilssioii on
liU uul in
Ifiirnlture
ll«'Ct,*njr a
[t'uiuge ?
COMMISSION, RROKERACE, IXSURANCR.
101
4. A provision in<'rcl«ant poltl on coinmlssion 7.50 Iwrn-lji
of iloiir at $1)'75 per imrrel. What \vu^i Win cultltul^^iOll at
24 plT CiMlt?
5. I paid an attornov (>„ por c«nt for collecting a debt of
$73-0-:io. Mow inucll did I rt'ceive:?
fi. I atn old <2:«'d tosril $2<»40 in bills on ih« Provincial bank«
n^nii w'liicli tiMi'e is a dir<;ouiit (d' *J j per Cent. How mucU
bankable nioiny will 1 rtcoive ulttr deducting ihe brokemge^
which i.« ^ p'T cent 1
7. Wy a<r«'nf in Havana pnrcha« d for nw a qnatitity of'
8U<rar at Cil c nts a ponnd. tor which I allow him a commis-
sion 1| per cent Hi^j commits on amonnlH to $42 (i^i : how
Jiiany barnd^ of sugar of 2«o lbs each did he purchaH*. and'*
how innch in<MO'y untst 1 .send hint t<.> pay tor ii, incindiug
his C(>inmi>siuM ?
8. What 1m the cost <d" 5t» shares of Great Western Rail-
road stuck, at ii^ pt-r cent below par, ihc shares bein^j $106-
eaclj. and the brokeraji*' h pi r cent.'
9. What is tin* valne ol 120 shares of Montreal Bank
Stock, it in'in^ at a premium of Ibi per cent, and the par-.
rainc being SloO a shai(? 1
10. A broker purchased t\»t Mr. A 2^0 shares of City Bank
Slock, at a pr inMim <d' «i^ p* r cent, and charged i p< r cent
hrokirage. If the shares" are $!000 each, ht>w much muue/
docH A pay foi- th<' st<H?k ?
11. A person wisluH to invest $:?000 in batik stock, which'
is at a discount of lo per cent. What anionul. at par value,
tun he pMrcliasj*
12. llo. nniny shares of Grand Trunk Railway .Stock can
t>ft l>onght 'or $«5J5k4. at an advance of 14 per cent on the
par vulne oi SKlO a share?
13 Wh<'n bank stock sells at a discount of 7,^ per cent,
tibat Hniount of stock, at par \alne. will §:i700 buy ?
11 raid $rjO for insurance on my dwelling, valued at
$7500. What was the rate per cent?
lo. What wcMild be the premium for itisuring a ship And
eari;o. value<l at $i47<!7 I. at Hh per cent? '
Ifi. What will it cost to insure a store wjirth $■'^.(110, at
\ per cent, and the block wurtU $7500, at I i>cr ccui ? * c
lU
Si ■
li-ll
I
tt
& '•■' I
103
COMrOUKD IXTERESt.
A
Compound InUresi ia wlien the interest is added
to tlie |»rinci|ml at llio end t>f' the ytniVy and on that
amount the interest found for nnoflier vear, and added
agjiin, and so on : that is called interest ujMm intere»i.
Ixvi.K. — Find the intrrest for 1 year, and add it to tb«
<prii>ci|ial. whiuh ualt tho auionnt for tho iiivst year; find
the inie.rest of thi« amount, which add as hefure. for th<i
aiiioum of tho neuond year, and so on for any number of
years required. Suhtraet (he original principal from the
last auuaint. and the renvainder will be the Compound
loierent for the whole time.
E\ A. MiM.K. — Required \ho amount oF $100 for 3 ycart
at t> per et?nt per annum, comjiound interest/?
1st Tritioipal Ij5l00'00 Amoinit SIOG-OO fV>r 1 vear.
2f/ Trinoipal 10« (K) Amount 112?>t) for 2 \Vara.
3^/ Trincipul 11230 Amount 1 ID- lOlG ft.ro years.
1. What 18 tho nmonnt of $125, for 4 years, at 5 ph
eoni per annum, compound interest ?
2. What ia tho ci»m|»ound interest of §=500, for 4 yeriTS
at jter cent per annum {
3. What will $1000 amount to in 4 years, at 7 per
eenr per annum, uou»p<»und interest *
4 What m the amount of $750 for 4 years, at 6 per
fienr f>er annum, coujpound interest ?
5. What ia tho compound interest of $870 90. for 3}
years, at (J per cent ptu' annum ]
(). What iH the C(nnp(»und interest of $500 for 2 year^^
. at 8 per cent per nimnm f
7. What i« the con>pnund interest of f 3758-50 for 3
years, ai 7 per cent per annum i
8. What \n the eomp<umd interest of $95037*50 for 7
years, m G per oeni pur unuum I
I added
on that
1 iid<led
interest,
it to th«
ar ; find
. for tha
luiber of
tVoni the
mipuuiid
3 ycart
ar.
iira.
^'ears.
at 5 pfei
4 ycriTs
it 7 per
it 6 per
), for 33
2 years,
»6 for 3
»0 for 7
103
. !
DISCOUXP.
Dlicownt is an allowance made ft)r the atlrance o#
moiioy npoti securities hefoi^e niitirrtty : l\m^^ a
liiereliatit holds a fn«?toniur*M pnmiisat^ry note fof
$100, payahle 3 months after ihiif, and wishing
to obtain tiie money for it, he takes it to his hanker,
who 'lives liim that amonnt less his char«re for the
advance. The sum received by the niorch*iit it
called its present worth,.
Case 1. — To find the Discount and Preaent Worth.
RrTLE— As lOO-f-the interest of $100 for the iirtit
ipecifieJ. is to the sum to be dhcounteiL r*JO is 100 to
the present w^rth rt»qiiireil. To find the discount, sub-
tract the present worth from tlte amount to be di»-
coanted.
The coTnmon m^tliod in actual prsictice is (though not
strictly correor) far more easy. Calculate the simple
hterestof ihe Bill lor the time ^^iven. juid subtract it from
Ihe amount, the result is the present worth.
KxAMPLK. -$1000 hill. 12 mouths to run. is to he dit-
VMinted at the rate of 12 pm* cent ; what is the di^coual
And what the present worth ]
Jiif the Rule. Bij the Com man Method,
112 : iooo : : 100 ^ $800 8G p. worth. $1000
then 1000 — a'J0.8u^§10J. 14 discount. J2
$i2:M).»dip<;nunt.
$1000— 120.00 = $880*
Which m'ik*»s a <liff»'rence in favor of iho banker by the
CommoT) inn hoi. and the lo!i«;er the tim<» tlu' y:r»'ater will
the dllff*renc« Vh» : but as baiikerM only <li^eount bills of 2
or ?> months th^ diff Tt^ntie bt»tween the true ami the conii-
nion m*4hoi is n'»t noficed ; if. beco?nes nhtv iinptrtant)
hov.'»»v(»r. in ne'^otintinj^ lon;»; loan;ji^i*n Mo!l;^:io»» or other
ISecuritieei, as will be «een by the following exorcises. » * '
m
m
1l
r!
'tf
I ''I
•it I
'4V
1
\iA
w
(i
II
101
DISCOUNT.
NoTK. — To prove tho corr<»ctnoss of thft true w.^-tlioii
above, it is t»v'i<i«int tlu» l»sitik»'r ni:ik<'s 1*2 jmt c^'ui on iho
tnoru'y he ri'raiiw. >in<l iii»> iiKMulkaiit 12 pi>r cciic on llie
niorit^v he iv^c-'ives : cal<nilaN> hoth. un<i ai'ltiiii;? them to-
gtither yoii will Hod the smn will con-e.^potiil with th«
iuterutit i>f the whole $1000 at ihe given rate and time.
• ExEKt'isKs. — Oi'^count the full-nvini* ^ocnritiea hy the
tn(€ method and then hy tlie common method. VVhut ur»
the net proceeds or presei.t vu/uc /
1.
2.
3.
4.
5.
C.
7. A
8.
9.
irv
11. A
12.
A Bill of ^'2")n :it 2 nionths. at 12 per cent p. aim
_ 375 3 — 20 —
_ 400
— 5 ('».'>
— 870
— 972
Mort;'a<'eof 120)
— 5720
— 9M){)
Debenture of 1' MM)
— 0470
9200
4
2.V
'^\
o
IS
1')
24
ao
13.' —
H y(»ars. at 4 per cent per unu'm
4^-5
5t - 3 - ,
Oi i}\ '_. •'
-i — —£ • ,,
20 — 2 ~
11 -- 2\
7| — 3 -. ' '
Case TT. — W^ren the mnnetf to hf inve^ifed. the rtde per ceift^
and the time are ficed. lo Ji-til tie amount the Secunly
i m list he drawn for.
Rule. — rind the interoj^t of $>'I00 at the ^\kcj\ rate and
time, add it to liK) for the innnm.t. \Uru ^ny — As 100: the
money to be invested : : amount of lOO.
Example. — For what «nm must a hill at 2 months ]>«
dniwn. HO that when di>c< muted at IS per cent its net
pruoeedd or present woitk ^hall he !^o7o ?
As 100 : 375 : : 103 to !^360.25 ihe umouot of the lill.
Exi
fn tht
ind at
in;i; pa
to ex(
ainouu
14.
15.
10.
17.
IS.fnd
19.
2).
21.1na
22.
23.
Case 11
time
Rui.R
hy the t
then — A
the rate
EVAM
years, v
vhor^ed
TIu
21. .Soon
25.
27.
h.'V \-'\7.
105
on tho
on ihe
leni to-
ith tho
time.
l)y tho
hut ur9
p. aan
linn in
inty
do i\r\<\
10: the
llhs ))«
Ita net
ExFunsKS — Vunous porso'*^ nla'»ft *]»(» following; sumf
In the h.intls of a hrok-r for ui"«*m ni^nt. »n th«^ nianiH<ir,
in J at th« PutoH Jin<l tiiuen. ns hi*i«»\x. hb -uc'eeds in fipd-
in;; parti«'s whu »*oiisetu to ;;ive ih« .sec'»rir'es ne''.e8.v}»r;»
to exactly ouctipy i1i« i'.*>j» hmvi* sums. ko«ul-«d tuj
ainouui for whicU eucli stiuuniy niasi ho druvi'n \
14.
15.
Ui.
17.
IS.
VJ.
2).
0*
iy\
In a Kill at 2 months, ut 12 per cent, $4C5
4
— 3
—
rnaMurtg.'igoal *i
yoiii'.H. iit
- 4V
InaDebenturoat2l
IS
21
3.)
2j
1.V
2V
'6\
900
786
874
40(Vi
6204
0425
10800
12()10
10000
hill.
Case TI!. — IVJ^en the pre^ient tr )//'/. the nmnw^t. and tht
tune is Liowny to Ji-nt w'nit rate //«>• been charged,
Uui.E — Siihtract th<» principal frosn tlic amount, divide
by the time, iho qUdiitMil is iho mr«r«st nuide in one year,
then — As the j;ivcn piinoipil : 100 : : this quotient to
the rate per cent.
KvAMPLR. — Secuniies to thn simMunt of $1650, for 5
yours, when Bold, produc** :^12>0; what wad the rut«
diorged * $lii.i I
12i»0 ■. i
T)4/ir> -
Then as 1230 : 100 : : 00 = 7^ per cent ' .
FIND TMK K\TK PKR t'BNT.
tl .Socarities amt'g. lo$lS '.O for 4 v.^ars. sell for $1480
2:>. — OVI 5nio.itha — 000
2^, - • •
27.
670
3CJ
1^ — _ 341
Vj!
lOi)
* Barter is llie rxclm!i«ri»ijjr of •MiO ^^^.'^in'^I*;* >i
Another, nihl diivfts nuM'tthaniH wut frnth'rH \wm tii
make the t'xc!iaii;j!^« vviihout kws to citfter pmrty.
Rui.K. — Finil tlu"! valun of iho i!<»m;n(»(li*y whose quantitj
isgivM'n: thcii titul wlutt qnittiiitjr of Uhi olh«r iit tht
proposf^d nitt; uan be bought lor thu »ainu luuxiey, and h
give* the auswer.
ExAMiM-K — What quantity of flax at 9 ctt». per lb. musi
be given io barter for 12 lbs. of iudt^o. at $*2.iy per lb. 'l
12 ibd. iri'li-^-) at $2 I'J per ib. eo?noM to )p2() 28 : tnerefoM
fts 9c/.v. : ilh. : : l5N26.2.St'/v. : 21)2 /is. the aurtwer.
1. Mow nunrh wlioat at $1.2") a bushel inui^t be giver
in barter fur oU Iju-bels of rve at 70 ci'ntH a btitihel '?
2. How much rice at 28,v per cwt. may be bartered
(or 3^ cwr. «»f j'ai>in8 at 5./. ptu* lb. f
3. How luuuh tea at 95 ct^nts per lb. tnust bo bartered
for 78 gallons of brandy, at 1?2. 1-) per gallon ?
4. A had H| cwr. of sugar at 12 etc*, per !>».. for which
B gave him 18 cwt. of flour j what waM the flour rated at
per poutid '?
5. B bar^erHd 3 hhds. of brandy eontainin* 69 gak
eaeh. at $1.05 p(»r gallon, to C fur 125 ydsi. of cloth ; what
wad tliB cloth per yani ?
D give.s K 25t) yardis of drugget, at 30 cts. per yard
for 319 lbs of pepper; what duos* the pepper aland him
in per pound ?
7. A had -11 ewt. of rice, at $4.20 per cwt.. for which
B gave liiuj $<st> in money, and (he rest in t»ugar ai 12J
cts. per 111 : Ijow mueh sugar did A reeoive 1
8. A farmer Inid 120 buHhel-s of wheat at $1 50 per
I^Hhel. fur vvbicb H gave him 100 bushels «>f btiiley. at 6S
•fM. per bu-(hel. and the balance in oatn at 40 cents pef
butihcl ; what quantity of otUo did the farmer receive I
w
dnct
the r(
scconc
here
Again
of the
Evoi
nunibei
EXTRA
Toe
to find
duce ih
RUT.K
jriven nu
each, bv
iv^\ir(\ a
towards
:i of the
lli'-qnoti
9, from
biaiader
Im« t«
ly.
quantity
ir ait thi
r lb. musi
I per lb/!
ifteretort
r.
be giver
ihel ?
bartered
bartered
for which
rated ut
69 gals,
[til ; what
|per yard
Land him
m w
hich
lir at 121
il 50 per
lloy. at 6S
Vritrt per
Iceive i
IXVOl.CTION — EVOLUTION.
IXVOLUTIOX.
m
When a nnmlHT is multiplied by itf^elf, the pro
duct is culled the power, and the imiiiiImt invdtiplied
the root Thus 2 X "2 -=■ 4 : here 4 is the stpiare o*
second powir of tbc tool 2. Ajraiii, *2 X 2 X2^=:8 :
here 8 is tbe «'ul)e or third pnwrr of the root 2.
Again, 2X2X'2X2=16, hero 10 is the tburtli power
of the root 2.
1. Find the Pocon«l power of 8.
2. Ut-qinrtHl the third p^wcr of 13.
, X liaise 32 to the fourth power.
4. Involve Ifl to tht! lil'th power.
5. luvulvo 38 to the sixlli i>ower.
EVOLUTION.
Evolution is the method of fnurmg the roots of
numbers.
EXTRACTIOX OF TTIE SECOND Otl SQUAIlE tioOT.
To cxtrsH't the sqiinrc root of any j»:iv«'U nnnd)er is
to find a iiunil)er, when multiplied by itself, will pro-
duce the ^iven number. • *
What is the ^ quare root (vf 106929 "?
RuT.K WITH ExAMei.K.— rvivldte th*?
given iuimlnr into p« T'Otls of two figiiros
each. l)y phicinjx '^ pt)int ov»r the unit
(ij;iin', Hiut ovrr ev««rv alteruat«* llfyure
towards the left. I'Miid t!ie square root,
liof the tirsi period 10. and phtce it in
th' quotient. Snl»M'nct the ^qujin* of it,
9, from »h • first period, and to the re-
buiiuder annex the lurxt )>enotb ^^t f<Mr
106920 (32T
C2) U9
124
U7}'
4529
4529
>:'■
"ivi'
"? 'i
1.,
f'ii y \\
rl
u
108
SQLAUR ROOT — CIBK ROOT.
% dividend. Doiililf ili^ root nlnisidy found. H. for a divisor,
Mid sli|>p(l^i!l^ ill*' iiiiir li,L!:iil'i>. !l. niii Hcd. lind imw ut'U'l) it,
riz. U, 1^ coiilHJiird ill tin* <iivi<leiid. It Ih cttiiiaiiitMi 2 titiu'(< ;
place tliu 2 tiiiMi iwf/i in th (|iioM«Mit and tin' divisor. Multi-
ply by il.2. llit'diviMtr. d'J.iiinl snlMrm-i ila- prodnct. I'J4. rmm
l!u' divi<|riid. |iriii<r down anoilicr pcriuii, unU procot'd thus
till all tilt' poridds ure liiuii^iii down. <i -
If tliero l)u n rcmuiiKku* nflcr nil tlio periods arc
nscci, pcriixls of ('i|du-i's nuiy hi? nii.'.ext'tl ; when
the restilt will l»o decimals. Slionl i I here be dc-
ciiuals ill the omvoh iiiiiiil>er, still tiie pointing is to
beo:in IVoni iln? unit's pi. in; of the integers^ and :i
point to he placed over every alternate ligure both
right and left.
The pqnan* root of a fraction is found by oxtractinn^ the
square root of the nnnicrator tor a new iinincrutor. and the
root of the (b-nonilnuior for tt lunv di'noininiit«)r ; if. how«*v«'r,
this caniKtt b(> done, let ttic fractiua be ri'duoed to udtcimalf
%ud ihc root extractrd as bfturc*.
. 1. What is the sqnaic r<iot of 'J0'J7<>?
2. What is th'.' sqnan; root of <)L2r)21 ? ;,
8. What is the square root of 1231321 ? . ,,
4. What is Hie square root of 20.*>2.()!) ?
6. What is the sqiian* root of 47!)r). 25731 ? , ,
(r. What is tint square root of 24ti74.i2C4 ?
7. What is the square root of ■^^\ ?
8. What is the sqiiure root of ^'3^5 1 ,
EXTRACTION OF THE TIIIPJ), OR CUBE ROOT.
To extrael the Cnhe Root of sinv oivni umnher
!s to find a imnihfr whirli, when innltlplied twice bjf
itself, will produce the giveu number.
-i^XZ
divisor,
)t't«'n it,
! tinu*»« ;
Multi.
J4. Iiom
;ed tbua
3fls arc
when
be dc-
g is to
uiui a
re both
tinj? t!»e
aiui the
io\v«»v«>r,
decimal,
; .
GOT.
mmboT
vice b/
CUBK ROOT.
Find the Cubu Root of 12812904.
109
HfLK WITH I'!X-
4M1M.K. •— Divid.' tho
j,'iv(Mi iiiniih''i' into
IHM'iods of lhn'<» ll^-
ui'<;S, b<'^i lining; at
ih(* place of units.
lMuc«; thi' cuIm* r«ii»t
of the llrsi iMTJnd
2. in the (|tioti«'iit.
And subtraei. itriciilits
8, from th«' Hr.-t \u-
riod. and hrinjrduwu
the next period t<tt' a
dividend, which in
4^12 ; to tin<l a di-
visor, inniiiply th«j
12812901(234
4»12
2X2=iXS00=1200
2x:<=iiX 30= ISO
ax;i = »
13^9X3=41(17
G45904
28«X3nO =158700
2:; x4X'*io= ii7(;o
4« = n;
1GH7(;X 4= C4.')90i
Fqnare »f the li<rnre placed in tlje quotient by H00.=r=r200,
liiid how often tiiis is coii!ain«d in the divid^'iid. vi%. 3 tiin* .*^
phice the 3 in th«' qiioti«'nt for ihest'cond li^rnres of the root
Multiply the pirt of the root formerly found, viz. 2. b^
the la:<t fij^un* placed in th»' root, viz 3. and the produ'^t hy
30,= 180; add this hm*! the squan' of the last Htrure placeil
in the root to the divisor. v*z 120.); multiply the .^^um of
ihene, 1.'{K9. by the lust H<rur'« plaee<l in tin* root. 3. and
Fulttract th(> pn»'l(U't. 4h>7. troin thi* divid< nd, 4812; bring
down another period for a new dividend, and proceed iu ths
lame munuur. * . t
In order to extract t!n» culv* root of a vulgar fraction reduct
it to a decimal, and then extract thi* root.
Iu mixed uumbtM's reduce the fractional part to a decitnaL
Find the cube ntot of the followiuif numljers : —
1. of
8:3M«
t). of
.'>27.34.37.')
2. —
.'> [X'l
7. —
7834.S748
3. —
389017
8.
.0:)31o737tf
4. - -..,
, 1092727
9.
4
5. —
84004519
10. —
7"
1
' )
1 >S:
no
DUODECIMAL MULTIPLICATION
Tills mle is nindi* use of hy artificers in tnctiKH -
injr tlieir work. The <li!neiisii)iis nre tnkeH in h-et^
iiu'Iu'R, niHJ parts. Tlie foot is divided into 12
parts called iiifh(>s ; tlie iticli into 12 parts euiled
8eeoiid.s ; Ike second^! into 12 p:»rts ealli-d thirds ;
and the thirds into 12 parts ealled lonrths. Three
seconds are nuirked thus, 3" ; thirds, thus, 3'" ^ and
fourths thus, 4"".
Multiply 7 feci C^ inches by 2 fuot 5^ iucb«(k
Rrf-K WITH RxAMiM.K. — I*laoe the ft. in. "
fiHltiplloruml rtlif uuiUiplicun*!. li't't 7 4i {♦*
IikUt fvrt. iiiclu't* aialor lnch<'s, Ac. 2 5 8 ' •
Ittaltiply tlx' umltipIicunM. <M'gitiniii|]f
U tin; hiwi'Ht t ru». }>. t»y tht' hi}rli(*st
lt»rm in tlu* inaUipli«T. 2. currvin,!? Wy
12 ; thiMj niultiply Wy the* n«'Xt Utwvr
ti^rm in th«' maltiplifr. viz. 6 iuclu's.
*«ikin}» cure. b<>u>*^v«'r. to put th<' pro-
duct oiM' place towjinls the ri^iht liaml. Do the naino w'tli iKt
next lower tonu, und so oa. Add ihe dlllcreat pioductd to
futber.
1. Multiply 7 fiTt 9 inchcR, by o feet (i inches.
2. Maltiply U feet 6 iiujheP 3", by 4 feet 8 inches 6".
3., Multiply V2 feet H iuche8 7", by 8 feet i inches 9",
* In«t<i>Md nt } <nr>h<>fl 0' nrr put down, bitcttUHe Umj ara (squitatoDi
tiM kMue U Uuutt with Um> J iuvU. - ■ ; i . '-
15 1 «
3 1 9
9
1 10
8 S
18 o 2" 6"' a"
4. M
6. M
6. M
7'o Jim
7. Fir
feet 4 ii
8. Fill
4 inches
9. Wb
(8 G feel
10. R(
luet 9 ini
11. A
ras tb«' I
U-eadth i.
12. Ho
p r Coot.
12 lett 4
To Jind i
2 iiiclie.M i(
It. R-q
truild, am:
nUOOF.OlMAL MULTIPUIATION'.
Ill
N
mc«K« •
I in t\•<^^
into 1*J
t8 called
thirds ;
. 'riir<;e
r
Ȥ.
9
io wrik iht
roducla to
6".
bs 9".
4. Multiply 4(i ft;el U iuchoa 8". by 12 IV.et 7".
6. Multiply 87 ftMit !)J iiichos. by 11 teta 10| incho».
6. Multiply (187 feut 7J inches, by 24 fuut 10] inches.
Tfl ^/irf the supvrficiui content mulliftltf the Ifiigth by tht
brvudtli. ■'
7. Finil tTjp Gontont of a board 8 feet 4 inches long and 3
and I ^^^^ "^ i"^*' ** ^"*^»^^d. ,
8. Find Him area of a table 10 fuet i) inches long, and 6 feci
4 inches broad.
9. Whut {?• Uh* price of a marl»i»» slnb. th»» l«"»n'tli nf which
is a feet 4 iiichi'i«. (he breudib ,i t'ect 2 inches, sif V.v. p r toot?
10. Rcqtiired the area of a square, the side «f it »^;ing 23
I'cet 9 inchcM 1
11. A priivn-ototM' was charpH nt !\s. 2»f. p<'r foot : what
ras th«' prief ijf it. ihr Irngih of it being 7 fret 2 inches, the
lUeudth 3 feoi (> ineht-s?
12. How much will it co«t to p-vvp a court-yard at 7.t. 8*/.
T foot. th«' leii;^th of it bei'ig lilj feet 'J inches, llio breadth
i fett 4 incht'rt?
To find the tolid content muh'tdv the len^ijh, bieCiulh, and
thii'/ini:u together.
n. "What is tlj(» solid content ot* a block of irmrldo 9 f'^ot
l2 iiiChe.M lonyr. ^) leet S iwclies broad, aiid 2 fi-et A incht-if thick?
«jquital«ni I It. R<M|uir«Ml tlio solid content of a box (i^ feet lung, 41 feet
llroad, and 3| feet di-t'p ''
I!
1 ;
>'{
n
^ II
112
DUOnKCIMAI. Sf'MTIIM.lCATloy.
1'. A loff of iiiiilioiriiiiy \h 72 r« «'t 7Jl ImcIm'* lonjj. 5 fi-f^k r\
InciicH oi'tMil, uiid ^ Ifci <>i inclio lliiek. Ki'i|tiircil ilb bolal
euutt.'iil?
10. What woiiM Ii C(i>f liiivinjr a o<'ll»r «lnjr ]Rf«'<'t4 ifrhri)
\0U]f. I'J Irrl t> iliclio lllDHtl. HIHI it li.Lt (i tlicllCb (li'f{), Ul 0(/.,
per bolid yard 1
17. U»'fjiiin'd llif f»oIi«l iMMUi'Ml of a \off of ImmcIi, 27 fee'
6 incht'H loii;;, 2 IVfi ;'» iia-lu's lauad. and 1 lout 2 inclici
thick ?
M
'b>
18. What Iff 11h' valin' of* n M<k<'k of prnnil*' f< IVrt lnch<f
lnn<r- '^ l'('«'t ' iiudicH bnmU. and 4 lft*t 2 iiicbca lUick, ut '»
(m/. the bulid iuoi ".
l^To
Kri.K
every I'l
n
•AiHI
12 ra)
12-
lli —
12 —
12 —
12 —
12— 1
'^-!
12-
12- 1
I'.O —
1:0*—
NO —
m.o —
rs{» __
too —
Whpii
I for u do
l.T
(^
U
H
— .
10
_
\)
—^
i:>
—
•
lu
-
iia
'n
M!
fit itb bul^u
It
MENTAL ARII'IIMETIC
iM't 4 ll'lMM?
■ t .
I'i'P, mK ti(/.,
I -To Jind the vafur of 12 aiticlcf. the price of one being
^ioen.
icli, 27 fiM»
fT*
ut 2 inclicii
Rri.K.— Ri'ckoii ♦,'vi'ry p"nii
y ill thu prici! a ftliilling. and
•'••! incliK
n< vHiiJc Ihe valiitt of 12 articluH ut lit. each h 127., or Is.
lUlck, at '»
Jinn.
Jln.f.
\
12 O 67. each (.«.
24® 77. ouch 14*.
I
«J 12— 87. — 8.y.
24 - (;j7. — lis. Cd,
12— i:w. — I As.
;jii_ !,,/. — 27ji.
12 — 4|7. — 4«. :W.
:wi 10.^7. :n«. r,7.
12 — r>kd. — 6.f. ♦>7.
12— iv. 4^7. -- i(;«. :u.
12 — 7: 7. — ' 7s. !)7.
12— I. V. 7^{7. — VXh. 1)7.
12 1.". 7. — IG.-*. 87.
21 -!.<«. 87. — 'Mil.
12— 1« 7. — Hi» <)7.
24— 2.S. 17. — f>0/t.
12— 1717. — 17jt. 1)7.
4N— I.V. 37. — ma.
12— 1!)J7. — \\h. iid.
7^-is. 87. — 121)*. \
1.0 __ 37. — 'M)a.
720 f)7. MOO*.
■ , * ■
I.O* 77. 70.V.
« (> - 77. — 4!)0.».
240— 87. — 1C(U.
j)()_ {]d. — 4bO».
mO— 77. — 210*.
lOKO- 77. — (;:{0*.
^si) — p,/. _ :m)s.
l.'OO - 87. — 80. \v.
100 — 1 17. — ojUj.
i;;20— i*7. — })yo*.
"Wh^n tliere am h r»'W ovor or ii mI.t tli<* «1ozMn. calculatt
for a duZfii, and add ur »iibti-iict us uny Ik* ivquircd.
Jus.
Ans.
n <^ 47.
each 4*. 47.
2*. fa>
47.
each 8*.
47.
11 57.
— A*. 10/.
2> —
Ud.
— ID*.
«7.
1 1 «7.
— 6*. ti7.
lA -
87.
— f)*.
07.
10— fi7.
— .'»*. .
22 —
77.
— 12.».
107.
D— 87.
— (I.t.
:i7 — 1.V
:{7.
— 40*.
8//.
i:> — 107.
— I'iH. (57.
:;:> —\s
47.
— 4(;*.
87.
* lu tliik ciutr ttuu Uic .'Udnii- lor uiie dozvii aiivl Uk« U Wa
1^
ill
1. 1
»*i
114
UIC.VTAL ARITIIMETIC.
II. — To find the price of a ffrosx. the price of one articlt
bein^ given. •
RrLK. — Reckon tbo p<»noe in tlie pr'of of otn* article »•
•hllliiijfu. atul tlitf iimn'»"r c»'" p^Mu'»'( in these t«hilliii2.s will be
Hit* price of u gross in sljilliugs.
Recalls*? takirijif t}i»* pt-nc*? in th'» prico as shillings is tlie
sanio as multiplyiiiy: by 12. and taking th«'St' ■^hillingH a.s p^'uco
Hptm is iIh* sanit' as multiplying by \'l another time, au»l li
Xl:i=li4=i gross.
1 gross (S> 4ti.
1 __ _ 2hf-
1 _- _aH
each 4N.<.
— :i0.t.
1 gross S]il. each 1)9*.
1 „ _ 91,/. _» 111,.
1 ._ _ll|,/. _ 14J&
1 — ~ 1::J//. — l^A
III. — To find the price per ftrore. the price of (*ne articU
OeiN^ given.
Rri.K.— Reckon a poiitid Tor fvcry shilling in tlw price
Thus* th<'r- b»'in!jr lO cwt. iu a ton, the price of I ton at 7l
td. per cwt, is 7/. H)s.
20 lb». ® t.f. per lb. 4/.
20 Tw. tl//. — ;V. lO.t.
40 <;>. :w. — 1-7. M)v.
60 2.*. :u. — (;/. 15.*.
80 l.v. C//. — 1 .s/.
IGO n.v. ^W. - - 2G/. o.*.
♦20^ibs.^r.^. p^Tib. mi.
v()0 T)*. bd. — T)')/.
401) 7.V. :{//. — 1 4r>/.
{■,{)() av. 9«/. — 292/ lOi.
800 12.». — 4 SO/.
1000 2.V. lid. — 1 12/. lOi
IV. — To find the value of 100 articles, the price of one
Oe.nfj^ given.
Rri.E — For ovory farthirig in \hv pric** tsiko a« many ponce
nnd twico as many shillings. Thns. 100 pfiicils at D^d. each
»8 12s. (j</.. <) being the nnnilH'r ol' farthings.
* Tn tilin cab« find the \-*\\ie of vtit Nccir, not! tak« it tea tinica for
on« artielt
i u
' article »•
1128 will be
inga is the
i^jjH as p^'uco
hne, uii'l 12
each DU*.
— 111*.
— 141*
— 14J*
f»/te articU
1 tl»(^ price
i luti at 1$
Am.
lb. <;()/.
— 145/.
— 'imi lOi.
— 4 so/.
— 112/. lOi
ice of one
many prnce
at i\d. each
I tea tiucf for
MENTAL ARTTHMRtra
IIS
Because, by taking a ])(»nny for m-ory farth'nqr is the same
IS iniiliiplyiti;: by 4. snul fsikins? 2 sh'llinjj:^ ("<»»• i'v*'ry farthing
in tliu baiuu ati multiplying by UU, and l)ii-f~'^='^^*
100 f® 2f/. each li;.v. «//.
KM) — 21^/. — iKv. lb/.
lUO — 35*/. — 21).-.. klJ.
100 ro) 4.\/. each Vus. (»//.
10 J — ;"•]//. — 47.V. 1!//.
100 — ^d. — bis. id.
V. — To find the price of one article^ the rate per dozen
beinf^ ^loen.
Rui.K; — Reckon a ponny for every shilling in the rate pef
tiiZMU.
Ans.
1 {3> 4,v. IW. pr»r doz. 4\ft,
1
Is. i'ui.
— Ihd.
1 —
lOv lb/.
h)U.
2
4.t. M.
— Hjr/.
n —
7.V. {id.
22^<i.
()
8.t.
4.*.
:j
\h.
H.S-. Or/.
I
Is.
— tJ*. 5c/.
r9 12.ti per doz. li/i.
_ 4,,. __ 4,i,
— 7». — Id.
— i:it; — 1«./.
— Ibv. — 147.
— 18.V. — ]^d.
— G.t. — 1-^/.
— Ss. — 2W.
VI. — To find the price of one articte, the price per gro»§
bem^ giuen.
RiTi.R — Reckon tiie shillings of the price as pence, ftil4
divide theiu l>v 12.
Bpcans' takinu: fho shi]!iM<r«« as p'Mic* and dividing them by
12 i» equal to dividing twice by 12, or 144.
Anft.
1 (Q 4^s. per gross 4*/.
1 _ 'Ms. — nd.
1 _ 3<i.v. — ';i\d.
I — 93#. — 7|f/.
An.f.
1 ^ OOi*. per gross ^d.
I _ inv. — !>Ai/.
1 _ in,, _ ]\y,
i — J 47*. — U^
il
iti
1 1-
lie
MRNTAL ARITHMETIO
Vll. — To find the vafue ofn nhiiife article at a certain rati
fH'i' ttiute.
Rule. — Reckon a Bitlliliig foi' every pound tii the price.
Jinn.
Jtn$.
lO 41.
per score 4.*.
20V.
5«.
P'T score 8*. <»/.
1 1)/.
— JIv.
1—7/.
7.S.
ti</. —
U.S. 4hd.
1 11/. lOs'.
— J».v. n</.
!-(;/
17.V.
Jl//.-
(KV.lO^d
i_n/. i.-,.v.
— Ml. \Ut.
1 :i/.
1 .is.
4</.-
H5. «/A
1—27/. nx
— 'iT*. IW.
1 - 7/.
(Is.
8./.-
7*. 4</.
1_30/. ir>.v.
— l\{)s, \hl.
2 1 'I/.
in.v.
—
2/. 12a. «</.
4 :*.")/. lAs.
U)d— "/.!<« '2,i.
40 -h/.
I7.S.
4//.-
17 /.1 4*. 8//,
6— S«:/. 1(.>.
N/ !>/. It. '.</.
HI—:)/
i:..s.
^,</.-
-ll/.aj».ll|(i
10— 'lii/. 18.V.
M—'^\i.\}tt.U.
^o— -/.
5if.
id.-
1)/. 0*. Ad.
VIII. — To find thf ttntuc of ainf vumhtr of nrt ides when
tUt pnee in fgiOcti tn pftice or ahillin^s.
Rn.K. — If llie price ho In pen*'. •. consider the number of
•rtich'S as pciiC"', iiml mnlti|»ly l»v iIh- p-nc * in th prce. If
the price he in sliilliii^^. eonsiiler tlif nnnilM r of articl<'H na
•liilliujr'^. arnl unilt ply hy lln* sliillin:is in ihf pric<% Tliu«,
!)♦» art oh'.** at it/. fa-Mi i<* 2l.v . h-eniisf iMi p nji* is 8.v.. and
*X:i=--*- A;iirn. M) arliclew ul ',\h. eacli is 12/., because 80#
iH4/., uud 4x;i:=sl2.
8fi
120
J 44
51
lOOA
Jln$.
Jlns.
3f/.
each !l.«,
40
(a)
'tS,
onch
id.
— fw/.
— '-').'*.
1<H)
Is.
—
35/.
— 7*/.
— '<)H,
1 10
—
lO.v.
—
70/.
— N/.
— lIllAT.
:;(H)
—
Nv.
—
12')/.
— iui.
— t'H.
1H)
—
]..*.
_
lOS/.
— 4//.
— -J /*.
t//.
!«»()
—
<;.v.
270/.
— M.
— (,7s.
h(;
—
10.V.
4:)/.
— i)d.
— 41*.
Oiji/.
lou
—
4«.
—
3a/.
rtain rati
3 price.
Jin 9.
)re 8*. <»'/.
Iff. 4kd.
Is. All,
1 2«. «*/.
7/.H*. 8//.
y/. 0*. 4<^.
//c/m txrAen
nnmhor of
pr ce. If
articb'i* hs
■ice. TIhh,
is Rv.. and
»fcause 80#
ncli
iH.
35/.
70/.
12')/.
lO.s/.
270/.
A'M.
Z6L
■t,-
in
II. i
i'i'
ANSWERS
NUMERATION.
I.] On''— Two— Three— Four— Five— Six— Seven— Eight-
Nine — Cipher.
2.] Tell— Kleven—Fonrt4»en— Sixteen — Nineteen — Twenty—
Forty-two —Eighteen— Seventeen.
8.) Two hundred— Four hundred and twenty — Six hundred
and seven — Nine hunih'»Ml and »Mgl!ty-six — Four iiundred
and seventy-three — Two hundred and torty-soveu —
Three hundred au<l sixty-four.
4.] Nino hundred and twelve — Eijiht hundred and seventy.
four — S»'ven hundred and ei^rhty-three — Six hundr d and
fifty — Two hundred and two— Six hundred and four-
Five hundred and ten.
5.] Four thousand — Two tijousand seven hundred — Eight
thousand six huiidr»;d and on«? — S«'ven thousand and
thirty-six — Two thousand one hundred aud one — Oue
thousand and sixty.
C] Oiie Jliousatid and ten— Seven thousand and thirty— Four
tlionsand six hundr d — Nine thousand one hundred and
eleven -Four tlnmsand and soveuty-six— Five thousand
' ei^ht hundred aud seventy.
f.] Twenty-six thousand atid twelve — Seventy thousand one
hundred and o le — Forty-two thousand on«* hundr d —
Thirty-six thousand Oiie hundred— Ninety thousand iw»
Vaudred and one.
■I I
'I
' f!)
,#'li
»
118
ANSWERS.' — NUMERATION.
%.] Spvph hnndr^'d tliousnnrl — Scn^en hundred Hnd one tliou'
Ban<l and twenty — Nine Inindred and lwenty««ix thou*
PHiid lour hnndred nnd t.wenty-srven — One hundred aud
four thousand two hundred and six.
9.] Nine millions — Nine mlllionp ser^n hnndred and sixty-four
thonstmd two hnndr d and sixty-ei^rht — Ei^ht inillionr
two hnndred and two thoiivand one hundred— Five mil-
lions twenty-three thousand and sixty-seven.
10.] Two millions six hnndred thousand and sixty — Four mil-
lions one hnndred and one thousand and ten — Two mil-
lions four tliowsaiid — One million four hundred and two,
thousand one hundred aud forty-nine.
11.] Forty millions — Twenty-nine millions six hundred and
two thousand six hnndred and ei^fhty-Si ven — Fifty mil-
lions twenty-six thousand and seventeen — One millioa
six hundred and seventy thousai»d aud twenty.
J2.] Nine hundred and forty-one millions two hundred and
8!Xty-eitrht thousand seven hundred and sixty-seven —
Two hundred and sixty-seven millions six hundred and
two thousand six hundr'd and seven — Four hundrtid and
one million four hundred and sixly-seveu tbou&aud 8lx
hundred and eighty.
13.] Two hundred and ninety-six millions twenty-six thousand
eight hurKired and seventy-six— Seven hundred aud tea
millions twenty thousand ami ten —Two hnndred and sev-
enty millions six hundied and three thousand and fifty.
14.] One thousand four hundred and two millions three hun-
dred and sixty thonsaml sevt-n hundred and forty — Threa
thonsatid four hundred and sixty millions seven hundred
and sixty thousand and ten — Four thousand and Iwent/
three millions six hnndred and one thousand four huu<
dr. d and ninety-seven.
15.] Sevrn thousand and forty-two millions six hnndred and
thn-e thou^alld xi'ven hundred and fourteen — Fivr t'lou-
Fand and seven*y-nine millions six hutidrcd and seven
thousainl ninn hundred and six — ihv tlionsand seven hua-
drcd aud four millions beventy thuuisaud isix hundred.
2]
5.]
«.]
«.]
7.]
AN'SWKRS — NOTATIO>f.
4i
one tliott*
«»ix thou«
idrud aud
sixty-four
it mi I Hour
Five mil-
Four mil-
-Two mil-
1 aud two
ndred and
Fifty fnit-
ne millioa
ndred and
ty-sevou —
I lid red and
iiidi'til and
ou&aud six
IC] Eigftty-onp tbotiRand four hundr <! and sixty-two millioni
tliiVM' hiiiidrcd ami sx lliniis.uid ami twelve — Foriy-six
thoui^and aiidscvt'ii rii lllonssix lniudrcd and «'|j;hty-8evea
tliousiitiil six liiiiidn>d mid ci^flify-oiu' — Mmly lour thou-
BUtid and t^ighly-Mix inilli(Mis tour Imiulrcd uud twynty-oiio
thouHiUnl tlirtH' liuttdrd and sixty. 't
!7.] Fourteen tliousaiid and twcnfy-thri'<» millions six hundred
and lbrty-oii»* thonsiml t.wo hiMdrci] mid one — Twenty
ih()4isii(id t'iixlit liiiiiilnMl and sixty inllioat) two ihonsand
and on(> — Forty thousand and two niillion» two hundred
and two.
18.] Nmv hundn**! and s«'Vf!n thousand and sixty millions two
hundred aud six (hou'^iind r.Ao liiiii<Iri'd aid four — Two
l!un«lr««d and tortv thousand and twniv six millions ono
huudi'ttl thcMi-saufl tw(» hinnlrcd and oiie — Five hundrvd
and ninety tliMUsand nine hutidn'<l and sixty indllous ou9
Uuudred aud twenty -iiix thousand and twouly.
,i
: if
x thofusand
id aud tea
ed and sev-
and fifty.
thre<» hun-
rty— Thne
au hundred
tid twent/
four buu<
nndred and
-Five t'lOU-
and peven
seven liua-
luadrcd.
NOTATION.
i
I.] 6_7— 9— R-~r)-10— ri~M— Ki-lS -20~li).
2.] 74~2G— :il— 4!l-r>.S— i;2-7(v— 77— 1)7— 84--05— 99.
s.] 100—104— 2 u-(;!H—7:)()—i)0^>—!»;n)-8;)2.
4.] 4000 ~■42'^•^-^>'^'t'l —{>'{):> -70:)0— 1> lO !_80SO— G707.
6.] 101)00 ~ LjotiO -- 1 !)U1 SI— 2d.M}:>— :^»0;j8— ^00 10—56502 —
70777.
«.] 400000 — 4000 10 — (100707 — 0S0000—25G975— 700707 -
9(54259.
7.] coooooo — r)4!i:rM)o — H{)U) 102 — 7 ior>7f;5 — 10010010 —
202 to o\ — 5;{0 >;iJo;{ — 85;;:) t8ii5:j — 20a I0o508
l)9aojJO0O.
'.■I
120
ANSWERS.
SIMPLE ADDITION.
1.
1185
25.
105
2.
124«
2(i.
293
8.
1348
27.
\408
^!' 4.
14<>5
28.
1475
5.
2249
21).
15388
i' «•
2072
30.
4257
r [..■■ 7.
2311
31.
27731
8.
285()
82.
l65K28a
9.
975
33.
78151214
10.
1035
34.
53()14G
11.
151 (>
35.
75075
12.
lt>5(i
30.
311013
13.
S4!I57
37.
$57821
14. ,
218(;7
38.
2246
15.
I>s0ii8
8«.
72
IB.
]<><)13
40.
204
17.
30154
41.
251
18.
ISO;) I
42.
68391
, 19.
2oi(;9
43.
2203
i 20.
14372
44.
$2197
1^ 21.
4110113
4({.
102
22.
351(124
6081
23.
27S538
47.
415
24.
24boU3
48.
$84
iXSWERS.
in
SIMPLE SUDTRACTION.
I.
18^
31.
704020138873
2.
470
32.
424^5-
(5325955
3,
342
33.
4I780194.')9a9
1.
4r>(i
31.
4108"
'9998308
6.
5:t(>
35.
457555
6.
37.">
3(;.
1205995
7.
4(>3
37.
3599244
8.
G3I
38.
57955
».
96
39.
$8072
W»
90
40.
171
11.
10175
41.
844
12.
iHiun
42.
172
13.
25972
4:^.
178
11.
70747
44.
lOS
15.
3(;!M9
45.
135
It.
78373
4fi.
790
17.
40::53
47,
1380517
la.
381199
48.
11
w.
22984
49.
130
10*
•J 5289
r)0.
740
21.
78359
51.
2830
22.
25292
62.
875334
23.
4f»2121935
63.
*4r
Wilsons,
24.
435195K59
54.
U 7291 4
25.
739::L'070
.55.
5320
26.
ri2<5J:3992
5«.
(02
27.
722m»f)4I2
57.
1794
2d.
91310919
58.
85
29.
filJ^841778!)i7
5».
131
10.
7t9bO8bU00J8
eu.
»•
^'M
ii
m
122
ANSWERS.
MIXKD QUE^^TIOXS IN ADDITION AND
SUliTUACTlUN.
6. 415 {fot pfife.
t>. 2lil remain. '
7. 12M").)li rxct'i'da by
8. $_87 rtmuiiiing.
1.
8:j loft.
i.
2720 n tiitiin.
8.
15 '>7 ivtiiniL'd.
4.
102 to Jjfo.
SIMPLE MCLTirMCATION
1 I
17101
23.
6fi82»
1 ^^
l:U')74
24.
393308
■•'•►
4:322<;5
2.5.
78G(;i6
4
21:580 J
2(>.
580962
: m
(;<)j7(>
27.
41)1(535
1 "H-
C72(08
23.
884943
f.
SSOMOI
29.
1179924
|. ^
74X71^0
30.
10815&7
I t.
60 -T)-) 7
:ji.
C823(>48
!•.
'lir2.'48
32.
1338(;360
It.
574875
33.
23249952
M.
6'"8(;(;8
34.
1122U09
13.
3r)(U84
35.
23150412
, H.
C128'.2
3(5.
1089(5344
ri 15.
787!44
37. ,
19912230
16.
bTrjUi
38.
13825056
17.
2(;2<5IJ8
31).
60518410
18.
4:j77:io
40.
22039992
19.
87A4M0
41.
67ti(57(]32
20.
o«;:{!!0(i
42.
71550144
21.
1050 '52
43
(53221592
22.
iyuu54
44.
. V 74G4480f
t Fnfe.
nain.
2t'('tlR by
nuiulng;.
688289
393308
78G(il6
689962
491()35
884943
1179924
10815&7
0)823048
1338(1366
23249952
U22U09
23150412
i:089()344
19912230
13825056
66518416
22039992
57t}f;7G32
71550144
(53221592
74644801
^.
♦0.
47.
#9.
fih
00.
6i.
62.
63.
64.
66.
b^.
67.
68.
6%
CO.
9h
AXSWF.R3. — SIMPLE DlVI3l02f.
P2I
29050420
(12.
175320'
48844096
63.
$'2'.)\^
84393932
64.
2592 te«t.
43U143168
65.
2303 U'iU'.rs,
7775(;()496
«6.
3168 boUlt%
359831X04
67. "■■■'■■
$3240>
6307:;7ii2
68.
4480 pop.
41281053
69.
865U pt'iioo.
24291591
70.
2144
2H0474U
71.
8105&
4(;3r.0';56
72.
78,1
675630377
73.
m
395491873
74.
1095 hotira
C49 135896
7.5.
569 iOI
64008924
76..
76800a
3704412714
77.
$15516«
403576660
78.
tllC90 uilet.
SIMPLE DIVISIOS?
t
6911 I
12.
714097,1— »
1
13752—4
13.
3906406— 4r
s.
13281-1
14.
68595.50
4.
11517—1
15.
12667006—5
5.
9553—2
16.
478066—?
6.
3186—2
17.
5894371—5
7.
6426 8
18. '
28236344— f
6.
4206 1
19.
18824229—2
0.
636890'i
20.
14118172— t
10.
63:V/.»55 2
21.
11291537—4
11.
13771812—3
22.
9412114—5
'1
i-i
u
191
1KSWKR3. — SIMPLE DIVISIOX.
23.
8067527
56
1613 38
21.
70:>JK)8«— 1
67.
1U7-513
25.
62747 45i— 2
58.
92-728
26.
6(H72(i8 \)
59.
181—26
27.
6133880 !)
60.
113-30
28.
4706057 5
61.
2«0-43
29.
s 87484011— 1
62.
1-19-387
80.
24!)8!)341—
63.
12;'»-319
31.
18742;)05— 3
64.
3.V)— .3
82.
1499360 1— 3
65.
2 M -21*5
33
12494670- a
iHi,
2Ji— sa
84.
10709717— • 4
67.
174 5a
35.
9371002- 7
68.
141- 2«5
36.
8329780- 3
69.
118-555
37.
7496802— 3
70.
209 41
88.
6815274 9
71.
632-155
39.
'■■■.. 6217385— 3
72.
101-816
40.
26654-14
73.
167-396
41.
41315—17
74.
216-:{55
42.
40364—12
75.
127-535
48.
24«4f>6— 2
76.
1080 t 74
44.
17862—35
77
10;i2-570
45.
8703— U
78.
9591-218
4i6.
6828—33
79.
9!Mrj-383
47.
4408—28
80.
72;U-312
48.
. 10!M)2— 31
81.
700-l.')07
49.
1889—64
82.
857-1713
60.
33)9-83
83.
3186—11
61.
3450 76
81.
9.k;-20U
52.
1767-22
85.
2:>13-U09
5:^
1726-18
86.
2587-1 2i'2
64.
KJ87- 8
87.
951-308
65.
1649—31
88.
I0i;l--2116
lU— 38
)7-'>l3
[)2-7i8-
SI— 26
-Ii)-:J87
.'»') — «<l
1 8-5 j5
>U9— 41
)82-la5
iOI-8U
lG7-»J)a
21()-:{55
127-53*
81)1—74
0;V2-570
51)1-218
2:u-:jr2
00-1507
;57-1713
;18(;— II
»5;i-20U
•>i:v-U09
•,H7-12»'2
j5i-:i>)H
[;l-21lG
AN3WF.R3.
n
M.
875— 2002
95.
45— 2
90.
4l8-74tJ»
9»».
3G bonrti.
91.
2252 -4l)0l)
9r.
2rtO— 2UJ09
92.
11— 1»5474
98.
20(i»i(><i()— SO
U.J.
2J0-l«8
9!>.
rj22()8— 31(1
91.
i 4
c;u- 7
lUO.
9^5— 23
1.
2.
8.
4,
1.
2.
8.
4.
5.
J.
2.
8.
4.
^.
8.
1.
2.
3.
4.
6.
8.
DECl.M.\L FRACTIONS.
ADDITION.
071.458
6.
80i5.()98
({.
1138.372
7.
1374.2784
8.
HUBTIU
crrox.
C7.517
fi.
8.015
7.
34.120/
8.
2!>7.or2l
9.
()G9.021
10.
MUI.TIPLH
JATION
.0729
7.
M.35GI
8.
77()t>.lll2
9.
.01118403
10.
.6(;42
11.
8.79
12.
DlVlb
iiox.
2.S803^-
7.
1.7844-
8.
10.3544-
9.
1.7H074-
10.
.02 1
11.
2.9U
12.
4541.03777
739(1.1403
6558.5850
1341.58517
182.7044
70.0346
810.8879
242.245787
3^7.2158
11044O.f;O2l
.4!)29(;l
78.^
3.ti4(;5
.40006
.76
19.02124-
9.1144-
3.8l<>(>94-
2 IHI4.
24KUIH4,
3.4G89
11
1' .'HI
4
IN
AK3frER9.
»i '■
1.
2.
S.
4.
S,
6.
7.
S.
1>.
10.
1.
5
2.
2
8.
2
4.
6
S.
i
1>iSK I.
2.
£.0720+
£.7!MM>'J5
S.
4.
£.»)(HU;-f
£0M5
6.
cwt. .S.67U2
7.
yard !.4Ui(;4-
wtM-k .0U1!«)8
8.
mile .a4:i7
9.
guinea .U1H8
0.
ounce .275
1.
acre .575
2.
tnilu .UUUU4
BBDUCTlOy.
1.
2.
3.
4.
6.
6.
7.
8.
0.
10.
II.
12.
13.
14.
15.
OAKB n.
iGk. :m. i
ch. 9ja.
3qro. lib. 9oz. ldr«
14()z. I5«lr.
161 bs. luoz. lldr.
8^(1.
4}<l.
22l)rs. 7min. 23sea
Iqr. 3iil8. 2 in.
25p(r.2yil8.irt.9llL
8o2. lodwt. lG(kk
15 <iranH.
IDdwt. I7gr. *•
l2oa. 7dr.
DECI.MAL CUURENCY.
$
215
11
27
1
42
23
231
71
50
35
eta.
00
O.if
5(ij
(»2J
9:j!
h7i
6(i[
43|
11.
12.
i:j.
14.
15.
1«.
17.
18.
19.
$3
2
18|
12J
93 m
87 0»
682 184
2 65
PRIME NUMBERS.
8
3
2
2
3
6
5
3
6
7
11
17
13
11
G.
7.
8.
9.
10.
2
2
2
2
2
3
5
5
3
2
5
7
7
6
6
31
19
23
6
7
L
2.
4.
6.
41
»"t
9oz. Idr,
In. 238ea
2 ill.
ls.irt.9(ii.
gr-
A'
$
CtSt
93
s*
87
o»
682
184
2
55
1
2J^
8
«i*
4
«»
2
1
31
19
2i{
6
7
«i
.M?: ir ANSWERS.
,-:i\A-'-> k
— .^
^^» COMMON MKASUUE. «
1
►
L
:Ui
<!.
n
2.
'i!i
7.
•f
».
48
8.
lis
124
4.
6(i
\).
6.
ca
10.
U
f
X
I.
i.
ii.
I.
2.
I,
4
I,
2.
3.
4.
5.
6.
7.
)MMON MUl.TIPl
2rv2
c.
1-0
7.
1:^0
8.
rO
0.
2bO
10.
CANCELLATION.
3f
6.
14
6.
48
7.
8}
8.
VULGAR FRACTIONS.
UKnLCriON'.—CASK I.
\
125
2780
714
41b9
4f
11. »i
6|
2487?
8.
1 f 939
C04L
9.
%UJi
227^1
10.
351
02.^',
11.
1 •*•*"»
9S^3
12.
104^.51
lODfJ
13.
isoisjj
1 1 .^ 3
14.
ivciKJi
t I
5l
?!i
12S
iNSWERS — \TIX3AR rRACTIOXS.
Mi
I
II '
15.
It
17.
18.
19.
2a
n.
t^
H
25.
ts.
27.
t8.
29.
CASE II.
15
2
30.
26
3
31.
8!)
6
32.
178
33.
9
in.3
31.
7'
' 1)707
35.
J5
ci::o
3G.
17
2fl:^.oi
37.
8(1
SO.-JJO
38.
3()
184^^7
39.
27
12:U)00
12G
85i(»:u
40.
4ll
7(285
41.
111
isoor>7
42.
2:J4
6U1248
43.
li'Zi
OASB UI.
CA8B IT.
JO
294
3fi8
14b5
iClo
819
352
1188
SP2
3-3
5304
e«325
33018
€8376
605880
"5890F
25056
9Z82
2(>1807
55575
17
23
58
4^
11
8^
10
58.
60.
1.
2.
3.
4.
5.
G.
ANSWEKS — VULGAR FRACTIONS
1^
J?.
294
if;8
1465
i(;i5
352
1188
S92
f):^Oi
33048
e8ii76
605880
25056
J)Z82
2<)1807
55575
44.
C5.
47.
18.
A9.
54.
B5.
56.
57.
68.
69.
IjS
lf:i5
11)1
i;'>io
m
55
J-8
1
ThO
240
2223 14<;.'{ 1716
60.
51.
52.
53.
2717 2717 2717
8073 4752 OCil
IMKiH iJir;^ !H>iiiI
315588 3255,S4
u
13
CAflB T.
03 56 48
84 84 84
3(0 5(i7 433
€18 (i48 648
15f)rO
44553G 44553(1 4455;i»)
310704
4455311
37<9;)38 38H3.!«)2 58(;i!):;4 25)199^9
84354(;t; 84354iM> 84;r)4(iH 8435406
105(;i 057803 1 Si)():r.5 1 (7 70 l(;;)2l)530
1111488075
12048530733 1204o.). 07:^3 1^0KS530733 K04H,530733
1738:'S'43 >8()40 201 1 70;;91 8IM) (;6l)(;58n7l252
b5738>.>-i.i.J.^O 857o82ol30b0
{)?<70OO7O840
857381:513080
3
8o7urf2543US0
17
ADDITIOV.
23
1.
1 98
* 1 ?T
68
2,
O 170
-1 AflT
4
3.
9 itn
11
4.
i
Ol tiA 1 1 3
1
3
5.
'
1 1 !»4«7 5
1
10
6.
"
«l 1 ; tf fM 5
1
7.
9.
1 174
I I 25
,53
14
11
n 5
Hi*
PT83
!«I7 5« '
7 n 4 »
i
'vlli
i69
t.
1
8.
4.
S.
t
t.
I.
i.
■i
1.
2.
3.
4.
6.
C.
4XswKnsi — VUI.0 A n rnACTioNU
I.
1.
auuTiiAurioN.
: >
5
0.
21j
28
7. '
31
9!)
8.
23 1
9.
73
ai
1115
U3 ^
JK]
10.
' i!-l7
11.
16 1^ ^
' 8^5
12.
C3f\
MUI/rir'MOATlON'.
15
«.
^A
U2
4 .
eojj
t
1U
8.
9.
17||
10.
sn
:)5i
11.
115,15
12.
isiSJi
1)1 vn
m)s.
n^
7.
t8
i
H.
gj
'ij
9.
^?
2,*A
10.
A"r
1!.
C5^
ili
12. ■
i
nBULCTION,
CONTINUKt.
IJLSB Tl.
8.
yj.painro.
ll?iis^
4. .
•3s fjvrthing
»ritf
6.
iiVii crowtt.
25.
20.
27.
28.
2Q.
ao.
ANSWERS.
m
1 "JL
1 5 I 3
15 1^
5A
60JJ
.* ^ cum' -ft,
193 farthing
crown.
6.
7.
8.
9.
10.
a.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
2G.
27.
28.
ao.
,'^ week,
•'j"** h(mr.
aoo^-704 dram,
mile.
• Iff!
CASK Vll.
3|" farthincr.
15|5 6 ounces.
»f» dwt.
T^% day.
CASE VIII. I
178. li -«d.
lOd.
4h.
10h.3i=^min.l0;f8ec.
lis. 10^— i'd.
irt. 4in.
9<)Z l.'^dwt.
13 ounooH.
3qr. lllb G(a 8,^dr.
Slur. 20per. 3yd. 2a.
tASS IS.
r^
.C2!>
.25
3.
4.
5.
Q.
7.
8.
9.
10.
11.
12.
1.
S.
3.
4.
5.
d
7.
«.
10.
CASE X.
i2|
.875
.833^
.1GG4|-
.5025
.01334.
.9-1114-
.72724-
.0715+
.00053 +
I*
ill'
_i
I 6J
TTiffI
_4I
I fltf
_?«
10 of
TtTTJf
ioa<l
i
PROMisrrot's Faercisks. •
1. [2x3x5] [2x3x11]
[2x2x2x3x3] [2x2x3
4-7] [3X3X7] [2<3x3]
[5x7] [2x2x2x^x3]
2. 28 .^^
3. 840
4. 3
I
i
,»
915 40J 85i f
iZ^
ANSWKRS.
6.
7.
8.
9.
10
11.
12.
13.
39
• 8
921
1
i
I
¥
4
I
12 13 12 12
9ewt. Iqr. 51b. SJoz.
44
t-Jt
14.
15.
16.
17.
18.
10.
20.
21.
300704
13(iz. 11 .{drams.
J[ of a mile.
Tyards 2qutirtcr8.
I
\
Trounces.
ADDITION OF MONEY.
1.
2.
8.
4.
1.
%
a.
i.
i.
1.
t.
s.
4.
I.
1
£
171
137
S-8
241
8.
17
17
10
JO
5
n
7
6.
7.
8.
9.
£
107
603
11912
17
SUBTRACTION OF MONEY.
£
48
18
68
89
€9
36
/».
//.
1H
9|
7.
19
18
2
3
8.
9.
IH
8f
10.
2
2
11.
17
8|
12.
£
80
l»i
18
38
17
30
MULTIPLICATION OF MONEY.
9
10
2
17
18
tf
14
19
()
12
£
liB
13U
399
4108
<»5U0
9.
14
17
(i
11
10
a
iP
n
ti
1*
7.
8.
9.
10.
11.
12.
d,
5
H
1
a
II!
Ill
£ 8, d.
6475 (> 4^
44130 15 11
904 8;t 3 I;
314848 12 JO
SO'iJJ,^? 1(» 91
410410 15 4
L
2.
3.
4.
6.
8.
7.
8.
9.
10.
U.
12.
13.
fifty.
drams.
lie.
][uiirtcr8.
1)7 9
03 10
12 2
17 17
5
^
1
18
8 14
8 10
7 «
to 12
ii.
d
111
£
8,
<f.
r)475
ti
4^
*no
15
11
iM8:i
3
n
4848
12 iO
'i«57
1(i
n
0110 16
4
*^
-'
ANSWERS.
13.
£112128
9
n
2a.
li.
dl9.&3
14
2
27.
15.
858:>
10
95
28.
IB.
U>i7
8
4
29.
17.
18
11
3
30.
18.
(iO
13
10
31.
19.
2<;8
2
r>4
32.
20.
lODG
2
43
33.
21.
910*
8
1 «^
3 k
22.
6505
<
2;'
35.
23.
5:i
18
8}
3(1.
24,
47
7
2?
37.
2.».
2S21
13
2j
>
131
L
2.
3.
4.
5.
6.
7.
8.
9.
10.
u.
12.
13.
a
15.
IG.
17.
£5208
9
5|
3.»z()4
7
9
81G37
2
4
^4
'>
4
4
10
j6
45
4
7|
f)01
17
tt
C38t>
11
Hi
37
14
20():?
I
^
20
13
DIVISION OF MONEY.
34 8
14 4
17 9
119 15
29 9
58 4
1080 19
834 5
60ri
789 IG
392 12
14 2
5 19
7 U
72
07 19
02 5
d.
10}
•~1
73-1
lOi-
82-
lU-
1_}
2V-J
0~j
7—1
Iff
18.
19.
20.
21.
22.
23.
2 k
25.
2G.
27.
28.
29.
31.
32.
33.
31.
3d.
490
723
778
458
730
19
4
63
2
1
8854
1
2
3
2
2
3
rf
9 3^
19 9}
17 101— «
4 9-
7
13
7
10
17
4
14
^2
h
It
S.
4
¥1
Hi .
8i-{
IJ— u
2 (>J— 34
G 10 9fir
3 94-3^
1 0— 4ir
134
ANSWERS. — RRDUCnOJf.
H.
Xfi 10
6.]— 531
52.
£ff 8
04 185
?t.
8 15
3 —454
53.
13 la
2
k
* 6
3} 101)
54.
9 4
7}— 9
d9.
17 9
n~i
.v>.
4 11
lU-39
10. '
1 5
84-<i2
6(;.
10 1
9^—109
41.
3 6
1 111
57.
9 10
DJ— 201
42.
3 5
10J~I94
58.
10 3
3^-495
4&
2
7i[— 184
61).
11
(li— 16
#1.
9
('4 \M
tJO.
•79 2
8
45
10 7
I.} -387
(!1.
8:>{
(
46
10
5J— (J()9
&1.
1(1
n— 12
47.
12 4
U-3
«3.
25000000 die.
4&
10 7
7^-3
«4.
2862 2220
49.
12 12
8|-V5
G5.
li 10
3| -388
fio.
17 Mi
10^— 8«
G6.
6
02-1916
■5
12 7
3 —64
'■
! '' ^ ^
REDU(
:tio
^,
i
n«g2 farthings.
i 15.
£188.1 lOfl.
t
6:i478 p
•nee.
\(i.
4U47H. (Id.
r.
350150 I'iiiihings.
: 17.
8737 10 Ihr<'«pence8.
%
1I88G5 h,
ilfpfoce.
18.
67552 (lv«>pt!
iices.
6.
(>9552 p
M1C«.
Oii21 fuurpi'nceB IJd.
^
7 ir)2() farthings.
\ 20.
319320^0 Hixpenct'8.
» '
87.')52 farthings.
|21.
38 1(>6 cr. 38.
A
10 ;92 p
fMice.
:22.
1188014 Bt»ven
ehilllngt.
f.
£\i'VM !0s.
|23.
1 24.
i
3H(;72 Hvi'penceB.
ia.
£444 13a. 3t!.
2282 cigtitponces fd.
II.
* K51 g
^. 18b.
!25.
HO 18 half mvs. 28.
^^.
^V*
' >l4«ci
•. 2b 10.1.
2«.
7327539 fHrihings,
I&
1130':7 fuiirp'>HC«H.
27.
28m) lUO farthii
i^«.
li.
•88U cruwus.
128.
206072 iiiiiepeuces.
2
7 J— 9
lU-39
5)i— 109
l^— 201
3J-495
HJ— 16
8
0-12
00000 (lie.
862—2220
3 J -38g
Oi-1916
ANSWERS.— WEKJirrS AND MEASURES.
29.
30.
81.
82.
33.
34.
35.
36.
37.
S8.
39.
23772'» tlir r lUrMnngs.
(il'Vj livtpuact'S.
17.51
2').0ii
2W.75
24.8i
18.r)i)
21.8!).J
9.27^
21.5:{J
13.27
40.
41.
41
43.
44.
4').
40.
47.
4«.
4JI.
60.
WEIGHTS AXI) MEASURES.
135
17.55
13.29J
17 53
U.25
21. (Ji
17.51
1350'
24.72
13.53
33. 93
13.27
i|
■': ^i
.
Avonu>ui*ois
wKiuur.
cwl.
qrs.
IbB.
08.
at. 1
1.
29
1
19
^ 1
2.
2
2
14
15
^ i
3.
tf
2
11
(1
npenccB.
4.
7
23
14
f
iHMices.
6.
40
2
14
•puncea 1 Jd.
6.
a
1
17
12
; 1
kuncfS.
7.
2
1
21
8
<^
)8.
8.
2
4
6
^^
m shillingt.
9.
8
2
27
9 7
peiices.
10.
9
3
4
9 |i
ilpcnces Jd.
11.
&11)
3
19
a
r KOVS. 23.
12.
21
13
12
<» ]
thiiigH.
13.
2S54
1
27
2
It
ihintr^
14.
4
1
12
3
7
eptiuces.
15.
211
3
1
4
t
135
AV^WEUS. — WEIGHTS AN'D MEA3URKS.
16.
17.
18.
19.
20.
21.
8 cvvt. :> qrs». 5 J lbs.
1 cwt ii (jrs. 20 lbs. J) oz. 6,\ dr
liTjl piiiei'ls.
] cwi. I qr. i:> IliR. 2 oz. 3jJ dr.
47.T ln)gslu;iuis. lUO rem.
rj2 tixis. lUowt. 3qr.s. Gibs.
22.
23.
' 21.
25.
2R.
27.
28.
29.
30.
SI.
32.
SX
84.
35.
3(;.
37.
38.
39.
4().
41.
TUOV
WKiailT.
Iba.
oz.
dwts.
grs.
194
4
IG
389
10
6
16
11
4
6
6
5
C)
15
4
1
u
8
11
11
6
80
7
8
8
3
14
>^>,*l
104
a
26-
G
16
12
mis.
u
118
4
92
I
16
LOXa MRASrKB.
fur.
29
2
4
m
5
3
5
5
per.
36
2
SO
8
18
6
2!)
18
33
yd«. ft.
3
4
^
'Ah
u
2
2
2
in
0^
D
1
I
r
;;
10 f
<3.
64.
C5.
66.
67.
6«.
;5.
76.
77.
IS.
19.
dr
in
10
ANBWERS-
—WEIGHTS
AN'D
MEASURES.
, 1
t
iM
•
CLOTH MKARUUe.
i
.1
o.
llPydfl. Oqrs
2iils.
48.
443yds. Iqrs. Onli.
IS.
3:;u
3
40.
20*
3
1 u
^9
4i.
9
3«
f)0.
47y
(Is.
1
i
45.
4
5J
.51.
10
1
1 ^
4(i.
148
1
52.
11-
-*{ suits.
47.
ID
i
tq,V\
RR OR LAND MEASURR.
.-
^
fiS.
KJacr
2nl.
Uper.
58.
Inc.
Ird.
9pcf
64.
18»
2
4
5J).
20
1
1«
55.
22
1
30
CO.
1
1
2«t\
56.
24
2
30
t;i.
G5
33 j
67.
2U
21
62.
2*. '6id,—
I2e7.
i
VRA^CKIS OK CAPACITT.
t3.
195q
m.
fibus
«h. Ip
€4.
3!»7
4
U
C5.
10
7
2J
66.
8
6
OJ
67.
175
1
68.
16
6
2
CO. 244qr«. 3ba»h. Opk»»
7U. 41 3 3}
71. lOIHfjals. Iqt. Ipt.
72. UifitxU. 2qt». Ipt. .'JjrU
73. 224lds. 4qrs. 5bsh. 3pkf
74. tJOligals. 2qts. Ipt
TIMK.
/5. 173Trs. 7wks. 5<1v5«.
76. 177dyf». IJlirs. 2Sinln.
?7. ]5yrs. 47\vks .^ilyp.
78. 2n«ly.«. I'hrs. MO,nin.
79. SCwks. i:ds. llhis. 16m.
80. 2wks. OdTs. inhrs.
81. 47lirs. 7iiiln. .SOs«»c.
82. 30ds. lOlirs. 2'.Mn. 4-'»^t,
83. 3471 2(^307 Becouda. ^
t38
ANawwta— wKir.nTS and measfres.
REDUCTION.
AVtMUDD'OIS WhUOIIT.
1.
I.
7.
9.
10.
11.
854 ll»fl.
15<!4 oz.
£1) lb. :t oz.
TROT WKIflHT.
67(5« Awt.
5 oz. 2 <lwt. 20 gr.
6184 ;rr.
€ spoons.
2H oz. 2 dwt. gr.
21 8poons.
APOTQECAIUKH WKIOIIT.
12. 27MOa'fainH.
13. 6oz. \At. Incr. 7gr.
14. 1S«5 scnipk'8.
15. 252 dayfl.
.>.
70:52 W)9.
21.
22.
2:i.
24.
CI.OTII MKASrUE.
2»!» yi!s. 2 Ills.
8 shins.— 8
7 suilri. — 8
.*.
LOXO MKASrilK.
fc
R
#'
16.
245 rO piTclu's.
17.
]m:v> vtls. in. 4 in.
:;0.
18.
2(M)<;4() yards.
:u.
19.
67200 tiiwfl.
a2.
20.
39tX)0 times.
33.
2">.
2<5.
27.
2ft.
2!).
MKASUKK Oi" CAPACITY.
I!»7 pints.
.'SK.-inrHls. Hqts. Ipt
3X(;3 p'cks.
]n>0 bushels.
20 hi gills.
TIME.
1004 hours,
.'ililys. 2(Hirs. rum.
r):)\ir4>i{) niinulcs.
3at)4U limea.
1.
2.
3.
4.
5.
6.
7.
3.
' \
irceU.
;AsrnE.
Im. 2 Ills.
s.— 8
.—8
• CAPACITY.
ints.
Is. Sql9. Ipt
P'cks.
hiishels.
gi\l3.
honr!».
*. 2(HirR. 57m.
ISO nilnutes.
iO limei.
1.
Z
3.
4.
5.
6.
7.
8.
9.
10.
U.
3.
4.
5.
6.
7.
1.
2.
3.
4.
5.
6.
7.
8.
AN3WKR8.
PUACTICK.
X7 7
2 13 U
2 M ft}
1 ir> lo}
$51)4. M)
$14« 12*
X4(iO 5 A
«.KU
6H7 5
$1351). 37J
$2.70
12.
13.
14.
15.
10.
17.
18.
10.
2<^.
21.
22.
139
$3 11
$547.5«
538 bushcl.H i p^rk.
$i<I2.2S
' ' $l«il7.0§
$3:V.)3 od
$135..n74
*38 134
iCGl 5
$3 00
iC82 10 «
TAUK AND TUI:T.
1, 40cwt. 2')rs. dfhs, net.
10
50
23
175
41
9
3
2
1
2
2
3J
25
12
15
8.
0.
10.
11.
12.
13.
14.
15.
bOcwI. 3/»x 7y6i.
21*
24
40
107
30
30
£03
3
1
2
2
1
7rt.
955
U
9M.
58cu*/. 2;i-.s. 5Ub$,
*
1. J10.25
BILLS OF PAUCKLS.
I 2. $14.45 I
SIMPLE FKOPOliriON.
3. $39.50
$12812\
2*' Hlil«H.
24 583 yardf.
1 1 1 .". diiys.
$15.03
3H.U37 bu^heid.
$83.75
2«
day.
9.
10.
11.
12.
13.
14.
15.
10.
23'} «lny«.
51 acres 1 ro<KL
1 In til r 22 mia.
$2,058
1002^,' lius^Uels
28* Mick*.
37a »'«'»*t.
240 aurca.
17.
IH.
10.
20.
21.
22.
2:5.
24.
25.
2*i.
27.
ANSV
•ERS.
f)r) pupils.
20.
4t) i;«'n!K.
:v).
IKin.n.s iniloB.
\\\.
$l«(»ilO.
3-2.
ls;vrjir» milea.
33.
S^17l W7
34.
4.,' vM'jirs.
35.
1^ d:ivs.
30.
2,2^ .liiys.
37.
25 o;l:r miles.
3H.
30 ^lavs.
3'J.
t320.tU
$220.80
45 )iii'iia.
74 .-^T vunls.
50.5025 pnlt^H.
1 • JltH per day.
105 tr«!t 2.« iu.
405 HUM J.
12 days.
7 day hour*
'6* iiioiiths.
14 luuuthd.
.\
COMrOUND PROrOIlTION
I
I.
s.
3.
4.
6.
0.
7.
8.
0.
10.
11.
14.
Jo.
16.
17.
18.
10.
$42501
J 200 00
J210 (»0
68^ Hiiitfl.
145 ini'ii.
10 ill)rs«*^(.
220i) num.
55 ;{ days.
$148.72^
$^20. 00
10! days.
720^ > iii«n.
1?^7^ miles.
72 ucreH.
lo davH.
021 'ijiys.
f30<IO
202.i jrallons.
150 taiioi'4.
20.
21.
22.
23.
24.
25.
2r>.
27.
2H.
30.
31.
32.
33.
34.
35.
3r».
37.
OCOO men.
50 men.
$471.04
3 ! ^ days.
180 niiMi.
COO ni»*n.
14j| days.
7^ (lunci's.
05.04 lbs.
32 horMes.
5 men.
135.535 days
800 lbs.
13« acres.
1205!^ mi!c8.
$100 70
$77.72
1^ luunilia.
1.
2.
9.
ID.
ANSWERS.
lil
3.80
unla.
11 IS |n'r ds\y.
t'r('t 2.« iu.
IIUMl.
ilsiyH.
siy \) hour*
iiiontliH.
lUUlltlid.
PARTITIVE PROPORTION.
1. A $1000,B $I200,C $800
2. $100, $80, $00
3. A $1714.28, B $285.71
4. $0000, $4000
5. $4030, $3980, $3980,
$4010
6. $3000, $5000, $7000
7. $5000, $2500, $3333,
$2500 and $6666
8. $162.50,
$270.83
9. 100, 140,
10. $161.53,
$193.84
11. $3333.33,
$3000,
19 4f»^3 A014 ,.,
1^. ^V-^ff, Ui^TJiJ, '^^oT
13. $1500 son, $3000 wi.
14. $400, $600
$210.00,
200
$64.61,
$3000,
$2066.60
70,' »
COMPOUND PARTITIVE PROPORTION.
00 men.
1 men.
171.04
« Jays.
\i) men.
M) ni*n.
If duys.
[ OUIHH1S.
).04 11)8.
'I horties.
men.
35.535 dayi
'.16 ll)s.
34 acres.
205!^ miles.
mo 70
77.72
l munihe.
1. $5.75, $7.77, $6.47
2. $16.38, $35.10, $18.72
3.$ 1577.84,$! 6(J9.99,$1753.16
4.
5.
$7
$60.79', $164.13'
$175.07'
1.
2.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
MEDIAL FcOPORTION.
CASE I.
8bush. corn, 7bush. oats.
71bs of first, Slbs ot second
3.
4.
5.
6.
^Ib of first, 3 Jibs second
12 J gals. 2Jgals.
7J acres of each.
5 tons hay, 8 tons straw
CASB 11.
lib at 8 cts., 1 at 10 cts., 3 at 14 cts.
8 bushels rye, 7 bushels oats, 8 bushels corn.
lib of each.
6 gallons brandy, 7 gallons wine, 5 gallons water.
3 calf, 2 cows, 1 ox, 1 colt.
251bs at 90 cts, 251bs at $1, and 601bs at $1.50.
3 gallons of water.
7 acres at $15, 5 acres at $22. 5 acres at $25.
4 at 36 cts, 36 at 2ft- eta, and 4 at 60 cts.
1 ak 18 cts, 1 at 20 cts, 2 at 25 ct».
US
ANSWERS.
CASE m.
1. lObush. at TOcts., 2^ at 48cts., 12| at 36cts., 40 at SOcta.
2. 201bs. of each.
3. 20 gallons of water.
4. 751bs. of each.
5. 20 bushels of barley, 61y®y bushels of oats.
6. 95 gallons of rum at 6s. 8d, and 30 gallons of water.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
CONJOINED PROPORTION.
1.
2.
52i bushels.
lolj
6.
7.
71^ months,
150 lbs.
3.
4tV
8.
144
4.
27^
9.
$92.37
5.
10 men.
10.
200 yards.
PERCE]
^TAGE.
1.
$6 96
11.
50 per cent.
2.
8 40
12.
, 25
3.
300 00
13.
10 cents.
4.
55 93
14.
$1185 18
5.
8 80
15.
675 30
7.
1 J per cent.
16.
300 00
8.
^
17.
4 28^
9.
83i
18.
3000 00
10.
l^
19.
2000 00
SIMPLE INTEREST.
$43 S7i
60 98
224 91
360 28
20 90
26 3i
458 88
42 24i
420 26
213 00
11.
12. '
13.
14.
15.
16.
17.
16.
19.
$181 25
11 04
132 77
26 95
416 IQ
1334 21
120 0«
40 09
8590 63
8.
1.
2.
3.
4.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
1.
3.
ANSWERS.
143
COMMISSION, INSURANCE, BROKERAGE.
iSOcta.
iter.
I.
2.
3.
4.
5.
6.
7. 158 bar.
8.
^]3o9 00
34 83
115 39
164 53
6835 28
2558 16
2412 66
5320 00
9.
10.
11.
12.
13.
14.
15.
16.
$21375 Of!
2135 00
3529 4 1
66 share* .^.
$4000 00
If per cent.
$5168 5:1
89 55
ths.
ds.
ter cent.
) cents.
85 18
75 30
OO 00
4 28^
00 00
00 00
;181 25
11 04
182 77
26 95
416 IC
1334 21
120 OS
40 09
B590 8?
1.
2.
3.
4.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
1.
'I.
3.
COMPOUND
INTEREST.
•
$516 59
5.
$198 83
131 23
6.
83 20
1310 79
7.
845 83
946 85
8.
48165 93
DISCC
)UNT.
$214 09
15.
$1055 7S
357 14
16.
853 IS
462 26
17.
1005 10
647 88
18.
6831 87
822 53
19.
6119 40
925 71
20.
7175 92
1071 42
21.
14202 00
2938 77
22.
16562 437
4948 09
23.
26500 00
8809 41
714 28
24.
6i-4-p»r ceat.J
6186 37
25.
20 —
^^ ^ \J \f \^ w
7621 39
26.
211+ -
474 30
27.
49J+ - .
J-'
BARTER.
28 bushels.
6cwt. 3qrs. 9ilb8.
201.21 pounds.
.05;i
6.
6.
7.
8.
$223 56
23J cents. ^
737.6 pounds.:
287^ bushel&J
U4
AK8WEB8.
INVOLOTION.
1.
.2.
^3.
I.
■>
^«
4.
O.
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
6.
7..
8.
64
2197
1048576
4.
6.
EVOLUTION.
176
789
1111
45.8
69.247-f-
6.
7.
8.
CUBE ROOT.
72
38
73
103
439
6.
7.
8.
9.
10.
247G099
129146796^
157.08
-I
12
14
37
37.6
19.86-f
.376
.829-1
1.93-f-
DUODECIMAL MULTIPLICATION,
ft in.
42 7
44 5
106 9
565 11
1040 8
17105 2
27 9
68 1
II III nil
6
7 6
9 8
9 8
4
4
2
4
4
8
4
6
6
10.
n.
12.
18.
14.
£7 Os. 4i— I f.
564ft. Oi?. 9"
£6 9s. 7^ f.
£126 9s. 4^— i f.
• 116 ft. 10 in. G"
100 ft. 4 in. 1" 6'"
16. 3419ft. 2in. 7" 2'" 10"" 6'""
16. . £2 Is. l^d.
17. 77 ft. 6in. 5"
18. £48 19s. 9|— I
THE END.
247C&99
)14679e^
I
7.08
-X
37.6
9.86-f
.376
.8294
1.93+
-If.
9"
f.
4-if.
in. 6"
[. 1" 6"'
' 10"" fi""*
id.
1.5"