IMAGE EVALUATION
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1
2
3
1
2
3
4
5
6
I
V\\ ^
Tl
I. Arithme
more cc
\u]«, eonsia
Innexeu.
II. VulgM
HI. Decimi
'■very plain ar
illntereat, Am
IV. Duodei
neasuring ar
V. A nolle
[In the foregoi
A new and
jreRdily calcu
I Salaries, &c.
The whole
I Remembranc
This Wwk
I ia recommeiK
I for prirate pe
B
A C(
D.
.\
I
TUTOR
5S
COMPENDTUM OF
JUINO
ANC
COMPLETE QUESTION-BOOK ;
C02JTAININ0,
11; n"'?' ^'"•!''"' "'"■^l" »™ '■»•« witk » treat dwlof pLinn... .nd permiculty.
[i.L'f.rSi'oTi rat'*""""'' P""»i">">""y •™SH for tl,. ...«i.. of .h, ,chol.,
TO WHICH ARE ADDED,
BY
FRANCIS WALKINGAME,
WRITINO-MASTER AND ACCOUNTANT.
TO WHICH IS ADDED,
A COMPENDIUM OF BOOK-KEEPING,
BY ISAAC FISHER.
NEW-YORK:
PUBLISHED BY
D. & J. 8ADLIER & CO., IfrS WILLIAM-STREET.
BOSTON :~I28 FEDERAL STREET.
AND 179 NOTRK-nA vTin BTncr^m Mn»n«».,A. .„ -
1 « 5 6 1
\{.
M
M
PREFACE.
The public, no doubt, will be surprised to find ttere is saiother
attempt made to publish a book of Arithmetic, when there are
such numbers already extant on the same subject, and several
of them that have so lately made their appearance in the world;
but I flatter myself, that the following reasons which induced
me to compile it, the method, and the conciseness of the rules,
which are laid down in so plain and familiar a manner, >vill
have some weight tow£.rds its having a favourable reception.
Having some time ago drawn up a set of rules and proper ques-
tions, with their answers annexed, for the use of my own school,
and divided them into several books, as well for more ease to
myself, as the readier improvement of my scholars, I found them
by experience, of infinite use ; for when a master takes upon
him that laborious, (though unnecessary,) method of writing out
the rules and questions in the children's books, he must either bo
toiling and slaving himself after fhe fatigue of the school is
over, to get ready the books for the next day, or else must lose
that time which would be much better spent in instructing and
opening the minds of his pupils. There was, however, still an
inconvenience which hindered them from giving me the satis-
faction I at first expected ; ue. where there are several boys in a
class, some one or other must wait till the boy who fii-st has the
book, finishes the writing out of those rules or questions he wants,
which detains the others from making that progress they other-
wise might, had they a proper book of rules and examples for
each ; to remedy which, I was prompted to compile one in order
to have It printed, tJiat might not only be of use to my own
school, but to such others as would have their scholars make a
quick progress. It will also be of ffreat use f^ a»oh ,.o«»i.,„.„ «-
A3
Jul
\h
PHEFACK.
have acquired some knowledge of numbe,. at school to make tl em
tberem, ,t will prove, after an impartial perusal, on account of if«
me book I shall not presume to say any thing more in (av„ur of
«.« work, but beg leave to refer the unpmudiced re.derT th!
^mark of a certain author,, concerning Jm^^ ' tl nlr'
His words are as follows:— ° ^ " "m naiure.
thereforer:' diffren^uVt ott^ JlCt wfTnol "':, 'T" =
^fm the same ^^tt^^^^^nr/^g- T^^^^^^
.akes^a much ^eair proJlTy L? t^^rrimt
To enter into a long detail of every rule, would tire the reader
»d swell the preface to an unusual length; I shall, therefore o^'
give a general ,dea of the method of proceeding, and leave til
^t to speak for i^elf ; which I hope the k™d rf der wild 1
«3wer the t,tle, and the re«.mmendatio„ given it. As to tht
* Dilworth.
PREPACB. ^
rules, they fo:iow in the same manner as the table of contents
specifies, and in much the same order as they are generally taught
m schools. I have gone through the four fundamental rules in In-
tege)-s first, before those of the several denominations; in order
that they being well undei-stood, the latter will be performed with
much more ^ease and dispatch, according to the rules shown, then
by the customary method of dotting. In multiplication I have
shown both the beauty and use of that excellent rule, in resolvmg.
most questions that occur in merchandising ; and have prefixed'
before Reduction, severaKBills of Parcels, which are applicable to
real busmess. In working Interest by Decimals, I have added tablfea.
to the rules, for the readier calculating of Annuities, &c. and have
not only shown the use, but the method of making them : as liko-
wise an Interest Table, calculated for the easier finding of the Inte*
rest of any sura of money at any rate per cent, by Multiphcatie*
and Addition only ; it is also useful in calculating Rates, Incomes,
and Servants' Wages, for any number of months, weeks, or daysj
and I may venture to say, I have gone through the whole with aa
much plainness and pei-spicuity, that there is none better extant.
I have nothing further to add, but a return of my sincere thanks,
to all those gentlemen, schoolmasters, and others, whose kind ap-
probation and encouragement have now established the use of this
book in almost every school of eminence throughout the kingdom r
but I think my gratitude more especially due to those who have
favoured me with their remarks ; tliough I must still beg of every-
candid and judicious reader, thafif he should, by chance, find a
transposition of a letter, or a fdse figure, to excuse it; for, not^
withstanding there has been great care taken in correcting, yet errore-
of the press will inevitably creep in ; and some may also have slip-
ped my observation ; in either of which cases the admonition of a
good-natured reader will be very acceptable to his nmch obliged,
and most obedient humble servant,
F. WALKmOAME..
fl
Units J
7«"' 12
Hundreds 123
Thousands 1,234
*>
3
5
8
To"
11
ii
15
19
20
6
8
10
12
6
9
*2
15
18
14
16
18
20
22
12 24
13 26
21
24
27
30
33
36
39
28 42
30 45
16 32 48
17 I 34 I 51
18 36 I 54
38 I 57
40 60
NUMERATION.
X. of Thousands. . ,, 12,345
C. of Thousands 123,450
JJJll'ons .*. 1,234,567
X. of Millions 12,345,673
MULTIPLICATION.
28
32
36
40
44
8
10
12
15
16
20
20
25
24
30
35
6
12
14
18
24
30
36
21
28
8| 9
35
40
45
50
48
52
56
55
1^
42
48
54
60
66
72
70
78
60
84
68
72
76
80
75
80
85
90
95
100
84
42
49
56
63
70
^6; 18
32
27
lOi 11
20j 22
30: 33
36
401 45
481 54
56
64
63
72
72
80
77I 88
84
96
81
12
3(
40,
50
55
60 66
70 77
80 88
_1?
60
72fl
90
99
90
84
_96J
99 lOsI
100. 110
108
91
.90
96
102
108
114
120
98
105
112
119
126
104
112
120
128
136
144
140
152
160
117
126
135
144
153
no; 121
120; 132
130 143
120
132
1441
140; 154
150 165
160, 176
162
171
180
170, 187
180, 198
190, 209
156
168
1801
192
2041
2161
2261
200, 220 240
NoTB.— This Table may be applied to Division by reversing it; as tlie
28 in 4 are 2, and 2s in 6 are 3, &c.
I £ S •
12,345
123,450
. 1,234,567
. 12,345,673
lOi
11
1^
20j
2ii
33
24
30;
36
iO,
44
4fi
30
30
ro
iO
55
66
7.7
88
60
84
96
^0,
99
108
>o.
110
120
o;
121
132
10,
!o:
132
143
144
156
Oi
154
165
168
180
0,
176
192
0,
187
204m
0,
198
216
1
0.
209
220
228
240
ing it; as the
ARITHMKTICAL TABLES.
VH
PENCK.
20d. are Is. 8d
TABLES OF MONEY.
24
2
30
.. 2
6
3G
.. 3
40
.. 3
4
48
.. 4
50
.. 4
2
60
.. 5
70
.. 5
10
72
.. 6
80d, are 6s. 8d,
HHIt,L.INC8.
84
90
96
100
108
110
120
130
1 140
7
7
8
8
9
9
10
10
11
6
4
2
10
8
20s, are £i Os.
30
40
50
60
70
80
90
100
110
1 10
2
2
3
3
4
4
5
5
10
10
10
10
1208. are £6 Os.
130
140
150
160
170
190
190
200
210
10
7
7
S
8
9
9
10
10
10
10
10
10
OF A POUND.
lOs.
6
5
4
3
2
2
1
1
Od.
8..
isl
..1
1
0....1
4....1
6. .. .1
1
o • • • • 1
8 a • • • 1
8 1 • . • 1
6....1
half
third
fourth
fifth
sixth
eighth
tent I
twelfth
twentieth
thirtieth
fortieth
PRACTICE TABLES.
OF A HHILLJNO.
6d. is 1 half
4 1 third
3 1 fourth
2 1. sixth
li..*. 1 eighth
1 1 twelfth
OF A TON.
10 cwt. 1 half
5 1 fourth
4 1 fifth
2i 1 eighih ,
2 1 tenth '
or A CWT.
qrs. lb.
2 or 56 is 1 half
1. .. ..28. ...1 fourth
16.... I seventh
14.... 1 eighth
OF A QUARTER.
Hlbs ...1 half
"7 1 fourth
4 \A seventh
3i««-« 1 eighth
CUSTOMARY WEIGHT OF GOODS.
A Firkin of Butter is 56 lbs
A Firkin of Soap 64
A Barrel of Soap 256
A Barrel of Butter 224
A Barrel of Candles 120
A Faggot of Steel 120
A Stone of Glass 5 lbs,
A Stone of Iron or Shot 14
A Barrel of A nchovies 30
A Barrel of Pot Ashes 200
A Seam of Glass, 24 Stone,
or-. 120
TROV WEIGHT.
24 gr. make 1 dwt.
20 riwt 1 ounce
12 oz 1 pound
TABLES OF WEIGHTS AND MEASURES.
AV0THECARIE8*
20 gr. make 1 scruple.
3 scr.. ..... 1 dram.
8 dr ...1 ounce
12 oz 1 pound
AVOIRDUPOIS.
16 dr. make 1 oz.
16 oz I lb.
14 lb 1 stone
28 lb 1 quarter
4 qrs 1 cwt.
on ^...i. 11.
•Wool weight.
7 lbs. make 1 clove
2 cloves....! stone
2 stone 1 tod
6i tods 1 wey
2 weys 1 sack
12 sacks 1 last
CLOTH MEAHURE.
24 inch make 1 nail
4 nails 1 quar.
3 quar 1 Fl. ell
4 quar I yard
5 quar 1 En. ell
quar 1 Fr. ell
HOLID MEAhURE.
1728 in. make 1 sol.
ft.
LAND MEAnVRC.
9 feet make 1 yard
30 yards .... 1 pole
40 poles 1 rood
4 roods .... 1 acre
LONG MEASURE.
3 bar. corn 1 inch
12 inches..! •foot
3 feet 1 yard
6 fsef 1 fathom
5i yards ... 1 pole
40 poles 1 furlong
8 fur 1 mile
3 miles ... 1 league
69 i miles. . . 1 degree
I
iviii
M
ARITHMKTUAL TABLKS.
Ot,D STANDARD
' ALE J
AND I3EER.
NEW STANDARD.
GiUs
3.93
3.SG
3.4(3
3.17
2.34
0.69
3.03
1.38
2.06
4 gills make 1 pint
2 P'nfs 1 quarf
4 quarts.... 1 gal
9 gallons.... 1 fir.
2 firkins 1 kild.
2 kilderkins. 1 bar.
U barrel.,. ... 1 hh.l
2 barrels 1 pun.
_3 barrels 1 butt
1.60
2.41
0.10
3.2S
1.Q2
3. S3
2.44
3.66
3.33
2 pints.. . 1
i quarts. .1
) gallons.. 1
J gallons..!
! gallons..!
' gallons..!
gallons..!
i hhds...!
pipes.. .!
quart
gallon
anksr
runlet
tierce
hogshead
puncheon
pipe
tun
B. P. G. Q. p. Gills
10 0.25
10 1.01
10 2.02
10 10 0.07
2 2 0.14
^0100 0.28
„8 1 0.50
33 2 24
S2 2 1 1.63
DRY MEASURE.
2 pints make 1 quart
4 quarts i a;allon
2 gallons. ,. i peck
4 pecks I bu.shel
2 bushels....! strike
4 bushels 1 gack
8 bushels 1 quarter
4 quarters... 1 chald
10 quarters... 1 last
3 3 0.21
£10 10 2.52
JOAL MEASURE.
Gills.
0.071
0.13
0.54
0.91
1.S2
3.64
1-45
3.27
2.91
3 bushels..! sack 2 3
36 bushels..! chaldron! 34 3
.Gills.
3.75
3.03
2.04
0.17
0.35
0.70
1 40
1.65
2.13
1 1 0.52
1 1 034
I ii
TAIVDARD.
^.
P.
ihlls.
1
0.07
0.13
0.54
1
0.91
1.S2
a 04
1
1.45
1
3.27
2.91
1
2.36
2.05
2.. 'is
1
3.87
1
3.70
1
3.r>5
1
340
1
3.11
1
2.22
■
Q
P.Gills. 1
1
3.7.")
3
1
3.02
3
1
2.04
3
0.17
i
0.35
)
0.70
)
1 40
)
1
1.G5
1
2.13
0.52
' 1 2.34
CONTENTS.
PART I.— ARITHMETIC IN WHOLE NUMBERS.
Page,
Introduction..... 11
Numeration 13
Integers, Addition 15
Subtraction 16
Multiplication 16
Division .*.... 19
Tables 21
Addition of several denomindtions28
Subtraction 34
M ultiplication 37
Division 42
Bills of Parcels. 44
Reduction 47
Single Rule of Three Direct. . . 53
Inverse.. 56
Double Rule of Three 58
Practice 60
Tare and Tret 67
Simple Interest 70
Commission 71
Purchasing of Stocks 71
Page.
Brokerage 71
Compound Interest 74
Rebate or Discount 75
Equation of Payments 76
Barter 1^
Profit and Loss 19
Fellowship 80
without Time 80
with Time 82
Alligation Medial 83
Alternate 85
Position, or Rule of False SB
Double 90
Exchange 91
Comparison of Weights and Mea-
sures 95
Conjoined Proportion 96
Progression, Arithmetical 97
Geometrical lOO
Permutation 104
PART n.— VULGAR FRACTIONS.
Reduction Iu6
Addition 112
Subtraction. 1 12
Multiplication 113
Division
The Rule of Three Direct. . . .
~ Inverse....
The Double Rule of Three. . .
i'
M
m
114
115
116
■
CONTENT*.
PART III.-.DECIMALS.
|i :
Numeration jj^*
Addition , ] jjo
Subtraction...., [[[ ug
Multiplication. . ; '.'.'/.'. 119
Contracted Multiplication...*.* 120
Division ^ ^ 221
-^ Contracted '. 122
Reduction 223
Decimal Tables of Coin.Weights,
and Measures 126
The Rule of Three .*.*.*.* 129
Extraction of the Square Root.* 130
Vulgar Fractions 131
r Mixed lumbers. 132
K^xtract of the Cube Root.... 134
—-Vulgar Fractions. . . 136
— Mixed ^Numbers..., 136
-Biquadrate Root. ... 13S
PpflTA
A general Rule for extracting the
Roots of all powers 133
Simple Inteiest .' 140
"; TT" for days 141
Annuities and Pensions, &,c. in
Arrears 543
Present worth of Annuit'ies.'.*.* 147
Annuities, &c. in Reversion.. . 150
Rebate or Discount 152
Equation of Payments ..] 154
Compound Interest 155
Annuities. &c. in Arrears..... 157
Present worth of Annuities... 160
Annuities, dec. in Reversion. . . 162
Purchasing Freehold or Real Es-
tates..... H34
r~7 in Reversion 165
Rebate or Discount 166
PART IV.~.DUODECIMALS.
Multiplication of Feet & Inches, 169
Measuring by the Foot Square, 171
Measuring by the Yard Square, 171
Measuring by the Square of 100
Feet 173
Measuring by the Rod 173
Muluplymg several Figures by
several, and the operation in
one line only 174
'F'f
PART V.-QUESTIONS.
A Collection of Questions, set
down promiscuously for the
greater trial of the foregoing
Rules f.... 176
A general Table for calculating
Interests, Rents, Incomes and
Servants' Wages
181
A COMPENDIUM OF BOOK-KEEPING
184
;
aZPLANATION OF THB CHAXACTBSfl.
EXPLANATION
=Equal.
— ^Minus, or Less,
-f Plus, or More.
X Multiplied by.
-r Divided b/.
2357
OF THE CHARAC
THIS COMPEN
The Sign of
signifies that 4
63
: : So ia.
7—2+5=10.
9—2+5=2.
The Sign of Sub! ^
is, 8 lessened 1^,2 is
The Sign of Addition; as, 4+4=8, that^,
4 added to 4 more, is equal to 8.
The Sign of Multiplication; as, 4X6=24,
that is, 4 multiplied by 6 is equal to 24.
The Sign of Division : as, 8-7-2=4, that is,
8 divided by 2 is equal to 4.
Numbers placed like a fraction do likewise
denote Division ; the upper number being the
dividend, and the lower the divisor.
The Sign of Proportion ; as, 2 : 4 : : 8:16,
that is, as 2 is to 4, so is 8 to 16.
Shows that the difference between 2 and Y
added to 6, is equal to 10.
Signifies that the sum of 2 and 5 taken from
9, is equal to 2.
Prefixed lo any number, signifies the Square
Root of that number is required.
Signifies the Cube, or Third Power.
Denotes the Biquadrate, or Fourth Power,
<fec.
1. e.
id est, that is.
M
»* *■
THB
TUTOR'S ASSISTANT;
BEING
A COMPENDIUM OF ARITHMETIC.
PART I.
ARITMETIC IN WHOLE NiJMBERS.
THE INTRODUCTION,
Arithmetic is tte Art or Science of computing by Nunh
bers, and has five principal or fundamental Rules, upon which
all its operations depend, viz : — •
Notation, or Numeration Addition, Subtraction, Mnir
riPLicATiON, and Division.
NUMERATION :
Teacheth the different value of Figures by their different Places^
and to read and write any Sum or number.
THE TABLE.
§ I
o 2
OM
8
9
8
o
;=3
2 2*^
o o i
omS
6 5 4
6
A
3 2 1
AAA
V V V
3
2
fi: I
u
ill i 1
NUMERATION.
£rtie'*;:„rTt:a„^"?<':i^^^^^^ *e righ. hand.
ooMisUng of three Rguros, or' rI, % "l""^' »«<»>» ! each
of each from the left hand L soT' ^'"'? ""^ «■«» %'"»
Tern, and the third aa so mlf ■ >'"'"? Hundreds, the next «.
THE APPLICATION.
«nd Fort^-five. T'""?"'""' Thousand, Two Hundred
Fi Hied'"'™'' ^- S-^O-" and Fort,-one ^o^and.
() Seven Hundred anr' T.. "'v^ "^^o-
^K?^dJ^"Sf^
lliousand, Five Hundred. ^^"""^' '^^"^ H"«<^red and Ten
Write down in Words
3« 2017
P 5P n 5201
Hm ^ (') 20766
(") 65700047 (H)
■dotation
T One.
II Two.
III Three.
IV Four.
V Five.
VI Six.
Vn Seven.
Vm Eght.
^^ ^^9th the followmg Numhm
P ?L'n'^ (") 5207054
() 754058 ("( oo'7iQn„
5G00030 M Xml
900061057 (^») ^^900790
*y Roman Letters.
IX Nine.
X Ten.
-X^I Eleven,
XH Twelve.
XIII Thirteen.
XI V fourteen.
XV Fifteen.
. XVI Sixteen.
ADDITION OF IN^EOBBS.
Uk
*e right Band,
Millions; each
'he first Figure
df» the next an
Js written over
2ad, Nine Hun-
of the rest.
Vumbera
xvn
XVIII
XIX
XX
XXX
XL
L
LX
LXX
LXXX
xc
c
00
Seventeen.
Eighteen..
Nineteen.
Twenty.
Tliirty.
Forty.
Fifty.
Sixty.
Seventy.
Eighty.
Ninety.
Hundred.
Two Hundred
Three Hundred. ^
' Four Hundred.
Five Hundred.
Six Hundred.
Seven Hundred.
Eight Hundred.
Nine Hundred.
One Thousand.
> One Thousand Eight
Hundred and Twelve.
MDOOCXXXVn One Thousand Eight
Hundred and Thirty
Seven.
COO
COCO
D
DC
DCO
DCCC
DGCCC •
M
MDCCCXII.
ty-six.
wo Hundred
'6 Thousand,
Fifty-seven
TO Hundred
ed and Ten
INTEGERS.
ADDITION •
Teacheth to add two or more Sums together, to make one wholo
or total Sum.
Rule. There must be due regard had in placing the Figures
one under the other, i. e. Units under Units, Tens under Tens,
&c. ; then beginning with the first row of Units, add them up to
the top ; when done, set down the Units, and carry the Tens to
the next, and so on; continuing to the last row, under which
set down the Total amount.
Proof. Begin at the top of the Sura, and reckon the Figures
downwards, the same as you add them up, and, if the same as
the first, the Sum is supposed to be right.
Qrs.
275
110
473
354
271
. 852
Months.
1234
7098
3314
6732
2546
6709
£
75245
37602
91474
32145
47258
21476
Years
(*) 271048
325476
107584
625608
754087
279736
/*^ "WKof tq flirk qiivr% cif J.^ 401 Q'7:1'7 ^.4.Ai. OOP,1 Q1 4 O^Mi
Am. 17206.
(') Add 246034, 298765, 47321, 68653, 64218, 6376, 9821,
id 640 together. Am, 730828. ,
b2 ^
%
i
m
SUBTBACTION OP INTEOE5S.
Jo\ hnllT-^-'^^-',?; ^^°*» ^' ^2H D. £391, and E.
( ; How many days are m the twelve Calendar Months ?
Ans. 366.
SUBTRACTION
Rule This being the reverse of Addition, you must borrow
Way u r rhl :is! ^''" "^^^ ^ «■-«■ ''-^» '— ^
(') (') (') (*) n /'^
From 271 47S4 42087 452705 271508 ^I^cLk
Take^ 2725 ^34096 327616 ?5247i 3150874
Rem. 117 " ' ~"
Proof 271 ■ ' ~
MULTIPLICATION
d?pf!?*»!''''' ^ tT^""^ *^^ ^'^^^^ ^f *^^ N"°^^rs given as
tl^JT.n::^'!^!''' '-'"^ ^"' compendiously performs
To this Rule belong three principal Members, viz.
1. ^e Multiplicand, or Number to be multiplied.
2. Ihe Multiplier, or Number by which you multiply.
8. Ihe 1 roduct, or Number produced by multiplying.
^^i"''^ ?-^" "^'^^ *^'^* ^^'S""'^ ^^hich stands in the Unit's place
fc r„ J^-n]^ n,P'''^"t ®'* ^^^" *^^« Units, and carry the
l^ens m mind, till you have multiplied the next Fimir« in fl.!
.«uiu,.iicarm oy the same J^igure in the Multiplier; to the nro"-
duct of which add the Tens you kept in mind, setting down ^e
Um^ and proceed as before, till the whole line is multfplied
XULTIPLICATION OF INTB0ER8.
Proof. By casting out the Nines ; or make the former Mul-
tiplicand the Multiplier, and the Multiplier the Multiplicand ; and
if the. Product of this operation be the same as before, the work
is i-ight.
MULTIPLICATION TABLE.
H
q
q
q
q
q
q
q
q
4
6
2
4
6
3
6
9
4
8
12
5
10
15
6
12
18
7
14
21
8
16
24
9
18
27
10
20
30
11
22
33
12
24
36
8 10 12
12 15 18
16 20 24
20 25 30
24 30 36
28 35 42
32 40 48
36 45 54
40 50 60
44 55 66
48 60 72
7
8
9
10
11
12
n
14
16
18
20
22
24
i
i
i
i
i
&
I
i
i
A
21
24
27
30
33
36
28
32
36
40
44
48
35
40
45
60
55
60
42
48
54
60
66
72
49
56
63
70
77
84
56
64
72
80
88
96
63
72
81
90
99
108
70
80
90
100
110
120
77
88
99
110
121
132
84
96
108
120
132
144
Multiplicand ( j 25104736 (») 52471021 {*) 79254375?!
MtJtiplier 2 3 4
Product 50209472
f 27104107 231047 7092516 3725104
5 6 7 8
4215466
9
2701057
10
(") 31040171
11
When the Multiplier is more than 12, and less than 20, multi.
ply by the Unit Figure in the Multiplier, adding to the Product
the back Figure to that you multiplied.
Bd
i") 6110592
13
MirLTIPUCATlOJr OF UtTBQMWL
(") 5107252 (") 76?S2in /m «„ w
^^ I ; /053210 (") 92057166
^^ V 16
I
n 6251721
17
9215324 ("\2'i^lqA^ ' n,^
j^ U ^571341 (»•) 3592104
^® 20
W"ng ,0 „^ the firatfiCTre of^lff'T"'," "'« Multiplier, ob-
you multiply by aZ X ^v^ ^>'^"«' ""der that Fi^re
Sum will Wf total Prodtt:'''''' ^'"^"'"^ '^'*^''^ »<» S
P m"!.'-''!^ f 1''«0'?1 by 5147.
U ?f" 'iPy "092«! 4 by 7419
( JWt,py 9S00985742 by 61870
( ) Multiply 170149S868S67 by 4768756
that the next Figure mLfb^wi *"',' ^""^ "'"^ ">"«' b« tatea
i. e. under the Figure y^u mulSpV bj.''''^ '""'" "^ "'' '*'' '""*'•
(") Multiply 671204
% 27009
5140836
3998428
1142408 .r
Product 15427648836
P u u-P,'^ ^561240325 b7670027~'
( ) Multiply 662710934 by 590030
L<ful-
DimrSION OF ZNTXOBm.
(•) Multiply 1379500
3400
19
53180
41385
4690300000
C*) Multiply 7271000 by 62600.
(") Multiply 74837000 by 975000,
Whon the Multiplier is a composite Number, i. e. if any two
Figures being multiplied together, will make that Number, then
multiply by one of those figures, and that Product being multi-
plied by the other will give the answer.
(*») Multiply 771039 by 35, or 7 times 5.
7X5=25
5397273
5
20986365
Multiply 921563 by 32,
Multiply 715241 by 56.
Multiply 7984956 by 144, . ^
DIVISION
Teaeheth to find how often one Number is contained in anoth^ ;
or, to divide any Number into what parts you plefise.
In this Rule there are three numbers real, and a fourth acci-
dent^: viz.
1. The Dividend, or Number to be divided :
2. The Divisor, or Number by which you divide :
3. The Quotient, or Numbej* that shows how often the Divisor
is contained in the Dividend :
4. Or accidental Number, is what remains when the work it
finished, and is of the same name as the Dividend.
Rule, Wlien the Divisor is less than 12, find how often it is
contained in the first Figure of the Dividend : set it down under
the Figure you dividetl, and carry the Overplus (if any) to the
next in the Dividend, as so many Tens ; then find how often the
Divisor is contained therein, set it down, and continue the same
%
m
VtVUlON or ir TKGCBS.
subtract from\TXL^a\^^ ^T"""^ ^'^^T^ '^' ^'^xi^ct
the next Figure in the DmI-? a^ Remainder bring down
Figures are SJ brought dow^^^^^ '"^ ^'""''^ «« ^f«'«' till the
the'^Kraind'^r^^^^^^^^^^^^ ^TZ p"'d ^^^^J^gether, adding
Dividend. ^ ^'^ ^''^ ^"^^"^^ ^" be the same as th!
Dividend. Rem.
O. Divisor 2)725107(1
Quotient 362553
2
(•) C)7210472( (.) 4)7210416(
Proof ^5HI^ <*) 5)7203287( (.) eliil^
(•) 7)2532701 (
O 8)2547325( (.) i^iHS^
Divisor. Dividend. Quotitnt.
(•) 29)4172377(143875 •
29
127
116
112
87
253
232
217
203
147
145
Rem. 2
29
1294S75
287750
2 rem.
4172377 Proof.
(*) Divide 7210473 by 37.
/jix ^. . *^««- 194877li
") Divide 42749467 by 347 ^"
/» 5f^?:^«?34097J43by5743.
(") Divide 1610478407
n Divide 4973401891 ^^ ^''^•
(») Divide 51704567374^ ^^^®^^'
/M\ rk- -J , by 4765043.
(") Divide 17453798946123741
by 31479461.
^ When there are Ciphers at th« ^n^ .r *i.^ t..._v .,
oe cut ott, and as many places from'"off' nit 'rJf'-T^'i 'j^*"^ T^^
must be annexed to the Rem^deTTt iJt ^''^'"^' ^"* ^'^
^^
VABLBs OP uovmr
(") 271100)254732121(939
(») 3731000)7524731729(2017
(") 5721100)7253472116(1261
(*) 215I000I63251041997(
29419
When the Divisor is a composite number, t. e. if any two Fi-
gures, being multiplied together, will make that number, then, by
dividing the Dividend by one of those Figures, and that Quotient
by the other, it will give the Quotient required. But as it some-
times happens, that there is a Remainder to each of the Quotients,
and neither of them the true one, it may be found by this
Rule. Multiply the first Divisor into the last Remainder, to
that Product add the first Remainder, which will give the true
one.
(") (") (")
Div. 3210473 by 27. 7210473 by 35. 6251043 by 42.
5761034 by 54.
118906 11 rem. 206013 18 rem. 148834 15 rem. 1066S5 44rem.
Marked
i Farthing
I Halfpenny
I Three Farthings
Farthings
4 =
- 48 =
960 =
MONEY.
4 Farthings make 1 'Penny d,
12 Pence 1 Shilling. . . .s.
20 Shillings 1 Pound £
1 Penny
12 = 1 Shilling
240 = 20 = 1 Pound.
SHILIilNGS. 1 PENC
S.
£ 8.
d.
s.
d.
20 ..
1 :
20
1
: 8
30 ..
1 : 10
24
2
:
40 ..
2 :
30
2
: 6
50 ..
2 : 10
36
3
•
60 ..
3 :
40
3
• 4
70 ..
3 : 10
48
4
80 ..
4 :
50
4 '
2
90 ..
4 : 10
60
70
5 .
5 :
lUU ..
5 :
10
110 ..
5 : 10
72
6
!
120 ..
6 :
80
6 i
8
130 ..
6 : 10
84
7 .
!
d.
90
96
100
108
110
120
130
132
140
144
150
160
9.
7
8
8
9
9
10
10
11
11
d.
6
4
2
10
n
8
I
12 t
12 : 6
13 : 4
■lU'il
TABtEa OF WEIOBTS.
TROY WEIGHT.
: '^'^^ 1 Pennjweigbt.
12 0unn;, .*^ ' 1 Ounce
1 Pound
Marked
f dwt.
2* =
480 =
• oz.
.lb.
1 Pennyweight
«;'7«A 20 = 1 Ounce
5760 :^ 240 = 12 =
are
25 lb. 18 a quarter of 100 ib. I cwt '^'^
20 cwt. I Ton of Gold or SUver.
Marked
Mr
j oz.
" ^^^IRDUPOIS WEIGHT
"^'•*™' "oko--..! Ounce......
16 Ounces , ^ .
28 Pounds , i;^""" ..lb
4 Quarters or .11 2 lb i w"""']^'; qr
20 Hundred Weighu'::.:;:! ^jf;^^^eight ?:;t.
Drams ' ' * ton,
.J^ = 1 Ounce
imZ ,11^ 28 ^^r.
28672 = 1792 = 112 Z ] ^""^
573440 = 35840 = 2240 == 80 ~ on ^""^^''^^ Weight
Tfi — ' ^^^ 1 Ton
- u::^ Tsor pLtt g-r,f -' '- ^'^ ^^^^^ 'u
A Firkin of Butter 'i'^xc. .. lb.
Soap ::::;• ^* ^ ^tone „f Iro„, gbot „,> *"•
Barrel of Anchovies ... so ^'"^™» ' ,"' f "
Soap a-iB 4 r. II ^"'«'ie'-'s Meat. . a
fiaisins ?i| t S*""" ?f Train Oil. ... n
A Puncheon of Prunes... 1120 "^ ^™^ °f Straw '*
A Fodder of T^ha
2 qrs.
• • .4.a cwt.
36 Trusses a Load
New TTflir
Old Ha/.....
66
Marked
[ dwl
dwt
oz.
• • • • • .lb. •
8, Electuaries
of fine Gold^
er, is H oz.
Marked
Mr
• j oz.
' • • . lb,
• • t qr.
• ..cwt
• • •ton.
Weight
1.
eigijt tli:*t
lb.
at or )
f 14
• • • • j
sat. . 8
• • • •
• • • •
» B e * ^\f
TABLES OF WEIGHTS.
Cheese and Butter.
A clove or Half Stone, 8 lb.
A Wey in Suffolk, ) lb. A Wey is Essex.
32 Cloves, or J 256 32 Cloves, oi
Wool.
lb.
A Clove 7
A Stone .,...,.,,,,,, , 14
AT(J ,.. 28
!'.'
lb.
8?
364
4368
A Wey is 6 Tods and
1 Stone, or
A Sack is 2 Weys, or
A Last is 12 Sacks, or
By this Weight is weighed anything of a coarse or drossy na-
ture; as all Grocery and Chandlery Wares; Bread, and all Me-
tals but Silver and Gold%
Note. One Pound Avoirdupois is equal to 14 oz. 11 dwts. 154
grs. Troy.
APOTHECARIES' WEIGHT.
^^arked
20 Grains make 1 Scruple a
3 Scruples i Dram 3
8 I^fams 1 Ounce 5
12 Ounces 1 Pound ..lb.
Grains
20 = 1 Scruple
60 = 3=1 Dram
480 = 24 = 8 =± 1 Ounce
6760 = 288 = 96 = 12 = 1 Pound.
Note. The Apothecaries mix their Medicines by this Rule,
but buy and sell their commodities by Avoirdupois Weight.
The Apothecaries' Pound and Ounce, and the Pound and
Ounce Troy, are the same, only differently divided and subdivi-
CLOTH MEASURE.
4 Nails, i make 1
3 Quarters 1
A r\ i
5 Quarters
Marked
)n.
fqr.
1 EnglishEU.
6 Quarters i French Ell ,
Quartf.r of a Yard
Flemish Ell /.:f1 K
.yd.
E. E.
.Fr.E
lard
••••••.*..•
TABLES OP MBASUBBS.
Inches
«i = 1 Nail
ftn ™ J *=* ^ Quarter
'45 * i^ *= ? = 1 Flemish EU
^ ^ ?? ^ ? =" 1 English Ell
34 « 24 « 6 s= 1 French Ell. -
LONG MEASURE.
:f";:^^^- -ke ,xnch ^:t1
1S^^ IFoor iin •
6 Feet * ^ Yard ^^f-
5iYardV..';:;;;;; j ^^''''"•••••••••••••'^''.'.""fth
*0 Poles ; J god. Pole or Perch **"d „
.^"••ws ::::::::::: Si[> ••^'"*
•J Miles '"-t mue
60 Miles... ;: League iii'ta
n 1 Degree i®*-
deg.
Barley Corns
3 ^ 1 Inch
36 = J2 ==
lOS =r 36 =
1 Foot
Mile.
594= 19S -_ ,«.— i.Yard
23760 = 7920 — fifin ^.^^'^ ^ Pole
190080 = dl^ - ,g» ; ,==0 = ^40 = . r„rt„jj^^
Jniy^rJon^t 'o Mil'f !"' "^ ^"'°"«»' "-'y. ^^ough con..
WINE MEASURE.
2 P^nts make
4 Quarts
10 Gallons
Marked
1 Quart )pt«.
1 Gallon..... ^^^?'
gal.
18 Gallons.*.'.'.*.' * } ^^^^^ of Brandy*.*.'.*.*. S'
31* Gallon* 1 Runlet ""'*•
42 r.!!!'ll!' Half an hAo-V::; ."?'?•
63
Gallons
" 'leaos
• ••....i.
Tierce
Hogshead.
' i hhd.
a pipeior4H'o*g;h;;d;.';:::;''-i p^pforButt
.tier,
.hhd.
1 Tun... ^^'•B*
TABLES OF MEASURES.
36
2 Pints make 1 Quart..
4 Quarts 1 Gallon .
Inches*
292= 1 Pint
571= 2= 1 Quart
231 = 8= 4= 1 Gallon
9702 = 330= 108= 42=1 Tierce
14553 = 504= 252= 63=1 i=l Hogshead
19404 = 072= 330= 84=2 =U=1 Puncheon
29106 =1008= 504=126=3 =2 =li=l Pipe
58212 =2010=1008=252=6 =4 =3 =2 = 1 Tun
All Brandies, Spirits, Perry, Cider, Mead, Vinegar, Honey,
and Oil, are measured by this measure ; as also Milk, not by
[ law, but cu'5tora only.
ALE AND BEER MEASURE.
Marked,
/pts.
^ qts.
gal.
8 Gallons... 1 Firkin of Ale A. fir
9 Gallons 1 Firkin of Beer B. fir.
2 Firkins I Kilderkin kil.
4 Firkins, or 2 Kilderkins 1 Barrel bar.
li Barrel, or 54 Gallons 1 Hogshead of Beer hhd.
2 Barrels 1 Puncheon pun.
3 Barrels, or 2 Hogsheads. ...... 1 Butt. ,butL
<" BESIL
Cubic Inches
354= 1 Pint
7(Ji= 2= 1 Quart
282 = 8= 4= 1 Gallon
2538 = 72= 36= 9= 1 Firkin
5070 =144= 72= 18= 2=1 Kilderkin
10152 =288=114= 30= 4=2=1 Barrel
1.5228 =432=216= 54= 6=3=1 4=1 Hogshead
20304 =570=2G3= 72= 8=4=2 =1^=1 Puncheon
30456 =804=432=108=12=6=3 =2 =li=l Butt
ALB.
Cubic Inches
35i= 1 Pint
704= 2= 1 Quart
282 = 8= 4= 1 Gallon
2256 = 64= 32= 8=1 Firkin
4512 =128= 04=10=2=1 Kilderkin
9024 =250=128=32=1=2=1 Barrel
• OROO
no J .
5=t3=:.3=i 3=1 nogsnead.
I
• By a late Act of Parliameqt.thechpacities of lh« Wine, the Ale and ^er, and the
Dry MeH8ure«. have heen reduced to one Standard For an accurate comparison of thaw
Measure*, with the old standiird Mcasuroa, the Student ii referred to the Table of th«
" Impnial Muuuru," at tke beginning of the work.
c
mv
ill
TABLES OP UEASUBES.
Btrong beer and small M IV ^^^^,f ^^ ^^ England, for ale^
to thf firkin. ^ ^^ ^^"^"* *^ ^' ^^''^^^ «nd 8^ gallons
^' ^'""a barr!.! ""nV?^™ •"' '''' ""^^' " ^2 gallons.
DRY MEASURE.
Marked
iqts.
...pot
. .gal
k.
strike
coom,
qr.
2 Pints matn , «
™*'^® 1 Quart
2 Quarts , « ,
2Pottles ; Po«le
2 Gallons .V;*. } g^lo"
4 Pecks 1 Peck
2Bu9heis**.*.;:;;:;:;;;;; ; ?"?f^^^ .''.'.'.'.'.'.'.'.tu.'
4 Bushels...., ....V;;:"*i conm «tri
JQrt:;s:'.^!""^^^^ -■•' Q-'^leV::::::;:::;::::----
^^^y' ....1 w.v: r^-
. ^ last
In London, 36 bushels make a chaldron.
Solid Inches
2681= 1 Gallon
637f= 2= 1 Peck
21601= 8= 4= 1 Bushel
4300^= 16= 8= 2= 1 Strike
8601|= 32= 16= 4- o-T , p
172031= 64= 32= t~ IZ o ^^"^
86016 =320=160=40=20=10^ 5-^ w'
172032 =640=320=80=40=20=10=2=?i
Last.
The Bushel in Water Measure is 5 Pecks.
A score of coals jg oi i i j
A sack of coals ^^ chaldrons,
A chaldron of coals ....;;; , | ^""f'^'
A load of corn ^ ®^^'^^-
A r-t "f ditto ^ hmh^h..
This mAfl«Mr?» * *^i*: * ; •/ • •.: V • • t .40 bushels.
UivlO
— measure is
The standard bushel
Hpplied to all dry goods.
18 m inches Wde, and 8 inches deep.
TABLES OF ]£SASX7SSS.
27
TIME.
60 Seconds make....l Minute.
60 Minutes 1 Hour. . .
24 Hours ..i Day....
7 Days 1 Week..
4 Weeks i Month.
13 Months, 1 day, 6 hours. . 1 Julian Year yr.
Marked
5 m.
.hour.
• day.
. week,
mo.
Seconds
60 = 1 Minute
3600 = 60 = 1 Hour
86400 = 1440 = . 24 = 1
604800 = 10080 = 168 = 7
2419200 = 40320 = 672 = 28
d. h.
31557600=525960=8766=365 : 6=
d. h.
31656937=525948=8765=365 : 5 ;
Day
= 1 Week
= 4 = 1 Month,
w. d. h.
=52: 1 :6=lJulianYear.
m. "
48 :57=1 Solar Year.
To know the days in each month, observe,
Tliirty days hath September,
April, June, and November,
February hath twenty-eight alone,
And all the rest have thirty and one ;
Except in Leap-Year, and then's the time
February's days are twenty and nine.
SQUARE MEASURE.
144 Inches make i
9 Feet
2™i fS;;.:::::::::::::::::::;::::::::;;} ^r""'"™""*
40 Kods J Rood
Roods, or 160 Rods, or 4840 yards' .' .* .* .' .* ,* 1 Acre of land
Acres.
Foot.
Yard.
4
640
30
100
V'-'*''' 1 Square Mile.
^"^^ 1 Yard of land.
^"«» 1 Hide of land.
C2
28
ADDITION OP MONEY.
Inches
., 144= 1 Foot
1296= 9 ^ 1 Yard
39204= 272i= 304.- i r> i
1568160=10890 =1210 ^r 40 -^1 P .
6272640=^43560 =48io =160' Zii^^f^^^^
bid'th'^ucra^^ «^-t ^-ve length and
I^umbing/glaLg, ia^' ^'"^'"^^' P^^^^""S> flooring, thatching,
SOLID MEASURE.
1728 Inches ,«,!,«
27 Feet "^""^ ^ Solid Foot,
40 Feet of round timb'er * ) ^ ^*""''' ^"^ ^"'^^ °^ earth.
Or, 50 Feet of hewn timber,' J •••• is .... I Ton or Load.
1 inch deep, is a stal^k of wood * ""'' '""""'^ ""^ « fe«'
fe a' coMott!" '■• ' ' '"' ''"'^' ^ f-' ''-'^. -d 4 feet dec,,
breS'tK td" "'" "^^"'^ "" '•''"8^ *•'■'' tav. length,
t;™7!; *"'''''' ™"^^' ^^° «^^«^'^^«-
as make one of the imxt^LTo.l- ^ """" <'ei""nination I
«naer the row added. and\£rvK'« O^? f^'.'^" K<'n'»i"<ler I
denomination, continuiCtre fal ^T"^ *" ""^ "<"" ^"P<=™' I
simple Addition. ^ • ■"" ^ ^^ ^^- *tich add aa in I
MONEY. I
f • "■ ^ '.**<. ^ *** . « I
» .. 17 .. 64 81.. 16.r tl"\l--ii "l •• ir. ..4i I
7- 0..3 75.. ,8.. 'n ll,-]t-^.i 35.. 10 .. 5, |
=> •• 14 .. -,{ 87 .. ,,, ,- 5g ■■, -r •• ' aa •• 19 7< ^
39.. o..,4 ■ ~^— ?ii^ii:^i_£L::Jl.:^4 •!
▲DDITION OP WBI6HTS.
MONEY.
« <•>
£ ».
d.
£
257 .. 1 ..
H
525
734 .. 3 ..
n
179
595 .. 5 ..
3
200
139 .. 14 ..
7i
975
207 .. 5 ..
4
254
798 .. 16 ..
7i
379
(•)
s. d.
.. 2 .. 44
• • 3 • • t)
.. 4 .. 74
• • o • • «>4
• • D • • 7
• • 4 . . 5 j
£ «. J.
21 .. 14 .. 74
75 .. 16 ..
79 .. 2 .. 44
57 .. 16 .. 5i
26 .. 13 .. 84
54 .. 2 .. 7
£ a.
73 .. 2
25 .. 13
96 .. 13
76 .. 17
97 .. 14
54 .. il
d.
" H
.. 7
.. 5t
.. 34
.. u
.. 74
(•)
£
s.
127
.. 4
525
.. 3
271
..
624
.. 9
379
.. 4
215
.. 5
.. f
(")
d.
£
ti.
d.
£
u
261
.. 17 ..
14
31
5
379
.. 13 ..•
5
75
5
257
.. 16 ..
74
39
1
184
.. 13 ..
5
97
3i
725
.. 2 ..
34
36
84
359
• • 6 . .
5
24
(")
s.
1
13
19
17
13
16
d.
H
1
74
34
5
34
£
27
]6
9
15
37
56
(")
fi.
13
12
13
2
19
J9
d.
5*
94
H
H
1
a
oz.
5
7
3
7
9
8
(0
dwt.
. 11 .
. 19 .
. 15 .
. 19 .
. 18 .
13 .
4
21
14
22
15
12
TROY WEIGHT.
lb. oz. dwt.
7 .. 1 .. 2
3 .. 2 .. 17
5 .. 1 .. 15
7 .. 10 .. 11
2 .. 7 .. 13
3 .. 11 .. 16
O
lb.
oz. dwt.
Rr.
5 ..
2 .. 15 ..
22
3 ..
11 .. 17 ..
14
3 ..
7 .. 15 ..
19
..
1 .. 13 ..
21
3 ..
9 .. 7 ..
23
5 ..
2 .. 15 ..
17
(*)
*.
d.
.. 3 ..
7
.. 17 ..
1
.. 15 ..
41
.. 10 ..
54
.. 19
''4
.. 17 ..
3i
lb. oz. dr.
152 .. 15 .. 15
272 .. 14 ,. 10
303 .. 15 .. 11
255 .. 10 .. 4
inio
835
13
13
AVOIRDUPOIS WETGHT.
(•)
cwt. qrs. lb.
25 .. 1 .. 17
72 .. 3 .. 20
54 .. 1 .. 16
24 .. 1 .. 16
17 .. .. i(^
55
16
(')
t. cwt. qrs. lb.
7 .. 17 .. 2 .. 12
5 .. 5 .. 3 .. 14
2 .. 4 .. 1 .. 17
3 . 18 .. 2 .. 19
7 .. y .. 3 .. 20
8
1
24
C3
90
ADDITION OF MEA8URBS.
APOTHECARIES' WEIGHT.
CLOTH MEASURE.
^35 .. 3 .. 3
70 .. 2 .. 2
,^5 .. 3 ..
176 .. 1 .. 3
26 .. .. 1
273 .. 2 .. i
(•)
E.E.
qr.
n.
272 ..
2 ..
1
152 ..
1 ..
2
79 ..
..
1
156 ..
2 ..
79 ..
3 ..
1
154 .,
2 ..
1
yd. feet
225 .. 1 .,
171 .. ..
52 .. 2 ..
S97 .. ..
154 .. 2 ..
137 .. 1
LONG MEASURE.
in. bar.
9 .. 1
3 .. 2
3 .. 2
10 .. 1
a.
726
219
1455
879
1195
(•)
r.
1
2
3
1
2
LAND MEASURE.
p.
31
17
14
21
14
(•)
a.
r.
1232 ..
1
327 ..
131 ..
2
1219 ..
I
JKn.
10V , ,
'4
p-
14
19
15
IS
17
ADDITION OF XBA8USE8.
m
ir- 8cr. gr.
* •• .. 12
7 .. 1 .. 17
2 •• .. 14
!••!.. 15
? - 2 .. 13
^ •• 1 .. 18
WINE MEASURE.
<:.
(•)
qr.
n.
•• 2 ..
1
• 1 ..
2
. ..
1
. 2 ..
. 3 ..
1
3 2 ..
1
u.. (*>
(•)
hhds. gals qts.
t. hhds. gals, qts
31 .. 57 .. 1
14 .. 3 .. 27 .. 2
97 .. 18 .. 2
19 .. 2 .. 56 .. 3
76 .. 13 .. 1
17 .. .. 39 .. 3
55 .. 46 .. 2
•
79 .. 2 .. 16 .. 1
o7 • • 38 • • 3
54 .. 1 .. 19 .. 2
55 .. 17 .. 1
97 .. 3 .. 54 .. 3
ALE AND BEER MEASURE.
(»)
(•)
(•)
A.B. fir. gal.
B.B. fir. gal.
hhds. gals, qts
25 .. 2 .. 7
37 • • 2 . . 8
76 .. 51 .. 2
17 .. 3 .. 5
54 .. 1 .. 7
57 . . 3 . . 3
96 .. 2 .. 6
y/ •• o •• o
97 .. 27 .. 3
75 .. 1 .. 4
78 .. 2 .. 5
22 .. 17 .. 2
96 .. 3 .. 7
47 .. .. 7
32 .. 19 .. 3
75 .. .. 5
*jO • • <6 • • d
55 .. 38 .. 3
DRY MEASURE.
fur.
j»o
• • 1 . .
19
.. 7 .,
S2
• . 5 , .
31
.. 6 .
12
. 6 .
17
. 5
21
(«
ch. bu. pks.
75 .. 2 .. 1
41 .. 24 .. I
29 .. 16 .. 1
70 .. 13 .. 2
54 .. 17 .. 3
79 .. 25 .. 1
last. wey. q. bu. r 41
38 .. 1 .. 4 .. 5 .. J
47 .. 1 .. 3 .. 6 .. 2
62 .. .. 2 .. 4 .. 3
45 .. 1 .. 4 .. 3 .. 3
78 .. 1 .. 1 .. 2 .. 2
29 .. 1 .. 3 .. 6 .. 2
• 1 . 14
• . 19
2 . 15
1 . IS
2 .. 17
(»)
w. d. h.
71 .. 3 .. 11
51 .. 2 .. 9
76 .. .. 21
95 .. 3 .. 21
79 .. 1 .. 15
TIME.
w. d. h. m. "
57 .. 2 .. 15 .. 42 .. 41
^5 .. 3 .. 21 .. 27 .. 51
76 i » Q » . ! 5 . . 9.1 oq
53 .. 2 .. 21 .. 42 .! 27
98 .. 2 .. 18 .. 47 .. 38
32
I
jii^;
ADDITION.
THJB APPLICATJON.
n ry ,.^ ^''^'^t JS the Slim of
"- •^<l. What do th.'e gotds'siandte ZT "'""' "><= ^^-^"^
^. There are two numbers fh« i . , ^"*- ^^7 : 10 : 3
Eldest sister's fortune, £138,]
»• A nobleman, before he „ *^f """• ''^^ "'em £25722
m'"S f his tradesmeit Ml, td™,' °'' '°"".' "^ "-'''^.3 of
I'e owed 82 guineas for rent i„ ht ^'*" '"'J""'-^' ''« ^""'1 that
to 1..S eonfoctioner, £12 : j 3 • 4 ^ "'"<: "'^'d^ant, £72 : 5
his t-iilor, £i 10 • 1, . fi . , ,-. * ' to "« draper, £47 • 1 o . o ' . '
ta"o,v-eli;u,dlery£8 /7\ t f T"=''-"«l^^^^ 5778^ t\' '.^
to his brewer, ist : 17. n 'Jt'"f "T""^'"""'!'''-. ^^O ■' 6 • R-
lOosiretokno.thamf^'LT?".'-^. ^.^ wage^'l^/^^'!;'
;k"S '^^ "'^ ^^- su- iioo,»vS hets'ri
-^w*. iJi 032 : 17 ; 3.
Ihebe47yeara
^ns. 1797.
»se of a quanti-
' a crown; B
It in all ?
^13 : 6 ;'3. .
^ several sums,
hur score and
fow much did
236 : 8 : 4.
tlie taxes are
£201 : 15.
\ second 519,
is tlie sum of
^ns. 14(38.
^54: 17, for
t the bargain
7 : 10 : 3.
0, their dif-
number, and
> 94 sum.
J'e than the
J and £11.
father leave
£13611,
'22.
^Icsirous of
found that
72 ; 5 : ;
: 2; to
I to his -
6 : 8;
to his
1 w]ien
-1 to take
17:3.
13
:
JO
5;
i :
oh
ADDITION. 33
10. A father was 24 years of a^e (allo^ving 13 months to a
(rear, and 28 days to a month) when his first child was born •
Detween the eldest 'and next born was 1 year, 11 months 14
lays; between the second and third were 2 years, 1 month 'and
15 days; between the third and fourth were 2 years, 10 months
md 25 days; when the fourch was 27 years, 9 months, and 12
lays old, how old 'was the father?
• ^ ^ins. 58 years, 7 months, 10 days.
11. A bankers clerk having been out with bills, biiuirs home
m account, that A paid him £7 : 5 : 2, B £15 • 18 • 6A C
£150 : 13 : 2^, D £17 : 6 : 8, E 5 guineas, 2 crown piec(^, 4
Ihalt-crowns, and 4s. 2d., F paid him only twenty groats, (> £7fJ •
115 : 9|, and H £121 : 12 : 4d. I desire to know how'much the
[whole amounted to, that he had to pay ?
-, o A 11 ^'**' ^^^^ • '^ ' H-
12. A nobleman had 'a service of plate, which consisted of
twenty dishes, weighing 203 oz. 8 dwts. ; thirty-six plates, W(n<rh.
ing 408 oz. 9 dwts.; five dozen of spoons, weighing 112 oz? 8
dwts.; six salts, and six pepperboxes, weighing 71 oz. 7 dwts •
kmves and forks, weighing 73 oz. 5 dwts.; two large cups, a
! tankard, and a mug, weighing 121 oz. 4 dwts.; a tea-kettle and
lamp weighing 131 oz. 7 dwts.; together with sundry other
small articles, weighing 105 oz. 6 dwts. I desire to know the
weight of the whole ?
,„ . , , -^ns. 102 lb. 2 oz. 13 dwts.
13 A hop-merchant buys five bag-s of hops, of which the fii-st
weighed 2 cwt. 3 qrs. 13 lb.; the second, 2 cwt 2 qrs 3 1 lb •
the third, 2 cwt. 3 qrs. 5 lb.; the fourth, 2 cwt. 3 qrs. 12 lb.';'
the fifth, 2 cwt 3 qrs. 15 lb. Besides these, he purchased t-o
pockets, each weighing 84 lb. I desire to know the wei^^ht of
the whole ? °
iA K c^7- ^ ^ns. 15 cwt 2 qrs.
^ 14. A, of Vienna, owes to B, of Liverpool, for goods receiNed
m January, the sum of £103 : 12 : 2; for goods received in Fe-
bruaiy, £93 : 3 : 4; for goods received in March, £121 • 17-
for goods received in April, £142 : 15 : 4; for goods received in
Alay, £171 : 15 : 10; for goods received in June, £142 : 12 : 6-
but tue latter .six months of the year, owing to the fallin'^ off in
the demands Pnr tha nrfn.loo ir. «*i.w»u i.^ ;i..„u ii,- '"^ .
only £205 : 7 : 2. I desire to know the amount of the whole
year's bill ?
• Ans. £981 : 3 : 4.
t4
jVBTRAonoir.
SUBTRACTION OP MONEY, «.eighiB & MEASUBEa
that as make one of the next s.^ri^'^^'.'*"'?" "« "'""y <>f
from .,,eh take thl lowe^f e To""'th*^tL" *" '"-'A^A
MONEY.
(')
Borrowed 715 .. 2 .. 7i
Paid 476 .. 3 .. si
Remains to pay 238 . . 18
lOi
Prsoof 715 .. 2
7i
£ *• <'•
87 .. 2 .. 10
79 .. 3 .. 7i
*> *.
3 .. 15
1 .. 14
d.
H
7
Lent 316 .. 3 .. 5J
Received 218 .. 2 .. ij
^^ " Q •• 8i 25 .. 5 .. 2I
£
321
257
o
s.
17
14
7
59
36
(')
*.
15
17
Paid in all
Remains to pay
(•)
^i ^ '- d. £
• ^i 71 .. 2 .. 4 527
• 2 19 .. 13 .. 71 139
Borrowed 25107 .. 15 .. 7
^ .^ 375 .. 5 .. 5k
Paid 259 . . 2 . . 7^
at 359 .. 13 .. 41
different 523 .. 17 .. 3
times 274 . . 15 . . 7J
325 .. 13 .. 5
». d.
• 3 .. 54
• 5 .. 7i
Lent 250156
271
6
Received 359 . . 15 . . 3
at 475 .. 13 .. 91
several 527 .. 15 .. 3]
payments 272 .. 16 .. 5
150 .. ..
MEASURES.
Y of the lower]
^ as many off
to the upper,
nee, and carry
arrowed.
*. d.
• 2 .. i|
1
(•)
*. d.
^ " 3 .. 44
• •• 5 .. 2i
iuBTKAcnoir. 86
TROY WEIGHT.
lb. oz. dwt. gr. lb. oz. dwt gr.
0) Bought 52 .. 1 .. 7 .. 2 (•) 7 .. 2 .. 2 .. 7
Sold 39 . . . . 15 . . 7 5 . . 7 . . 1 . . 8
Unsold
AVOIRDUPOIS WEIGHT.
lb. oz. dr. cwt. qrs. lb. t. cwt. qrs. lb
(•) 35 .. 10 .. 5 (*\ 35 .. 1 .. 21 <•) 21 .. 1 .. 2 .. 7
29 .. 12 .. 7 25 .. 1 .. 10 9 .. 1 .. 3 .. 5
APOTHECARIES WEIGHT.
lb. oz. dr. scr. lb. oz. dr. scr. gr
(») 5 .. 2 .. J .. (») 9 .. 7 .. 2 .. 1 .. IS
2..5..2..1 5..7..3..1..16
Fl.E. qr, n.
(>) 35 .. 2 .. 2
17 .. 2 .. 1
CLOTH MEASURE.
yd. qr. n.
(«) 71 .. 1 .. 2
o . < « • • 1
E.E. qr. n.
(•) 35 .. 2 .. 1
14 .. 3 .. 2
LONG MEASURE.
yds. ft. in. bar.
O 107 .. 2 .. 10 ., 1
78 .. 2 .. 11 .. 2v
lea. mi. fur. po.
(•) 147 .. 2 .. 6 .. 29
58 .. 2 .. 7 .. 33
LAND MEASURE.
a. 1
O 175 .. 1 .
^M
1'
27
27
9 r. p
(•) 325 .. 2 .. ]
279
tirBTRAeriopK,
:'a >ttlailfc ..-t
WINE MEASURE.
hhd. gal. tg
28..39..3.:i <•)
tun- tlid. ptil. ,,^
4'^ •• 2 .. 37 .. a'
17 .. 3 .. 49 .. 3
A.B. fir. eal.
O 25 . . 1 . .*^2 •
21 .. 1 .. ft
ALE AND BEER MEASURE.
O
BB. fir. gal.
37 ,. 2 ..*i
25 .. 1 .. 7
hhd.
(•) 27
12
gal. qt.|
27 .. 1 '
50 .. a
q«. bir! n
O 72 .. 1 .. I'
35 .. 2 .. 3
DRY MEASURE.
q«. bu. p.
O 65 .. 2 .. 1
57 .. 2 .. 3
(•) 79 .. 3 ..
54 .. 7 .. 1
TIME.
yrs.
O 79
ino- w. ds.
8 .. 2 .. 4
23 .. 9 .. 3 .. 5.
/#
. ^f. inf#.
(") 24 .. 42 .. 43
19 .. 53 .. 47
THE APPLICATION.
«. A man wa. bor„ i„ the year :,83. what wa, hi, age i„ ,he ,ear ,,,,1 ,
JhZtrn in tmr""' '"'"="" "•« »«= of a man born inlTiO^Ind
S. A Merchant had five debforq a t> r. T^ »»*. .
•.- ^no.. B. c. D. and tr:at.''iV3?- ^^b^! :!;° JCa-;-"
^ i»ru •^W.f. i;419
to 12 ,c-o;e and £U r'a'I^^Cir.E^Tiir'''""''' ™ ''^
^n». £45 ; 14.
wmmmnitv n ii i Mt, ),
COMPOUND MULTIPLICATION,
37
ihd.
gal
27 .
. 27
12 .
. 50
qt.l
1
3
ch.
79
54
bo.
• • 3 , ,
• • 7 • ,
•
p
1
«
mffr.
-• 42 .. 45
' 53 .. 47
le year 1781?
•^ns. 58,
in 1710, and
''ins. 56.
gether owed
"s del.t ?
na. £i\g,
'ing of taxes
£45:14.
15. What is the difference between £9154, and the amount of JC754 added
I to £305?
Ans. £8095.
6. A horse in his furniture ig worth £37 : 5 ; out of it, 14 guineas ; how
much does tlie price of the furniture exceed that of the horse ?
• Ans. £7 : 17.
7. A merchant at his out-setting in trade, owed £750; he had in cash,
coniniodities, the stocks, and good debts, £12510 : 7 ; he cleared, the first
[year, by commerce, £152 : 3 ? 0; what is the neat balarce at the twelve
months' end ?
Ans. £12212 : 10 : 6.
a A gentleman dying, left £ <5247 between two daughters, the younger
who was to have 15 tliousand, 15 hundred, and twice £15. What was the
elder sister's fortune ?
Ans. £28717.
9. A tradesman happening to fail in business, called all his creditors to-
gether, and found he owed to A, £63 : 7 : 6 ; to B, £J05 : 10; to C, £34 •
5:2; to D, £28 : 16 : 5; to E, £14 : 15 : 8 ; to F, £112 : 9; and to G,
£J 13 : VI : 9. His creditors found the value of his stock to be £212 : 6,
and that he had owing to him, in good book debts, £112 : 8 : 3, besides
£■21 : 10 : 5 money in hand. As his creditors took all his effects into their
hands, I desire to know whether they were losers or gainers, and how
much ?
Ans. The creditors lost £146 : 11 : 10.
10. My correspondent at Seville, in Spain, sends me the following ac-
count of money received, at different sales, for goods sent him by me, viz •
Beeswax, to the value of £37 : 15 : 4 ; stockings, £37 : 6 : 7 ; tobacco, £125'-
11:6? linen cloth, £112:14:8; tin, £113 : 10 : 5. My correspondent, at
the Siime time, informs me, that he has shipped, agreeably to my order,
wines to the value of £250 : 15; fruit to the value of £51 : 12 : 6; figs,
£19 : 17 : 6; oil, £19 : 12 : 4; and Spanish wool, to the value of £115 :
15 : 6. I desire to know how the account stands between us, and who is
the debtor ?
Ans. Due to my Spanish correspondent, £23 : 14 ; 4.
MULTIPLICATION OF SEVERAL DENOMINATIONS.
RuLR.— Multiply the first Denomination by the quantity given, divide
the product by as many of that as make one of the next, se't down the re-
mainder, and add the quotient to the next superior, after it is multiplied.
Tf thff given quantity is above 19, multiply by any two numbers, which
multiplied together will make the same number; but if no two numbers
multiplied together will make the exact number, then multiply the top
line by as many as is wanting, adding it to the last product.
D
"!
tOtL
..MHilL
88
COMPOUND MULTIPLICATION.
Proof. By Division.
(')
£
s.
d.
35:
12 :
7i
2
71 :
5 :
n
£ a. d.
75: 13: li
3
1. 18 yards of cloth, at 9s. Gd.
per yard. o
0X2=IR ,
4:5:0
3
£ 9. d.
62:5 : 4i
4
£ s. d.
67 : 2 s 4|
5
8 : 11 :0
2. 20 lb. of tea, at £1 : 2 : 6
per lb. o
8X3X =20 !
i>:0:0
3
27 : :
Top line X2=2 :5:0
29 : 5 :
3. 21 ells of Ilollnnd, at Vs. S^d. per ell.
4. 35 firkins of butter, at I5s. 3^d. per firkin.
6. 76 lb. of nutmegs, at Is. 23d. per lb.
6. 37 yards of tabby, at 9s. 7d. per yard.
H ci^ , c ^ o Facit, £17: 144 7.
7. 97 cwt. of cheese, at JCl : 5 : 3 per cvvt.
ft ^Q 1 r „ ^"^^^ -^122 : 9 : 3.
8. 43 dozen of candles, at Cs. 4d. per dozen.
lo^u ei) i . , Facit, £13: 12:4.
9. 127 lb. of Boliea tea, at 12s. 3d. per lb.
10. 135 gallons of rum, at 78. 6d. per gallon.
n H . ,, ^ J. , Facit, £60 : i : 3.
11. 74 ells of diaper, at Is. 4tid. per ell.
12. G dozen pair of gloves, at Is. lOd. per pair.
Facit, £0 : 12.
When the given quantity consists of i, ^, or |.
Rule. Divide the given price (or the price of one) by 4 for i bv 2 for 1
them to the product, and their sum will bo the answer re^iui ed
COMPOUND MULTIPLICATION,
39
(•)
£ s. d.
57 : 2 ! 4|
5
13. 25i ells of holland, at 3 : 4id. por ell.
5
5X5 = 25
- —
ea, at £l
:2
: 6 ^
8 j
:
iO
:0 1
3 1
e
27 :
X2=2 :
Oi
:0 1
:0 1
29:
5:
1
1:1: 10^.
t : 16 : 2i.
^ : 2 : 2^.
1: Uil.
22 : 9 : 3.
3 : 12 : 4
7 : 15 : 9.
)0 : 1 : 3.
55 : 1 : 9.
£0 : 12.
01' 4. by 2 for
y '-' Tor i, add
red.
^
10: lOi
5
4:4:4^ = 25
0:l:8i = J
4:G:0^ = 25i
14. 75 J elk of diaper, at Is. 3d. per ell.
Facit, £4 : 14 : 4J.
15. 19 J ells of dain.'isk, at 4s. 3d. per ell.
Facit, £4 : 2 : lOj.
16. 35 J ells of dowla.s, at Is. 4d. per ell.
Facit, £2:7:4.
17. H cwt. of Malaga raisins, at £l : 1 : 6 per cwt.
Facit, £7 : 16 : 10 J.
18. 6 J barrels of herrings, at £3 : 15 : 7 per barn^I.
Facit, £24: 11 : 3^.
19. 35i cwt. doubled refined sugar, at £4 : 15 : por cwt.
Facit, £109: 10:3.
20. 154i cwt. of tobacco, at £4 : 17 : 10 per cwt.
Facit, £755 : 15 : 3.
21. Il7i gallons of arrack, at 128. Od. i)or gallon.
Facit, £73 : 5 : 7 J.
23. 85^ cwt. of cheese, at £l : 7 : 8 por cwt.
Facit, £118: 12:5.
23. 29i lb. of fine hyson tea, at £l : 3 : per lb.
Facit, £34 : 7 : 4A.
24. I7f yards of superfine scarlet drab, at £l : 3 : i)cr yard.
Facit, £20: 17: 1^.
26. 37i yards of rich brocaded silk, at 12s. 4d. per ynnl.
Facit, £23 : 2 : 6.
26. 50 1 cwt. of sugar, at £2 : 18 : 7 per cwt.
Facit, £160:4 :7i.
27. 96i cwc. of currants, at £2 : 15 : per cwt.
Facit, £207 : 15 : 9.
28. 45| lb. of Beiladino silk, at 188. 6d. per lb.
nn H, , , , Facit, £42 : 6 : 4i.
29. 87f bushels of wheat, 5it 4s. 3d. per bushel.
Facit, £18:12:11*.
d2
40
COMPOOWD MULTIPLICATION.
80. 1201 cwt. of hops, at £4 : 7 : 6 per cwt.
31. 407 ya*„f cloth, at 3s. 9Jcl, per v^f ^''' = ' = '*•
32. 729 ells of cloth, at 7s. 7i<l. per ell. ^"'' ^" •' ' ' '^■
33. 2008 yards of lace, at 9s. 5id. per 5!'' ^'" = ' = '*•
Facit, £977 : 19 : 10.
THE APPLICATION.
o.oto each man ; what was the value of tJie prize «
, cuiu wnat lb their sum and product ?
4. W,.at difference hotter! Vf' ^^"? ®^''' ^"""^""^ «2208.
twice mv-cight,^/; iLlrLv pSeir ^■='" '-"^ ^f'^. -<•
required* ' ^'^ ^^0.'/^'' '"™ "'"' l'™''"'^' a™
6. The sum of two numben ' i! 300 7' T''f l'""^"'''
what is th.r ..rod^^^^^^^^^ tpqUeTihtl^utetf" ".^^
men, and 207 battalion,, e'nd 500 Z " '""'>■ '"•='' '*"
diers, supposing th.at in 7 hitrtC 'a 'rr73"3 J*-^""^''™ ^* :
0: A merchant liad £19118 tn h. ' f'",' ^^^'^^ * ^^ •' ^•
t^^ther lie cleared £loll^yL^ ^^J^f^ "^^ ' ^'^ ? ^^-
^52715 : 10 : 6 a year- bn tlut l' H" ,^ '''"'' ^"^ '"''^^^'^ ?^f»J
had tlie misfortune tt. I. ■^i""'' ^''' ''^' "^ ^'^''^'^J'^^ ^'-^
year, what wjis his real fortune at 12 yeai-s' end ? '^ " * ' ** ^
^W5. X33984 : 8 : 6.
pieces,
year;
COMPOUND MULTIPLICATION.
"4^
: 3 : 2^.
: 3 : 5i.
: 19 : 10.
18 men, so
5:0: 0.
loiinted tc
prize ?
: 15 : 0.
and Iialf a
; 62208.
I fifty, and
>oduct.
37 times
rod net are
Voduct.
em 144;
Ference.
each 157
active sol-
44800.
with his
■t having I
ach quiil I
14 : 0.
' 5 years
^de good
ivadoj h'?.
:4:6a
8:6.
i
10. In some parts of the kingdom, they weigh their coals by a
machine in the nature of a steel-yard, waggon and all. Three
of these draughts together amount to 137 cwt. 2 qrs. 10 lb., and
tlie tare or weight of the waggon is 13 cwt. 1 qr. ; how many
coals had the customer in 12 such draujihts?
Ans. 391 cwt. 1 qr. 12 lb.
11. A certain gentleman lays up every year £294 : 12 : 6,
and spends daily £1 : 12 : 6. I desire to know what is his an-
nual income? Ans. £887 : 15 : 0.
12. A tradesman gave his daughter, as a marriagoj portion, a
scrutoiro, in which there were twelve drawers, in each drawer
were six divisions, in each division there were £o0, four crown
pieces, and eight half-crown pieces; how much had she to her
tbrtune? ^W5. £3744.
13. Admitting that I pay eight guineas and half-a-crown for a
quarter's r<3nt, and am allowed quarterly 15s. for repairs, what
does my apartment cost me annually, and how much in seven
years? ^HS. In 1 year, £31 : 2. In 7, £217 : 14.
14. A robbery being committed on the liighway, an assessment
was made on a neighbouring Hundred for the sum of £380 : 16 :
6, of which four parishes paid each £37 : 14 : 2, four hamlets
£31 : 4 : 2 each, and the four townships £18 : 12 : 6 each; how
nnich was the deficiency? Ans. £36 : 12 : 2.
15. A gentleman, at his decease, left his widow £4560 ; to a
public charity he bequeathed £572 : 10; to each of his four ne-
phews, £750 ; 10; to each of his four nieces, £375 : 12 : 6; to
thirty poor housekeepers, "ten guineas each, and 150 guineas to
his executor. What sum must he have been possessed of at the
time of his death, to answer all these legacies ?
A71S. £10109 : 10 : 0.
16. Admit 20 to be the remainder of a division sum, 423 the
quotient, the divisor the sura of bo'h, and 19 more, what was the
nunibei of the dividend? Ans. 195446.
EXAMPLES OF WEIGHTS AND MEASURES.
Multiply 9 lb. 10 oz. 15 dwts. 19 grs. by 9.
n Multiply 23 tons, 9 cwt. 3 qrs. 18'lb. by 7.
(®) Mniti|)iy 107 yards, 3 qrs. 2 nails, by 10.
Multiply 33 ale bar. 2 firk. 3 gal. by 11.
Multiply 27 beer bar. 2 firk. 4 gal. 3 qts. by 12.
•) Multiply 110 miles, fur. 26 poles, by 12.
1)3
43
DIVISION.
DIVISION OF SEVi^ML DENOMINATIOKS.
5! T^;.,:j_ ii
My "emains.'ml.ufdv'irbv '«?"""''''■''" °° ""^ k" hand and if'
.one of that, which Jd tl X iT'Vt '-'i"^ "<"" '''^^ ."ak!
. 'K. ,
^)!^4( 3)3f:r:,'( J\f, /\<i.
7^77^ ■ -^ *)^^( 5)52: 7 :0(
O Divide £1407: 17: J bv 243
h Divide £197430,2' 5'.^7iV^.Vf^
^ ♦'^ • o . 7^ by 214723.
THE APPLICATIOjf.
. •!• If a man spends £2^^ • o
■3 that per month ? ^ ' • 2 : o in twelve months' time, what
^vep|te *«^ = « •• ^1 for nine pieces J^^^^^ = f, ^
^rJSfl^r:'?? :t'? "^ - ""^^-d of ^!::Z; iVote
.tth£rp:^-.:?r-----o:o-.;^-?i.
J;^--5:3:4for30ha,esofc,oth,ir-t,^;?i;,
8. A pnze of £7257 : 3 • fi !, t„ i ^''*- -^IS : 5 : 8J
«00 sadors, what is each man's sIL'e? ' '^"""^ '""^ed amongst
?• There are 2545 hnll^^i ^ , ^^s- £14 • in . qi
DIVISION.
4S
^TIOJVS.
'eft hand, and if ^
't less as make
before.
is' time, what
1:8: 61
' 3 : 4, what
1:12: 8.
> what did I
* : 2 ; 11.
t what rate
^1 : V : 3.
len 120 are
/ 5 : Of.
'ire to l^now
: 3 : 8^.
that for 2
: 5 : 81
tl amongst
10 : 3^.
>f'0 men, I
^e of each
1 share.
10. A gentleman lias a garden walled in, containing 9625
lyards, the breadth was 35 yards, what was the length ?
Ans. 275.
11. A club in London, consisting of 25 gentlemen, joined for
la lottery ticket of £10 value, which came up a prize of £4000.
I desire to know what each man contributed, and what each
I man's share came to ?
Ans. Each contributed 8s., each share £160.
12. A trader cleared £1156, equally, in 17 years, how much
did he lay by in a year? Ans. £68.
13. Another cleared £2805 in 7^ years, what was his yeaily
Increase q^ tbitunfi ?
Ans. £374.
14- What number added to the 43d part of 4429, will raise it
to 240? Ans. 137.
15. Divide 20s. between A, B, and C, in such sort that A may
have 2s. less than B, and C 2s. more than B ?
Ans. A 4s. 8d., B 6s. 8d., C. 8s. 8d.
16. If there are 1000 men to a regiment, and but 50 officers
how many private men are there to on^ officer ?
Ans. 19.
17. What number is that, which multiplied by 7847, wil.
make the product 3013248 ? Ans. 384.
18. The quotient is 1083, the divisor 28604, what was the di-
vidend if Hhe remainder came out 1788 ?
Ans. 30979920.
19; An army, consisting of 20,000 men, took and plundered
a city of £12,000. What was each man's share, the whole
being equally divided among them ?
Ans. 128.
20. My purse and money, said Dick to Harry, are worth 12r.
8d., but the money is worth seven times the pui-se. What did
tlie purse contain? Ans. lis. Id.
21. A merchant bought two lots of tobacco, which weighed
12 cwt. 3 qrs. 15 lb., for £114 : 15 : 6. Their difference in
point of weight, wjis 1 cwt. 2 qrs. 13 lb., and of price, £7 : 16
6. I desire to know their respective weights and value ?
Ans. Less weight, 5 cwt. 2 qrs. 15 lb. Price, £53 : 10,
Greiiter weight, 7 cwt. 1 qr. Price, £61 : 5 : 6.
22. Dividfl 1000 crowns in such a niannor betwctn A, B, and
C, that A may receive 129 more than B, and B 178 less than CL
Am. A 360, B 231, C 409.
4A
BILLS OP PARCELS.
EXAMPLES or WEIGnie AND MEASURES.
1. Dividc3 83 lb. 5 oz. 10 dvvts. 11 p.. by 8
2. Divnc e 29 tons, 17 cwt. m-s. 18 lb L o
S. DivKo 114 yards, 3 qrs. 2 l.ails, b^! 1?
4. Dmdol017n,iH6V38Hos,^>yll ^
JutSltsf ^^^^^"' ' --ths, 3Us, ^ days, 11 hou., 27
BILLS OF PARCELS. .
HOSIERS*.
Mr. John Thomas,
BoiigJit of Samuel Green.
8 Pair of worsted atockinrrg ^f !* . f"
5 Pair of thVad ditto. . . f 'y^^'-'tlt ^'' ^^'' ^
3 Pair of black silk ditto ' i ? ' i "
6 Pair of milled hose.!::: ^^^^ ••
4 Pair of cotton ditto I'.i
2 Yards of fine flannel / '
May 1, 18
8 per yard
£1 : 12 : 2
MERCERS*.
O Mr. Isaac Grant,
Bought of John Sims,
15
18
d.
May 3, 18
Vards of satin „* q . ^
Yards of flowered silk ! . . .i ! . ..'.H :* 4.!''^
16 i ards of sai-senet « . °
13 Yards
• • • • t
3 : 2,
xds of Genoa velvet ' 9^ '. a
23 Yards of lutestring ..'/.. q l q.
iJC2 : 2 : 5
BILLS OF PARCELS.
46
LINEN drapers'.
IC) Mr. Simon Surety,
Bought of Josiah Short. June 4, 18
s. d.
4 Yards of cambric at. . . 12 : G per yard £
12 Yards of muslin 8:3
15 Yards of printed Hnen 5 : 4 •
2 Dozen of naplvins ...,2:3 each ...
14 Ells of diaper 1:7 per cU . .
85 Ells of dowlas 1 : li
£17 : 4 : C^
MILLINERS.
(*) Mrs. Bright,
Bought of Lucy Brown.
£ s.
18 Yards of fine lace at. ..0:12
5 Pair of fine kid gloves. . . . . .0 *. 2
12 Fans of French mounts : 3
2 Fine lace tippets 3 : 3
4 Dozen Irish lamb : 1
6 Sets of knots : 2
June 14, 18
d.
3 per yard £
2 per pair
6 each ...
:0
: 3 per pair
: 6 per set. .
£22
WOOLLEN DRAPERS'.
(•) Mr. Thomas Sage,
Bought of Ellis Smith.
17 Yards of fine serge. . . .at. . .0 :
18 Yards of drugget :
15 Yards of superfine scarlet .. .1 :
Yards of black :
Yards of shalloon .0 :
16
25
11
June 20, 18
d.
; 9 per yard £
;
;0
;
; 9
: 6
..•...•
£59 : 5 :
I'l
iMi
i
46
BILLS OF PARCELS.
^^'^ Giles HarnX "^^"^^'^—^
l^«"glit of Abel Smith.
f Calfskins , ^. ^. "^"'^^'^^
^^5 SlH-ep ditto ...;.; '•**... 3 : 9 per skin £
^^' Coloured jitto. . . ^'^
15 Buck ditto... 1 : 8
17 I^ussia Ifides ^ ^ •" 6 . . , .
120 Lamb Skins.;;;; ^0:7....;;;
i-Si
£38:17:5
( ) Mr. Richai-d Groves,
Bought of Francis Elliot.
25 lb. of Jump sno-ar s. d.
2 loaves of doubFe r;fineV V * ' "^ '' ^* P^^ lb. £
14 lb. of rice... ^ •" • H^
28ib.ofMaiaga;;i;i;;;;;; I- «
15 lb. of currants ^' 5
^ ^'^•^f wackpe;);;;:::;;;;;;;;;0; 5^
July 5, 18
cheesemongers'.
(*) Mr. Cliarles Cross,
I^ought of Samuel Grant,
^3:2. 3i
8 lb. of Cambrido-e huttor ^' ^•
^l ">. of new checfse ' ^^- • -0 : 6 per lb. £
5 I'lr. of butter, wt 28* IK ^ ' ^ • •
5 aeshh-e d^^^^^^^^^ 0:5|..
2 Warwickshire ditto, 15 lb ^ ' ^ ' •
12 lb. of cream cheese ^ •' ^ • .
^ 0:6 ..
July G, 18
£3 : 14 : 5
reduction. 47
corn-chandlers'.
(•) Mr. Abraham Doyley,
Bought of Isaac Jones. July 20, 18
d.
[Tares, 19 bushels at. , 1 : 10 per bushel £>
Pease, 18 bushels 3 : 9^
Malt, Y <iu.irters 25 : per quarter
Hops, 15 lb 1 : 5 por lb. . . .
j Oats, G <[rs 2 : 4 per bushel
Beans, 12 bushels .....4: 8 ........
£23 •.7:4
REDUCTION pp pp
Is the bringing or reducing numbers of one denornination into
other munbers of another denomination, retaining the same value,
and is performed by multiplication and division.
First, All great names are brought into small, by multiplying
with so many of the less as make one of the greater.
Secondly, All small names are brought into great, by dividing
with so many of the less iis make one of the greater.
▲ TAULE OF SUCU COINS AS ARE CURL NT IN ENGLAND.
£ s. d.
Guinea 1 : l : o
Half ditto 0:10:0
Sovereign , 1 : :
Half ditto 0:10:0
Crown : 5 :
Half ditto 0: 2:6
Shilling : 1:0
Note. There are several pieces which speak their own
value; such as sixpence, fourpence, threepence, twopence, penny,
halfpenny, farthing.
1. In £8, how many shillings and pence!
20
160 shillings.
12
1920
48
Ml
III
W
BEDUCTION.
2. In £12, how manv shill
ings, pence, and fartliino-s ?
8 InSlT^QAf .!,• 1 ^^^*- 240s. 2880(1. 11520 far.
«. m 311520 farthings, how many pounds ]
4. How many farthings are there in 21 guinelT ^^^^ '' ^^*
5 Tn i!T7 . K . oi 1 « -^ws. 21108.
o. in iJ5 . 14 . 1, how many shillinjjs and pence!
». In 17940 pence, how many crowns? ""''■ '"if ^ol"
8. In 15 crowns, how many shillings and sixpence.?
9. In 57 half-crowns, how many pen^^^'Sd'tth' "rr"""-
in T« Ko ^^*- l^lOd. G840 farthino-s
tow^nitZr? " "»y>^^'f— '. ^hill,„gs, ^Id'^rence,
»280 tahin"T^ f^""' ^'""'"S^- -/ P--!^. - 'tit™ • h.
12. How m'any g„.ne,. in 21168 fJCj^"'- '"''■ ^''■
13. :a 16573 farthings, how many pouni ? ^'"^ '' ^"■"^^•
14. In 6169 p„„ce, how many shillings ancf ^^.fiV ' ' '*•
15. Jn 6840 farthmgs, how many pence and h.-df-crowns ?
16 In 2149^ f *T,- 1. ^^^' '^^1^^- 5V half-crowns.
lin^; Ja pr,^a^|"e-ht\Tarn= "^'Tr^f "
17. How many shilhngs, crownsjand pounds, in 60 ^.ink',.'
18. Reduco 76 moidores into JZ^Z^ZZ""-' '''■
19. Reduce £102 : 12 into shillings aifd^moS; f "^ ^ ''■
.a^^-pLr '''■'--' - -;•— trs^iifi:;rhow
22. Seven men brono-ht £^^ - m i, • . "f^""' "^^"'^ ' ^^-
changed for guineaJZ'wLf J muft l^ I't taH f'' " ^" ^^^
^WA'. 103 guineas, 7s. over.
23.
24.
26.
21.
28.
29.
15 gr.
33.
REDUCTION.
49
11520 far.
iJ324 : 10.
IS. 21108.
''S. 10573.
s. 0109(1.
Ans. 299.
sixpences.
farthinors.
and pence,
f. 21424.
8 there in
Os. £18.
gunieas.
; 5 : 3^.
14 : 1.
^ns?
crowns.
»wns, shil-
im. 52.
uineas ?
s, £03.
2 : 12.
>idores.
ire tliei*e
1. over,
ig.^, how
) : 18.
to bo ex-
over.
23. If 103 guineas and seven shillings are to be divided
amongst seven men, how many pounds sterling is that each ?
Ans. £15 : 10.
24. A certain person had 25 purses, and in each purse 12 gui-
neas, a crown, and a raoidore, how many pounds sterling had he
in all ?
Ans. £355.
25. A gentleman, in his will, left £50 to the poor, and ordered
that ^ should be given to ancient men, each to have 5s. — ^ to
poor women, each to have 2s. Od. — \ to poor boys, each to have
Is, — 1 to poor ^'irls, each to have 9d. and the remainder to the
person who distributed it I demand how many of each sort
there were, and what the person who distributed the money had
for his trouble I
Ans. 66 men, 100 women, 200 boys, 222 girls,
£2 : 13 : 6 for the person's trouble.
TROY WEIGHT.
26. In 27 ounces of gold, how many grains?
Ans. 12960.
27. In 12960 grains of gold, how many ounces?
Ans. 27.
28. In 3 lb. 10 oz. 7 dwts. 5 gr. how many grains ?
Ans. 22253.
29. In 8 ingots of silver, each weighing 7 lb. 4 oz. 17 dwts.
15 gr. how many ounces, pennyweights, and grains ?
Ans. 711 oz. 14221 dwts. 341304 gr.
30. How many ingots, of 7 lb. 4 oz. 17 dwts. 15 gr. each, are
there in 341304 gi-ains? Ans. 8 ingots.
31. Bought 7 ingots of silver, each containing 23 lb. 5 oz. 7
dwts. how many grains? Ans. 945336.
32. A gentleman sent a tankard to his goldsmith, that weighed
50 oz. 8 dw^ts. and ordered him to make it into spoons, each to
weigh 2 oz. 16 dwts. how many had he?
Ans. 18.
33. A gentleman delivered to a goldsmith 137 oz. 6 dwts. 9
gr. of silver, and ordered him to make it into tankards of 17 oz.
15 dwts. 10 gr. each; spoons of 21 oz. 11 dwts. 13 gr. per dcz.
salts of 3 oz. 10 dwts. each; and forks of 21 oz. 11 dwts. 13 gr.
per doz. and for every tankard to have one salt, a dozen of spoons,
and a dozen of forks ; what is the number of each he must have ?
Ans. 2 of each sort, 8 oz. 9 dwts. 9 ^r. over.
E
I'
4
! I
.11
fiEDUCTION
AVOIRDUPOIS WEIGHT
add onJ'hSr"' """"''' '"•" "■""»"- """«il.'^ by 3. and divide b^ 5 „
tral^'niThrd'" P""""' ""° S-»'. n.ul.iply by 2, and divide by 3. or . ^
I2 dS.::."""^^ """%• ?"-»
i<f GI0S3. or IM doz. . . i n,-^^t n
24 Sheets.... ^^leat G oss.
20 Quires ;;; J g'^""^-
2 Reams ^*^^"?,-
1 Roll.
34. In 14769 ounces how many cwt. ?
35. Reduce 8 cvvt ors 27 Ih i • "^''*' ^ ''"'^- ^ '^'•- ^7 lb. 1 oz.
'"• '' ''• ' °^- ^r^'^S--^' P«"-'«, and ounces.
36. Boueht 32 bi<.q of k , ^"^ ^•■^- ^'^^ lb. 14769 oz
^'. In 34 ton. n ow.. I ,.. ,« „. ,„„ „,„,-^::„:;r'- ' 1^- '0 'b.
38. In 547 great poun*. how many co.m„„ p,„„j, , •""'• '«'" "^
39. in 27 c„t of raisin, h<„. „,„, p„„,, „, ,^ ,f- «^0 lb. 8 „..
40. In 9 cwt. 2 qrs. 14 lb of Jn,<;„„ u * '^"•'' ^^S.
4 »• -i^ ID. oi mdigo, how many pounds ?
41. Bouerht 27 ba^s of linn. i « *^"*- 1(>'?9 lb.
lb., how mLy cwtfn ,he Thik ? ' ' '^'^ ' "'• ''' "■■ »"'J »"«' bag of 137
42. How many pounds in 97 l,„ i .. , ■^"''- *" ™'- ' I"- "> 'b.
SI cwt. > ^ P"™"' •" 2' hogsheads of tobacco, each weighing neat
«. In =52 common pounds of silfc. bow n,a„y great pount'' ''''"
^U. How .any p,rce,s of sugar of t5 lb. 2 „.. are there in tflwt'f ,,
^««. 113 parcels, and 12 lb. 14 OZ. over.
heel by a great
Jrefore,
livide by S or
i by 3, or 9 \.
REDUCTION. 51
APOTHECARIES' WEIGHT.
46. Ir. 27 lo. 7 oz. 2 dr. 1 scr. how many gra'ns?
Ans. 159020.
46. How many lb. oz. dr. scr. are there in 159020 grains?
Ans. 27 lb. 7 oz. 2 dr. 1 scr.
CLOTH MEASURE.
m
i
■ lb. 1 oz.
and ounce*.
14769 oz.
ther of 150
ir. 10 lb.
'8111 lb,
lb. 8 oz.
«.«. 16S. ,
1073 lb. *
►ag of 131
. 10 lb.
hing neat
26460
s. 368.
wt. 1 qr.
over.
47. In 27 yards, how many nails ? Ans. 432.
48. In 75 English ells, how many yards ?
A71S. 93 yards, 3 qrs.
49. In 93f yards, how many English ells? *:^;>:. 75.
60. In 24 pieces, each containing 32 Flemish ells, ho"? ^lany
English ells ? Ans. 460 English ells, 4 qrs.
51. In 17 pieces of cloth, each 27 Flemish ells, how many
yards ? Ans. 344 yards, 1 qr.
62. Bought 27 pieces of English stuff, each 27 ells, how many
yards? Ans. 911 yards, 1 qr.
53. In 911 1: yards, how many English ells?
Ans. 729.
54. In 12 bales of cloth, each 25 pieces, each 15 English ells,
how many yards ? Ans. 5625.
LONG MEASURE.
65. In 57 miles, how many furlongs and poles ?
Ans. 456 furlongs, 18240 poles.
56. In 7 miles, how many feet, inches, and barley-corns ?
Ans. 36960 ft. 443520 in. 1330560 b. corns.
67. In 18240 poles, how many furlongs and miles?
Ans. 456 furlongs, 57 miles.
58. In 72 leagues, how many yards? Ans. 380160.
59. In 380160 yards, how many miles and leagues?
Ans. 216 miles, 72 leagues.
60. If from London to York be accounted 50 leagues, I de-
mand how many miles, yards, feet, inches, and barley-corns ?
Ans. 150 miles, 264000 yards, 792000 feet,
9504000 inches, 28512000 barley-corns.
61. How often will the wheel of a coach, that is 17 feet in
circumference, turn in 100 miles ?
Ans. 3l058|4 times round.
£2
8S
t
#
ml.
r
itBDUCTION.
£.fcn,fera;L^^^^^^^ the worfa, the'
LAND MEASURE.
«3. In 27 acres, how ma„^ roods and perches'
64. In 4320 perches, how mJZL"? ""^''' *^^° ^"'^'^■
poMat rrd tijip^s^ri « --^^^ ^^ i
l^ow ,„an^ perches he wK 14?"'" '" ^•. ^ "--« «» W
-!»«• 40 shares, 42 perches rem.
WINE MEASURE
'' '""="'"' ^ '""' "^ P-' -> how .an, .anons and pints,
h.«, ^",^896 gallons of Camre L ^"'- ^ tuna,
heads, and of each an equal nur^^ ^"^ """'? P>« "nd hogs.
whow.:;tzen':'a:httadr ^-"^ ''^-^ *^e:uT
^n«. 28 d<Ken of each.
ALE AND BEER MEASURE.
71- In 46 barrels of beer, how many pi„„.
''• '" '" '""'^ ">' «'«' "- >»», gallons and ^Zt^T'''
''■ '" '^ ^"S^''-* of ale, how maijaf- '''° ^**
»<• In 108 barrels of ale, how many hogsheads f ^'"^ '"^
Ans, 74J
81. fc
I Saviour'i
82. I
many dj
83. F
how raa
84. F
and dayi
Teachetl
proporti(
Rule,
such ord
the sam
numbers
tioued.
the world, the
' 69 miles and
jarley-corns.
8IN0LE KVLE OF THREE DIRECT.
DRY MEASURE.
58
20 perches.
Ans. 27.
gf 37 acres. 1
«ire to know
ins. 3521.
f 75 perches
l> 4 acres, 2
cres, 1 rood,
n?
ches rem.
^nd pints ?
BO pints.
• 5 tuns,
and hop^-
Qs over.
f>f a pipe
• desire to
»f each.
75. In 120 quarters of wheat, how many bushels, pecks, gal-
Jons and quarts ?
Ans. 960 bushels, 3840 pecks, 7680 gallons, ?0720 qts.
76. In 30720 quarts of corn, how many quarters?
Ans. 120.
77. In 20 chaldrons of coals, how many pecks?
Ans. 2880.
78. In 273 lasts of corn, how many pecks ?
Ans. 87360.
TIME.
79. In 72015 hours, how many weels?
Ans. 428 weeks, 4 days, 15 hours.
80. How many days is it since the birth of our Saviour, to
"Christmas, 1794? Ans. 655258^.
81. Stowe writes, London was built 1108 years before our
[Saviour's birth, how many hours is it since to Christmas, 1794 ?
Ans. 25438932 hours.
! 82. From November 17, 1738, to September 12, 1739, how
many days? Ans. 299.
83. From July 18, 1749, to December 27 of the same year,
how many days? Ans. 162.
84. From July 18, 1723, to April 18, 1750, how many yearj
and days? Ans. 26 years, 9770^ days,
reckoning 365 days 6 hours a year.
THE SINGLE RULE OF THREE DIRECT.
13248,
?
JOqta.
. loa*
Teacheth by three numbers given to find out a fourth, in such
proportion to the third, as the second is to the first.
Rule. Fii-st state the question, that is, place the numbers in
such order, that the fii*st and third be of one kind, and the second
the same as the number required; then bring the fii-st and third
numbers into one name, and the second into the lowest term mcn-
tioued. Multiply the second and third numbers together, and
e3
I
•i
■ Mi
llfi
i
IW
M
•INOLB BULB OP THREB DIRECT.
EXAMPLES.
1. If 1 lb of sugar cost 4hd, what cost 51 lb?
1 : 4i : : 54
4 18
~ -^w*- £l : : 3.
18 4)972
12)213
208. 3d.
2. If a gallon of beer cost lOd., what is that per barrel ? "
-^ns. £1 : 10.
3. If a pair of shoes cost 4s. 6.. what will 12 dozen come to .'
>ans. £32:8.
, J; '* -«^ y-d of cloth cost 15s. 6d.. what will 32 yards cost at the saino
•dns. £-24 : 10.
5. If 32 yards of cloth cost £24 : 16. what is the value of a >ard ?
-^Jis. 15s. 6d.
8. If I give £4 : 18 for 1 cwt of ,„gar. at what rata did I bu, it per lb !
•/ins. luid.
tJdL\)VlZu> '""°"'' "■=" '" ^"'- '"' »«'• M. per ell, ,vhat i.
^ns. £^50.
8. What will 23 cwt. 3 qr,. 14 lb. of tobacco come to. at I.',J,1. per lb f
•^ns. £181 :3 :3
«„ou„Uof' "■' ""' °' ■""'""• "' «- »!''• P^' yard, what d„c. it
An. £!) : 5 ! Oi, 2 rem.
^^10. Bough. 1, cwt. 1 qr. 14 lb. of iron, at 31 per lb. what doe, it come
^ns. £20 : 7 : Oi.
11. If coffee is sold for 5id. per ounce, what must be given for 2 cwt '
Jina. £82 : 2 : 8.
12. How many yards of cloth 'may be bought for £oi . , , , , /
3* yards cost £2: 14: 3? i„, 27"vard. Tnf- , m'J*' "^'^^"^
-^ns. 4 1 yards, J qrs. 1 nail, 84 rem
31^. Y ^ "'"*• ^'^ ^^''^''^ «^«««« <^«^t £1 : 14 : 8. what m...st F .fvn 'for
•^ns. Is. 1(1.
.o"e to/"""' ' ""• "* "•• « - °f "O "•0. V >•" ™ '■• """' <'"e» it
■dm. los. Uid. 112 rem.
SINGLE BULE OF THREE DIRECT.
55
15. If a gentleman's income is £500 a year, and he spends lOs. 4d. per
day, hi.w much does he lay by at the year's end ? jIhs. jCU? : 3 : 4.
10. It I buy 14 yards of cloth for 10 guineas, how many Flemish elLi
can I l)uv for £283 : 17 : 6 at the same rate ?
^ns. 504 Fl. ells, 2 qrs.
17. if 504 Flemish ells, 2 quarters, cost £283 : 17 : 6, at what rate did
I pay lor M yards ?
j?«». IDs. lOd.
18. Gave £1 : I : S for 3 lb. of coffee, what must be given for 2<J lb. 4 oz. ?
Ans. £10 : 11 : 3.
19. If one English ell 2 qrs. cost 43. 7d. what will 39i yards cost at th«
game rate .■■
JIns. £5:3: 54, 5 rem.
20. If one ounce of gold is worth £5:4: 2, what is the \%>rth of ot\»
grain .' Jlns. 2^(1. 20 rem.
21. If 14 yards of broad cloth cost £9 : 12, what is the purchase of 75
yards ? ' Ans. 51 : 8 : G|, 6 rem.
22. If 27 yards of Holland cost £5 : 13 : 6, how many ells English can
I buy for £100 ? Aits. 384.
23. If 1 cwt. cost £12 : 12 : 6, what must I give for 14 cwt 1 qr. 19 lb.
Ans. £182 : : Hi, 8 rem.
24. Bought 7 yards of cloth for 17s. 8d. what must be given for 5 piecea,
each coiitiiiiiing 27^ yards.
A71S. £17 : 7 : 04, 2 rem.
25. If 7 oz. 1 1 dwts. of gold bo worth £35, what is the value of 14 lb.
9 oz. 12 dwt. 10 gr. at the same rate ?
Ans. £823 : 9 : 3|, 552 rem.
20. A draper bought 420 yards of broad cloth, at the rate of 148. 10|d
per ell English, how much did he pay for the whole ?
An^. 250 : 5.
27. A gentleman bought a wedge of gold, which weighed 14 lb. 3 oz
8 dwts. for the sum of £514 : 4, at what rate did he pay for it per oz. ?
Ans £3.
28. A grocer bought 4 hogsheads of sugar, each weighing neat 6 cwt. 2
qrs. 14 lb which cost him £2:8:0 per cwt. ; what is the value of the 4
hogsheads ?
Ans. £04 : 5 : 3.
29. A draper bought 8 packs of cloth, 'each containing 4 parcels, each
parcel V) pieces, and each piece 26 yards, and gave after the rate of £4 :
16 for 6 yards ; 1 desire to know what the 8 packs stood him to ?
Ans. £6656.
30. If 24 lb. of raisins cost 68. 6d. what will IS frails cost, each weigh-
ing neat 3 qrs. 1 8 lb. ?
Ans. £24 : 17 : 3,
31. If 1 oz. of silver be worth Ss. what is the price of 14 ingots, each
weighing 7 lb. 5 oz. 10 dwts.
Ans. £313 : 5.
32. What is the price of a pack of wool, weighing 2 cwt. I qr= 19 lb. at
88. 6d. per stone ?
Ans. £8:4: 64, 10 rem.
33. Bought 59 cwt. 9 qrs. 24 lb. of tobacco, at £2 : 17 : 4 per cwt. ; what
does it come to ? ^n». £171 : 3 : 74 80 reia.
ill!
>'il:(
56
JtVLE OP THREE INVERSE.
o f^^^^"2rlit 171 tons of lead nr Via
and other incident clmro-es £4 ' in t ^'^ *''"' P^'^ ca"Taffe
»ead, and what it stands me in p^r lb ? '^''''' *^' ^"^"^ ^^ ^
^ 35 If a pair ^l^^^^^^f ^32 rem. per lb.
I buy for i;43 : 5 ? ^^ ^^ 10 groats, how many dozen mav
V
36. Bought ^7 do/en ^^ m c „^^*' ^1 clozen, 7A pair
Pe' 3 lb. wLt did ZyU, '^,f -"^K '"fer the rj^m.
. 31 If an ounce of fine gold i, .J"/' 5 ='« = **. 1 «"n.
•ngob ^ eaoh ,vei?hi„g 3 ^ t ''/° 1 '"' f^ ^ IC «-lmt come V
•""fo^ „ ;''■ !' S---, at the same
38. If my },e,se stands me in M T ■^,'°" = 1* = ^i-
be the charge of 11 horses for the year P "^ ^''«' "''^' »•«'
89. A factor boH-ylit rk „• . ^"*- ^J58 : 18 : 6i
19 •• 4, at 4s. lod "^t va,r?/ ''"T' I!'™'' ^«' him i^iV :
-ere. and how many 'e„s ^^J ^^^J"- -"7 y-<ls the«,
■'2l*in'r«-'^'''^"^'«^«Mquarte.
40. A gentloman 1 ; 1 '''""• '" » P'''*'"'-
I desire to kn^Iw m ',, T ™"""^ "^ ^8»« -^ " Per annum
40 uwdores ? '^ gumcas, and g,ve to the poor quarterlv
^M. £1 : U : 8, 44 rem. ^
III
I
i
THE RULE OF THREE INVERSE.
Inverse pRopoRTrr^xr ;„ i
luires more. Cereli ;Trs"is'"T '1""^f '«''• ■""^ '^^ ^e-
second And llss requi 1 ' / ' '"''I" *" •*" '<^^' "'an the
*f «'^fi«t, and 4 i^sThTfo,;rth tr"'^"'^'' '^™ -^ '^
the second. ^ '^ '"""h term to be greater thao
fon to the second L tlL tfdt 2,"t"tL:^" ""' ™"' P™"*
paid carnage
value of the
™- per lb.
^ dozen mav
m
> ^i pair,
fate of 17d.
h 1 rem.
lat come 7
It the same
, what will I
18 : 6|.
im £517 :
ards there
uarters,
r annum,
the year's
quarterly
rem.
less re-
is greatr
han the
is less
er than
ind di-
propor-
BULB OF THREE XNVEHSB.
EXAMPLES.
57
1. If 8 men can do a piece of work in 12 days, how many
[days can 16 men perform the same in? Ans. 6 days.
8. 12 . . 16 . 6
8
16)96(6 days.
2. If 64 mep can build a house in 90 days, how many can do
the same in 60 days ?
Jns. 97} men.
3. If, when a peck of wheat is sold for 2s., the penny loaf
weighs 8 oz., how much must it weigh when the peck is worth
but Is. 6d. ?
Ans. lOf oz.
4. How many pieces of money, of 20s. value, are equal to
240 pieces of 12s. each? Ans. 144.
6. How many yards, of three quarters wide, are equal in mea»
sure to 30 yards, of 5 quarters wide ? Ans. 60.
6. If I lend my friend £200 for 12 months, how long ought
he to lend me £160, to requite my kindness ?
Ans. 16 months.
7. If for 24s. I have 1200 lb. carried 36 miles, how many
pounds can I have carried 24 miles for the same money ?
4ns. 1800 lb.
8. If 108 workmen finish a piece of work in 12 days, how
many are sufficient to finish it in 3 days ?
Ans. 432.
9. An army besieging a town, in which were 1000 soldiers,
with provisions for 3 months, how many soldiers departed, when
the provisions lasted them 6 months ?
Ans. 500.
10. If £20 worth of wine is sufficient to serve an ordinary of
100 men, when the tun is sold for j£30, how many will £20
worth suffice, when the tun is sold but for £24 ?
Ans. 126.
11. A courier makes a journey in 24 days, when the day is
but 12 hours long, how many days will he be going the same
journey, when the day is 16 hours long?
Ans. 18 days.
Ki
■ :■•
m
6&
nil!
DOUBLE RULE OB THREE.
12 How much plush is sufficient for a cloak, which has in it
Will 34 men take to do the same ? / ' ""' "^ny aays
^^^*- ^ d/ys; 4 hours, 56 min. ^V, at 12 hours for a day
14. Borrowed of raj friend £64 for 8 months inrl i.. l, 7'
casion another time to borrow of me for T2 monTl . T
must I lend him to requite his f^rm" ktdnelr me) ''" ""'
Ans. 4166 yards, 2 qra. 2 nails, 2 rem.
1. If 14
)e sufiiciei
1.
2.
By
h
As 1
da
As ]
2.
hen
If 8r
3 be tc
THE DOUBLE RULE OF THREE,
Is so called because it is composed of 5 numbers ^iven to find n
a supposition ; the two last, aidant '" ^''' ''""' ^'^
J. Place the other t»o terms under .heir"like in the supposi-
5^i^^:.rn-t^j^rr'rftt^i^-
tY^^'Jlf"' b^ank foils under the first or second term. mnlnVl.
PuooF. By two single rules of three.
DOUBLE BULB OF THBEE.
59
EXAMPLES.
1. If 14 horses eat 56 bushels of oats in 16 days, how many bushels will
)e sufficient for 20 horses for 24 days
By two single rules,
hor. bu. hor. bu.
1. As 14 . 56 .. 20 . 80
days bu. days. bu.
2. As 16 . 80 . . 24 . 120
or in one stating, worked thus :
hor. days bu.
14 . 16 . 56 56X20X24
20 . 24 . — =120
14X16
2. If 8 men in 14 days can mow 1 J 2 acres of grass, how many men must
Ithere be to mow 2000 acres in 10 days ?
acres, days, acres, days.
1. As 112 . 14 .. 2000 . 250
days. men. days, men.
2. As 250 . 8 . . 10 . 200
me*
■Ia':
— . 10
acres.
. 112.8X14X2000
-^s^OO
. 2000 112X10
3. If £100 in 12 months gain £6 interest, how much will £75 gain in
|9 months. ^««- £3:7:6.
4. If a carrier receives £2 : 2 for the carriage of 3 cwt. 150 miles, how
Imuch ought he to receive for the carriage of 7 cwt. 3 qrs. 14 lb. for 50 miles ?
' • ^ns. £1 : 16 : 9.
5. If a regiment of soldiers, consisting of 136 men, consume 351 quar-
Iters of wheat in 403 days, how many quarters of wheat will 11232 soldiers
consume in 56 days ?
Ans. 15031 qrs. 864 rem.
6. If 40 acres of grass be mowed by 8 men in 7 days, how many acres
I can be mowed by 24 men in 28 days ? Jins. 480.
7. If 403. will pay 8 men fox 5 days' work, how much will pay 32 men
for 24 days' work ? -^ns. £38 : 8.
^ 8. If £100 in 12 months gain £6 interest, what principal will gain £3 :
7 : 6 in 9 months ? ^»J^ £75.
9. If a regiment, consisting of 939 soldiers, consume 351 qrs. of wheat
in a 168 days, how many soldiers will consume 1404 qrs. in 56 days .'
Ans, 11268.
10. If a family consisting of 7 persons, drink out 2 kilderkins of beer in
12 days, how many kilderkins will another family of 14 persons drink out
in S days ? -^ns. 2 kil. 12 gal.
11. If the carriage of 60 cwt. 20 miles, cost £14 : 10, what weight can I
have carried 30 miles for £5 : 8 : 9, at the same rate of carriage ?
Ans. 15 cwt.
12, If 2 horses eat 8 bushels of oats in 16 days, how many horses will eat
uu 3000 nuarters in 24 davs ?
Ans. 4fX)0.
13, If £100 in 12 months gain £1 interest, what is the interest of £571
for 6 years ?
Jlns. £239 : 16 : 45, 20 rem.
Pa'
■JjH,
i
i#:
mm
60
I*.
a
PRACTICE.
Ans. £9:2: 0^.
PRACTICE
All questions in tliis rule are performed bv UVn.c. nV .
Of a Pound.
s. d.
10 : ..is...^
6:8 ^
5
4
3
2
2
1
.... .1
4 f
« I
_i_
8 _i
Of a shilling.
G
Of a Ton.
cwt.
10.. is.. 4
Of a Hundred j
qrs. lb.
" ..i^...| M".. IS... i 2 or 56 is i
3
2
5. .
1
••§■
••12
u
w
Of a Quarter.
To" I ^4 lb 1
1 II
4 1
3i I
-5i^£,t- ^;:vrai?i:3t ?
O^isi)57041b.ati
12)142G
210)1118:10
Facit,i;5:18:10
^695 at ^
Facit, £16:0:7^
O 5470 at ^
Facit, £11:7:11
C) 6547 at I
Faci^\£20 : 9 : 2^
C) 4573 at f
Facit, £14 : 5 : 9f
Tjizx^-i-'^'^^.^-'Ss^ti
i« tV '
2
Facit, i
l^is i
2I(
1 Facit, £1
'(») 5432i
Facit, £3
(*) 6254
Facit, £^
C) 2351
Facit, £]
C) 7210
Facit, £C
2710
Facit, £i
(') 3251
Facit, £i
{') 2715
Facit, £t
{'") 700'.
Facit, £
(") 214^
Facit, £1
(") 700<
Facit, £
PRACTICE.
61
es, what must!
£9:2: Oi.
[') is tV '754'7 at Id.
sons concern-j
g aliquot, or|
are avoided;
)f a Hundred. I
rs. lb.
2 or 56 is ^j
1 or 28. ..i
a4...|
f a Quarter.!
t lb 1:
^ I:
•••... .4;
2 •••••••J I
vide by the j
5, it will 1:^ I
210)6218
: 11
Facit, £.31 : 8
: 11.
(»)lisyV375latUd
i is i 312 : Y
•78 : li
210)3910 :
8t
Facit, £19 : 10
8i
(") 325*7 at 4d.
Facit, £54 : 5 : 8.
('*) 2056 at 4|d.
Facit, £36 : 8 : 2.
{") 3/52 at 4^d.
Faeit, £70 : 7 : 0.
n 2107 at4^d.
Facit, £41:14:0^
at 1
JO : 9 : 2i
1
at f
4 : 5 : 9f
1
fe the ali
'ether, and
(*) 54325 at l^d.
[Facit, £339 : 10 : 7^.
(*) 6254 at l^d.
Facit, £45 : 12 : 0^
{') 2351 at 2d.
Facit, £19 : 11 : 10.
C) 7210 at 2id.
Facit, £67:11 :10i
(') 2710 at 2^d.
Facit, £28 : 4 : 7.
3250 at 2td.
Facit, £37 : 4 : 9^.
(») 2715 at 3d.
Facit, £33 : 18 : 9.
n 7062 at 3id.
Facit, £95 : 12 : 7^
(") 2147 at 3^
Facit, £31:6 : 2^.
(") 7000 at 3§d.
Faeit, £109 : 7 : 6.
(") 3210 at 5d.
Facit, £66 : 17 : 6.
n 2715 at5H
Facit, £59 : 7 : 9f ,
n 3120 at 5id.
Facit, £71 : 10 : 0.
{'") 7521 at 5id.
Facit, £180 : 3 : 9i
(") 3271 at 6d.
Facit, £81 : 15 : 6.
(") 7914at 6id.
Facit, £206 : 1 : 10^
(") 3250 at 6|d.
Facit, £88 : : 5.
(") 2708 at 6 Id.
Facit, £76 : 3 : 3.
n 3271 at 7d.
Faeit, £95 : 8 : 1.
(") 3254 at 7id.
Facit, £98:5 : Hi
(-') 2701 at 7^d.
Facit, £84 : 8 : 1^.'
F
(") 3714 at 7|d.
Facit, £119: 18:7^.
(") 2710 at 8d.
Facit, £90 : 6 : 8.
('") 3514 at 8id.
Facit, £120: 15 :10J.
{'') 2759 at 8^d.
Fiicit, £97 : 14 : 3^.
n 9872 at 8H
Facit, £359 : 18 : 4.
(") 5272 at 9d.
Facit, £197 : 14 : 0.
(") 6325 at 9id.
Facit, £243 : 15 : 6^.
{'') 7924 at 9^d.
Facit, £313 : 13 : 2.
(="■) 2150 at 9^d.
Facit, £87 : 6 : lOf
('') 6325 at lOd.
Facit, £263 : 10 : 10.
n 5724 at lO^d.
Facit, £244 : 9 : 3.
n 6327 at lO^d.
Facit, £270 : 4 : 3|.
(") 3254 at lO^d.
Fiicit, £142 : 7 : 3.
{*') 7291 at 10|d.
Facit, £326 : 11 : 6^.
{'') 3250 at lid.
Fiicit, £149 : 4 : 8.
ft.
§ ■
11'
if'l
03
Fa
PBACTICB.
;■) 72S4 at md. |n3754atlUd. inW2aMTW
act, £340 : : 7J. I Facit, £179 : 17* : 7. j hlll'lloo :^fh.
li^''Z!',T'Z "'" P™" '' """•' """> o"" «Wlling,mKl less
Price ^ ?; ; f " !'"'■.,•;.'• f^"*-"' »i"' «« n.ucl,«f1he ri v^
pnce Oh IS more than a s ii n.r wlii.-li ■i.l.l t„ ii,„ • ° •
and divide by 20, it will give & anlwe.' ' ^'''" ^""'^^^^'
OilV2106atl2|d,
43 : 10|
210)21419 : 10^
Facit, £107:9: 10^.
C) 3215 at Is. l|d
Facit, £177:9 :10i
(') 279"oi;nri7d7
Fa<!it, £156 : 18 : 9.
Facit, £452 : 16 : 8.
3750 at Is. 2d.
Facit, £218 : 15 : 0.
{') 329nnr2Adr
Facit, £195 : 8 : Of.
M")9254atls. 2^cr
Facit, £559 : 1 : 11,
(") 7250 at Is. 2^d.
Facit, £445: 11 : 5^
(") V591 at Is. 3d.
Facit, £474 : 8 : 9.
n 6325 at Is. 3^d.
Facit, £401 : 18:0^.
(") sm^tuTsu
Facit, £340 : 8 : 4^^d.
0-KV37l5atl2|d.
154 : 9^
210)38619: 9^
Facit, £193 : 9 : 9-^.
n 3254 at Is. 3^d.
Facit,£213:10:10|.
('") 2915 at Is. 4d.
Facit, £194 : 6 : 8.
n 3270 at Is. 4|d.
Facit, £221 : 8 : 1|.
n 2712 at 12U
Facit, £144 : 1 : 6.
n 2107 at Is. Id.
Facit, £114 : 2 : 7.
n 7103 at Is. 6id.
Facit, £540 : 2 : 5^.
n 3254 at Is. e^d
Facit, £250 : 16 : 7.
('') 7059 at Is. 4|d.
Facit, £485 : 6 : l|.
('") 2750 at Is. 4^d.
Facit, £191:18: 6J.
n 3725 at Is. 5d
(") 7925 at Is. 6fd.
Facit, £619 : 2 : 9|.
n 9271 at Is. 7d.
Facit, £733 : 19 : 1.
O 7210 at Is. 7^1"
Facit, £578 : 6 : 0^.
n2310at Is. 7H
Facit, £263 : 17 : 1. Wcit, £W : 13 f 9.
n V250 at Is. 5^d.
Facit, £521 : 1 : lo^.
n 2597 at Is. 5Ul
Facit, £189 : 7 : 3^.
Facit, £533 : 4 : 9^.
Facit, £564 : 6 :
{") 2504 at Is. 7fd.
Facit, £206 : 1 : 2.
('') 7152 at Is. 8d.
Facit, £596 : : 0.
n 2905 at Is. 8^d.
Facit, £245 : 2 : 2|.
n 7104 aTTTs^
Facit, £606 : 16 : 0.
(") 1004 at Is. 8fd.
Facit, £86 : 16 : 1.
n 2104 at Is. 9d.
Fticit, £184 : 2 : 0.
(") 2571 at Is. Oid.
Facit, £227 : 12 : 9i
n 2104 at Is. dhd.
Facit, £188 : 9 : 8.
n 7506 at Is. 9|d.
Facit, £080 : 4 : 7^.
PRACTICE.
(") 1071 at Is. lOd.
Facit, £98 : 3 : 6.
(*•) 5200 at Is. 10-id
Facit, £482 : ^ : 8.
(") 2117 at Is. 10|d.
Facit, £198 : 9 : 4i
(") 1007 at Is. lOi
Facit, £95 : 9 : U.
(") 5000 at Is, lid.
Facit, £479 : 3 : 4.
(") 2105 at
Facit, £203
63
Is. lUd.
: 18 : 5^.
(") lOOC at
Facit, £98 :
Is. IIH
10 : 1.
(*') 2705 at
Facit, £267
Is. llH
:13:7i
('') 5000 at
Facit, £489 : 11 : 8.
Is. ll|d.
(") 4000 at
Facit, £395
Is. llH
: 16 : 8.
Rule 4. When the price consists of any even number of
shillings under 20, multiply the given quantity by lialf the price,
doubling the first figure of the product for shillings, and the rest
of the product will be pounds.
{•) 2750 at 2s.
Facit, £275 : : 0.
n 3254 at 4s.
Facit, £650 : 16 : 0.
(') 2710 at 6s.
Facit, £813 : : 0.
(') 1572 at 8s.
Facit, £628 : 16 ; 0.
(') 2102 ac 10s.
Facit, £1051 : : 0.
(•) 2101 at 12s.
Facit, £1260 : 12 : 0.
C) 5271 at 14s.
Facit, £3689 : 14 : 0.
n 3123 at 16s.
Facit, £2498 : 8 : 0.
(») 1075 at 16s.
Facit, £860 : : 0.
(") 1621 at 183.
Facit, £1458 : 18 : 0.
Note. When the
price is 10s. take half
of the quantity, and
if any remains, it is
10s.
Rule 5. When the price consists of odd shillings, multiply
the given quantity by the price, and divide by 20, the quotient
will be the answer.
{') 2703 at Is.
Facit, £135 : 3 : 0.
(») 3270 at 38.
3
0.
3271 at 5s.
Facit, £817 : 15 : 0.
;:r ™gi
2t0)98ii0
Facit, £490 : 10 :
f2
•f *^B
ii^
mm\i'.
ml
III
64
(*) 2715 at Is.
Facit, £950 : 6 : 0.
3214 at 9s.
Facit, £1446 : G : 0.
(') 2710 at lis.
Fitcit, £1490 : 10 : 0.
PRACTICE.
3179 at 13s.
Facit, £2066 : 7 : 0.
C) 2150 at 15s.
Facit, £1612: 10:0.
("')2l50atl9s.
Facit, £2042: 10:0.
(") 7157 at 19,s.
Facit, £0799 : 3 : 0.
(") 3142 at 17s.
Facit, £2670: 14 :0.j
Note. When the price is 5s. divide the quantity by 4 and
if any remain, it is 5s. ^ ^ ^ ' ^"^
Rule 6. When the price is shillings and pence, and they the
ahquo part of a pound, divide by the aliquot pa t, and TtMni
give the answer at once; but if they are' not an aliquot plrL
then multiply the quantity by the shillino., atid take\a.t/for
the rest, add them together, and divide by 20. ^
(') 7514 at 4s. 7d
Facit, £1721 : 19: 2.
*. d.
6:8
i
(•) 2710 at 6s. 8d.
Facit, £903 : 6 : 8.
d.
2
210
3150 at 3s. 4d.
Facit, £525 : : 0.
2715 at 2s. 6d.
Facit, £339 : 7 : 6.
7150 at Is. 8d.
Facit, £595 : 16 : 8.
n 3215 at Is. 4d.
Facit, £214 : 6 : 8.
i
O 7211 at Is. 3d.
Facit, £4 50 : 13 : 9.
2710 at 3s. 2d.
3
8130
451 : 8
C) 2517 at 5s. 3d.
Facit, £660:14:3.
n 2547 at 7s. 3id.
Facit,£928:ll:10i.
(") 3271 at 5s. 9id.
Facit, £943 : 16 : 4|.
n2103at I5s.4^d.
Facit,£l616:13:7^.
n 7152 at 17s, 6|d.
Facit, £6280 : 7 : 0.
85811 : 8
Facit, £429 : 1 : 8.
C*)25]0atl4:7id.
Facit, £1832: 16:5^
n37l5at9.s. 4^d
Facit, £1741 : 8 : 1^.
(") 2572 at 13 : 7^d.
Facit, £1752 : 3 : 6.
(") 7251 at 14s. 8id.
Facit,£5324:l9:0i
Rule 7.
[he quantii
lliey are e'
\dd them t
2dly, ^^
)ence the
)ounds, an
3dlv, ^
pings, and
■)Ound red
[he quanti
together, a
JsToTE.
hree figun
4
1
s
s. d.
2:6
i
6
1
s ,
PBACTICB.
6S
(") 3210 31158.7101.
Facit, £2511 . 3 . 1|.
1 2710 at 19s. 2id.
I Facit, £2602.14. 7.
Rule 7. 1st, When the price is pounds and sliillings, multiply
[he quantity by the pounds, and proceed with the shillings, if
[hey are even, as the fourth rule ; if odd, take the aliquot parts,
jidJ them together, the sum will be the answer.
2dly, When pounds, shillings, and pence, and the shillings and
)ence the aliquot parts of a pound, multiply the quantity by the
)ounds, and take parts for the rest.
3dly, When the price is pounds, shillings, pence, and far-
things, and the shillings and pence are not the aliquot parts of a
)ound reduce the pounds and shillings into shillings, multiply
[he quantity by the shillings, take parts for the rest, add them
together, and divide by 20.
JsToTE. When the given 'quantity consists of no more than
three figures, proceed as in Compound Multiplication.
\s, d.
12:6
6
1
5
[') 7215 at £7. 4.0.
7
50505
1443
£51948
(') 2104 at £5.3.0
5
10520
263
52.12
£10835 . 12
(') 2107 at £2.8.0.
Facit, £5056.16.0.
(*) 7150 at £5 .6.0.
Facit, £37926. 16.0.
F3
6
n
2
i
210
27l0at£2.3.7i.
43
116530
1355
338.9
1182213.9
Facit, £5911 .3.9.
(')3215at£l .17.0.
Facit, £5947. 15.0.
2107 at £1.1 3.0.
Facit, £3476.11 . 0.
n 3215 at £4.6.8.
Facit, £1393 1.1 3. 4.
(») 2154 at £7.1 .3.
Facit. £15212.12.6.
1:
; t
III
' 4
%
(4
r,, -.
I .
■ \ 'I
66
i
ti
PBACTICB.
2. At £1 . 4 . 9 per cwt,
diGose to ? .
3. Sold 85 cwt. 1 qr. lo
what does it come to ?
4. Hops at X'4 . 6 '. 8 per
Iqr. 18 1b.? ^
5. At £1 . 1 . 4 p,>^ ^^^^
15 ib. of Mala^ra raisins ?
0. Bought 78 cwt. 3 ai-8.
cwt., what did I give for the
^vhat comes IV cwt. 1 qr. 17 lb. of
„ ^W5. £21 .10.8
lb.ofcheese,at £1.7.8 per cwt,
^W5. £118.1 0*
cwt., what must be given for 72 cwt
'^iia. 13 the value of 27 cwt. 2 qrs
19 n ^ ^''*. £2D. 9.0? '
^^^^^''^' ^?w. £227. 14^
TARE AND TKET.
6Y
It
I. Sold 56 cwt. 1 qr. lY lb. of sugar, at £2 : 15 : 9 the cwt.,
ehat does it come to ? ^ns. £157:4; 4^
8 Tobacco at £3 : 17 : 10 the cwt, what is the worth of 97
Ut"l5lb.? Ans.£Sl8 :0'.S.
9. At £4 : 14 : 6 the cwt., what is the value of 37 cwt. 2 qrs.
13 lb. of double refined sugar? „ ^^ . ,
Ans. £177 : 14 : 8^.
10. Bouo-ht suirar at £3 : 14 : 6 the cwt., what did I give foi
|15 cwt. 1 q". 10 lb.? ^ns. £57 : 2 : 9.
II. At £4 : 15 : 4 the cwt., the value of 172 cwt. 3 qrs. 12 lb.
|of tobacco is required? ^ns. £823 : 19 : 0^
12. Soap at £3 : 11 : 6 the cwt., what is the value of 53 cwt
\l^\\jj Jns. £190 : : 4.
TARE AND TRET.
i
rr
11
. i
The allowances usually made in this Weighty are Tare^ Tret^
and Cloff.
.CI
Tare is an allowance made to the buyer for the weight of the
box, barrel, bag, &c., which contains the goods bought, and is
eiAher
At so much per box, bag, barrel, <kc.
At so much per cwt., or *
At so much in the gross weight.
Tret is an allowance of 4 lb. in every 104 lb. for waste, dust,
&c., made by the merchant to the buyer.
ClofF is an allowance of 2 lb. to the citizens of London, on
every draught above 3 cwt. on some sort of goods.
Gross weight is the whole weight of any sort of goods, and
that which contains it.
Suttle is when part of the allowance is deducted from the gross.
Koat is ^ho nni'o ■vvfio-ht when all allowances a.e deducted.
Rule 1. AVlien the tare is at so much per bag, barrel, «fec.,
multijily the number of bags, barrels, (fee. by the tare, and sub-
tract the product from the gross, the remainder is neat.
n
• u
'M
«
C8
TARE AND TRET.
m
divM^by 1^5. ''^"'^ ^'"'^ ^"'^ ^^"^"^' "^"^^'P^7 ^y 2, and|
Uiil\t\l II?'!' "". 'm t'' ""^^ r'^'^^'"" ^ ^^*- 2 qrs. 5 lb. gross,
taie at 23 lb. per frail, how much neat weiglit ?
23 ^^*- 37 cwt. 1 qr. 14 lb.
7 ^ • ^ * ^ or, 5 . 2 . 5
. A ^ 23
28)101(5
140—
21
38 . 3 . '7=gross
1.1. 21=tare
37 . 1 . 14=neat
6 . 1 . 10
* 1
37 . 1 . 14
2. What is the neat weight of 25 hogsheads of tobacco weio-h-
mg gross 163 cwt. 2 qrs. 15 lb., tare 100 lb. per hogsS ? ^
o T 1^1 ^ ^'^*'- 141 cwt'l qr. 7 lb
3 lb' J^. I '^' ^^ P^PP^'-, each 85 lb. 4 oz. gross, tare per bag,
3 lb. 5 oz. how many pounds neat ? ^^^^^ \ 3 j J^ "'
«..mT ^; .^'^^^'", *^'^. ^^'^ ^' ^^ «^ ^«"ch i" the whole jrro'^s
wcnght, subtract the given tare from the gross, the remainckr is
^ 4. What is the neat weight of 5 hogsheads of tobacco wein-h-
mg gross 75 cwt. 1 qr. 14 lb., tare in th? whole 752 Ib.T ^
K T »7r 1 , ,. ^ ^^"'^- ^*S cwt. 2 qrs. 18 lb
whole 697 lb. liow much neat weight J Am. 60 cwt. 1 qr
Rule 3. When the tare is at so much nor cwt., divide the
po., wo,g,t by the aliquot ,,arte of a cwt., which subt. ct frl
the gross, to remainder is neat.
^"wi \ '•''■.1' •'^' ^ '^'" tV. 14 lb. is i 16 lb. is i. •
2 a..'^ lb! '^rtt"ir .rSctt!.' ""'" "' ™™''^''^-^'' « ^"^
8.2.6
9X2 = 18
76 . 3T17
2
14=1 153 . 3 . 6
19 . . 25^
134 . 2T~8|
TARE AND TRET.
69
a
1. In 25 barrels of figs, each 2 cwt. 1 qr. gross, tare per cwt
IG lb., how much neat weight? Ans. 48 cwt. qr. 24 lb.
8. What is the neat weight of 9 hogsheads of nutmegs, each
weighing gross 8 cwt. 3 qrs. 14 lb., tare 16 lb. per cwt.
Ans. 68 cwt. 1 qr. 24 lb.
Rule 4. When tret is allowed with tare, divide the pounds
suttle by 20, the quotient is the tret, which subtract from the sub-
tle, the remainder is neat.
9. Tn 1 butt of currants, weighing 12 cwt. 2 qrs. 24 lb. gross,
tare 14 lb. per cwt., tret 4 lb. per 104 lb., how many pounds neat?
12 . 2 . 24
4
60
28
14=|- 1424 gross.
178 tare.
26)1246 suttlo.
47 tret.
It-
i
%h
4
•i1
f 1 1
1199 neat.
10. Tn 7 cwt. 3 qrs. 27 lb. gross, tare 36 lb., tret 4 lb. per 104
lb., how many pounds neat ?
Ans. 826 lb.
11. Tn 152 cwt. 1 qr. 3 lb. gross, tare 10 lb. per cwt, tret 4 lb.
per 104 lb., how much neat weight?
Ans. 133 cwt. 1 qr. 12 lb.
TiuT.E 5. Wlicn cloff is allowed, multiply the cwts. suttlo by
2, divide the product by 3, the quotient will be the pounds cloff,
which subtract from the suttle, the remainder will be neat.
12. What is the neat weight of 3 hogsheads of tobacco, weigh-
ing 15 cwt. 3 qrs. 20 lb. gross, tare 7 lb. per cwt., tret 4 lb. per
104 1b., cloff 2 lb. for 3 cwt.?
Ans. 14 cwt. 1 qr. 3 lb.
\--V\
70
INTEREST.
''^tV 15 . 3 . 20 gross
3 . 27i tare.
26)14 . 3 . 2Qi sutfle
3 . S tret.
14 . 1 . I2i suttle.
9i cloff.
14. 1 . 3
neat weight; ' '"■ 1'"' ■^ cw(., how much
MIS. 34 cwl. 3 qis. 8 lb.
SIMPLE INTEREST,
d^tet^^S'sS time'"''"^ " '■°"'"™"" °' »"^ -" "^ ™-ey for a
The Amount u'the l^incipTltrfVn e "t »d<ieV „U',Ter'"' ""'°"""-
anXrare:':„,---pr7;te"^
ded"hr:o'a.^l;'^'i;lVtt';reS',.l-?;uti'''^ p- -" ^' ^'--'-''^ivi.
^or several Tears.
2.' Multiply the interest of one year by the niirnhp,- nf „ • •
question and the product will be the a./swe' °^ ^'^^'-s g'venin the
mon
Rule of th ;e Direct.
EXAMPLES
1 What is the interest of £375 for
5
ayoar, at 5 per cent, per annum?
18175
20
15100 ^»5. £18 . 15 . 0.
2 What is the
3 What is the
interest of £2(58 for 1
interest
year, at 4 per cent, per annum .'
of £945 . 10. for a year, at 4
'^/M. £10 . 14 . 41.
percent, per annum?
^n«. 37 . 16 . 41
4.
What
yaars
p
5.
What
annum ?
G.
What
5 years ?
7.
My c
amount of J
2ipe
r cent.
8.
If I a
mand
on thf
9
At 11
Stock
>
10.
At 10
14.'
11.
At 96
12.
At £
Stock
?
INTEREST.
71
4. What is the interest of £547 . 15, at 5 per cent, per annum, for 3
ly^ars • ^ns. £82 .3.3.
5. What is the interest of £254 . 17 . C, for 5 years, at 4 por cent, per
I annum? ^«s. £50 . 19 . 6.
6. What is the interest of £556 . 13 . 4, at 5 per cent, per annum, for
1 5 years ? Ans. £139 . 3 . 4.
7. My correspondent writes me word, that he has b<n)ght goods to #he
amount of £754 . 16 on my account, what does his commission come to at
|2i percent.? ./?n*. £18 . 17 . 4|.
8. If I allow my factor 3| per cent, for commission, what may he de-
[mand on the laying out £876 . 5 . 10 ? Jlns. £32 . 17 . 2i.
9 At 1104 per cent., what is the purchase of £2051 . IG. South Sea
I Stock? Jlns. £22V)Ci . s . 4.
10. At 104| per cent. South Sea annuities, what is tlie purchase of 1797 .
!l4? .^«». £1876 . 6 . 111.
11. At 96| per cent, what is the purchase of £577 . 19, Bank annuities ?
Atis. £559 , 3 . 3|.
12. At £124| per cent., what is the purchase of £758 . 17 . 10, India
"^tock ? £915 . 15 . 44.
h
I' I
r- '
Br.OKAGE,
Is an allowance to brokers, for helping merchants or factors to persons, to
buy or sell them goods.
Uui.E. Divide the sum given by 100, and take pails from the quotient
with tlie rate per cent.
13. If I employ a broker to sell goods for me, to the value of £2575 .
17 . G, what is the brokage at 4s. per cent. ?
, 25175.17.6
20
4s.=' 25 .15.2
15117
12
2110
^ns. £5 . 3 . 04
14. When a broker sells goods to the amount of £7105 . 5 . 10, whal
may he demand for brokage, if he is allowed 5s. Gd, per contW
^ns. £19 . 10 . 9i.
15. If a broker is employed to buy a quantity of goods to the value of
£975 .6.4, what is the brokage, at Gs. Gd. per centi ?
Atis. £3 . 3 . 4i
16. What is the interest of £547 .2.4, for 5i years, at 4 per cent, per
annum ? Ans. £120 . 7 . 3i,
17. What is I
larters ?
! interest of £257 .5.1, at 4 per c(
A
18. What is the interest of £479 . 5 for 5i years, at 5 per cent, per an-
qus
£18. 0. U.
nutn
^ns. £125 . 16 . 04
X:
h.,v
w-
72
l» w
t (
if '
INTEREST.
19. What ia the interest of £576 • 2 • ft fnr '71 ,.«
cent, per annum. *^ 'o • ^ . 6 for 7f years, at 4^ pj
20. What is the interest of £279 • U^Tjlf '' '^' '' f^' J
annum, for 3^ years? *^'^ • ^^ • 8 at 5^ per cent, p^
A7is. £oi : 7 : 10.
When the interest is required for any number of Weeks.
KuLE. As 52 weeks are to the Interest nf t>in ^'
a year, so arc the weeks given for thoSsf^lfJ''^'' "'"
pJl^r^^:,^^'^"^' "' '''' ■■''■■' f- 20 weeks, at
22. What is the amount of £375 • 6 • ftAV '^= ^"i' .
per cent, per a„n„™. it' ii^TO :t; S^!
When the Interest is for any number of days.
Rule. As 305 days are to the interest „f (1>„ „:
year, so are the da/given to the i"4"^cd^ ™" '"'" "^^
2 .'7 Vot 5 yii:: m d^; r"™- "'='' '^ *•= ""--' »f ^»8s
24. mat is the interest of £2726 1 1"ft 4?^^ ' '^ V^' i
annum, f„r three years, 154 days ? •■'•*•■" ^s per cent, pej
^w. £419 . 15 . 6i
When the Amount, Time and Hate per cent, are yiven to find
t/ie r'nncipal.
to £100 '^\ol r'""' "^/- '' ""^ ^^^ '^'^ ^"^ time .iven • i.
to £100 . . so IS tlie amount given : to the principal required '
25. What principal beinjr put to interest, will amount >^ Pim i
10 m 5 yeai-s, at 3 per cent, per annum ? ^ ^^^^ '^
3X6+100=£I15. I00..402 10
20 20
2300
8050
100
23!00)8050I0Q(£;?50 Ans.
INTEREST.
73
26. What principal being put to interest f^r 9 years, •will
imount to £734 : 8, at 4 per cent, per annum?
Ans. £540.
27. What principal being put to interest for 7 years, at 5 per
cent, per annum, will amount to £334 : 16?
Ans. £248.
When the principal, Bate per cent, and Amount are given,
to find the Time.
Rule. As the interest of the principal for 1 year : is to 1 year : :
|bo is the whole interest : to the time required.
28. In what time will £360 i aiount to £402 . 10, at 3 per cent,
[per annum ?
360 As 10 . 10 ; 1 : : 52 . 10 : 6
3 20 20
10150 210 21i0) 10510(5 years. ^ns. 402 . 10
20 105 350.10
10100 52.10
29. Tn what time will £540 amount to £734 : 8, at 4 per cent,
per annum ? Ans. 9 years.
30. In what time will £248 amount to £334 : 16, at 5 per
cent, per annum ? Ans. 7 3^ears.
When the Principal, Amount, and TimCy are given, to find the
Rate per cent.
Rule. As the principal : is to the interest for the whole time : :
BO is £100 : to the interest for the san^j time. Divide that in-
terest by the time, and the quotient will be the rate per cent.
31. At what rate per cent, will 350 amount to £402 :10 m
6 years' time ?
350 As 350 : 52 . 10 : : 100 : £15
20
52 . 10
1050
100
36i0)10500iO(300s.=£l5-f-5 = 3 per cent.
32. At what rate* per cent, will £248 amount to £334 : 10 in
7 years' time ? Ayis. 5 per cent.
}^.
h:
»;
f ' i
74
INTEREST.
33. At what rate per cent, will £540 amount to £734 : 8 in 9
yeai-s'time? .4/is. 4 per cent.
COMPOUND INTEREST,
Ts that which arises both from the principal and interest; that
is, when the interest on money becomes due, and not paid, tlie
same interest is allowed on that interest unpaid, as was on the
principal before.
Rule 1. Find the first years' interest, which add to the princi-
pal ; then find the interest of that sum, which add as k^fore, and
so on for the number of years.
^ 2. Subtract the given sum from the last amount, and it will
give the compound interest required.
EXAMPLES.
1. ^Y[\at is the compound interest of £500 forborne 3 years,
at 5 per cent, per annum ?
500 500 • 525
^25 26 . . 5
25100
525 = 1st jesv. 55 1 .. 5 = 2d year.
5
2G125
20
5l00
2*7156.
20
11125
12
— 551 ..5
5 27. 11. .3
578. 16..3=3dyear.
prin. sub
500
3!00
78 . 16 . . 3=inter.for3years.
2. What is the amount of £400 forborne 3^ years, at 6 per
cent. \m' annum, compound interest? Ans. £490 : 13 : 11^:.
3. What will £650 amount to in 5 years, at 5 per cent, per
annum, compound interest? Ans. £829 : 11 : 7^.
4. What is the amount of £550 : 10 for 3 yeara and 6 months,
at 6 per cent, per annum, compound interest ?
Ans. £675 : 6 : d.
• K
5. What is the compound interest of £764 for 4 years and 9
months, at 6 per cent, per annum ? Ans. £243 : 18:8.
6. What is the compound interest of £57 : 10 : 6 for 5 yeare,
1 months, and 1 5 days, at 6 per cent, per aiinum ?
Ans. £18 : 3 : 8f.
REBATE OR DISCOUNT.
75
7. What is the compound interest of £259 : 10 for 3 years, 9
months, and 10 days, at 4^ per cent, per annum?
Jns. £46 : 19 : 10^.
REBATE OR DISCOUNT,
Is the abating of so much money on a debt, to be received be-
fore it is due, as that money, if put to interest, would gain in the
same time, and at the same rate. As £100 present money would
diseharge a debt of £105, to be paid a year to come, rebate being
made at 5 per cent.
Rule. As £100 with the interest for the time given : is to
that interest : : so is the sura given : to the rebate required.
Subtract the rebate from the given sum, and the remainder
will be the present worth.
EXAMPLES.
1. Wliat is the discount and present worth of £487 : 12 for 6
months, at 3 per cent, per annum ?
em=^6 .
3
100
103
As 103:0;:487 : 12
20 20
2060
9752
3
487 : 12 principal.
14 : 4 rebate.
£ s.
20610)292516(14 . 4 rebate.
206
Ans. £473 : 8 present worth.
865
824
416=48.
2. What is the present payment of £357 : 10, which was
agreed to be paid 9 months lience, at 5 per cent. })er annum ?
Ans. £S4 4:11:7.
3. What is the discount of £275 : 10 for 7 months, at 5 per
cent. ])er annum ?
g2
Ans. £7 : 16 : li
ri
f-|
I
J
78
Hiii
m
EQUATION OF PAYMENTS.
4. Boui^ht goods to the value of £109 : 10, to be naid if ni'nJ
months what present money will discharge th'e same,^i I 1 "] '
lowed 6 jer cent, per annum discount ? , x am ai
7 Sold goods for £875 : 5 : 6, to be paid f Inths tte
what IS the present worth at 4^ per eont. ? '
8. Wlfat 18 the present worth of £500, payable in 10 months
at 6 per cent, per annum ? ^^, j.^'^^
d„!'i . "" T'^ '"''^^ "'^"'>' '-''" ^ ^^^«i^'^ for a note of £75
due 15 months hence, at 5 per cent. ? ^^ ^'o,
in WK . Ml 1 , ^^*- ^'^0 : 11 : 9i.
10. H hat will be the present worth of £l50, payable at 3
four months ^. .. one third at four months, one thi rd^^Ts Inhs
and one third at 12 months, at 5 per cent, discount? '
11 an J X ., , . ^ns. £145 : 3 : 8^.
11. Sold goods to tbe value of £575 : 10, to be paid at 2 three
months, what must be discounted for prese'nt payment, at 5 per
12. VVhat is the present M-orth of £500 at 4 per cent £lO0
being to be paid down, and the rest at 2 six montli ? '
^ns. £488 : 7 : 8^.
EQUATION OF PAYMENTS,
Is when several sums are duo at different times, to find a mean
fame for paying the whole debt; to do which this' is the common"
RiTLE. Multiply eacli term by its time, and divide the sum
of the product, by the whole debt, the quotient is accounted the
tDcali U1I10>
KQUATION OF PAYMENTS.
n
t]
EXAMPLES.
1
1. A owes B £200, whereof £40 is to be paid at 3 months,
I £00 at 5 months, and £100 at 10 months; at wluit time may the
whole debt be paid together, without prejudice to either?
I;.
£
m.
40
X
3
= 120
60
X
5
= 300
100
X
10
2l(
= 1000
30)14120
7 months
tV.
2. B owes C £800, whereof £200 is to be paid at 3 months,
£100 at 4 months, £300 at 5 months, and £200 at 6 months;
but they af^reeing to make but one payment of the whole, I de-
mand what time that must be ?
Ans. 4 months, 18 days.
3. I bought of K a quantity of goods, to the value of £360,
which was to have been paid as follows: £120 at 2 months, and
£200 at 4 months, and the rest at 5 months ; but they afterwards
agreed to have it paid at one mean time ; the time is demanded.
Ans. 3 months, 13 days.
4. A merchant bought goods to the value of £500, to pay £100
at the end of 3 months, £150 at the end of 6 months, and £250 at
the end of 12 months; but afterwards they agreed to discharge
the debt at one payment; at what time was this payment ir ide^
Ans. 8 months, 12 day^-f
5. H is indebted to L a certain sum, which is to be paid at
dilforent payments, that is, ^ at 2 months, -^ at 3 months, ^ at 4
months, ^ at 5 months, |^ at 6 months, and the rest at 7 months j
but they agree that the whole should be paid at one equated time*
what is that time 2
Ans. 4 months, 1: quarter. ,
6. A is indebted to B £120, whereof i is to be paid al 3
months, ^ at G months, and th.e rest at 9 months; what is the
equated time of the whole payment ?
Ans. 5 months, 7 days.
g3 ^
f«^ hi
'f^'
78
BARTER.
BARTER
Is the exchanging of one commodity for another, and informjl
the traders so to proportionate their goods, that neither raaj
sustam loss. J
Rule 1st. Find the vakie of that commodity whose quantitv
18 given ; then find what quantity of the other, at the rate prd
posed, you may have for the same money. f
2dly. When one h.i-^ goods at a certain price, ready money,
but in bartering, advanct. it to something more, find what the
other ought to rate his goo. at, in proportion to that advancJ
and then proceed as before. ^'
m
EXAMPLES.
n;:i!
!!i|
1. What quantity of chocolate, at
4«. per lb. must be delivered in barter
tor 2 cwt., of tea, at Us. per lb. ?
2 cwt,
112
224 lb.
9 price.
4)2016 the value of the tea.
504 lb. of chocolate.
2. A and B barter ; A hath 20 cwt
of prunes, at4d. per lb. ready moneyj
but in barter will have 5d. per lb. andf
B. hath hops worth 32s, per cwt,,
ready money ; what ought B. to raU
his hops at in barter, and what quan-
tity must be given for the 20 cwt., of
prunes ? '
112 As4:5::33|
20 5
s.
40
12
2240
5
-cwt. qr. lb.
4)160
408.
4810)112010(23 . 1 . g'll Ans.
96 *'
160
144
10=1 qr. 9 lb. j^
must receive the difference and hfw^iteh^' ^""^ '^'"'' ">'<"°*"l>'l
Jl7is. B. miiflf rerpivp of A Xfo o
J'ntl Im ^ner'lh'.' if ^''^1 ^^' "^ "P'^^'' ^^ ^^id. per lb. ; B hati gin- 1
pepper.' ^ ' ""^ """"^^ Sanger must he deliver in barter forV
'^ns. 3 lb. 1 ozM
..rfc.l
PKOFIT AND LOSS.
7»
6 How many dozen of candles, at 53. 2d. per dozen, must be delivered
in barter for three cwt. 2 qrs. 16 lb. of tallow, at 373. 4d. per cwt. .'
' J^ns. 26 dozen 3 Ib.fJ
7 A hath 608 yards of cloth, worth 14c. psr yavi, for which B giveth
I him £125 . 12. in ready money, and sr. cwt. " -irs. 24 lb. of bees'-wax.
The question is, what did B reckon his be s'-wi : at per cwt. ?
8 A and B barter ; A hath 320 dozen of cauJies, at 43. 6d. per dozen ;
for which B giveth him £30 in money, an«' m • rest in cotton, at 8d per
lb : I desire to know how much cotton I' ,y> ■ ; .^ besides the money ?
■' Ans. 11 cwt. 1 qr.
9. If B hath cotton, at Is. 2d. per lb., how much must he give A for 114
lb. of tobacco, at 6d. per lb. z, ^o lu i a
Ans. 48 Ib.yf.
10. C hath nutmegs worth 7s. 6d. per lb. ready money, but in barter will
have 8s. per lb. ; and D hath leaf tobacco worth 9d. per lb. ready money ;
how much must D rate his tobacco at per lb. that his profit may be equiva-
t •
v#^^
11
PROFIT AND LOSS
Is a Rule that discovers what is got or lost in the buying or selling
of goods, and instructs us to raise and lower the price, so as to
gain so much per cent, or otherwise.
The questions in this Rule are performed by the Rule of Three.
M9I
EXAMPLES.
1. If a yard of cloth is bought for
Us. and sold for 12s. 6d. what is the
gain per cent. ?
As 11 : 1 : 6 : : 100
12
12.3
U .0
1.6
18
20
2000
18
11)36000
12)3272y\
210)2712 . 8
Ana. £13 . 12 . SrV
2. If 60 ells of Holland cost £18
what must 1 ell be sold for to gain 8
per cent. ?
As 100 : 18 : : 108
108
1100)19144
20
8180
12
0160
12X5=60
12)19 . 8 . 9i
5)1 , 12 . 41
. 6 . 54
2140
-Ans. 6s. 5|d
1:1
,t!i
I
V
HI
Ml
80
FELLOWSHIP.
^J. ^ rf 1 lb. of tobacco COS. m. and i, ,„ld fov 20d. wha. i, ,he gain pj
wasV/^-ird,"'. ''°"' "" '"" f" ^5«»- -d a. 12 per cenf ^-In^^i. J
., 5. If a yard of cloth is bou-ht for 13s 4d ,n,l a m • '^.^' '^^'^^- I
18 the gain p^i- cent. ? ^- *"^ ^^^'^ ^gam for l(5s. whati
6. if Hi lb. of iron rn<-t oia ca k . -^>^i- £20. I
15 per cent. ? °'^ ^^' ^'^•' ^^^^ must 1 cwt. be sold for to g^inl
7. If 375 yards of broad cloth be sold for £icn f^"' ^^ ■ ^^ ■ n
In! it cost per yard ' ^""^ '^'^^^^ ''"'^ 2U per cent, profit,
" " ' Ans. jgl . ] . 9 ,
8. Sold 1 cwt. of hona for 4>a ^K * xu '^"*- j£l . 1 . 9i
What would have been he ^at pi? cent' .f I td ''!', t '' .P^*- ^^"t" P-""'!^
%am percent, it 1 had sold them for jES^per cut '
. 0, If 90 ells of cambric cost £m \, u *^'**- ^^48 . 2 . li i. '
gain 18 per cent. .' ^ '^^"' ^°^ "^"^^ '""^t I sell it per yard to
10 A plumber sold lOfotherof leid for ^oni i. , ,_ *^'**- ^-«- "''f'-
cwt.) and gained after the rate of i?9 in ^'^ ' ^^' ^^^^ ^^^^er being 'M
per cwt. .^ ^^^^ "^ ^\2 . 10 per cent. ; what did it cost bin!
_ 11. IJought 436 yards of plntK „«^ li. ^ ■^w«. 18s, 8d
■t ro. ,0. u. pe.. jj] wbt:!'i^Ve'"yir„f1b?•wti^/ '-"' -" -"
13. Bought 124 yards of linen for i-J?' I, ^ ,. ^ns. £W2 \o»s.
per yard to gain 15 per cent " ' ^ ''^""^^ ^'^^^ ^^^^^ l>^ «-etailed
^/«. £10.7.6 proat, and 25 per cent. '
FELLOWSHIP *
proportion to Ws'i.rinciplirroS.tocr "' "" «"'" "' '-' -
cJftor'r^rau: i::;.tfI;T r^ *? *"<'^<^ -"-g^t i-
ciency of a^sete or cftS. ^ "^J"'"'' "''^" ">«■* » "d*
FELLOWSHIP IS Eir„™ WITH OH WITHOUT TIME.
FELLOWSHIP WITHOUT TIME
Proof A. 11 ij *i i " ^^ "^'^ ^'^''^'"<^ ^f the ffain or loss
th« gain or la« ; to l,i« sh^l i, tl' ' "^ " '"'^' "'^"' ^•'«' '
euaic UJ
A 60 : 50
21
' 6IO)100li
£16 . 13 .
2. Tfireer
I and C £40 ;
3. A, B, a
j C £500 ; am
1 to his stock :
4. Four n
■] £349, D£l
! iaerchant's s
5. Three
!v3 £4(50, a
what is eacl
6. A mer
and to E £I
but £675 . :
At
7. Four \
C ^, and D
man's share
8. Two \
£27,200, w
tax ; where
of the mon
the said est
M
FELLOWSHIP.
EXAMPLES
81
1. Two merchants trade together; A puts into stock £20, and B £40,
Ithey gained £50 ; what is each person's share thereof?
A 60 : 50 ! : 20
20
610)10010
£16 . 13 . 4
20+40=60
As 60 : 50 : : 40
40
33 . 6 . S, B's share.
16 . 13 . 4, A's share.
610)20010
£33 . 6 . S
50 . 0.0 proof.
2. Ttiree merchants trade together, A, B, and C ; A puts in £20, B £30,
and C £40 ; they gained "ISO : what is each man's part of the gain ?
Ans. A £40 ; B £60 ; C £80
3. A, B, and C, enter into partnership ; A puts in £364, B £482, and
C £500 ; and they gained £807 ; what is each man's share in proportion
to his stock ?
Ans. A £234 . 9 . 34— rem. 70 ; B £310 . 9 . 5— rem. 248 ;
C £322 . 1 . 3i— rem. 1028.
4. Four merchants, B, C, D, and E make a stock ; B puts in £227, C
£349, D £115, and K £439 ; in trading they gained £428 : I demand each
merchant's share of the gain ?
Ans. B £85 . 19 . 6^—690 ; C £132 . 3 . 9—120 ; D. £43 .
11 . U— 250 ; E £166 . 5 . 64—70.
5. Three persons, D, E, and F, join in company ; D's stock was £750,
E's £4(50, and F's £500 ; and at th'^ end of 12 months they gained £684 :
what is each man's particular share of the gain ?
A?is. D £300, E £184, and F. £200.
6. A merchant is indebted to B £275 . 14, to C £304 . 7, to D £152,
and to E £104 . 6 ; but upon his decease, bis estate is found to be worth
but £075 . 15 : how must it be divided among his creditors ?
Ans. B's share £222 . 15 . 2—6584 ; C's £215 . 18 . U— 15750 •
D's £122 . 16 . 21—12227 ; and E's £84 . 5 . 5—15620.
7. Four persons trade together in a joint stock, of which A has i, B 4,
C ^, and D ^ ; and at the end of 6 months they gain £100 : what is each
man's share of the said gain ?
Ans. A £35 . 1 . 9-48 ; B £26 . 6 . 3|— 36 ; C £21 . 1 . Oi
—120; and D £17 . 10 . lOi— 24.
S. Two persons purchased an estate of £1700 per annum, freehold, for
£27,200, when money was at 6 per cent, interest, and 4s. per pound, land-
tax ; whereof D paid £15,000, and E the rest ; sometime after, the interest
of the money falling to 5 per cent, and 2s. per pound land-tax, they sell
the said estate for 24 pears' purchase ; I ^csirc to knovv eaen person's shaie ?
Ans. D £22,500 ; K £18 "00.
. \M
i
l«i liJi
>H
01 «
"2 7*
"4 2T*
FELLOWSHIP.
Stocks^; ^fiTv^ ^'i^li; *^''"' "^'^'' '"^ ^'^^^'^ ^^^ ^"^^^""t of theiJ
stocks IS £647 and they are m proportion as 4, 6, and 8 arc to
one another, and the amount of the gain is equal 'to D^s stock
what IS each man's stock and gain? , '
Ans. D's stock £143 . 15 . 6J-f gain, 31 . 19
J-s 215. 13 .4 47. 18
Fs 287.ll.iyL.... 63.18
10. D, E, and F, join stocks in trade; the amount of thpirl
:^cLrs IT; ^' ^^^^ "^' ^''^ ^^' -^ ^'^ ^« -^- -
^n.. D's stock £18.15; E's £31.5; and Fs £50.
FELLOWSHIP WITH TIME.
time . IS to the whole gam or loss ; : so is each man's product •
to his share of the gain or loss. proauct .
Pboop. As in fellowship without time.
2,', M,
EXAMPLES.
month^ and e1*?'. 'T r'"^*^^^?; ^ ?"*« in £40 for three
montns, and h ^75 for four months ; and they gained £7o •
what IS each man's share of the gain ? ^ ^ '
Ans. D £20, E £50.
40X3 = 120 As 420 : 70 : : 120 As 420 • 70 • • '^(\c^
75X4=300 120 -«^s ^-iu . /u . . 300
420
4210)840)0(20
840
4210)210010(50
2100
2 Three merchants join in company; D puts in stock £195
tl mat's ;tw!:f IL git ' ''''' ''''''' ^''' '''-' -^-^ %
Ans. D's £102 . 6 . 4-5008 ; E's £148 . 1 uJ!
-o«ou;;; HOu i' a JE;n4 . 10 . 6| — 14707
ALLIGATION.
3. Three merchants join in company for 18 months; D put in
£500, and at five months' end takes out £200 ; at ten months'
end puts in £300, and at the end of 14 months takes out £130 :
E puts in £400, and at the end of 3 months £270 more ; at 9
months he takes out £140, but puts in £100 at the end of 12
months, and withdraws £99 at the end of 15 months: F puts in
£900, and at 6 months takes out £200^; at the end of 11 moiiths
puts in £500, but takes out that and £100 more at the end of 13
months. They gained £200 : I desire to know each man's share
of the gain ?
Ans, D £50 : 1 : 6— 21*720 ; E £62 : 12 : 5^—29859 ; and
F £87 : : 0^—14167.
4. D, E, and F, hold a piece of ground in common, for which
they are to pay £36 : 10 : 6. D puts in 23 oxen 27 days; E 21
oxen 35 days; and F 16 oxen 23 days. What is each man to
pay of the said rent ?
Ans. D £13 : 3 : U— 624; E £15 : 11 : 5—1688; and F
£7 : 15 : 11—1136.
ALLIGATION
ALLIGATION IS EITHER MEDIAL OR ALTERNATE.
ALLIGATION MEDIAL
Is when the price and quantititc *»f several simples are given
to be mixed, to find the mean p-ice of that mixture.
Rule. As the whole .position : is to its total value : : so
is any part of the oompo'^iuo: : to its mean price.
Proof. Find the value of the whole mixture at the mean rate,
and if it agrees with the total value of the several quantitias afc
tb<'ir respective prices, the work is right.
84
ALLIGATION.
li
EXAMPLES.
As 96 : 288 : : 1 : 3
20X5 = 100
36X3 = 108
40X2= 80
06
288
Ans. 38.
8cl. per irillon nnrl o^ i ^f ,'. ^^ ^^^^^"^ ^^ «^eny, at 6s.
eJ- f ,r-^ --g'^d * "wt. of sugar, at 56^ I'^w'/tlt 7
value of 8 hu^i^l^lAi^J.f ^' <'™^'^>-- ™-' - 'he
5. If I mix 27 bushels of wheat at s'^''fi/,'„;^' ^^'\'''^-- ..
6. A vintner mixes 20 gallons of Dort .i t^'lf' ^^'^^f,'
with 12 gallons of white Jfe" 1^"V
p^fiVn %^rt-"^""'' li"' \^ gaiiorof^ij^, f "r6d
per gallon. What is a gallon of this mixture worth ?
-7. A refiner having 12 lb. of silver bullion ^T ^'' !^'^-^^- , ,
melt it with 8 lb. of 7 oz. fine and J lb nf « ^'' ^"'' ''^"^^
the iiaeness of 1 lb. of that 2ture ? ' ''' ^"' ' ^^^"""^^
.8. A tobacconist would nnx 50 lb^of\ob'4o^f n /' ^"•,.
with 30 lb. at I4d per lb 2-. lb -.f ooi ^"^^^9^' "^, ^^^'- pt^'' 'b.
per lb What .vn in V *^ ^'^' P^' '^' ^"^^ ^7 lb. at 28.
per 10. Wiiat will 1 lb. of this mixture bo worth «
-n-iii
io;
it-
i.ii
ALLIGATION.
85
J
bushel, and
s of bailey,
I bushel of
per gallon,
ei-iy, at 6s.
per gallon.
2^cl.|f
tvt. with 1
em-aiid the
.8.9.
t*28s. per
I", and 24
lat is the
2icl.A.
'^hel, with
ushels of
lel of this
31* gallon,
■allons of
t 4s. 6d.
f<l.|f
le, would
required
16 gr,
. per lb.
lb. at 28.
ALLIGATION ALTERNATE
h when the price of several things are given, to find such quanti-
ties of thera to make a mixture, that may bear a price pro-
pounded.
In ordering the rates and the g'ven price, observe,
1. Place them one under the other, 1 8 — . 2
and the propounded price or mean 22^*^~^ — ^
rate at the left hand of them, thus, 24_l
28
4
2
2. Link the several rates together by 2 and 2, always observ-
ino" to join a greater and a less than the mean.
°3. Against each extreme place the difference of the mean and
its yoke fellow.
When the prices of the several simples and the mean rate are
given without any quantity, to find how much of each simple is
required to compose the mixture.
Rule. Take the difference between each price and the mean
rate, and set them alternately, they will be the answer required.
Proof. . y Alligation Medial.
EXAMPLES.
1. A vintner would mix four soits of wine together, of 18d.,
20d., 24d., and 28d. per quart, what quantity of each must he
have, to ^sell the mixture at 22d. per quart ?
28_J
Proof.
2 of 18d. = 36d.
6 of 20d. = 120
4 of 24d. = 96
2 of 28d. = 56
I
14
)308
2 2d.
22
or thus,
18 6 of 18d
20
24_.l
28 _
Proof.
= 108d.
2 of 20d. = 40
2 of 24d. = 48
4 of 28d. = 112
14
)308
22d.
Note. Question^ in this rnlc pAimit of .i- great variety of an-
swers, according to the manner of linking them.
2. A grocer would mix sugar at 4d., Od., and lOd. per lb., so
as to sell the compound for' 8d. per ib. ; what quantity of each
must he take ?
Ans. 2 ib. at 4d., 2 ib. at Od., and 6 lb. at lOo.
i •
V ■
iMu
r
>.\
;.;•'■!
^ '-li
^ ' ;
rJtm „ii
itl
ht.i'ir
I ' 'IB''
'.II'
86
ALLIGATION PARTIAL.
8 1 desire io know how much tea, at ICs Us 9s anrl ft«
per lb, w,ll compose a ,nixturo worth lOs. per Jb. ? ' '
^i^^. lib. at IGs, 2 lb. 14s., 6 lb! at 9s., and
4. A t^tr.ner would mi^ T ,S ^^i^ -^ 'V!^!/ ^'- 1 ']' ,
rye at 4s. per bushel, and oat«l Ss tVbutl t TJ ^2"^'
fixture worth 2s, Cd. per bushel. 11^^ .tlrl^^l^ 7tt
Jns. G busJiels of barley, 6 of rve and SO nf nnfc
6. A tobacconist would mix tobacco at 2s Is fid «nfl U ^A
per lb., so as the compound mav bear a dHop of u «1 ^u
What quantity of each sort must he take' ^ ' '^* P'' ^^•
Ans. 1 lb. at 2s., 4 lb. at Is. 6d., and 4 lb. at Is. 3d.
ALLIGATION PARTIAL,
01 them and the mean rate are given to find the several auanti-
ties of the rest m projiortion to that given ^
*>,/' !^''/];^^'T.'?r ""^ ^^'^^ '""P^« ^^^'osP qviantity is given • to
he rest o the d.tFerences severally : : so is the quantity^ ven '• to
the several quantities required. ^ ^
EXAMPLES.
,♦ 1;/ tobacconist being determined to mix 20 lb. of tobacco
at I5d. per lb., with others at IGd. per lb., 18d. per lb and 22d
per lb.; how many pounds of each sort must he tak"; to m'ke
one pound of that mixture worth 17d.?
Answer. ^root
16 5 20 lb. at 15d. = .^ood. Ag 5
,h1C_
^M8-J
22
1 4 lb. at IGd. = 64d. As 6
1 4 1b. at 18d. =. 72d. As 5
2 8 lb. at 22d. = 170d.
1 : : 20 : 4
1 : : 20 : 4
2 : : 20 : 8
Ans, 30 lb.
■ .1 ii\i.
ALLIGATION TOTAL.
87
2 A farmer would mix 20 bushels of wheat at 60d. per bush-
el with rye at 36d., barley at 24a., and oats at 18d. per bushel.
How much must he take of each sort, to make the composi-
tion worth 32d. per bushel ? , , , ,, H^ V. u 1
Ans. 20 bushels of wheat, 35 bushels of rye, 10 bushela
of barley, and 10 bushels of oats.
3 A distiller would mix 40 gallons of French Brandy, at 12s.
per * gallon, with English at 7s., and spirits at 4s. per gallon.
What quantity of each sort must he take to afford it for 8s. per
^^ ^^ Ans. 40 gallons French, 32 English, and 32 spirits.
4 A grocer would mix teas at 12s., lOs., and 6s., with 20 lb.
at 4s. per lb. How much of each sort must he take to make
the composition worth 8s. per lb.?
Ans. 20 lb. at 4s., 10 lb. at 6s., 10 lb. at lOs., 20 lb. at 12s.
5 A wine merchant is desirous of mixing 18 gallons of Ca-
nary, at 6s. 9d. per gallon with Malaga, at 7s. 6d. per ga on,
shm'v at 5s. per gallon, and white wine at 4s. 3d. per galloni
How much of each sort must he take that the mixture may bo
sold for 6s. per gallon 1 , ^ ,r i -. oi ^ ci
Ans. 18 gallons of Canary, 31^ of Malaga, 13i of Sherry,
and 27 of white wine.
ALLIGATION TOTAL
UAI
Is when the price of each simple, the quantity to be compound-
ed, and the mean rate are given, to find how much of each sort
will make that quantity.
Rule. Take the difference between each price, and the mean
rate as before. Then, , .. , j/r
As ihe sum of the differences : is to each particular ditter-
•nee : : so is the quantity given : to the quantity required.
ft
EXAMPLES.
1. A grocer has four sorts of sugar, viz., at 12d., lOd., 6d., and
4d. per lb.; and would make a composition of 144 lb. worth 8d.
^-I tv T ;i.vo;-,. ♦/-. hnfxxv vahiit nuaiititv of each he must take?
^ h3
r 11
I-
88
fm
POSITION, OB THE HUIB OP FALSE.
Proof.
48 at ]2cl. 576=As 12
24 at lOd. 240= As 12
24 at 6d. 144=A8 12
48 at 4d. 192= As 12
4
2
2
4
144
144
144
144
48
24
24
48
52 144 )ll52(8d.
Wlmt quantity must there be of each ? ' ''' ^' "^
of 60 gallons to he w Jl, I ' ,V '"'"''^ "^''^ » '"'''•«'«
each mu?t helkt?'^ ^°"'' ''• f'' S""""- What quantity of
^'"' t'^nlT fij}'*^ ^'".^' ^ S'tlloos of Flemish,
I . 6 gallons of Malaga, and 5 gallons of Canary.
*■ A silversmith had four sorts of jrold vW of Oi „ .
fine nf 99 9n nr.A i c . /» e*^'^* viz., oi zi carata
eacrs:rf,:,^eirso'a,rot™ "42:^7,1^frr"'t"f
much must iTe take of each < ' ""'*'' ^"'- H"''
Ans. 4 0.. of 24 4 oz. of 22, 4 oz. of 20, and 30 oz.
ot 15 carats fine.
take for each parcel? ^ ^""^ """='' "^ ^'^'' «»'' *d he
^«». 12 lb. of 8.,. 80 lb. of 8s.
8 lb. of 5s. « lb. of 5,_
J lb. of 4s. 6 lb. of ^
28 lb. at 69. per lb. 42 lb. at Ts. per lb.
POSITION, OE THE RULE OP FALSE,
*s;vr^\*''Ui' t' r:;3™?t "'""^^•.'"^«" «' P'"-"-
SiHGM and Double ^ ^' «. divided into two parH
«?*t*Si«r?^5|
POSITION OR THB RULE OF FALHH.
69
SINGLE POSITION,
[s, by using one supposed number, and working witb it. as the
true one, you find the real number required, by the following
Rule. As the total of the errors : is to the true total : : so is
the supposed number : to the true one required.
Pjioof. Add the several parts of the sum together, and if it
agrees with the sum it is right.
EXAMPLES.
1. A schoolmaster being asked how many scholars ho had, said,
If I had as many, half as many, and one quarter as many more,
I should have 88. How many had he ? Ans. 32.
Suppose he had. .40 As 110 : 88 : : 40 32
.as many.... 40 40 32
half as many 20 16
i as many . . 10 Ill0)352l0(32 8
33
110
22
22
88 proof.
2. A person having about him a certain number of Portugal
pieces, said, If the third, fourth, and 6th of them were added
together, they would make 54. I desire to know how many he
had? Ans. 12.
3. A gentleman bought a chaise, horse, and harness, for £60,
the horse came to twice the price of the harness, and the chaise
to twice the price of the horse and harness. What did he give
for each ?
Am. Horse £13 : 6 : 8, Harness £6 : 13 : 4, Chaise £40.
4 A, B and C, being determined to buy a quantity of goods
which would cost them £120, agreed among themselves that B
should have a third part more than A, and a fourth part more
tJian B. I desire to know what each man must pay ?
Ans. A £30, B £40, C £50.
h3
P
90
POSITION, OR THE RULE OP FALSE.
terest, aiul at the end of 10 vol-FZ ''':\i'^' ''^"'•"'n, simple in.
t-est, £300. What ^l J^Cle^U "'V^^Xll^/;!^^"
DOUDLE POSITION
be tlius ordered :— ^^ / ""^7 are, with their errors, to
tho quotient will bo th^ a^^-"" "^ ""■"■ l"'"''""'^ ^o' ■•' dividend,
EXAMPLES.
n.4^i^;c^olSt^::;'V::;;d^d'^ '^'^v ^^t^ - that b
must each have? ' ^^ ^^ ™^'*^ *'^^*» I^; liow much
'"C Bind 46 Thens.i,.poseAhad.50
and C ^1 ^^'''' ^^ »""«t have 56
140 too little by 60.
sup. errors.
40 60
50 '^ 30
3000 1200
1200
60
30
30 divisor.
310)180(0
60 Ans. for A.
170 too little by 30.
60 A
66 B
74
200 proof.
covt tots,!':' fort;, yTc """"!"" ''<"«•"• "-"» 0-
it will double the wd^ht V tho CT " P"' "" *''« ^"^ ™P.
greater c„p, it will te'?hriee S hSt I T' ,™'' ^''^ <"• '••«
is the weight of each cup ? ^ "^ ** '"^^ <="P- What
-^»». 3 ounces less, i greater.
BXCHANOB.
91
3. A gentleman bought a house, with a garden, and a horse in
I tiie stable, for £500 ; now lie paid 4 times the price of the horse
for the garden, and 5 times the i)rice of the garden for the hoViSe.
What was the value of the house, garden, and hoi-se, separately t
Ans. horse £20, garden £80, house £400.
4. Three persons* discoursed concerning their ages: says H,
I am 30 years of age ; says K, I am as old as H and i of L ; and
says L, I am as old as you both. What was the age of each
peraon ?
Ans. H 30, K 50, and L 80.
5. D, E, and F, playing at cards, staketl 324 crowns ; but dis-
puting about the tricks, each pan took as many as ho could : D
got a certivin number; E as many as D, and 15 more; and F got
a fifth part of both their sums added together. How many did
each get ?
Ans. D 127i, E 142^, and F 54.
6. A gentkraan going into a garden, meets with some ladies,
and says to tliem, Good morning to you 10 fair maids. Sir, you
mistake, answered one of them, we are not 10; but if we were
twice as many more as we are, we should be as many above 10
as we are now under. How many were they 3r • *
Ans. 5.
EXCHAN^GE
Is receiving money in one country for the same value paid in
another.
Tlie par of exchange is always fixed and certain, it being the
intrinsic value of foreign money, compared with sterling; but
the course of exchange rises and falls upon various occasions.
L FRANCE.
They keep Lu^ir accounts at Paris, Lyons, and Rouen, in livres,
sols, and deniers, and exchange by the crown = 4s. 6d. at par.
Note. 12 deniers make 1 sol.
20 sols 1 livre.
3 livres 1 crown.
! 4
'I 4
a^.
V^,
iMAGE EVALUATION
TEST TARGET (MT-3)
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4i_s
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f<'' C^x
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sr A^ mp.
Q!r
i/.l
1.0
I.I
1.25
6"
IIIIIM
2.0
11111=
1.4 IIIIII.6
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'c^
A
' cp
Photographic
Sciences
Corporation
<l^
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V
23 WEST MAIN STREET
WEBSTER, N.Y. M580
(716) 872-4503
6^
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A.
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92
EXCHANGE.
To change French into Sterling.
Rule. As 1 crown : is to the given rate : : so is the French
sum : to the sterling required.
To change Sterling into French.
Rule. As the rate of exchange : is to 1 crown : : so is the
sterhng sum : to the French required. *
EXAMPLES.
1. How many crowns must be paid at Paris, to receive in
London £180 exchanged at 4s. 6d. per crown ?
d. c. £
As 54 : 1 : : 180 : 800.
240
54)43200(800 crowns.
432
2. How much sterling must be paid in London, to receive in
raris 758 crowns, exchanged at 56d. per crown ?
q A t, . . T , . Ans £11Q: 17 : 4.
3. A merchant m London remits £176 : 17 : 4, to his corres-
pondent at Paris ; what is the value in French crowns, at 56d
per crown ? ^^; ^^g '
4. Change 725 crowns, 17 sols, 7 deniers, at 54^d. per crown,
mto sterling, what is the sum? Ans. £164 • 14 • 0|d ^^S-
ohtf^'tlfif^^^ '^^[^^ «*«rfi»g. into French crowns,"ex-
change at di^d. per crown ? '
Ans. 725 cro\vns, 17 sols, 7 J^V <3eniers.
n. SPAIN.
They keep their accounts at Madrid, Cadiz and Seville, in
dollars rials and maravedies, and exchange by the piece of eUt
=4s. od. at par. <^ .^ r &
Note. 34 maravedies make 1 rial.
, f ^.^]^ 1 piastre or piece of eight.
lOnals 1 dollar.
Rule. As with France.
EXAMPLES.
«f I'a^ "'G'-c^ant at Cadiz remits to London 2547 pieces of eight.
at 66d. per piece, how much sterling is the sum ?
Am. £594 : 6.
> is the French
, to receive in
, to receive in
EXCHANOB. 03
I. How many pieces of eight, at 56d. each, will answer a bill
of je594 : 6, sterling ] Ans. 2547.
8. If I pay a bill here of £2500, what Spanish money may I
Oraw my bill for at Madrid, exchange at SV^d. per piece of eight?
Ans. 10434 pieces of eight, 6 rials, 8 mar. |f
III. ITALY.
They keep their accounts at Genoa and Leghorn, in livres,
sols, and deniers, and exchange by the piece of eight, or dollar
=4s. 6d. at par.
Note. 12 deniers make 1 sol.
20 sols 1 livre
5 livres 1 piece of eight at Genoa.
6 livres 1 piece of eight at Leghorn.
N. B. The exchange at Florence is by ducatoons ; the exchange at Venice
by ducats
Note. 6 solidi make 1 gross.
24 gross 1 ducat
Rule. Same as before.
9. How much sterling money may a person receive in London, if h«
pays in Genoa 976 dollars, at 53d, per dollar ? Ans. £215 . 10 . 8.
19. A factor has sold goods at Florence, for 250 ducatoons, at 5 Id. each ;
what is the value in pounds sterling ? Ans, £56 .5.0.
II. If 275 ducats, at 4s, 5d. each, be remitted from Venice to London ;
what is the value in pounds sterling ? Ans. £60 . 14 . 7.
12. A gentleman travelling Would exchange £60 . 14 . 7, sterling, for
Venice ducats, at 43. 5d. each ; how many must he receive ?
Ans. 275.
IV. PORTUGAL.
They keep their accounts at Oporto and Lisbon, in reas, and
exchange by the milrea=Gs. 8^d. at par.
Note. 1000 reas make 1 milrea.
Rule. The same as with France.
EXAMPLES
13. A gentleman being desirous to remit to his correspondent in London
2750 milreas, exchange at 6s. 5d. per milrea; how much sterling will he
be the creditor for in London ? Ans. £882 . 5 . 10.
14. A .merchant at Oporto remits to London 4S66 milreas, an' j83 reas,
at 53. Sjd. exchange per milrea ; how much sterling must be paid in Lon-
don for this remittance } Ans. £1193 . 17 . 6|, 0375.
15. If I pay a bill in London of £1193 . 17 . 65, 0375, what must 1 dravT
for on my correspondent in Lisbon, exchange at 58. 5|d. per milrea ?
Ans. 4366 milreas, 183 reas.
:ir
M
0i
i'l:
■d
EXCHANGE.
V. HOLLAND, FLANDERS, AND GERMANY.
aa in England ; ^Ct'gZ: S^ ^''^' ""^ ^"^^^
exchange with us in our poufd, at 33s!'Slemfshf :r;r ' "'"1
Note. 8 pennings make , .,„.,
1 guilder or florin.
ALSO,
20 schellings, or 6 guilders. . . i pound
To change Flemish into Sterling,
Bun^: to tlt«i~r' '" »- P-"-! = = - - the Flemish
^0 cAawye Sterling into Flemish
given -^ i: He::Sl"sS"ugi.r '"^ ^'"" "'«= = ^ '' ^I^^ ^""S
EXAMPLES.
how -inrpSTrSl^^^^^^ ^ b'? «f ^^54 .10.0 sterling,
per pouPd sterling .' ' ^^"^ '"'"' the exchange, at 33^ oa. Flemish
. 17. A merchant in Rotterdam remits jEiIg?" f ^^^q 'J,^ ' ^' ^^^'"^^h.
in London, how much sterling monTvmtfhl^* V^' Flemish, to be paid
at 33s Od Flemish per pouSd TerlZ^?^"' ^' '^'"^ ^''' '^^ "'^'^i^"'^^ ^''^^S
18. If r pay in London £852 lo %' „*^ri:„„ , '^''•*- ^754 . 10.
I draw for at Amsterdam. exchan^P «/ ^j u^\ T ""^"^ guilders must
^n«. 852 . 12 . 6.
To convert Sank Money into Current, and the cMrary
The Zoic: .^tto„*':n7and Tothr" "T. *« «"™»^
generaIl,f..om3toCperc:nU„tou?„7ttBil'^'"' ""<' "
^0 cAaw^e j?aw^ into Current Money
EXCHAN6B.
To change Current Money into Bank.
95
Rule. As 100 with the agio is added : is
to 100 Bank : : so is
Current money given : to the Bank required.
20. Change 794 guilders, 15 stivers, Current Money, into Bank
florins agio 4f per cent.
Ans. 761 guilders. 8 stivers, ll|f^ pennings.
21. Change 761 gui' 'ers, 9 stivers Bank, into Current Money,
agio 4f per cent.
Ans. 794 guilders, 15 stivers, 4y='^ pennings.
VI. IRELAND.
22. A gentleman remits to Ireland £575 : 15, sterling, what
will he receive there, the exchange being at 10 per cent. ?
Ans. £633 : 6 ; 6.
23. What must be paid in London for a remittance of £633 :
6 : 6, Irish, exchange at 10 per cent. ? Ans. bl5 : 15.
COMPARISON OF WEIGHTS AND MEASURE S.
EXAMPLES.
. If 50 Dutch pence be worth 65 French pence, how many
Dutch pence are equal to 350 French pence?
Ans. 269^f .
2. If 12 yards at London make 8 ells at Paris, how many ells
at Paris will make 64 yards at London ?
Ana. 42j8j.
3. If 30 lb. at London make 28 lb. at Amsterdam, how many
lb. at London will be equal to 350 lb. at Amsterdam ?
Ans. 375.
4. If 95 lb. Flemish make 100 lb. English, how many lb. En-
glish are equal to 275 lb. Flemish.
Ans. 289ff.
CONJOINED PROPORTION,
Is when the. coin, weights, or measures of several countries are
compared in the same question ; or, it is linking together a varie-
ty of proportions.
When it is required to iind how many of the first sort of coin,
weight, or measure, mentioned in the question, are oqual to a
given quantity of the last.
i'i.
96
PHOPOHTIOW.
ply the first row coilZm, fir . ^- m ^ ""^ ''f ''i *<"> """Wl
a divisor. «»>u«ually for a dividend, and the second fo,l
requfrr ^^ "" """^ ^'"Sle Rules of ITiree as the questioj
EXAMPLES.
are equal & 72 lb. atleShorn^^'"'™' '""' """^ «'• «' ^^-donl
Left.
20
Right.
23
155
180
12
20X155X72 = 223200
23X180=4I40)223200(53J3;|.
at AmLerdt 12^ Ib'ari'houl! "• f ^'^''''''"•' ""^ ^"O ">■
are equal to 401b. at xiioluseT '' ^"^ "'"^ '"• "' ^""^on
Ans. 40 lb.
an^lL'rar4i:i;rtoTell%'^?rr ^' ^^»"''--
ces at Venice are equal to ?6 ells EngHsh F"^^"^' ^"^ "'""y '"■''•
Am. 25^^^.
at tn?!tetdam make°"m aTn ','•'^ f ^"^'^'d'"-. and 90 lb.
are equal to mtJZlif '') '"" "^"^ "'• "' '^''<'-
weStJ'JfeSi^ln'lio^ed '^ ZZ " l^' '^^ ^'^ "' -"'
quantity of the first. ^ 1"^"°"' "^ «q«al to a
han''d!'a'ndfeUhett":±rst:lH™'":lf' f"?'™''"'' »' ">» 'e«
tipiy the fi.t row frr?d:;i^or,r the" Z:!t:':t^,^. """■
PROGRESSION. 97
EXAMPLES.
5. If 12 lb. at. London make 10 lb. at Amsterdam, and 100 IL.
Lt Amsterdam 120 lb. at Thoulouse, how many lb. at Thoulouse
iio equal 'o 40 lb. at London ? ^ws. 40 lb.
6. If 40 lb. at London make 36 lb. at Amsterdam, and 90 lb.
It Amsteidam 116 lb. at Dantzick, bow many lb. at Dantzick are
equal to 122 lb. at London? Ans. Ul^^l^.
PROGRESSION
CONSISTS OF TWO PARTS
ARITHMETICAL AND GEOMETRICAL.
ARITHMETICAL PROGRESSION
lis when a rank of numbers increase or decrease regularly by the
continual adding or subtracting of equal numbers ; as 1, 2, 3, 4,
5, 6, are in Arfthraetical Progression by the continual increasing
I or adding of one; 11, 9, 7, 5, 3, 1, by the continual decreasing
or subtracting of two.
Note. "When any even number of terms differ by Arithme-
tical Progression, the sum of the two extremes will be equal
to the two middle numbers, or any two means equally distant
from the extremes; as 2, 4, 6, 8, 10, 12, where 6 + 8, the two
middle numbei-s, are=12+2, the two extremes, and=10-{-4 the
two means=14.
When the number of terms are odd, the double of the middle
term will be equal to the two extremes; or of any two means
equally distant from the middle term ; as 1, 2, 3, 4, 6, where the
double number of 3 = 54-1=2 + 4 = 6.
In Arithmetical Progression five things are to bo observed, viz.
1. The first term; better expressed thus, F.
2. The last term, L.
3. The number of terms, N.
4 The equal difference, D ,
5. The sum of all terms, S.
Any three of which being given, the other two may be found.
The first, second, and third tern)s given, to find the fifth.
Rule. Multiply the sum of the two extremes by half the
number of terms, or multiiJiv half the sum of the two extremes
m
PHOORESSIOiV.
I. F L y a re given to find S.
F4-Lx~=a
2
EXAMPLES,
hoisf °" many strokes does the ha,„„er of a clock strike in l^l
12+1=13, then 13X6=78.
«ngly, and returns .ith eve,y egl^thett "t^X M ^^^
-^»«- 5 miles, 1300 yards.
Tbe first, second, and third terms ,iven, to find the fourth
FLN are given to. find D.
L — F
-=0.
EXAMPLES.
the'-eMer32!'1h?incrr; t m-T.'' >"«- <"''. -"
was the common di4re~ their "^T'"' ^'"S'^^'on, '„ha.
32-4=28, then 28^8 = 1+4 common difference.
day. and"*:; b'^t^^UTe tttv'° " ""•'"■" J"- '" ''
an e,„a. excess, so that the ttXt];re^| -ry^-^^y .,
what
1.
PROGRESSION.
09
B total of all the!
ock strike in 12
>r the first yard
unt to ?
Ans. £5 . 2.
itiy a yard as-
a basket, what
hese 100 eggs
'Ut it in ?
1300 yards.
e fourth,
mainder divi-
iars old, and
'ession, what
Ans. 4.
ence.
place in 12
'Very day hy
>e 58 miles,
what is the daily increase, and how many miles distant is that
place from London ? Ans. 5 daily increase.
Therefore, as three miles is the firet day's journey,
3-|-5 = 8 the second day.
84-5 = 13 the third day, &c.
The whole distance is 366 miles.
The first, second, and ff>ui-th terms given, to find the third.
Rule. From the second subtract the first, the remainder divide
by the fourth, and to the quotient add 1, gives the third ; or thus,
III. F L D are given to find N.
L— F
— +1=N.
D
EXAMPLES.
6. A person travelling into the country, went 3 miles the first
day, and increased every day 5 miles, till at last he went 58 miles
m one day ; how many days did he travel ? Ans. 12.
58—3 = 55-7-5 = 11 + 1 = 12 the number of days.
Y. A man being asked how many sons he had, said, that the
yoangest was 4 years old, and the oldest 32 ; and that he increas-
ed one in his family every 4 years, how many had he ?
Ans. 8
The second, third, and fourth terms given to find the first.
Rule. Multiply the fourth by the thii-d made less by one, the
product subtracted from the second gives the first : or thus,
IV.
L N D are given to find F.
L— DxN— 1=F.
EXAMPLES.
8. A man in 10 days went from London to a certain town in
the country, every day's journey increasing the former by 4, and
the last he went was 46 miles, what the first?
Ans. 10 miles,
4V10 — 1=:S6. then 46 — 36 = 10. the first day's lournev.
12
mv
100
PROGRESSION.
it«.
i'Li'"Z^^ Tsml''f'' "' « --'•'" times, so n, J
by 6, the last nHe-' «tt'"vf,' thSr """""^ "ifT'l
Tlio fourth, third, and fifth given, to find the fet
sub's h.5r;t SL'^o'Vo'ii'^' ™," ?T."'-' '■-«-
less I gives the fi,i^:or thus, ""''"'''"'' ''^ ""^ ""''''I
V. JSr D S are given to find F.
SDxN— 1
~F.
EXAMPLES.
ex<^!d IhT foriHrr.^ i" :' ,f ' r '^' p"^'"^-"^- -'•■ •«
ment on any one tKt o'n „)M *'""«. »<; be^t""- '•'<' first pay
pemn have for hi ptl?" ''" '"'° ^'''"'' " ■^- What will W
^ ■ -4ws. £8.
4 X 12—1
300-12=30, then 30 £« fi,. a .
' — *8 the first payment.
The first, third, and fourth, given to find the second. '
seLid. or thus' "'"^'^ ""^^'^ '" '^^ ^'^^ ^^^« ti^«
FN D are given to find L.
ND— D4-F=L.
EXAMPLES.
be^LSe%!!d\S:i;:?^l^t:^tr'rir^^^^^^^^^
-,. „„ Ans. 158.
20X8-8=152, then 152+6=158, the last number.
GEOMETRICAL PROGRESSION
Is the increasing or decreasing of any i-ank of ni.mKnr= i
2. and 16,\ 4, 2, d^r;^ by the dwi'r"' '^ ""^ ""'";P"'='
PROGRESSION.
101
Note. When any number of terms is continued in Geome-
trical Progression, the product of the two extremes will be equal
to any two means, equally dist-mt from the extremes': as 2, 4, 8,
16, 32, 64, where 64X- av<f = 4X32, and 8X16 — 128.
When the number of the terms are odd, the middle term multi-
plied into itself will be equal to the two extremes, or any two
raoans equally distant from it, as 2, 4, 8, 16, 32, where 2X32 =
4X16 = 8X8 = 64.
In Geometrical Progression the same 5 thing? are to be obser-
ved as are in Arithmetical, viz.
• 1. The first term.
2. The last term.
3. The number of terms.
4. The equal difference or ratio.
5. The sum of all the terms.
Note. As the last term in a long series of numbers is very
tedious to come at, by continual multiplication ; therefore, for the
reader finding it out, there is a series of numbei*s made use of
in Aritlimetical Proportion, called indices, beginning with an
unit, whose common difference is one ; whatever number of in-
dices you make use of, set as many numbers (in such Geomet-
rical Proportion, as is given in the question) under them.
. 1, 2, 3, 4, 5, 6, Indices.
2, 4, 8, 16, 82, 64, Numbei-s in Geometrical Proportion.
But if the firet term in Geometrical Proportion be differeut
from the ratio, the indices must begin with a cipher.
^g 0, 1, 2, 3, 4, 5, 6, Indices.
1, 2, 4, 8, 16, 32, 64, Numbers in Geometrical Proportion.
When the Indices begin with a cipher, the sum of the indices
made choice of must always be one less than the number of terms
given in the question ; for 1 in the indic-s is over the second
term, and 2 over the third, <fec.
Add any two of the indices together, and that sum will agree
with the product of their respective terms.
As in the first table of Indices 24-5= ^
Geometrical Proportion 4X32 = 128
Then the second 24-4= 6
4X16= 64
13
103
PBOORESSION.
j*
ratb S.'^Zf^'/r^''''"'"" P'-'^^^-g <■■•»"> unity, the
EXAMPLES.
^n*. £2.2.8.
16=4
0> 1, 2, 3, 4, Exponents 16 = 4
1, 2, 4, 8, 16, No. of terms.-
For 4+4+3=11, No. of terms less 1
256=8
8=3
4)2048=11 No. of far.
12)512
2(0)412 . 8
£2.2.8
2. A country gentleman goinff to a fair tn K,„. c^
meets, ^v'ith a p.rson who had 23 • he demanrlpd fl7 ■ % a"'"'
and was answLd £16 a pilVth gtZt btds^i'jr^'^-'"'
and he would buy all ; the^the'r tells'h^mTrouH „ot 'be Xn"
PSOORESSIOir.
103
RuLB. Proceed as in the last, only observe, that every product
must be divided by the first term.
EXAMPLES.
3. A sum of money is to be divided among eight persons, the
first to have £20, the next £60, and so in triple proportion ; what
will the last have ? Ans. £43740.
540X540 14580X60
20; ei; 180; 540; =^^^80, then- =43740
20 20
3 + 3+1 = 7, one less than the number of terms.
4. A gentleman dying, left nine sons, to whom and to his exe
cutors he bequeathed his estate in the manner following : To his
executors £50, his youngest son was to have as much more as
the executors, and each son to exceed the next younger by as
much more ; what was the eldest son's proportion ?
Ans. £25600.
The first term, ratio, and number of terms given, to find the
sum of all the terms.
Rule. Find the last term as before, then subtract the first
from it, and divide the remainder by the ratio, less 1 ; to the quo-
tient of which add the p-reater, gives the sum required.
EXAMPLES.
5. A servant skilled in numbers, agreed with a gentleman to
serve him twelve months, provided he would give him a farthing
for his first month's service, a penny for the second, and 4d. for
the third, &c., what did Ws wages amount to ?
Ans. £5825 . 8 . 5^.
266X256=65536, then 65536X64=4194304
0, 1, 2, 3, 4, 4194304—1
1, 4, 16, 64, 250, =1398101, then
4+4+3 = 11 No. of terms less 1, 4 — 1
1398101+4194304=5592405 farthings.
6. A man bought a horse, and by agreement was to give a far-
thing for the first nail, three for the second, &c., there were four
shoes, and ii each shoe 8 nails ; what was the worth of the horse ?
Ans. £965114681693 . 13 . 4.
304
PERMUTATION.
Ist"
M<
Iff
was lier })ortion? ^ -^ ^"^" ^^^ ^ 7^*^""; ^vliat
^w*. i;204 . 15.
man to "TS 2*2 "vXI '" l""'",',™' '«^'*'' »■'"' « ««'*
tJ.e fii-st vir fi , ^ I ^ "'^' »"''' '"■»'"«1<"1 iaco, for 2 ,,i„3
d4f';^ k^::;i; >:, j :„ ;i/r"it,: ;?«'"■'"" "'"""'■''" = ■
sale tiw, s«,>posinVtKr!.'\itrx7^:;'.:ir' '^ "'°
^WA*. Iho laco sola fbr i;;]2G880 .0.0.
Gain i;32G732 . . Q.
PER¥UTATiON
Is tho changing or varying of tlio order of things.
^ EXAMPLES.
hom-8 ? innrntts, cind the year to contain 3G5 days, 6
^.ng, ccl n xi,n, ^u, to wiiich tho scholar airroes WhuV t;."," ." i"-^
the scholar stay with tho gcntleniau ? ^ ^' ^""^ ^'"^
^n*. 6040 days.
105
^ow-year's day,;
tortion, prouiis-
r 1 ^enr ; what
. il204 . 15.
witli a gentle
lice, for 2 pins
l)io])oition ; I
18 won; valued
or lost by the
yard,
880 . . 9.
732 . . 9.
tlicr, and Iho
Is; and how
10 changes
365 days, 6
470001600
need, is =91
40
THE
TUTOE'S ASSISTAIT.
PART II.
VULGAR FRACTIONS.
A KUACTiON is a part or parts of an unit, and written with two
figures, with a line between them, jis ^, a, f, &c.
The figure above the lino is cjilled the numerator, and the un-
der one the denominator; whieh shows how many j)arLs tho
unit IS divided into : and the numerator sliows how many of
tliose parts are meant by the fraction.
There are four sorts of vulgar fractions : proper, improper,
compound, and mixed, viz. i i >
1. A PROPER FRACTION is wheu the numerator is less than
the denominator, as J, f, I, lo., i« i, Slc.
2. An IMPROPER FRACTION is wheu tho numerator is equal
to, or greater than tiie denominaior, jis i, ^, j|, i.^j ^fcc.
- " -«-•'•--.-. x.xACi,t,n r, tiKj iraetion of a fraction, and
known by the word of, as i of f of f of J^ of ^^, &c.
4. A MIXED NUMRER, or FRACTION, is composed of a whole
number and fraction, as 8f, 17^, 8J|, &c.
i
I;
f
^t
t^
106 REDUCTION OP VULGAR FRACTIONS.
REDUCTION OF VULGAR FRACTIONS.
1. To reduce fractions to a common denominator.
ex^li\^lfA^ """'"'"'"'' '"^^ '^^ '^' denominator,!
except Its own, for a numerator; and all the denominators for
a common denommator. Or, "'uiudiors, loi
2. Multiply the common denominator by the several eiven
nu.nc-rato,-s, separately, and divide their product bv the served
dei-onnnators, the quotient, will be the now numeral
EXAMPLES.
1. Keduce f and 4 to a common denominator.
1st num. 2d num. ^^''''^ ^« ^"^ ^^•
l^vV^ .^X^-l^, then 4X7=.28 den.=|f and 4f .
2. heduce I f, and a, to a common denominator.
Facit -Si 11 AS.
3. Reduce h a, j\- and f, to a common denominatoV. "*"*'
_ Facit, ^11 A 2 3.10 2.016 a.8 8
4. Reduce J» a 1 nnrl 3 f^ „ 3 3ao» 3 36 0', 3 36 oj taeo-
*• ^^^<^"ce Jo-, ^, I, and f , to a common denominator.
_ Facit i|l 8 8 40 J'JI.O. 84
6. Reduce « a 3 nnrl i f« „ « ' 1 e a ff» 1 e e ^? 1 e a > Te s ff-
o. jvcauce 3, f, ^, and ^, to a common denonnnator.
Facit, #?a ^6 5 6 4 105
6 Red imp i « a o«;i 3 ^^ « "'840' 840' 8To» ilf-
o. xicuuce ^, ^, I, and f , to a common denominator.
Facit, 7'%'W, 4-2.J11 j5_4_o_ inofl
' 2 16 0? 2 1 6 o> 2T0 o» 5i e 0"
2. lo reduce a vulgar fraction to its lowest terms.
Rule. Find a common measure by dividing the lower term
by the upper, and that divisor by the remainder folloW ,^
nothnig remam: the last divisor is the common measure Mho
divKle both parte of the fraction by the common measurl an
the quotient will give the fraction required.
Not. If the comnion measure happens to be one, the fraction
s already m its lowest term: and when a fraction hath ciphe,-s at
the right hand, it may be abbreviated by cutthig them off, as ^If
EXAMPLES.
1. Reduce §f to its lowest terms.
24^32(1
24
Com. measure, 8)24(3 Facit,
REDUCTION OF VULGAR FRACTIONg.
107
8. Reduce y'/s to its lowest terms.
9. Reduce f |f to its lowest terms,
10. Reduce ||f to its lowest terms,
11. Reduce m to its lowest terms,
12. Reduce |^f | to its lowest terras.
Facit, -^j.
Facit, VL3y.
Facit, ^.
Facit, f f.
Facit, f .
3. To reduce a mixed number to au improper fraction.
Rule, Multiply the whole number by the denominator of
die fraction, and to the product add the numerator for a new
numerator, which place over the denominator.
Note, To express a whole number fraction-ways set 1 for the
denominator ffiven.
O
EXAMPLES.
13. Reduce 18| to an improper fraction.
Facit, If A.
Facit, i|i5.
Facit, ^\K
Facit, y.
Facit, a I A.
Facit, &f.f 1.
18x7+3 = 129 new numerator=ifa.
14. Reduce 56if to an improper fraction.
15. Reduce 183/y to an improper fraction.
16. Reduce 13 a to an improper fraction.
17. Reduce 2V| to an improper fraction.
18. Reduce 514|^ to an improper fraction.
4. To reduce an improper fraction to its proper terms.
Rule. Divide the upper term by the lower.
EXAMPLES.
19. Reduce J-f «- to its proper terms.
129-7.-184.
20. Reduce J-||i to its proper terms.
21. Reduce ^{^ to its proper terms.
22. Reduce ^ to its proper terms.
23. Reduce aA£ to its proper terms.
24. Reduce ^\^^ to its proper terms.
6. To reduce a compound fraction to a single one.
HuLE. Multiply all the numerators for a new numeraV ^r.
Jind all the denominators for a ne^y denominator.
Reduce the new fraction to its tSVest terms by Rr'e 2.
Facit, 18f
Facit, 6Gif.
Facit, 183^y.
Facit, 13f.
Facit, 27a.,
Facit, 614^.
Is'
Ml
h i
108
SEDUCTION OP VULGAR FB ACTIONS.
EXAMPLES.
25. Reduce f of f of f to a single fraction.
2X3X5= 30
Facit, —reduced to the lowest tenn=i-
3X5X8=120 ^'
26. Reduce f of 4 of ii to a single fraction.
T?o/ii» 32 55
27. Reduce H of U of U to a single fraction' "'~'^"-
2.8. Reduce J of f of ^ to a single fractio!!""' ' •^*=*--
29. Reduce 1 of f of J to a single fraction. *''''*' ^''"^"
Facit i5i 7
80. Reduce f of ^ of j\ to a single fraction. ' ^« «-^5-
Facit, eVo^eV-
^'J"* J''^^''''^'f^^c^''ons of one denomination to the fraction of I
another, but greater, retaining the same value.
Rule Reduce the given fraction to a compound one, by com-
pa rg ,t with all tlie denominations between it «nd tha denol
nation which you would reduce it to; then reduce that compos i
traction to a sin.ole one. 'i>^um \
EXAMPLES.
31. Reduce | of a penny to the fraction, of a pound.
32. Reduce } of r. penny to the frTcdon of I'^pound"''"^*'
33. Reduce | of a dwt. to the fraction of a lb. troj.""''^' ^'^'
F'loit Sl.
34. Reduce 4 of a lb. avoirdupois to the fraction of a'cwl"^"
Facit, :yiy.
1. To reduce fractions of one denomination to the fraction of
another, b'-t less, retaining the same value.
Rule Multiply the numerator by the parts contained in the
several denomn,atK>ns between it, and tl.at^-ou woul H dl
to, for a new numerator, and place it over the given denonSol
REDUCTION OF VULGAR FRACTIONS.
109
!io fraction of
EXAMPLES.
35. Ke<.luce j^\^ of a pound to the fraction of a penny.
Facit, |.
^ TX 20X 12 = 1680 ifiA reduced to its lowest term=f
S(]. Ucduco -^l^ of a pound to the fraction of a penny.
,- u 1 » Facit, |.
3 1. Keduce j^\^ of a pound troy, to the fraction of a nenny-
38. Reduce ^f ^ of a cwt. to the fraction of a lb. ' *'
Facit, ^.
8. To reduce fractions of one denomination to anothor of the
same value, having a numerator given of the required fraction.
ItLLE. As the numerator of the given fraction : is to its deno-
linmator : : so is the numerator of the intended fraction : to ita
|deiJummator.
EXAMPLES.
30. Reduce § to a fraction of the same value, whose numera-
|tor sha.l be 12. As 2 : 3 : : 12 : 18. Facit, jf.
40. Reduce 4 to a fraction of the same value, whose numera-
|tor shall be 25. p.^^.,-,.^ 24
41. Reduce 4 to a fraction of the same value, whose nmnera-
|tor shall be 47. 47
Facit,
65f.
9. To reduce fractions of one denomination to another of the
Isaino value, having the denominator given of the fractions re-
Iquired.
PiULE. As the denominator of the given fraction : is to its
numerator : : so is the denominator of the intended fraction • to
jits numerator.
EXAMPLES.
42. Reduce f to a fraction of the same value, whose denomi-
luator sliall be 18. As 3 : 2 : : 18 : 12. Facit, {K
43. Reduce f to a fraction of the same value,, whose i'fiJmi-
Itor shall hp. n.'i. p.-. o,
41. Keduce 4 to a fraction of the same value, whose denomi-
itor shall be C5f . 47
4'
\
Facit,
65f
no
II*
ft
4
REDUCTION OF VULGAR FRACTIONS.
10. To rrduc^ a ,inixorl fraction to a sinr^le one.
TluLB When the numerator is the intoirral part, multiplvi
by the aenorninator of the fractional i,art, add\na; in the nunierat
or tiio fractional part for a new numerator; tiien niultit)!v the d
nominator of the fraction by the denominator of the fraction
part tor a new denominator. ^
EXAMPLES.
45. Reduce— to a simple fraction. Facit ii4=ii
3 ()X " + 2 = 110 numerator.
48X3 =144 denominator.
234
46. R(^,duce — to a simple fraction.
38
When the denominator is the integral part, multiply it bv tli
denonmu.tor of the fractional part, adding in the numerator of
the fractional part for a new denominator; then multiply thJ
iiumerator of the fraction by the denominator of the frac-tioiiJ
part for a new numerator. ■
/ EXAMPLES.
47
47. Reduce — to a simple fraction. Facit aiss _s
Oof ' '^'■^^ ''
19
48. Reduce — to a simple fraction.
44^
n. To find the proper quantity of a fraction in the knows
parts of an integer, I
^ Rui.K. l\ftiltiply the nuniorator by the ccmmon parts of tliJ
int-ger, and divide by the denominator.
EXAMPLES.
49. Reduce f of a pound sterling to its proper quantity.
3X20 = 60—4=158. p\jj,j|.' igg
60. Reduce f of a shilling to its proper quantity.
Facitj 4d. 3i qrs.
61. Reduce 4 ot a pound avoirdupois to its proper quantity
63.
R
64.
E
55.
R
56.
R
57.
R
68.
R(
59.
R<
>
60.
Hi
12.
To
lenomina
RrLE.
ionod for
the
sai
qui re
d.
Facit JL7_ — 3
52. Reduce | of a cwt. to its proper quantity
Facit, 9 oz. 2^ dr.
Facit, 3 qrs. 3 lb. 1 oz. 12 J dr.
62.
lie
03.
Re(
64.
R<^(
65.
Rec
66.
Rec
n.
Rec
68.
Red
09.
Rec
JIEDUCTION OF VULGAR FRACTIONS.
Ill
63. Reduce f of a pound troy to its proper quantity.
> . „ , . - „ „ Facit, 7 oz. 4 dwts.
54. Ueduce f of an ell English to its proper quantity.
_. p , . . ., . I^^'icit, 2 qrs. 3 a nails.
5o. Jteduce f of a mile to its proper quai.tity.
Kc Tf 1 . c . ■^'''^^*'^' ^ ^"''- ^^ poles.
60. Keduce f of an aero to its proper quantity.
fcH r» 1 « i. , , , •^''*^'^' - ^^^^^y 20 poles.
5/. Ivxluce f of a hogshead of wine to its proper quantity.
CO r> 1 n Pixdt, 54 gallons.
58. Keduce f of a ban-el of beer to its proper quantity.
rn r. 1 ^ l^'ixdl, 1 2 gallons.
59. Keduce -,% of a chaldron of coals to its proper quantity.
^A i> 1 « . ^'^^^'^^ ^5 bushels.
00. Jveduce | of a month to its proper time.
Facit, 2 Aveeks, 2 days, 19 hours, 12 minutes. •
12. To reduce any given quantity to the fraction of any greater
penoniination, retaining the same value.
RrLR. Reduce the given quantity to the lowest term mon-
lioneil tor a numerator, under which set the integral part reduced
jo the same term, for a denominator, and it wiirgive the fraction
Required.
EXAMPLES.
61. Reduce 15s. to the %l4g<ion of a pound sterhng.
02. Reduce 4. 31 qrs. textile fraction of a shiUirig. ' '' "
Facit 2:.
C3. Reduce 9 oz. 2f dr. to the fraction of a pound avoirdupois.
n. 1^ , , Facit, 4.
64. K<:^duce 3 qi-s. 3 lb. 1 oz. 12f dr. to the fraction of a cwt.
-^ ,^ , . Facit, J.
65. Keduce 7 oz. 4 dwts. to the fraction of a pound troy.
66. Reduce 2 qrs, 3i nails to the fraction of an English ell.
. Facit, 4.
•^7. Keduce 6 fur. 16 poles to the fraction of a mile.
68. Reduce 2 roods 20 poles to the fraction of an acre.
rn r» i Facit, |.
CO. Reduce 54 gallons to the fraction of a hogshead of wine.
Facit, f .
ft '
'I'l
(l^S
M".
:i-.r
112
SUBTRACTION OF VULGAR FRACTIONS.
10. deduce 12 gallons to the fraction of a barrel of beer.
Facit, 1.
71. Reduce fifteen bushels to the fraction of a chaldron of coals,
Ti Facit, j^j.
72. Reduce 2 weeks, 2 days, 19 hours, 12 minutes, to thJ
fraction of a month. Facit, ^.
ADDITION OF VULGAR FRACTIONS.
Rule. Reduce the given fractions to a common denominator!
then add all the numerators together, under which place the com]
mon denominator.
EXAMPLES.
1. Add f and 4 together.
2. Add i f and f together.
3. Add 1, ii and f together.
4. Add 7| and f together.
Facit,i4+M=lf = lA.
Facit, liff.
Facit, m
Facit, 8y'j.
Facit, |i.
Facit. n^V-
6. Add ^ and f of f together.
6. Add 5f, Gi and 4^ together.
2. When the fractions are of several denominations, rediw|
them to their proper quantity, and add as before.
7. Add f of a pound to f of a shiiJin^. Facit, 15s. lOd.
8. Add ^ of a penny to f of a ^^ Facit, 133. 4^(1.
9. Add ^ of a pound troy to } oWR ounce.
Facit 9 oz. 3 dwts. 8 grs.
10. Add A of a ton to | of a lb.
Facit, 16 cwt. qrs. lb. 13 oz. 5^ dr.
11. Add f of a chaldron to f of a bushel.
Facit, 24 bushels 3 pecks.
12. Add I of a yard to ^ of an inch,
Facit, inch. 2 bar. corns.
SUBTRACTION OF VULGAR FRACTIONS.
Rule. Reduce tho given fraction to a common denominator,!
then subtract the less numerator from the greater, and place
remainder over the common denominator.
Rule.
rules of
a new n\
ator.
1.
Mu
2.
]\Tu
3.
I'l It
4.
Mu
6.
Mu
6.
Mu
MULTIPLICATION.
118
2. When the lower fraction is greater than the upper, sub-
tract the numerator of the lower fraction from the denominator,
and to tliat difference add the upper numerator, carrying one to
the unit's place of the lower whole number.
21-
-20=1 num.
Facit, ^\,
Facit, -li.
Facit, 4|f.
Facit, //^.
Facit, ^i|.
Facit, (J3j.
EXAMPLES.
1. From f take 4. 3X7 = 21. 5X4 = 20.
4X7 = 28 den.
2. From | take f of f.
3. From 5f take -j^g-.
4. From 3| take f.
5. From if take | of f .
6. From '34^ take f of %.
3. When the fractions are of several denominations, reduce
them to their proper quantities, and subtract as before.
7. From | of a pound take ^ of a shilling. Facit, 14s. 3d.
8. From § of a shilling take ^ of a penny. Facit, l^dL
9. From | of a lb. troy take | of an ounce.
Facit, 8 oz. 16 dwts. 16 grs.
10. From f of a ton take | of a lb.
Facit, 15 cwt. 3 qrs. 27 lb. 2 oz. lOf drs.
11. From f of a chaldron, take % of a bushel.
Facit, 23 bushels, 1 peck.
12. From | of a yard, take f of an inch.
Facit, 6 in. 1 b. com.
MULTlPLICATIOrToF VULGAR FRACTIOxNS.
Rule. Prepare the given numbers (if they require it) by tho
rulosof Reduction; then multi])ly all the numerat- rs tofjether for
a new numerator, and aiyhe denorainatoi-s for a new "denomia-
ator.
EXAMPLES.
1. Multiply I by f.
Facit, 3X3 = 9 num. 4X5 = 20 den.— J»r.
2. Mnltir.lv 1 Kv ^ Y'A6i, |f
I OS
iug,
2. Multii>ly 1 by §.
4. Muhi|)Iy 43Uy6j by 18-|
6. Multiply ^^ by 'i of f of f .
6. Multiply ^^ by I of t of f
Facit, 672gi'y.
Facit, 7935^.
Facit, ^»\ = H.
Facit, 3.
'y '-,!
f'\
1**1
k3
114
SINGLE RULE OF THREE DIRECT
1. Multiply f of f by f of l
8. Multiply ^ of I by -f.
9. Multiply 5f by |.
10. Multiply 24 by f.
11. Multiply ^ of 9 by |.
12. Multiply 9^ by f.
Facit, f
Facit, J/y.
Facit, 431.
Facit, 16.
Facit, 5ff.
Facit, 31.
DIVISION OF VULGAR FRACTIONS.
Rule. Prepare the given numbere (if they require it) by tbel 3. If
rules of Reduction, and invert the divisor, then proceed as in I cost ?
Multiplication. ■ 4 If
r
m 4
St. I
f'
EXAMPLES.
1. Divide ^^ by |.
Facit, 5X9=45 num. 3X20:
2. Divide 14 by f .
8. Divide 6723V by 13f
4. Divide 193o^ by 18^.
5. Divide f by f of ^ of I
6. Divide f of 16 by 4 of i
1. Divide i of f by f of f .
8. Divide 9/2 by ^- of 7.
9. Divide /g^ by 4^.
10. Divide 16 by 24.
11. Divide 520oy\ by f of 91.
12. Divide 3} by 9^ '^
■ 60 den.— If =f.
Facit, |.
Facit, 48|.
Facit, 430|.
Facit, i^j.
Facis, 19 |i.
Facit,! A = |.
Facit, 2if
Facit, ^.
-Facit, f.
Facit, 111
Facit, }.
THE SINGLE RULE OF THREE LIRECT, IN VULGAR
FRACTIONS.
^ Rule. Reduce the numbers as before directed in RM"^>Jnn.l
^Z. f 1 ?™ ;" ^^^' proportion, then multiply the tiir(.'
terms continually together, and the product will be the answer.
BINQI.E fiVLB OF THBEE INVERSE.
lift
Facit, f
Facit, J/y.
Facit, 431.
Facit, 16.
Facit, 5|f.
Facit, 31.
DNS.
[uiro it) by thel
t proceed as in I
Facit, |.
Facit, 48|.
Facit, 430|.
Facit, VV.
''acis, 19 |i.
acit, fA = |.
Facit, 2if
Facit, ^.
-Facit, f.
Facit, 7 If
Facit, |.
:n vulgar!
in Reduction:
numbers, and |
iply the ihw \
le ausw.>r.
EXAMPLES.
1. If f of a yard cost | of £1, what will ^^ of a yard come to
lat that rate ? Am. ^| = 153.
yd. £ yd. £
^s^ : f :: A : if = 153.
for 4 X 5 X 9 = 180 num. 5 v< j,_^,5. 4Um5.£
and 3X8 X 10 =^40 den. "^^»« «» ^;«oVao*-
2. If f of a yard cost f of £1, what will |^ of, a yard cost?
Ans. 14s. 8d.
3. If ^ of a yard of lawn cost 7s. 3d., what will 10^ yards
cost? Ans. £4 : 19 : 10||.
4. If I lb. cost fs. how many pounds will f of Is. buy ?
Ans. 1 lb.2f9 = 3V«
5. If f ell of Holland cost i of £1, what will 12f ells cost at
the same rate? Ans. £7:0:8^ ^f.
6. If 12^ yards of cloth cost 15s. 9d., what will 48 J cost at the
same rate? Ans. £3 : : 9^ y'/^.
7. If ^^ of a cwt. cost 284s. what will 7^ cwt. cost at the same
rate? ^ns. £118 : 6 : 8.
8. If 3 yards of broad cloth cost £2|, what will 10^ yards
cost? Ans. £9 : 12.
9. If I: of a yard cost f of £1, what will | of an ell English
come to at the same rate ? Ans. £2.
10. If 1 lb. of cochineal cost £l : 5, what will 36y\ lb. come
to? Ans. £45 : 17 : 6.
11. If 1 yard of broad cloth cost 15|s., what will 4 pieces cost^
Ans. £85 : 14
34 H
or
each containing 27^ yards ?
12. Bought 3^ pieces of silk, each containing 24f ells, at 6s,
9|(1. per ell. I desire to know what the whole quantity cost?
Ans. £25 : 17
H
lit.
CUII
THE SINGLE RULE OF THREE INVERSE, IN
VULGAR FRACTIONS.
EXAMPLES.
1. If 48 men can build a wall in 24|- days, how many men
the sarne in 192 davs? Ans. Qt-^~
ay;
'Tee
2. If 25 |s. will pay for the carriage of 1 cwt. 145^ miles, hpw.
far may 6^ cwt. be carried for the same money
2
Ans. 22^y miles.
I
\:
f
%
J a.i'
I
3
116
m.
!■
THE DOUBLE ROIE OF THREB.
«ide, to .nak; auother of Zll^^L^^ "" "''"'' *» * rJ
weighs but 2| oz ? ''''^' '^^'^'^ » P^n^y white loaf
-dn*. 15 yards.
THE DOUBLE RULE OF THREE, IN VULGAR
FRACTIONS.
' EXAMPLES.
!• If a carrier receivos £9 i ^.^ *t.
miles, ho^v-much ought helo^iL^vp 5' tr"'^ ^^ ^ ^^^- '^O
H q.^. 50 miles? ^ '"^^''^ ^^' *^^« ^•«'-"«i?e of 7 cwt
2. If £100 in 12 months ^ain £^ ' . /? ^* ' ^^ ' ^•
gain £3f in 9 months^ ^ "" ^"^ '''^'''^> ^^^^ principal will
3. If 9 students spend £lOi in 1« ^ i ^^'''' ^'^•
students spend in 30 Ws. ''^ ''^37171^1' ''
helped them? ^ *''' ^^^ ^^>'«' ^^^^n their two sons
qu'; to ^n'll^T"^'^' ^^^" ^'^' -^^* «- tii/l/s^;,
6 If the caniage of 60 cwt. 20 miles cost /ui TT'''" .
can I have carried 30 miles for £'5 z. a ^^' '"^^'^^ ^^'^'^t
T« • -dn*. 15 cwt.
parts,
117
be sufficient to
which js I y^rdj
'««• 4 1 yards,
iiours, in how
THE
TUTOR'S ASSISTANT.
mshel of wheat I
nny white loaf
«*. ]5s. 4|d.
K will line 7^
i*. 15 yards.
l^ULGAR
^ 3 cwt. 150
t?e of 7 cwt
'1 : 16 : 9.
principal will
Aiis. X75.
inch will 20
4JL6
145 J*
earned 4|s.
*ir two sons
: H: 4.
ill £13^ re-
^ months,
tvhat weight
^ 15 cwt.
PART III.
DECIMAL FRACTIONS.
In Decimal Fractions the integer or
one yard, one gallon, &c. is supposed
parts, and those parts into tenths, and
So that the denominator of a deci
consist of an unit, with as many ci
places, therefore is never set down ;
guished from the whole members by
which stands for Vo. .25 for J/^, ,123
But the diflferent value of figures
lowing table.
whole thing, a.s one pound,
to be divided into 10 equal
so on without end.
mal being always known to
phers as the numerator has
the parts being only distin-
a comma prefixed: thus ,5
for -1-2JL
^"' 100 0* ^
appears plainer by the fol-
Whole numbers. Decimal parts.
7654321 ,2 34567
S ss » r
o
a
CO
S3 as
o o o o o o
<t> ^
^ s
a>
g-
p o
g-
tr o
O S3
g-
From whicli it plainly appears, that as whole numbers increase
in a ten-fold proportion to th* left hand, so decimal parts decrease
in a ten-fold proportion to the right hand ; so that ciphers placed
in
'%
118
ADDITION OF DECIMALS.
li'-
before decimal parts dccroa'so flwo'i. ,-oi.,^ u
To ? j'-'"^ IS t) l)tUtS OI 100 or —5. • nnr 4„ - \ ,. • '
^^A„d 52,275275275 is called' a 'compouko n.cuHa.^o „kc-
In all circulating numbers, dash the last figure.
ADDITION OF DECIMALS.
KuLE. In setting down the proposed numbers to \^ icUoA
away o hnd t TT'":' v' '"P'"''''"'"? P"""^' ^>"«l' ""S''
to thcr respect, ve values; then add them as in while numbelf^
EXAMPLES.
1. Add '72,5+32,071+2,1574+371,4 + 2,75.
2. Add 30,07 + 2,0071+50,432 + 7 1 ' ^''^'' '''''^''•
3. Add 3,5+47,25 + 027,01+2,0073 + 1,5.
r A r S:V^ + '*'''^1 ^^24 + 31,4o2+,3075.
p An ;^^+27,514+l,005+725 + 7,32.
6. Add 27,5 + 52+3 2G75+,574I +2720
MULTIPLICATION OF DECIMALS.
119
11 number of
JRRINO DECI-
SUBTRACTION OF DECIMALS.
R.LK. Subtraction of decimals differs but little ^J^^
numbers, only in placing the numbers, vvhich must be caiefully
observed, as in addition.
EXAMPLES.
1. From ,2Y54 take ,2371.
2. From 2,37 take 1,70.
3. From 271 take 21o,7.
4. From 270,2 take 75,4075.
5. From 571 take 54,72.
C. From 625 take 70,91.
7. From 23.415 take ,3742.
S. From ,107 take ,0007
MULTIPLICATION OF DECIMALS.
Rule. Place the factors, and multiply tbem as i" ^^'^^^Ic nmn-
belaud from the product towards the nght hand, cut of as
^rny%es for decimals as there are in both actors tog.the;
Tut if tiiere should not be so many places in the product, .ui>-
ply the defect with ciphers to the lett hand.
EXAMPLES
1. Multiply ,2305 by ,2435. Facit, ,05758775.
2. Multiply 2071 by 2,27.
3. Multiply 27,15 by 25,3.
4. Multiply 72347 by 23,15.
5. Multiply 17105 by ,3257.
6. Multiply 17105 by ,0237.
7. Multiply 27,35 by 7,70071.
8. Multiply 57,21 by ,0075.
9. Multiply ,007 by ,007.
10. Multiply 20,15 by ,2705.
11. Multiply ,907 by ,0025.
When any number of decimals is to be multiplied by 10, 100,
1000 &c it is only removirii,^ the separatrng point m the multi-
Sn; many plLs toward the ri^t hmul ^ ^l^^^}';:;i
in the multiplier : thus, ,578X10-5,78. ,578X 100_o,/8 , ,o.8
X1000=578; and ,578X10000 = 5780.
CONTRACTED MULTIPLICATION OF DECIMALS.
RuLK. Put the unit's place of the multiplier uu^hv that place
of the multiplicand that is intended to be kept in the F'>; ;'^' ; ^''j;"
invert the order of all the other figures, i. c. write them all the
■SI
1'^
♦ I ri
1
CONTRACTED MULTIPLICATION.
alZt, iT'"'! •" .7""''''^"° ""' ^g"™ '«ft 0'" CT«>-y time ncM
EXAMPLES.
foufpla1^'Sof''f^'^? ''y f'^34^' »"'' •«' *ere be only
lour places ot aecinials in the product. ^
Contracted way.
384,6721.58
5438.63
Go.Timon way.
384,672158
36,8345
115401647
23080329
3077377
115402
15387
1923
1923
15386
115401
3077377
23080329
115401647
14169,2065
14169,2066
360790
88632
6474
264
48
4
038510
Facit, 14169,2065.
of tiS"'^ '''''''' "^ '"''*''• »^ ■-? ^.fy^z '""'■^'
,,,,.., ^ I^acit, 105,6994.
14. Multiply 2,38645 by 8,2175, and .eave only four places
'^t"^^ . Faci[, 19,6ll)7
Dli;!') ; -^ ^'"^^^'^^^^^ ^^ ^^^^^'*' '-^"^ ^'^ '^''^'<^ ^^ only one
pla^e of decuiials ^^,^ ,^. •! ,
(>. Multiply 375,13758 by 16,7324, and leave only four plac.s
'^''""*'^'- Facit, 6270,9520.
onlv four
of
17. Multiply 395,3756 by ,75642, and let tliere be
places of decimal;
Facit, 299,0099.
DIVISION OP DECIMALS.
121
DIVISION OF DECIMALS.
This Rule is also worked as in whole numbers ; the only dif-
ficulty is in valuing the quotient, which is done by any of the fol-
lowing rules :
Rule I. The first figure in the quotient is always of the same
value with that figure of the dividend, whiph answers or stands
over the place of units in the divisor.
2. The quotient must always have so many decimal places,
as the dividend has more than the divisor.
Note 1. If the divisor and dividend have both the same num-
ber of decimal parts, the quotient will be a whole number.
2. If the dividend hath not so many places of decimals as are
:n the divisor, then so many ciphei-s must be annexed to the divi-
dend as will make them equal, and the quotient will then be a
wiiole number.
3. But if, when the division is done, the quotient has not so
many figures as it should have places of decimals, then so manj
Jiphers must be prefixed as there are places wanting.
EXAMPLES.
1. Divide 85643,825 by 6,321.
2. Divide 48 by 144
3. Divide 217,75 by 65.
4. Divide 125 by ,1045.
5. Divide 709 by 2,574.
C. Divide 5,714 by 8275.
I.
Facit, 13549.
7. Divide 7382,54 by 6,4252.
8. Divide ,0851648 by 423.
9. Divide 267,15975 by 13,26.
10. Divide 72,1564 by ,1347.
11. Divide 715 by ,3075.
VVhen numbers are to be divided by 10, 100, 1000, 10,000,
(fee. It is performed by placing the separating point in the dividend
*J many places towards the left hand, as there are ciphers in the
divisor.
1-^
t- i\
i
If i
!
* ,1
Tims, 5784-^ 10=578,4.
6784-M 00=57,84.
5784-r- 1000=5,784.
6784-M0,000=,5784.
It 1
123
CONTRACTED DIVISION.
11 '
1^
CONTRACTED DIVISION OF DECIMALS.
RifLK. By tlH3 fii*st rulo find what is tlie value of the fii^st fij^ure
in the qiioiic t : then by knowing the lii-st figure's denomination,
the decimal 'laces may be reduced to any number, by taking as
many of tJK icft hand figures of tlie dividend as will answer them ;
and in dividing, omit one figure of the divisor at each following
operation.
Note. That in multiplying every figure left out in the divisor,
you must carry 1, if it be 5 or upwards, to 15 ; if 15, or upwards,
to 26, carry 2 ; if 25, or upwards, to 35, carry 3, &c.
EXAMPLES.
12. Divide 721,17562 by 2,257432, and let there be only three
places of decimals in the quotient.
Contracted. Common way.
2;357432)721, 17562(319,467 2,257432)721,17562(319,467
6772296 6772296
439460
225743
213717..
203169..
10548...
9030...
1518....
1354....
i64
158
9
6
13. Diude 8,758615 by 5,2714167.
14. Divide 51717591 by 8,7586.
16. Divide 25,1367 by 217,35.
16. Divide 51,47542 by ,123415.
IV. Divide 70,23 by 7,9863.
18. Divide 27,104 by 3,712.
439460
225743
2
2
213717
203168
00
88
10548
9029
1518
1354
163
158
120
728
3920
4592
93280
02024
6
91256
ILS.
e fii-st fijrure
^nomination,
by taking aa
[isvvor them ;
ch following
\ tlie divisor,
or np wards.
)e only three
way.
502(319,407
96
60
43
2
o
17
68
00
88
48
29
120
728
18
54
3920
4592 ^
63
58
93280
02024
6
91256
BBDUCTION OF DECISIALS. 123
REDUCTION OF DECIMALS.
To reduce a Vulgar Fraction to a Decimal.
Rule. Add ciphers to the numerator, and divide by the do-
nominator, the quotient is the decimal fraction required.
EXAMPLES
1.
Reduce \ to a decimal.
4)1,00(25 Facit.
2.
Reduce ^ to a decimal.
Facit, ,5.
3.
Reduce % to a decimal.
Facit, ,75.
4.
Reduce f to a decimal.
Facit, ,375.
5.
Reduce 2^ to a decimal.
Facit, ,1 923070 -h.
6.
Reduce \\ of |f . to a decimal.
Facit, ,6043950+.
Note. If the ji^iven parts are of several denominations, they
may be reduced either by so many distinct operations ai. there
are different parts, or by first reducing them into their lowest
denomination, and then divide as before ; or,
2ndly. Bring the lowest into decimals of the next superior de-
nomination, and on the right hand of the decimal found, place the
parts given of the next superior denomination ; so proceeding till
you bring out the decimal parts of the highest integer required, by
still dividing the product by the next superior denominator ; or,
Sdly. To reduce shilling's, pence, and Hirthings. If the num-
ber of shillings bo even, take half for the first place of decimals,
and let the second and third places be filled with the farthings
contained in the remaining pence and fartliings, always remem-
bering to add 1, when the number is, or exceeds 25. But if the
number of shillings be odd, the second place of decimals must
be increased by 6.
7. Reduce 5s. to the decimal of a £,
8. Reduce ^s. to the decimal of a £.
9. Reduce 16s. to the decimal of a X.
l2
Facit, ,26.
Facit, ,45.
Facit, ,8.
s;.'*
^ I
.1..
Ir.
i*f
:t
m
ml
H!
4
rli
124 REDUCTION OF DECIMALS.
10. Reduce 8s. 4d. to the decimal of a £.
11. Reduce 16s. T^d. to the decimal of a £.
first.
IGs. VH
12
199
4
960)799(8322916
second.
4)3,00
12)7,75
210)16,64583
,8322916
third.
2)16
,832
Facit, ,4166.
Facit, ,8322916.
7|d.
4
31
12. Reduce 19s. 5^d. to the decimal of a £.
Facit, 972916.
13. Reduce 12 grains to the decimal of a lb. troy.
Facit, ,002083.
14. Reduce 12 drams to the decimal of a lb. avoirdupois.
Facit, ,046875.
15. Reduce 2 qi-s. 14 lb. to the decimal of a cwt.
Facit, ,625.
JO. Reduce two furlongs to the decimal of a league.
Facit, ,0833.
17. Reduce 2 quarts, 1 pint, to the decimal of a gallon.
Facit, ,625.
18. Rccluco 4 gallons, 2 quarts of Wine, to the decimal of a
hogshead. Facit, ,071428+.
19. Reduce 2 gallons, 1 quart of beer, to the decimal of a bar-
rel. Facit, ,0625.
20. Reduce 52 days to the decimal of a year.
Facit, ,142465 -f.
To find the value oj any Decimal Fraction in the known parts
of an Integer.
Rule. Multiply the decimal given, by the number of parts of
tlip. v.oxi ijiff'rior dt^nornination, cutting off the docimaI§ from th«
product ; then multiply the remainder by the next inferior deno-
mination ; thus proceeding till you have brought in the leasl
known parts of an integer.
REDUCTION OP DECIMALS.
125
EXAMPLES.
21. What is the value of ,8322916 of a lb. ?
Ans. 16s. 7^d.+.
20
. 16,6458320
12
7,7499840
4
2,9999360
22. What is the value of ,002084 of a lb. troy ?
Ans. 12,00384 gr.
23. What is the value of ,046875 of a lb. avoirdupois ?
Ann. 12 dr.
24. What is the value of ,625 of a cwt. ?
Ans. 2 qrs. 14 lb.
25. What is the value of ,625 of a gallon ?
Ans. 2 qre. 1 pint
26. What is the value of ,071428 of a hogshead of wine ?
Ans. 4 gallons 1 quart, ,999856.
27. What is the value of ,0625 of a barrel of beer ?
Ans. 2 gallons 1 quart.
28. What is the value of ,142465 of a year ? •
Ans. 61,999725 days.
L3 ■
%l
;l
h
126
DECIMAL TAULKS OF COIN, M'EIOHT, AND MEASURE.
TABLE I.
English Coin.
iJ 1 the Integer.
Sh.
19
IS
17
16
15
14
13
12
11
10
Dec.
,95
.9
,S5
,8
,75
,7
,65
,6
,55
,5
Sh.
9
8
7
6
5
4
3
2
1
Dec.
,45
,4
,35
,3
,25
.2
,15
.1
,05
Pence.
6
5
4
3
2
1
Decimals.
,025
,020833
,016666
,0125
,008333
,004166
Farth.
3
2
1
Decimals.
,003125
,0020833
,0010116
TABLE II.
English Coin. 1 Sh.
Long" Measure. 1 Foot,
the Integer.
Pence &
Inches.
6
5
4
3
2
1
Decimals.
,OOuoJ J
25
!l 66666
,083333
Farfh.
3
2
1
Decimals.
,0625
,011666
,020833
TABLE III.
Troy Weight.
1 lb. the Integer.
Ounces the same as
Pence in the last
Table.
Dwts
10
9
. 8
7
6
5
4
3
2
1
Decimals.
,041666
,0375
,033333
,029166
025
',020833
,016666
,0125
,008333
,004166
Grains.
Decimals.
12
,052
11
.022916
10
,020833
9
,01875
8
,016666
7
,014583
6
,0125
5
,010416
4
,008333
3
,00625
2
,004 1 (i6
1
,002(J83
TABLE IV.
Avoir. Weight.
112 lbs. the Integer.
Grains.
12
11
10
9
8
7
6
5
4
3
9
Decimals.
,002083
,001910
,001736
,001562
,001380
,001215
,001012
,000868
,000694
,000521
,000347
,000173
1 oz. the Integer.
Pennyweights the same
as Shillings in the first
Table.
Qrs.
Decimals
3
,75
2
,5
1
,25
Pounds.
14
13 .
12
11
10
9
8
7
6
5
4
3
2
1
Decimals.
,125
,116071
,107143
,098214
,089286
,080357
,071428
,0625
,053571
,041643
,035714
,026786
,017857
,008928
Ounces.
8
7
Decimals
,004464
,003006
U
Avo
1
T)un'
Dra
L.I
1
Gail
K
127
SURE.
Decimals.
,022910
,020833
,01873
,01(1000
,0Nr)&3
,0125
,010^110
,OOS:J33
,00025
,004 1 00
,0020.'-3
.E IV.
Weight.
le Integer.
Decimals.
,75
,5
_^25
Decimals.
,125
,110071
,107M3
,098211
,089280
,080357
,071428
,0025
,053571
,041043
,035714
,020780
,017857
,008928
Decimals.
,004404
,003000
DKCIMAL TABLES OF COIN, WKIOHT, AND MEASURE.
,003348
5
,002790
4
,002232
3
,001074
2
,001 no
I
,000558
4 0z.
Decimals.
3
,000418
2
,000279
1
,000139
TABLE V.
Avoirdupois weight.
1 lb. the Integer.
Ounces.
8
7
(\
5
4
3
2
1
Decimals.
.5
,4375
,375
,3125
,25
,1875
,125
,0025
Drams.
8
%
6
5
4
3
2
1
Decimals.
,03125
,027343
,023437
,019531
,015025
,011718
,007812
,003906
TABLE VI.
LIQUID MEASURE
1 tun the Integer.
Gallons.
100
90
Decimals.
,390825
,357142
bO
70
GO
50
40
30
20
10
9
8
7
6
.1
4
3
2
1
,317400
,27
,238095
,198112
,158730
,119047
,079365
,0-^9082
,035714
,031746
,027
,023809
,019841
,015873
,011904
,007936
,003908
Pint-j.
4
3
2
1
Decimals.
,001984
,001488
,000992
,009490
Hogshead the
Integer.
Gallons.
30
20
10
9
8
7
6
5
4
3
2
1
Decimals.
,470190
,317100
,158730
,M2857
,120984
,111111
,095238
,07i)305
,003492
,047019
,031746
,015873
Tmts.
3
2
1
Decimals.
,005952
,003968
,001984
TABLE VII.
Measures.
Liquid, Dry.
1 Gal. 1 Qr.
Integer.
Pts.
Decimals.
Bush
A
,5
4
3
,375
3
2
,25
2
1
,125
1
Q. pt
3
2
1
Decimals.
,09375
,0025
,03125
Pck.
3
2
1
Decimals.
,0234375
,015025
,0078125
Q. Pks.
3
2
1
Decimals.
,005859
,003900
,001953
Pints.
3
2
1
TABLE VIL.
Long Measure.
1 Mile the Integer.
Yards.
1000
900
800
700
600
Decimals.
,568182
,511364
,454545
,397727
,340909
l^^
128
DECIMAL TAHLKS OF COIN, WKIOHT, AND MKASUKE.
DECIMAL TA
5iJiJ
1 ,2ftl0'.>l
4W
,'227'27-J
3(J0 •
,170151
2(.)(J
,lL'{(i;ji)
luo
,050818
UO
,051130
SO
,015151
70
,03U773
60
,03-lUUl
50
,0-iS4l)'J
40
,02->727
30
,017015
90
,011301
10
,005682
9
,0(J5114
8
,001515
7
,003i<77
6
,00310f>
5
,0028-11
4
,002273
3
,001704
2
1
,0011 Co
,000508
Feet.
2
1
Decimals.
,0003787
,0001891
Indies.
6
3
1
Decimals,
,0000917
,0000174
,0000153
TABLE IX.
Time.
1 year the Integer.
Months the same as
Pence in the second
Table.
Decimals.
1 ,000WO
,821918
,517915
,273973
,240575
70
(>0
50
40
30
20
10
9
8
7
6
5
4
3
2
1
,219178
,191781
,104383
,13098*)
,10958y
,082192
,054794
,027397
,024057
,021918
,019178
,010438
,013098
,010959
,008219
,005479
,002739
1 day the Integer.
Hours.
12
11
10
9
8
7
6
5
4
3
2
1
Decimals.
,5
,458333
,410066
,375
,333333
,291006
,25
,208333
,160006
,125
,083.^33
,041600
Minutes.
30
20
10
9
8
7
6
5
4
3
2
1
Decimals.
,020833
,013888
,000944
,00625
,005555
,004801
,004166
,003472
,002777
,002083
,0U1389
,000004
TABLE X.
Cloth meahure.
1 yard the Integer.
Quarters the same as
Table 4.
Nails.
o
Decimals.
,125
,0025
TABLE XI.
Lead Weight.
A Foth. the Integer.
Hund.
10
9
3
7
6
5
4
3
2
1
Decimals.
,512820
,401538
,410256
,358974
,307092
,250410
,205123
,153840
,102564
,05!-:2«J2
Qrs.
2
1
Decimals.
,025041
,012820
Pounds.
14
13
12
11
10
9
8
7
6
IJ
4
3
2
1
Decimals.
,0(J04 1 02
,0059523
,0054945
,0050306
,0045787
,0041208
,0030030
,0032051
,0027472
,0022893
,0018315
,001 3736
,0009157
,0004578
THB BULB OF THREE IN DECIMALS.
129
THE RULE OF THREE IN DECIMALS.
EXAMPLES.
If 26 J yards cost £3 : 16 : 3, what will 32^ yards come to?
Ans. £4 : 12 : 9^.
yds. £ yds.
26,5 : 3,8125 : : 32,25 :
32,25
26,5)122,953125{4,63974 = £4 : 12 : 9^.
2. What will the pay of 540 men come to, at £l : 5 : 6 per
oian- A71S. £688 : 10.
3. If 7f yards of cloth cost £2:12:9, what will 140i yards
of the same cost? Ans. £47 : 16 : 3 2,4 qrs.
4. If a chest of sugar, weighii^-r 7 cwt. 2 qrs. 14 lb. cost £36 :
12 : 9, what will 2 cwt. 1 qr. 2i lb. of the same cost?
Ans. £11 : 14 : 2 3,5 qi-s.
6. A grocer buys 24 ton 12 cwt. 2 qrs. 14 lb. 12 oz. of tobac-
co for £3678 : 6 : 4, what will 1 oz. come to? Ans. Id.
6. What will 326^ lb. of tobacco come to, when 1^ lb. is sold
for 3s. 6d. ? Ans. £38:1:3.
7. What is the worth of 19 oz. 3 dwts. 5 grs. of gold, at £2 :
19 per oz.? Ans. £56 : 10 : 5 2,99 qrs.
8. What is the worth ©f 827| yards of painting, at 10|d. per
^^^^\^^, Ans.£3Q :4:3 1,5 qrs.
9. If I lent my friend £34 for f of a year, how much ought he
to lend me y\ of a year to requite my kindness ? Ans.°5l.
10. If I of a yard of cloth, that is 2^ yards broad, make a gar-
ment, how much that is f of a yard wide will make the same ?
_, _. ' Ans. 2,109375 yards.
11. If 1 ounce of silver cost 5s. 6d., what is the price of a Um-
kard that weighs 1 lb. 10 oz. 10 dwts. 4 grs. ?
Ans. £6 : 3 : 9 2,2 qrs.
^ 12. If 1 lb. of tobacco cost I5d. what cost 3 ho'xsheads wei-^h-
rng together 15 cwt. 1 qr. 19 lb. ? Ans. £m : 18 : 9°
13. If 1 cwt. of currants cost £2:9: 6, what will 45 cwt. 3
qrs. 14 lb. cost at the same rate? Ans. £il3 : 10 : 9|.
14. Bought 6 chests of sugar, each 6 cwt. 3 qrs. at £2:16 per
L. |,
cwt., what do they come to ?
Ans. £113 : 8.
lao
EXTHACTION OP THE SQUARE ROOT.
15. Bought a tankard for £10 : 12, at tho rate of 58. Ad. per
ounce, what was tho weight ?
Ans. 39 oz. 15 dwt
16. Gave £187 : 3 : 3, for 25 cwt. 3 qrs. 14 lb. of tobacco,
at what rate did I buy it per lb. ?
Am. Is. 3^d.
17. Bouorht 29 'b. 4 oz. of coffee, for £10 : 11 : 3, what is the
value of 3 lb. ? Ans. £1:1:8.
18. If I give Is. Id. for 3^ lb. cheese, what will l)c the value
of 1 cwt.? Ans. £l : 14 : 8.
EXTRACTION OF THE SQUARE ROOT.
m
Extracting the Square Root is to find out such a number as, being
multiplied into itself, the product will be equal to the given num-
ber.
Rule. First, Point the given number, beginning at the unit's
place, then proceed to the hundreds, and so upon every second
figure tliroughout.
Secondly. Seek the greatest square number in the first point
towards the left hand, placing the square number under the first
point, and the root thereof in the quotient; subtract the square
number from the first point, and to the remainder bring down
the next point and call that the resolvend.
Thirdly. Double the quotient, and place it for a divisor on the
left hand of the resolvend ; seek how often the divisor is contain-
ed in the resolvend ; (preserving always the unit's place) and put
the answer in the quotient, and also on the right-hand side of the
divisor ; then multiply by the figure last put in the quotient, and
subtract the product from the resolvend ; bring down the next
point to the remainder if there be any more) and proceed as be-
fore.
Roots.
Squares.
1. 2. 3. 4. 5. 6. 7. 8 9.
4. 9. 16. 25. 36. 49. 64. 81.
EXTRACTION OF THE SQUARE ROOT. 181
Ans. 345.
EXAMPLES.
1. What is the square root of 119025 ?
119025(345
9
64)290
256
685)3425
3425
2. What is the square root of 106929 ? Ans. 327+.
3. What is the square root of 22C8741 ? Ans. 1506,23-j-.
4. What is the square root of 7596796 ? Ans. 2756,228-f-
5. What is the square root of 36372961 ? Ans. 6031.
6. What is the square root of 22071204 ? Ans. 4698.
When the given number consists of a whole number and deci-
mals together, make the number of decimals even, by adding ci-
phers to them ; so that there may be a point fall on the unit's
place of the whole number.
7. What is the
8. AVhat is the
9. What is the
10. What is the
11. What is the
12. What is the
square
square
square
square
square
square
root of
root of
root of
root of
root of
root of
3271,4007?
4795,25731?
4,372594?
2,2710957?
,00032754?
1,270059?
Ans. 57,19+.
^7is. 69,247+.
Ans. 2,091+.
Ans. 1,50101+.
^ns. ,01809 + .
Ans. 1,1269 +
To extract the Square Boot of a Vulgar Fraction.
Rule. Reduce the fraction to its lowest terms, then extract
the square root of the numerator, for a new numerator, and the
square root of the denominator, for a new denominator.
If the fraction be a surd (i. e.) a number where a root can ne-
ver be exactly found, reduce it to a decimal, and extract the root
from it.
EXAMPLES.
£301?
£184'
13. What is the square root of
14. What is the square root of fi||?
15. What is the square root of xVsVt •
Ans. f .
Ans. |..
Ans. |.
I'
*
I ^! - .
133
EXTn ACTION OF THE l^QUABE ROOT.
SURDS.
I?
16. What is the square root of ||f ?
17. What is the square root of m ?
18. What is the square root of f Jf ?
Ans. ,898024-.
Ans. ,86(302+.
Ans. ,933094-.
To extract the Square Hoot of a mixed number.
Rule. Reduce the fractional part of a mixed number to its
lowest term, and then the mixed number to an improper fraction.
2. Extract the root of the numeratoiSvand denominator for a
new numerator and denominator.
If the mixed number given be a surd, reduce the fractional
part to a decimal, annex it to the whole number, and extract the
square root therefrom.
EXAMPLES.
19. What is the square root of 5l|-»- ?
20. What is the square root of 27/^ ?
21. What is the square root of 9ja
SURDS.
22. What is the square root of 85-|-f ?
23. What is the square root of 8^ ?
24. What is the square root of 6| ?
Ans. 7^.
Ans. 5\.
Ans. 3^.
Ans. 9,27+.
Ans. 2,95 19-t-.
Ans. 2,5819-1-.
To find a mean i^voportional between any two given numbers.
RuLK. The square root of the product of the given number
is the mean proportional sought.
EXAMPLES.
6. What is the mean ])roportional between 3 and 12 ?
Ans. 3 X 12 = 36, then ^36 = 6 the mean proportional.
6. What is the mean proportional between 4276 and 842 ?
Ans. 1897,4+.
To find the side of a square equal in area to any given
otcX/cr/ttcco,
RuLK. The square root of the content of any given superficies
is the side of the square equal sought.
)8024-.
30024-.
33094-.
r.
ber to its
• fraction.
ator for a
fractional
extract the
ins. 1}.
ins. 5^.
[ns. 34.
9,27+.
519+.
819 + .
'imbers.
1 number
tional.
342?
)V,4+.
iven
iuperficiea
EXTRACTION OF THE SQUARE ROOT.
EXAMPLES.
133
27. If the content of a given circle be 160, what is the side of
tlie square equal ? ^W5. 12,64911.
28. If the area of a circle is 750, what is the side of the square
equal? ^ris. 27,38012.
The area of the circle given to jind the Diameter.
Rule. As 355 : 452, or, as 1 : 1,273239 : : so is the area : to
the square of the diameter; — or, multiply the square root of the
area by 1,12837, and the product will be the diameter
EXAMPLES.
29. What length of cord will be tit to tie to a cow's tail, the
other end fixed in the ground, to let her have liberty of eating
ail acre of grass, and no more, supposing the cow and tail to
measure 5| yards? Am. 6,136 perches.
The area of a circle given, to find the periphery^ or
circumference, ,
Rule. As 113 : 1420, or, as 1 : 12,56637 : : the area to the
square of the p<Ti|)hery; — or, multiply the Sijuare root of the
arc;a by 3,5449, and the product is the circumference.
EXAMPLES.
30. When the area is 12, what is the circumference?
Am. 12,279.
31. When the area is 160, what is the periphery ?
Ans. 44,839.
Any two sides of a right-angled triangle given, to find the third
side.
I. Tl
IC ViiWZ tXliU
pcrj
mil
dicul
ar given 10
una t
hypothenuse.
Hulk. Thn s(|uare root of the sum of the squares of the base
and perpendicular, is the length of the hypotlicnuse,
M
f
I i
M
n
s
I
■
4
I
134
EXTRACTION OF THE SQUARE ROOT.
EXAMPLES.
32. The top of a castle from the ground is 45 yards high, and
surrounded with a ditch 00 yards broad; what lunoth must a lad-
der be to reach from the outside of the ditch lo the top of the
^^^^- ^n.. 75 yards.
Ditcli.
<D
-)->
i
S3
J-f
3
'^ Sc
13
<v. >->
a
-5
53
a»
w
Ba »0 yards.
S3. The wall of a i wn is 25 feet high, which is surrounded
by a moat of 30 feet m breadth: I desire to know the lencrth of
a ladder that w)ll reach from the outside of the moat to the top
^^^^^^^^^^"? ^n*. 39,05 feet. ^
The hypothenuse arid perpendicular ffiven, to find the base.
KuLE. The square root of the difference of the squares of the
bypothenuse and perpendicular, is the length of the base.
The base and hypothenuse given, to find the perpendicular.
Rule. The square root of the difference of the squares of the
hypjHhenuse and base, is the height of the perpendicular.
JN. Ji. Ihe two last questions may be varied for examples to
tno two last proposiiions. '^
Any number of men being given, to form them into a square
battle, or to find the number of rank and file.
Rule. The square root of the natibcr of men given, is \h
number of men cither in rank or file.
34. An army consisting of 331770 men, I desire to know how
many rank and hie 2 Ans. 6^.
oo. .V conaiu square pavement contains 48841 square stones,
all ot the same size. I demand how many are contained in one
r.
ynwh high, and
>th must a lad-
tho top of the
ns. 75 yards.
is surrounded
the length of
oat to the top
. 39,05 feet.
d the base.
squares of the
base.
>endicular.
squares of the
iular.
r examples to
to a square
Jile.
given, is the
to knr)\v how
Ans. 516.
square stones,
taiiji'd in one
Ans. 221.
EXTRACTION OF Tl| P i L'ilE uOOT.
EXTRACl'ION OF THE CUBE ROOT.
135
To extract the Cube Root is to find out one luin.b.M-, which be
inrr multiphcd nito itself, and then into that product, pimhicoth
the given number.
Rule. 1. I>oint every tliird figure of the cube given, betrinnino-
at the units place; seek the greatest cube to thc^ first point, and
subtract It therefrom ; put the root in the quotient, and brin-.- down
the figures in the next point to the remainder, for a Rksolv^^nd
2 huul a Divisor by multiplying tho ^,quare of the quotient
by 3. _ bee how often it is contained in the n."solvcnd, reiectincr
the units and tens, and put the answer in the quotient. "
3. To find the Subtrahend. 1. Cube the last firrure in the
quotient. 2. Multiply all the figures in the quotient by 3, except
the last, and that product by the square of the last. .3. Muitir/lv
the divisor by the last figure. Add these products to-n-tluM-, for
the subtrahend, which eubtract from the resolvend ; to the re-
mainder bring down the next point, and proceed as before.
Roots. 1. 2. 3. 4. 5. G. 7. 8. 9.
Cubes. 1. 8. 27. 64. 125. 216. 343. 512. 729.
EXAMPLES.
1. What is the cube root of 99252847 ?
Dlvisor-
99252847(463
64 =cube of 4
S(^uare of 4X3=48)35252 resolvend.
Divisor-
216=cubo of 6.
432 = 4 X 3 X by square of 6.
288 = di visor X by 6.
33336 subtrahend.
Square of 46X3 = 6348)1916847 resolvend.
27=cube of 3.
1 242 = 40 X 3 X by square of 3.
19044 =divisorXby 3.
1916847 subtrahend.
* -f
If A
%
s%.
'f
136
EXTRACTION OP THE CUBE ROOT.
I
2. What is the cube root of 380017 ?
3. What is the cube root of 57'.^5',iS0 ?
;U. What is the cube root of ;?24f)l759 ?
5. What is the cube root of 84(504519 ?
6. What is the cube root of 25!:>0y4072 ?
V. "v7hat is the cube root of 4822«544 ?
8. What is the cube root of 2705403G008 ?
9. What is the cube root of 22009810125 ?
10. What is the cube root of 122615327232 ?
11. What is the cube root of 219365327791 ?
12. What is the cube root of G73373097125 ?
Ans.
Ans.
Ans.
Ans.
Ans.
Ans.
73.
ITD.
319.
439.
(i38.
301.
Ans. 3002.
Ans. 2805.
Ans. 4908.
Ans. 6031.
Ans. 8705.
Wlien the given number consists of a whole number ami deci-
mals together, make the number of decimals to consist of 3, 6, 9,
&€. places, by adding ciphers thereto, so that there may be a
point fell on the unit's place of the whole number.
13. What is the cube root of 12,077876 ? Ans. 2,35.
14. What is the cube root of 36155,02756? Ans. 33,06+.
15. What is the cube root of ,001900624 ? Ans. ,124.
16. What is the cube root of 15926,972504 ? Ans. 3,215+!
17. What is the cube root of 15926,972504? Ans. 25,10+.
18. What is the cube root of ,053157376 ? Ans. ,376.
To extract tke cube root of a vulvar fraction.
Rule. Reduce the fraction to its lowest terms, then extract
the cube root of its numerator and denominator, for a new nu-
merator and denominator ; but if the fraction be a surd, reduce
it to a decimal, and then extract the root from it ?
EXAMPLES.
19. What is the cube root of f f -« ?
20. AVhat is the cube root of y^^V ?
21. What is the cube root of if|§ ?
Ans. ^.
Ans. ^.
Ans. |.
SURDS.
22. What is the cube root of | ?
23. What is the cube root of ^- ?
24. What is the cube root of I ?
Ans. ,829+.
Ans. ,822+".
3' -^««. ,873+.
To extract the cube root of a mixed number.
Rule. Reduce the fractional part to its lowest terms, and then
the mixed number to an improper fractio.5, extract the cube root
of the numerator and denominator for a new numerator and done
St
EXTRACTION OF THE CUBE ROOT.
137
minator ; but if the mixed number given be a surd, reduce the
fractional part to a decimal, annex it to the whole number, and
extract the root therefrom.
EXAMPLES.
25. What is the cube root of 121a ?
26. What is the cube root of Sl^^j?
27 What is the cube root of 405 A^ ?
SURDS.
28. What is the cube root of 1} ?
29. What is the cube root of 9 J- ?
80. What is the cube root of 8^ ?
THE APPLICATION.
Ans. 2^
Ans. 3f
Ans. 7|.
Ans, 1,93+.
Ans. 2,092-f-.
Ans. 2,05 7-|-.
1. If a cubical piece of timber be 47 inches long, 47 inches
broad, and 47 inches deep,, how many cubical inches doth it con-
^""^ ^, , Ans. 103823.
2. There is a cellar dug, that is 12 feet every way, in h.'nglh,
breadth, and depth; how many solid feet of earth were takt-n'out
^^^^^^ . Ans. 1728.
3. There is a stone of a cubic form, which contains 389017
Bolid feet, what is the superficial content of one of its sides ?
Ans. 5329.
Between two. numbers given, to find two mean proportionals.
Rule. Divide the greater extreme by the less, and the cube
root of the quotient multiplied by the less extreme, gives the less
mean ; multij.ly the said cube root by the less mean, and the pro-
duct will be the greater mean proportional.
EXAMPLES.
4. What are the two mean proportionals between 6 and 162 ?
Ans. 18 and 54.
5. What are the two mean proportionals between 4 and 108 ?
Ans. 12 and 36.
To find the side of a cube that shall he equal in soliditv to an^>
given solid, as a globe, cylinder, prism, cone, <jtc.
Rule. The cube root of the solid content of any solid body
given, is the side of the cube of equal solidity.
m3
■r.
-p-
I
mi
138
EXTRACTING ROOTS OF ALL POWERS.
m
i;
EXAMPLES.
6 If the solid content of a globe is 10G48, what is the side of
a cube of equal sohditj ? ^^^^_ 22.
The side of a cube beinq fjiven, to find the side of a cube that
shall be double, treble, <&c. in quantity to the cube given.
Rule Cube the side given, and Tiinltiply it by 2, 3, <fec., the
cube root of the product is the side sou<riit. -^ ' ' ^•' ^"^
EXAMPLES.
v. There is a cubical vessel, whose side is 12 inches and it is
requn-ed to find the side of another vessel, that is to contain three
times as imich? yin.. 17,306.
EXTRACTING OF THE BIQUADRATE ROOT.
To extract the Biquadrate Root, is to find out a number, which
bemg involved four tunes into itself, will produce the givei num-
Rule First extract the square root of the given number, and
then extract the square root of that square root, and it will dve
the biqiadrate root required. ^
EXAMPLES.
1. What is the biquadrate of 27 ? Ans. 531441.
2. U hat IS the biquadrate of 76 ? Ans. 33362176
3. What IS the biquadrate of 275 ? Ans. 6719140625*
4. VViiat IS the biquadrate root of 531441 ? Ans. 27
6. What is the biquadrate root of 33362176 ? Ans. 16
6. What is the biquadrate root of 5719140625 ? Atis. 21 5.
A GENERAL RULE FOR EXTRACTING THE ROOTS
OF ALL POWERS.
1. Prepare the number given for extraction, bv pointing off
from the unit's place as the root required directs.
■' — -"- -^e,"'*-' "« ii'O «v0i;, ^rnicu suuiruct rrom the
given number.
3. Bring down the first figure in the next point to the remain-
der, and call it the dividend.
EXTRACTING ROOTS OP ALL POWERS.
139
4. Involve the root into the next inferior power to that which
is given, multi[)ly it by the given power, and call it the divisor.
0. Find a quotient figure by common division, and annex it to
tlie root ; then involve the whole root into *^he given power, and
call that the subtrahend. •
0. Subtract that number from as many points of the given
power as are brought down, beginning at the lower place, and
to the remainder bring down the first figure of the next point for
a new dividend.
1. Find a new divisor, and proceed in all i*«yects as before.
EXAMPLES.
1. What is the square root of 141376 ?
141376(376
9
6)51 dividend.
1369 subtrahend.
3X 2=6 4VMrvu>r.
37x 37 = laf^o w^btrahend.
* 37X 2 = 74 /I'^S'^ir.
376X376=141?''«^ wbtrahend
• 74)447 dividend.
141376 subtrahend.
2. What is the cube root of 53157376 ?
i--
IE ROOTS
53157376(376
27
27)261 dividend.
50653 subtrahend.
4107)25043 dividend.
63157376 subtrahend.
3X 3X 3=27 divisor.
37X 37X 37 = 50653 subtrahend.
37 X 37 X 3 = 4107 divisor.
376X376X376 = 63157376 subtrahend
I'i
M
3
s*ii
fe
*.
»:,
;.:*»»
' SIMPLE INTEREST.
3. What is the biquadrate of 19087173376 ?
19987173376(376
81
108)1188 dividends
1874161 subtrahend.
202612)1245503 dividend.
19987173076 subtrahend.
3X 3X 3X 4=108 divisor.
37X 37X 37x 37 = 1874161 subtrahend.
3<X 37X 37X 4=202612 divisor.
376><: 376X376X376 = 19987173376 subtrahend.
SIMPLE INTEREST.
There are five letters to be observed in Simple Interest, -vift
P. the Principal. *
T. the Time.
R. the Ratio, or rate per cent.
I. the Interest.
A. the Amount. ,
A TABLE OF RATIOS
3
,03
3^
,035
4
,04
^
,045
5
,05
8
,08
sh
,085
9
,09
H
,095
10
,1
Note. The Ratio is the simplefnterest of £1 for
Ifie rate per cent, proposed, and is found thus
one year, at
£ £ £
As 200 : 3 : : 1
2. '
for 6 j
3. '
Dum, i
4.
cent. ]
6.
aiH
0.
montl
,03
As 100 : 3,6 : : 1 : ,036.
SIMFLE INTEREST.
141
end.
btrahend.
rnterestj'vias
,08
,085
,09
,095
J ^
one year, at
35.
When the p-incipal^ time, and ate per cent, are given^ to find
the infer est.
RuLK. Multiply the principal, time, and rate together, and it
will give the interest required.
NoTK. The proposition and rule aro better expressed thus :—
I. When P K T are given to find I.
Rule. prt=I.
Note. When two or more letters are put together like a word,
they are to be multiplied one into another.
EXAMPLES.
1. What is the interest of £915 : 10, for 3 years, at 5 per cent,
per annum. Ans. 945,5 X,OoX 3 = 141,825, or £141 : 16 : 6.
2. What is the interest of £547 : 14, at 4 per cent, per antuim,
for C years-? Ans. £131 : 8 : 11, 2 qrs. ,08.
3. What is the interest of £796 : 15, at 4^ per cent, per an-
num, for 5 years? Ans. 179 : 5 : 4 2 qrs.
4. What is the interest of £397 : 9 : 5, for 2\ years, at 3^ per
cent, per annum? Ans. £34 : 15 : 6 3,5499 qrs.
5. What is the interest of £554 : 17 : 6, for 3 years, 8 months,
at 4^ ])er cent, per annum ? Ans. £91 : 11 : 1 ,2
0. What is the interest of £236 : 18 : 8, for three jears, 8
months, at 5^ per cent, per annum? Ans. £47 : 15 : 7^, ,293.
When the interest is for any numbe^' of days only.
Rule Multiply the interest of £1 for a day, at the given rate,
by the principal and number of days, it will give the answer.
INTEREST OF £1 FOR ONE DAY.
per cent.
3
4
H
5
5^-
6
Decimals.
,00008219178
,00009589041
,00010958904
,00012328767
,000)3698030
,00015068493
,00016438356
per cent.
6.}
7
8
02
9
Decimals.
,00017808219
,00019178082
,00020547945
,00021917808
,00023287671
,00024657534
,00026027397
NoTP^ The above table is thus found : —
As 365 : ,03 : : 1
,0000821
,00009589041
78. And as 365 : ,035 : : 1
f
f' >
* n : I
(fee.
%, W'
jl
fi
M
142
SliMPLE INTEREST.
EXAMPLES.
V. What is the interest of £240, for ion Hnv« nt a
I... an.nun ? Ans. ,OOOI09.580oix 240X 12 l^a' J" ?'
0. Wi.Ht is the interest of £725 • 15 fnrlT) '^^ • /^ ^ U-
per r.nnuni ? '< <^i ^/-o . 15, for 74 d.-.ys, at 4 per cent.
10. What is the interest of i!lon f.. n "f' "^^^ 'r^^ = ^^^'
to tiio 9tli of AfM,.., f I ' ^'^"^ ^^'^' I'^t of June, 177o
JtJi ot ALuch following, at 5 per cent, per annum ? '
^ns. £3 : 16 : llf.
ir. AVhcn P IZ T arc given to find A.
Rule, prt + p=A.
EXAMPLES.
per a„„I';f "■" ^"^ = ''- "•"-" ^ •; ^ y«-, at 4J per cent
^^^5. £370: 19: 11 2,8 qrs.
year which are CaUriho^e di;:' "^'' 'f ''''^''' ^^^ <>^ «
per an.r;f "" ^'^^ ^ ^^' ^-^"^f ^<' i?,f^ ^-^ at 4 per con.
H. What will £273 : 18, amount^ t ^4^;-.', 'I^^J^^s
per cent, per annu,n ? Ans. £310:14: r3,3508006rqrf '
III. AVhen A R T are given to find P.
a
Rule. — ^=P.
rt+l.
EXAMPLES.
• 10 • n o « L K ' ' 'Z^^,'""' ""^ ""'^■i^'»t, will anjount to £376
1.* . 11 2,8 ,n 5 years, at 3^ per cent, per annum?
Ans. £320 : 17.
SIMPLE INTEHEST.
148
fit 4 per cent.
£3:3: If
lays, at 6 per
: 13: 11|.
at 4 per cent.
5:17: 8}^.
'f June, 1775,
uin ?
: 16: Ul
' 4^ per cent
5 3,04 qrs.
3^ per cent
il 2,8 qrs.
years, reduce
I parts of a
t 4 per cent
i ,02 qrs.
5 (lays, at 3
0064 qrs.
nt to £30
•
579 : 12.
It to £376
20: 17.
Vr. What principal, bein^ put to interest, will amount to
£1130 : 9 : Oi ,02 qi-s. in 5^ years, at 4 per cent, per annum ?
Ans. £020 : 12.
18. Wliat principal will amount to £310 : 14 : 1 3,35080064
ars. iu 4 years, 175 days, at 3 per cent, per annum I
^ ^ A?is. £273 : 18.
IV. When A P T are giveu to find R.
a— p
Rule. ■=R.
pt.
EXAMPLES.
19. At what rate per cent, will £279 : 12, amount to £367 :
13 : 5 3,04 qrs. in 7 years'^ ,„.k «
Ans, 307,074—270,0 = 88,074, 275,0 xV = 19o7,2,
then 88,074-r-10o7,2 = ,045 or 4^ per cent.
20. At what rate per cent, will £320 : 17, amount to £376 :
19 : 11 2,8 qrs. in 5 years? -Ans. 3-h F^* cf"^-
21. At what rate per cent, will £926 : 12, amount to £1130 :
9 : Oi ,92 qrs. in 5^ years ? -^w*- 4 per cent.
22. At what rate per cent, will £273 : 18, amount to £310 :
14 : 1 3,35080064 qrs. in 4 yeare, 175 days?
Ans. 3 per cent
V. When APR are given to find T.
a — p
Rule. =T.
' ^*^' EXAMPLES.
23. In what time will £279 : 12, amount to £367 : 13 : 5 3,04
qrs. at 4 4 per cent. ? .
^ws. 307,674-279,0 = 88,074. 27^,6 X ,045 = 12,5820, then
88,074-r 12,5820 = 7 years.
24. In what time will £320 : 17, amount to 370 : 19 : 11 2,8
qrs. at 3^ per cent. ? ^If • /^ yeai-s.
25. In what time will £926 : 12, amount to £1130 : 9 : Of
,92 (p-3. at 4 per cent. ? ^'''jX^''''f!' i
2G. In what time will £273 : 18, amount to £310 : 14 : 1
3,35080064 qrs. at 3 per cent. ? Ans. 4 years, 175 days.
ANNUITIES OR PENSIONS, &c. IN ARREARS
Annuities or pensions, c\rc. are said to be in arrears, when thc'
arc payable or due, cither yearly, half-yearly, or quarterly, fti .
are u.'ipnid for any number of payments.
t! "
k
•V I
♦ •!..,
144
SIMPLE INTEREST.
Note. U represents the annuity, pension, or ycaily rent, T
R A as before. •/ j '^
I U U T are given to find A
ttu — til
Rule. X r : + tu=A.
EXAMPLES.
21. If a salary of £150 k^ forborne 6 years at 5 per cent, what
will It amount to? Ans, £825.
3000
6X5X1-50— 5X150=3000 then X ,0o + 5X 150=£825
2
28. If £250 yearly pension be forborne 1 years, what ',ill it
amount to in that time at 6 per cent. ? Arts. £2065.
29. There is a house let upon lease for 5^ years, at £60 per
annum, what will be the amount of the whole time at 4^ per
^^^- • Ans. £363 : 8 : 3.
30. Suppose an annual pension of £28 remain unpaid for 8
years, what would it amount to at 5 per cent. ?
XT ^^', ^^*- ^263 : 4.
JNoTE. \\heTi the annuities, Ac. are to be paid half-y early or
quarterly, then "^
For half-yearly payments, take half of the ratio, half of the
annuity, &c., and twice the number of years — and
For quarterly payments, take a fourth part of the ratio, a fourth
part of the annuity, &c., and four times the number of yeai-s,
and work as before. /
EXAMPLES.
81. If a salary of £l50, payable every half-year, remains un-
paid for 5 years, what will it amount to in that time at 5 per
<^ent- ? Ans. £834 : 7 : 6.
32. If a salary of £150, payable every quarter, was left unpaid
for 5 years, what would it amount to in that time at 5 per cent. /
Ans. £839 : 1 : 3.
Note. It may be observed by comparing these la^t oxami-Ies,
the amount of the half-yearly payments are more advantageous
thaji the yearly, and the quarterly more than the hali-yeaily.
IL When ART are given to find U.
UuLE.-
2a
ttr— tr-f2t
=U.
'caily rent, T
)er cent, what
drts, £825.
:150=£825.
, what 'vill it
IS. £2005.
, at £60 per
e at 4^ jjcr
«3 : 8 : 3.
inpaitl for 8
£263 : 4.
ulf-)early or
half of the
itio, a fourth
ber of yx'ixrs,
remains un-
ne at 5 per
14 : 7 : 6.
left unpaid
per cent. }
9:1:3.
it oxanipies,
Ivantatreous
iiiiily.
SIMPLE INTEREST.
145
33. If a salary amounted to JE825 in fivo years, at 5 per cent
what was the sahiry? Ar^. iiloO.
825X2=1660 5X5X,05—5X,054.5X2=:11 thJn 1650 -j-
11 =£150.
34. If a house is to be let upon a lease for 5^ years, and the
amount for that time is £363 : S : 3, at 4^ per cent, what is the
yearly rent? A71S. £60.
35. If a pension amounted to £2065, in 7 years, at 6 per cent,
what was the pension ? Am. 250.
36. Suppose the amount of a pension be £263 : 4 in 8 years, at
5 per cent, what wjis the pension ? Ans. £28.
Note. When the payments are half-yearly, then take 4 a, and
half of the ratio, and twice the number of years ; and if quarterl}'-,
then take 8 a, one fourth of the ratio, and four times the number
of years, .and proceed as before.
37. If the amount of a salary, payable half-yearly, for 5 years,
at 5 per cent, be i2S34 : 7 : 6, what was the salary ? Ans. £ 150.
38. If the amount of an annuity, payable quarterly, be £839 :
1 : 3, for 5 years, at 6 per cent, what wiis the annuity i
Ans. jeiSO.
III. When U A T are given to find R.
2a— 2ut
Rule.— =R.
utt — ut
EXAMPLES.
39. If a salary of £150 per annum, amount to iE825, in 5 years,
what is the rate per cent. ? Ans. 5 per cent.
150
825-1-2—150+5+2=150 then = 05
150X5X5—150X5
40. If a house be let upon a lease for 5^ years, at £60 per an-
num, and the amount for that time be £363 : 8 : 3, what is the
rate per cent. ? Ans. 4^ per cent.
41. If a pension of £250 per annum, amounts to £2065 in 1
jrears, what is the rate i)er cent, f Ans. 6 per cent.
42. Suppose he amount of a yearly pension of £28, be £263 :
4, in 8 years, what is the rate per cent ? Ans. 5 per cent
per
N
I-
,1
f ii j
SIMPLE INTEREST,
NoTR. When the payments are half-3'early, take 4 a — 4 iit for
a <:Hvi<l«'iKl, and work with half the annuity, and double the num-
ber of years for a di\i-or; if quarterly, take S a — 8 ut, and work
with a fourth of the annuity, and four times the number of years.
43. If a salary of £150 'per annum, payable half-yearly,
amounts to £834 : 7 : 6, in 5 years, what is the rate })er cent. ?
Ans. 5 per cent.
44. If an annuity of £i50 per annum, payable quarterly
amounts to £839 : 1 : 3, in 5 yeai-s, what is the rate per cent. ?
Ans, 5 per cent.
IV. When U A R are given to find T.
Rule. First,-
2a XX
-l=x then: ^ 1-
:T.
ur
EXAMPLES.
4 2
45. In what time will a salary of £150 per annum, amount to
£825, at 5 per cent. ? Ans. 5 years.
2 820X2 39X39
1 = 39 = 220 =380,25
,05 150 X, 05 4
39
^220 + 380 ,25=24 ,5 =5 years.
2
40. If a house is let upon a lease for a certain time, for £60
per annum, and amounts to £363 : 8 : 3, at 4| per cent., what
time was it let for ? Ans. 5^ years.
4*7. If a pension of £250 per annum, being forborne a certain
time, amounts to ^2065, at per cent, what was the time of
forbearance 'i Ans. 1 years.
48. In what time will a yearly pension of j£2&, amount to
£203 : 4, at 5 per cent. ? Ans. 8 years.
Note. If the i)ayments are half-yearly, take half the ratio, anJ
half the ammity ; if quarterly, one fourth of the ratio, and one
fourth of the annuity; and T will be equal to those half-yearly
or quarterly payments.
49. If an ainuiity of £150 per annum, payable half-yearly,
amounts to £834 : 7 : 6, at 5 per cent., what time was the pay-
ment forborne 3 Ans. 6 yeara.
50. Il
£839 :
Note.
1. Wl
t
Rule.
61. V!
5 years {
5X5X^
52. "V^
years wo
53. A^
1 years,
54. ^^
ney, at 5
Note.
annuities
ments.
65. ^^
5 years, j
Note.
the pres(
than yea
11. W
Rule.-
4 a — 4 lit for
ible the num-
iit, mid work
ibor of 3'ears.
5 half-yearly,
per cent. ?
5 per cent,
jle quarterly,
per cent. ?
5 per cent.
SIMPLE INTEREST.
147
m, amount to
'IS. 5 years.
;80,25
sars.
:ime, for £60
ir cent, what
f. 5^ years,
orne a certain
. the time of
ns. 1 years.
5, amount to
yis. 8 years.
the ratio, anJ
atio, and one
se half-yearly
e half-yearly,
was the pay-
ns. 5 years.
50. If a yearly pension of £150, payable quarterly, amounts to
£839 : 1 : 3, at 5 per cent., what was the time of forbearance ?
Ans. 6 years.
PRESENT WORTH OF ANNUITIES.
XoTE. P represents the present worth ; U T R as before.
1. When U T R are given to find P.
ttr— tr + 2t
Rule. : x u=P.
2tr -1-2
EXARIPLES.
61. What is the present worth of £150 per annum, to continue
5 years at 5 per cent. « Ans. £660.
5X5X,05— 5 X ,054-5X2 = 11 ,5 X ,05X2+2=2,5 then ll-H
2,5XloO=£660.
52. What is the yearly rent of a house of £60, to continue 5^
years worth in ready money, at 4| per cent. ?
Ans. £291 : 6 : 3.
53. What is the present worth of £250 per annum, to continue
1 years, at 6 per cent? Ans. £1454 : 4 • 6.
54. What is a pension of £28 per annum, worth in ready mo-
ney, at 5 per cent, for 8 years? Ans. £188.
Note. The same thing is to be observed as in the first rule of
annuities in arrears, concerning half-yearly and quarterly pay-
ments.
65. What is the present worth of £150, payable quarterly, for
5 years, at 5 per cent? Ans. £671 : 5.
Note. By comparing the last examples, it will be found that
the present worth of half-yearly payments is more advantageous
than yearly, and quarterly than half-yearly.
11. When V T U are given to find U.
tr + 1
Rule. : X 2p=U.
ttr— tr + 2t
n3
148
SIMPLE INTEREST.
EXAMPLES.
50. If the present worth of a salary be £660, to continue 5
years, at 5 cent., wliat is tlie salary? jins. £150.
IX ,05-f 1 = 1,25 5 X T) X ,05t7-5 xT'T+To = 11.
1,25*"'
X 660 X 2 = £150.
11
_ 67. There is a house let upon lease for 5| years to come, I de-
sn-e to know the yearly rent, when the present wortli, at Ah ner
cent., is £291 : 6 : 3? ^.^^^.^ £60.
58. What annuity is that which, for 1 years' continuniice, at 6
per cent., i>roduces £N54 : 4 : 6 present worth? Ans. £250.
59. What annuity is that which, for 8 years' continuance, nro-
ducos £188 for the present worth, at 5 per cent. ? Jus. £28.
Note. When the payments are half-yearly, take half the ratio
twice the number of years, and multiply by 4 p ; and wlien niiar-
t(.'rly, take one fourth of tlic ratio, and four times the number of
years, and multiply by 8 p.
00. There is an annuity payable half-yearly, for 5 years to
come, what is the j'early rent, when the present worth, at 5 per
c<M.t., is £667 : 10? Am.£]ryO
61. Ihere is an annuity payable quarterly, for 5 years to come,
I desire to know the yearly income, when the present worth, at
5 per cent., is £671 :5? ^ws. £150.
III. When U P T are given to find R.
ut— p X 2
Rule. =R.
2pt + ut— ttu
EXAMPLES.
62. At what rate per cent, will an annuity of £150 per annum,
to continue 5 years, produce the present worth of £660 ?
Alls. 5 per cent.
150X6-660X2 = l80,2X000X5-f5X 150-5X5X150=3000
then 180 -7- 3 600 =,05 =5 per cent.
63. If a yearly rent of £60 per annum, to continue 5| yenre,
produces ^291 : : 3, for the present worth, what is the rate
P^^ <^e»t. ? jins. 4i per cent.
66. It
ving 5 y
cent. ?
07. Il
ving 5 I
cent. ?
to continue 5
Ans. £150.
10= 11.
= £150.
to come, I de-
bli, at 4 1 per
Ans. £60.
iinunnee, at 6
Ans. £250.
tlniiaiico, pro-
Ans. £28.
half the ratio,
d vvlien quar-
iG number of
r 5 years to
rth, at 5 per
im. £150.
ears to come,
}nt wortli, at
ins. £150.
) per annum,
10?
} per cent.
< 150=3000
ne 6^ years,
is tlio rate
f per cent.
SIMPLE I]STEREST.
149
64. If an annuity of £250 per annum, to continue 7 years,
produces £1454 : 4 : 6, for the present worth, what is the rate
per cent. ? ' Ans. G per cent.
65. If a pension of £28 per annum, to continue 8 years, pro
duces £188 for the presen^vorth, what is the rate i)er cent. ?
•- Ans. 5 per cent.
Note. When tlie annuities, or rents, &c. are to be paid half-
yearly, or quarterly, then
For half-yearly payments, take half of the annuity, &c. and
twice the number of years, the quotient will be the ratio of half
the rate per cent. — and
For quarterly payments, tiike a fourth part of the annuity, &c.
and four times the number of years, the quotient will be the ratio
of the fourth part of the rate per cent.
66. If an annuity of £150 per annum, payable half-yearly, ha-
ving 5 years to come, is sold for £667 : 10, what is the rate per
cent. ? Ans. 5 per cent.
67. If an annuity of £150 per annum, payable quarterly, ha-
ving 5 years to come, is sold for £671 : 5, what is the rate per
cent. ? Ans. 5 per cent.
IV. When U P R are given to find T.
2 2p 2p XX X
Rule. 1 =x then ^ 1 =T,
r n ur 4 2
EXAMPLES.
68. If an annuity of £150 per annum, produces £660 for the
present worth, at 5 per cent., what is the time of its continu-
ance?
660X2
,05 150
30,2X30,2
—1=30,2
A71S. 5 years.
660X2
=176
150 X, 05
= 228,01 then ^228,01 + 176=20,1
30,2
20,1 =5 yeara.
2
m3
150
SIMPLE INTEREST.
i
,i Sf:
69. For wli.it time may a salary of £G0 bo ])urchased for
£291 : 6 : 3 at 4J^ per cent. ? Ans. 5^ years.
70. For what time may ^2250 per annum, be i»iirchascd for
£1454 : 4 : G, at G per cent. ? Ans. 7 yeai"s.
71. For what time may a pension of £28 per annum, be pur-
chased for £188, at 5 per cent. ? Aiis. 8 years.
Note. When the jiayments are half-yearly, then U will be
equal to half the annuity, tfec. It half the ratio, and T the num-
ber of payments : and.
When tlie payments arc quarterly, U will be equal to one
fourth part of the annuity, &c. R the fourth of the ratio, and T
the number of payments.
72. If an annuity of £150 per annum, payable half-yearly, is
sold for £667 : 10, at 5 per cent., I desire to know the number
of payments, and the time to come ?
Ans. 10 payments, 5 yeai*s.
73. An annuity of £150 per annum, payable quarterly, is sold
for £G7l : 5, at 5 per cent., what is the number of payments, and
time to come ? Ans. 20 payments, 5 years.
ANNUITIES, &c. TAKEN IN REVERSION.
1. To find (he present worth of an annuity, <fec. taken in re-
version.
Rule*. Find the present worth of the ttr — tr-f-2t
yearly sum at the given rate and for the : X u=P.
time of its continuance ; thus, 2tr-f-2
2. Change P into A, and Hnd what prin-
cipal, being put to interest, will amount to a
A at the same rate, and for the time to =P,
come before the annuity &c. commences ; tr-j- 1
thus,
EXAMPLES.
74. What is the present worth of an annuity of £150 per an-
num, to continue 5 years, but not to commence till the end of 4
years, allowing 5 per cent, t.^ the purchaser ? Ans. £550.
6 X 5 X ,05 — 5 X ,05 4- 2 X •-> = 4^4 V 1 50 — 660
6X,05X2-|-2
4X,06-fl
=560.
75. W
to contimi
of 5 years
7G. A
luim, for i
willing to
iii'i'seut w<
77. A
person of
is 21 ; he
per cent.,
2. Tof
liULB 1
worth at
before the
2. Cha
nuity boil
Baine rate
ance; thu
78. A
does not <
allowing
come ?
550 X 4
79. Tl
coimnenc
for £152
cliiuser, w
80. A
which do
the same
cent, to t
;»urehased for
?. 5^ years.
i>iircl»asccl for
IS. 7 yoai-s.
nuin, be pur-
is. 8 ycara.
in U will be
T the num*
squal to one
ratio, and T
lalf-yearly, is
»■ the number
s, 5 yeai*s.
•terly, is sold
fiynionts, and
s, 5 years.
HON.
taken in re-
2t
- : X U=:P.
p.
SIMPLE INTEREST.
151
1 50 per an-
ho end of 4
ns. £550.
-=660.
75. What is the present worth of a lease of £50 per annum,
to continue! 4 years, but which is not to commence till the end
of 5 years, allowing 4 per cent.' to the purchaser?
Anv. £152 : 5 : 11 3 qrs.
VO. A person having the promise of a pension of £20 per an-
num, for 8 years, but not to commence till the end of 4 years, is
willing to dispose of the same at 5 per cent., what will be the
liv.'seut worth? Ans. £l 1 1 : 18 : 1 ,14 + .
77. A legacy of £40 per annum being left for 6 years, to a
person of 15 years of age, but which is not to commence till he
is 21 ; he, wanting money, is desirous of selling the same at 4
per cent, what is the present worth ?
Ans. £171 : 13 : 11 ,07506.
2. To find the yearly income of an annuity, &c. in revereion.
ptr-f-p=A.
liuLK 1. Find the amount of the present
worth at tlie given rate, and for die time
before the reversion ; thus,
2. Change A into P, and find what an-
nuity being sold, will produce P at the
Biune rate, and for the time of its continu-
ance; thus,
EXAMPLES.
tr-fl
ttr— tr-f2t
•:X2p=U.
78. A person having an annuity left him for 5 years, which
does not commence till the end of 4 years, disposed of it for £550,
allowing 5 per cent, to the purchaser, what was the yearly in-
come? Ans. £150.
5 X ,05 -I- 1,
550 X 4 X ,05 + 550 = GGO 5 X 5 X ,05—5 X ,05 + 6 X 2=
,113036 X C60 X 2 = £150.
79. There is a lease of a house taken for 4 years, but not to
connnence till the end of 5 years, the lessee would sell the same
for £152 : 6, present payment, allowing 4 per cent, to the pur-
cliiuser, what is the yearly rent? -^ins. x50.
80. A person having the promise of a pension for 8 yearn,
which does not commence till the end of 4 years, has disposed of
the same for £111 : 18 : 1 ,14 present money, allowing 6 per
cent, to the purchaser, what was the pension ? Ans. £20.
152
REBATE OR DISCOUNT.
81. There is ji certain lei^acy left to a person of 15 years of age,
whicli is to be continued for 6 years, but not to commence till he
arrives at the age of 21 ; he, wanting a sum of money, sells it for
£1*71 : 14, allowing- 4 ]>er cent, to the buyer, what was the an-
nuity left him ? Ans. £40.
REBATE OR DISCOUNT.
Note. S represents the Sum to be discounted.
P the Present worth.
T the Time.
R the Katio. *
I. When S T R are given to find P.
s
Rule. = P.
tr+1
due 5 m{
payment,
8. A
months li
much wa
III. ^
Rule."
9. At
hence, pr
EXAMPLES.
t. "What is the present worth of £357 : 10, to be paid 9 months
hence, at 5 per cent? Ans. £344 : 11 : 6^ ,108.
2. What is the present worth of £275 : 10, due 7 months
hence, at 5 per cent. ^ Ans. £267 : 13 : 10^^^.
3. What is the present worth of £875 : 5 : 6, due at 5 months
hence, at 4^ per cent. ? Ans. £859 : 3 : 3^ y|^.
4. How much ready money can I receive for a note of £75,
due 15 months hence, at 5 per cent. ?
Ans. £70 : 11 : 9 ,l764d,
II. When P T R are given to find S.
Rule. ptr-{-p=S.
EXAMPLES.
5. If the present worth of a sum of money, due 9 months
hence, allowing 5 per cent., be £344 : 11 : 6 3,168 qrs., what
was the sum first due ? Ans. £357 : 10.
344,5783 X ,75 X ,05-f 344,5783 = £357 : 10.
6. A person owing a certain sum, payable 7 months hencr.
agrees with the creditor to pay him down £267 : 13 : lO^j'i^, al-
lowing 5 per cent, for present jiayment, what is the debt ?
A71S. £275 : 10.
1, A person receives £859 : 3 : S^j^-j for a sum of money I 14. 1
10. A
hence, pr
11. A
hence, pr
12. A
produce
IV. ^
Rule.
years of age,
nenee till he
', sells it for
was the au-
4w5. £40.
id 9
months
I 7
,108.
months
: IO^Vt-
at 5 months
: 3^
T63-
of £75,
9 ,l764d.
i 9 months
i qrs., what
1357 : 10.
10.
mths hence,
•10 3 8 ol.
l>t?
1275 : 10.
n of money
BEBATE OR DISCOUNT,
153
due 5 months hence, allowing the debtor 4]^ per cent, for present
payment, what was the sum due? Ans. £875 : 5 : 6.
8. A person paid £70 : 11 : 9 ,1764d. for a debt due 15
months hence, he being allowed 5 per cent, for the discount, how
much was the debt ? Ans. £75
III. When S P T are given to find R.
s— p
Rule. =R. *
tp
EXAMPLES.
9. At what rate per cent, will £357 : 10, paj-abL months
hence, produce £344 : 11 : 6 3,108 qrs. for present payment?
3575,-344,5783
. z=,05=5 per cent.
344,5783 X ,75
10. At whai rate per cent, will £275 : 10, payable 7 months
hence, produce £267 : 13 : lOg^^ for the present payment?
Ans. 5 per cent.
11. At what rate per cent, will £875 15:0, payable 5 months
hence, produce the present payment of £859 : 3 : 3^ jf ^ ?
Ans. 4^ per cent.
12. At what rate per cent, will £75, payable 15 months hence,
produce the present payment of £70 : 11 : 9 ,l764d. ?
Ans. 5 per cent
IV. When S P R are given to find T.
s— p
Rule. = T.
rp
EXAMPLES.
13. The present worth of £357 : 10, due at a certain time to
come, is £344 : 11 : 6 3,108 qrs. at 5 per cent., in what time
should the sum have been paid without any rebate ?
Ans. 9 months.
357,5—344,5783
:,75=9 mouths.
344,5783 X ,05
14. The present worth of £275 : 10, due at a certain time to
154
EQUATION OF PAYMENTS.
come, is £267 : 13 : lOJ^J^, at
the sum have been paid witlujut
15. A person receives £859
due at a certain time to come,
desire to know in what time the
Q(* witliout any rebate ?
10. I liave received £70 : 1
allowinaf the person 5 per cent,
know when the debt would have
5 per cent., in what time should
any rebate ?
~ Ans. 7 months.
: 3 : 3f ,0184, for £875 : 5 : Q,
allov.ing 4| per cent, discount, I
debt should have been dischar<i'-
Ans. 5 months.
1 : 9 ,l7C4d. for a debt of £75,
for prompt payment, I desire to
been payable without the rebate!
Ans. 15 months.
hi
U.'
EQUATION OF PAYMENTS.
To find the equated time for the payment of a sum of money
due at several times.
Rule. Find the present worth of each pay- s
ment for its respective time ; thus, =P
tr+1
Add all the present worths together, then, s — p=D.
d
and =E
pr
EXAMPLES.
1. D owes E £200, whereof £40 is to be paid at three months,
£60 at si.x months, and £100 at nine months ; at what time mcay
the whole debt be paid together, rebate being made at 5 per cent. ?
Ans. 6 months, 26 days.
40 60 100
=39,5061 =58,5365 =96,3855
1,0125
1,025
1,0375
then 200—39,5061 + 58,5365-1-96,3855=5,5719
6,5719
=,57315=6 months, 26 days.
194,4281 X ,05.
2. D owes E £800, wliareof £200 is to bn paid in 3 months.
£200 at 4 months, and £400 at 6 months ; but they, agreeing to
make but one payment of the whole, at the rate of 5 per cent.
rebate, the true equated time is demanded ?
Ans. 4 months, 22 days.
I
COMPOUND INTEREST.
155
time should
1 inontlis.
£875 : 5 : 6,
;. discount, I
:en dischai'fi'-
5 months,
iebt of £7o,
, I desire to
t the rebate?
5 months.
m of money
tr+1
J— p=D.
d
=E
pr
iree months,
it time mcay
5 per cent.?
, 26 days.
,3855
5,5719
1 3 months,
no-reein^; to
5 per cent.
22 days.
3. E owes F £1200, which is to be paid as follows: £200
down, £500 at the end of 10 months, and the rest at the end of
20 months ; but they, agreeing to have one payment of the whole,
rebate at 3 per cent., the true equated time is demanded ?
Ans. I year, 11 days.
COMPOUND INTEREST.
The letters made use of in Compound Interest, are,
A the Amount.
P the Principal.
T the Time.
R the Amount of £l for 1 year at any given rate ;
which is thus found :
As 100 : 105 : : 1 : 1,05. As 100 : 105,5 : : 1 : 1,055.
A Table of the amount of £1 for one year.
RATES
PER CENT.
AMOUNTS
of£1.
RATES
PER CENT.
6
ei
7
7i
AMOUNTS
OF £1.
RATES
PER CENT.
AMOUNTS
OF £1
3
3i
4
4i
5
1,03
1,035
1,04
1,045
1,05
1,055
1,06
1,005
1,07
1,075
8
8i
9
9i
10
1,08
1,085
1,09
1,095
1,1
Table showing fhe aviount of £1 for any number of year%
under 31, ct^ 5 and 6 per cent, per annum.
YEARS.
5 RATES. 6
YEARS.
5 R.\TE3. 6
1
1,05000
1,06000
16
2,18287
2,54035
2
1,10250
1,12300
17
2,29201
2,69277
3
1, 15762
1,19101
18
2,40662
2,85134
4
1,21550
1,26247
19
2,52695
3,02560
5
1,27028
1,33822
20
2,65329
3,20713
6
1,34000
1,41852
21
2,78596
3,39956
7
1,4071.0
1,50303
22
2,92526
3,60353
8
1,47745
1,59385
23
3,07152
3,81975
9
1,55132
1,68948
24
3,22510
4,01893
10
1,«2SS9
1,79084
25
3,38635
4,29187
11
1, 71034
1,89829
26
3,55507
4,54938
12
1,79585
2,01219
27
3,73345
4,82234
13
1,SS.')05
2,13292
28
3,92013
5,11168
14
1,97993
2,26(190
29
4,11613
5,41S38
15
2,07892
2,39655
30
4,32194
5,74349
h
* '\
4
156
COMPOUND INTEREST.
to
Note. The preceding table is thus made — As 100 : 106 : : 1 •
1,05, for the first year; then, As 100 : 105 : : 1,05 : 1,1025, so
cond year, &c.
I. When P T R are given to find A.
Rule. pXrt=A.
EXAMPLES.
1. What will £225 amount to in 3 years' time, at 5 per cent,
per annum ?
Ans. 1,05X1,05X1,05=1,157625, then 1,157625X225=
£260 : 9 : 3 3 qrs.
2. What will £200 amount to in 4 years, at 5 per cent, per
*""""^ • Ans. £243 2,025s.
3. What will £450 amount to in 5 years, at 4 per cent, per
a"""'" '^' Ans. £547 : 9 : 10 2,0538368 qrs.
4. What will £500 amount to in 4 yeai-s, at 5-^ per ceut. per
annum
Ans. £619 : 8 : 2 3,8323 qrs.
II. When A R T are given to find P.
a
Rule. =P
rt
EXAMPLES.
5. What principal, being put to interest, will amount to £260 :
9:33 qrs. in 3 years, at 5 per cent, per annum ?
260,465625
1,05 X 1,05X 1,05 = 1,157625 -=£225.
1,157625
6. What principal, being put to interest, will amount to £243
2,025s. in 4 years, at 5 per cent, per annum ? Ans. £200.
7. What principa. will amount to £547 : 9 : 10 2,0538368 qrs.
in 5 years, at 4 per cent, per annum ? Ans. £ 150.
8 What principal will amount to £619 : 8 : 2 3,8323 qrs. in 4
years, at o^ per cent, per annum ? Ans. £500.
III. When P A T are given to find R.
a \yhich being extracted by the rule of exi
Rule. — =rt tion, (the time given to the question shov
9. A1
qrs. in 3
10. A1
in 4 year
11. Al
2,05383f
12. Ai
3,8323 q
IV. Vs
Rule.-
13. In
5 per cer
260,465(
the power) will give R
COMPOUND INTEREST.
157
: 106 : : 1 •
1,1025, 80
t 5 per cent.
125X225=
: 3 3 qrs.
er cent, per
3 2,025s.
er cent, per
8368 qrs.
>er ceut. per
8323 qrs.
it to £260 :
3.
nt to £243
ns. £200.
538368 qrs.
IS. £150.
23 qrs. in 4
IS. £500.
of extrac-
on showing
EXAMPLES.
9. At what rate per cent, \vill £225 amount to £200 : 9 : 3,3
qrs. in 3 years ? ^ ^ns. 5 per cent.
260,465325
=1,157625, the cube root of which
225
(it being the 3d power) =1,05=5 per cent.
10. At what rate per cent, will £200 amount to £243 : 2,025s.
in 4 years ? -4w5. 5 per cent.
11. At what rat« per cent, will £450 amount to £547 : 9 : 10
2,0538368 qrs. in 5 years ? Ans. 4 per cent.
12. At what rate per cent, will £500 amount to £619 : 8 : 2
3,8323 qrs. in 4 years ? Ans. 6| per cent
IV. When P A R are given to find T.
a which being continually divided by R till no-
RuLE. — =rt thing remains, the number of those divisions
p will be equal to T.
EXAMPLES.
13. In'what time will £225 amount to £260 : 9 : 3 3 qrs. ftt
5 per cent. ?
260,465625 1,157625 1,1025 1,05
. = 1,157625 = 1,1025 =1,05
225 1,05 . 1,05 1,06
= 1, the number of divisions being three times sought.
14. In what time will £200 amount to £243 2,025s. at 5 per
cent. ? Ans. 4 years.
15.' In what time will £450 amount to £547 : 9 : 10 2,0538368
qi-s. at 4 per cent. ? Ans. 5 years.
16. In what time will £500 amount to £619 : 8 : 2 3,8323
qi-s. at 5^ per cent. ? Ans. 4 years.
ANNUITIES, OR PENSIONS, IN ARREARS.
Note. U represents the annuity, pension, or yearly rent
A R T as before.
,;.A''
^U.i
'4
m
158
COMPOUND INTEREST.
A Table showing the amount of £1 annualhj^ for any number
of years under oi, at 5 and 6 ^^cr cent. ^;er annum.
YEARH.
5 RATK3. 6
Yr.AR!*,
5 RATK3. 6 1
1
1,0')(JUU
1,00000
10
23,65719
35,67252
2
2,U50OU
2,(X)0(X)
17
25,84036
28,21288
3
3,15250
3,18360
18
28,18238
3U,90565
4 -
4,31012
4,37461
19
30,53900
33,75999
5
5,525r,3
5,63709
20
33,06595
36,78559
6
6,80191
6,97532
21
35,71925
39,99272
7
8,1-1200
8,39383
22
33,50521
43,39229
8
9,51<H0
9,897-16
23
41,43047
46,9y582
9
11,02656
11,49131
24
<1 4 ,50 199
50,81557
10
12,577Sli
13,18079
25
47,72709
51,86151
11
14,20678
H,9716J
26
51,11345
59,15638
12
J5,yi712
16,86991
27
54,66912
63,70576
13
17,7121)8
18,88213
28
58,40258
68,52811
. U
19,5U86S
21,01506
29
62,32271
73,63979
15
21.57856
23,27597
30
66,43884
79,05818
Note. The above table is made thus : — take the first year's
amount, which is £1, multiply it by 1,05 + 1 =2,05 = second
year's amount, which also multiply by 1,054-I=2,l525=third
year's amount.
T. When U T R are given to find A.
ur"*
-u
RULE.-
=A, or by the table thus :
"irr
Multiply the amount of £1 for the number of years, and at the
rate per cent, given in the question, by the annuity, pension,
<fec. and it will give the answer.
EXAMPLES.
17. What will an annuity of £50 per annum, payable yearly,
amount to in 4 years, at 5 per cent. ?
Ans. 1,05 X 1,05 X 1,05 X 1,05 X 50=60,7*7531250
60,7753125—50
tJien ^- =£215 : 10 : 1 2 qrs.; or,
1,05—1
by the table thus, 4,31012X50=£215 : 10 : 1 1,76 qrs.
18. What will a pension of £45 per annum, payable yearly,
amount to in 5 years, at 5 per cent. ?
Ans. je248 : 13 : 3,27 qrs.
COMPOUND INTEREST.
159
19. If a salary of £40 per annum, to be paid yearly, be "for-
borne years, at 6 per cent., what is the amount ?
Ans. £279 : : 3,0579609Gd.
20. If an annuity of £75 per annum, payable yearly, be omit-
ted to be paid for 10 years, at 6 per cent., what is the amount?
Jns. £988 : 11 : 2,222d.
II. When A R T are given to find U.
ar — a
Rule. =U.
rt— 1
EXAMPLES.
21. What annuity, being forborne 4 years, will amount to
£215 : 10 : 1 2 qrs. at 5 per cent.?
215,50G25X 1,05— 215,50025
Ans. — -— =£50.
1,05X1,05X1,05X1,05—1
22. What pension, being forborne 5 years, will amount to
£248 : 13 : 3,27 qrs. at 5 per cent. ? Ans. 45.
23. What salary, being omitted to be paid 6 years, will amount
to £279 : : 3,05790096d. at 6 per cent.? Ans. £40.
24. If the payment of an annuity, being forborne 10 years,
amount to £988 : 11 : 2,22d. at 6 per cent., what is the annuity?
Ans. £75.
III. When U A R are given to find T.
ar-j-u — a which being continually divided by R till
Rule. --=rt nothing remains, the number of those
u divisions will be equal to T.
EXAMPLES.
25. In what time will £50 per annum amount to £215 : 10 :
1 2 qrs. at 5 per cent, for non-payment ?
Ans. 215,5062"5X 1,05 + 50 215,5062j =l,2]550625.
50
which being continually divided by R, the number of the divi-
sions will be =4 years.
26. In what time will £45 per annum amount to £248 : 13
327 qrs. allowing 5 per cent, for forbearance of payment?
Ans. 5 years.
02
..1 i
160
COMPOUND INTEREST.
21. In what time will £40 per annum amount to £279 : :
3,0579G096d. at 6 per cent. ? Ans. 6 years.
28. In what time will £75 per annum amount to £988 : 11 :
2,22(1. allowing 6 per cent, tor forbearance of payment ?
Ans. 10 yeai-s.
PRESENT WORTH OF. ANNUITIES, PENSIONS, &c.
A Table showing the present loorth of £1 annuity, for any num-
ber of years under 31, rebate at 5 and 6 per cent.
YEARS.
5 RATES. 6
YEARS.
5 RA'
i'KS. 6
1
0,95235
0,94339
16
10,83777
10,10589
2
1,85911
1,83339
17
11,27406
10,47726
3
2,72321
2,G7o0l
18
1 1 ,68958
10,82760
4
3,54595
3,46510
19
12,03532
11,15811
5
4,32947
4,21236
20
12,46221
11,46992
6
5,07509
4,91732
21
12,82115
11,76407
7
5,78037
5,58238
22
13,16300
12,01158
8
6,40321
6,20979
23
13,48857
12,30338
9
7,107^2
6,80109
24
13,79864
12,55036
10
7,72173
7,30008
25
14,09391
12,78336
11
8,30041
7,88687
26
14,37518
13,00317
12
8,80325
8,38384
27
14,64303
13,21053
13
9,39357
8,85208
28
14,89812
13,40616
14
9,8986 '
9,29498
29
15,14107
13,59072
15
10,37965
9,71225
30
15,37245
13,76483
Note. The above table is thus made : — divide £1 by 1,06 =
,95238, the present worth of the first year, which-M,05=90753,
added to the first year's present worth= 1,85941, the second
year's present worth ; then, 90703-M,Oo, and the quotient added
to 185941 = 2,72327, third year's present worth.
I. When U T R are given to find P.
u
u
Rule.
=P.
r— 1
or by the table thus :
present worth of £l annuity for the time and rate
per cent, given by the annuity.
Bwer.
anni
pension, &c., it will give the an-
COMPOUND INTEREST.
161
£279 : :
6 years.
;988 : 11 :
lO years.
, &c.
any num-
mt.
__
,n7-2t)
,827(30
,15811
,40992
,70.407
.oiins
,30338
,5.')030
,78330
,00317
,2 ions
.'lOGIO
,59072
,70183
by 1,06 =
5=90'753,
be second
ient added
e and rate
ve tho ail-
EXAMPLES.
29. What is the present worth of an annuity of £30 per aii-
num, to continue 7 years, at 6 per cent. ?
Ans. £167 : 9 : 5 ,184d.
10,0483
30
1,50363
= 167,4716.
-=19,9517
30—19,9517 = 10,0483
By the table 5,58238X30=167,4714.
1,06—1
30. What is the present worth of a pension of £40 per annum,
to continue 8 years, at 5 per cent. ?
Ans, £258 : 10 : 6 3,264 qrs.
31. What is the present worth of a salary of 35, to continue
7 years, at 6 per cent. ? Ans. £195 : 7 : 7 3,968 qrs.
32. What is the yearly rent of £50, to continue 5 years, worth
in ready money, at 5 per cent. ? Ans. £216 : 9 : 5 2,56 qrs.
II. When P T R are given to find U.
prtXr — pr*
Rule. =U.
rt— .1
EXAMPLES.
33. If an annuity be purchased for £167 : 9 : 5 184d. to be
continued 7 years, at 6 per cent, what is the annuity ?
Ans. 167,4716X1,50363X1,06—167,4716X1,50363
=£30.
1,50363—1
34. If tho present payment of £258 : 10 : 6 3,264 qrs. be
made for a salary of 8 years to come, at 5 per cent., what is the
salary? ^"^' ^'*^'
35. If the present payment of £195 : 7 : 7 3,968 qrs. be re-
quired for a pension for '7 years to come, at 6 per cent., what ia
the pension? Ans. £^b.
36. If tho present worth of an annuity 5 years to come, be
£216 : 9 : 5 2,56 qi-s. at 5 per cent., what is the annuity?
Ans. £50.
03
•a
I
fc
4. 1 =
f4
162
COMrOUND INTEREST,
III. When U P R are given to find T.
u which bein;^ continually divided by R till
Rule. =rt nothing remains, the number of those di-
p+u — pr visions will be equal to T.
EXAMPLES.
37. How long may a lease of £30 yearly rent be had for
£1G7 : 9 : 5 ,184d. allowing 6 per cent, to the purchaser?
30
167,47164-30—177,5198
which being continually
I SOSe*? divided, the number of
' those divisions will be=
to T=7 years.
38. If £258 : 10 : 6 3,264 qrs. is ppid down for a lease of £40
per annum, at 5 per cent., how long is the lease purchased for ?
Ans. 8 years.
39. If a house is let upon lease for £35 per annum, and the
lessee makes present payment of £195 : 7 : 8, ho being allowed
6 per cent., I demand how long the lease is purchased for 2
Ans. 1 yeai-s.
"40. For what time is a lease of £50 per annum, purchased
when present payment is made of £?16 : 9 : 5 2,56 qrs. at 5 per
cent. ? Ans. 5 years.
ANNUITIES, LEASES, &c. TAKEN IN REVERSION.
To find the present worth of annuities^ leases, d'c. taken in
reversion.
41. WI
per annun
Che end of
40
1,41852
42. Wl
per annujT
of 3 years
43. Th.
yet in beir
m reversic
pi red, wha
sion, allow
To find I
Rule.
worth at
fore the ar
Change
being sole
and for th
be the yea
Rule. Find the present worth of the annui-
ty, &c. at the given rate and for the time of its
continuance : thus,
2. Change P into A, and find what principal
being j>ut to intorest will amount to P at the
Bame rate, and for the time to come before the
annuity commences, which will be the present
worth of the annuity, «&c. : thus
u
u-
=p.
r— 1
a
44. Wl
to continu
at 6 per c
I
i by R till
f those di-
B had for
r?
ontinually
umber of
will be=
36 of £40
!d for ?
3 years.
I, and the
y allowed
. •
J yeare.
purchased
. at 5 per
t years.
RSION.
ken in
11
=P.
-1
=P.
COMPOUN.i) INTEREST.
EXAMPLES.
163
41. What is the present worth of a reversion of a lease of £40
per annum, to continue for six years, but not to commence till
Che end of 2 years, allowing 6 per cent, to the purchaser ?
Am. £175 : 1 : 1 2 ,048 qrs.
40 40—28,1984 196,6933
=28,1984 =196,6933
1,41852 1,06—1 1,1236
= 175,0563.
42. What is the present worth of a reversion of a lease of £60
p(^r annum, to continue 7 years, but not to commence till the end
of 3 years, allowing 5 per cent, to the purchaser ?
Ans. £299 : 18 : 2,8d.
43. There is a lease of a house at £30 per annum, which is
yet in being for 4 years, and the lessee is desirous to take a lease
m reversion for 7 years, to begin when the old lease shall be ex-
pired, what will be the present worth of the said lease in rever-
sion, allowing 5 per cent, to the purchaser ?
Ans, £142 : 16 : 3 2,688 qrs.
To find the yearly income of an annuity, <&c. taken in reversion.
Rule. Find the amount of the present
worth at the given rate, and for the time be-
fore the annuity commences : thus, pr*=A.
Change A into P, and find what yearly rent
being sold will produce P at the same rate,
and for the time of its continuance, which will pr*Xr — prt.
be the yearly sum required : thus, =U.
r»— 1.
EXAMPLES.
44. Wliat annuity to bo entered upon 2 years lience, and then
to continue 6 years, may be purchased for £175 : 1 : 1 2,048 qrs*
at 6 per cent. ?
Ans.. 175,0563 v 1.1 23G = 1 96,6933
hen 196,0933 X 1,41852 X 1,00— 279',01337
=£40.
1,41852—1
k'V
i;
i
164
C03IP0UND INTEREST.
45. The present wortli of a lease of a house is £209 : 18 : 2 8d
taken in reversion for 7 years, but not to commence till the enc
of 3 years, allowing 5 per cent, to the purchaser, what is the
yearly rent?
Ans. 60.
46. There is a lease of a house in being for 4 years, and tlio
lessee being minded to take a lease in reversion for 7 yeai-s, to
begin when the old lease shall be expir-'d, paid down £142 : 16 :
3 2,688 qi-s. what was the yearly rent of the house, when the les-
see was allowed 5 per cent, for present payment? Ans. £30.
PURCHASING FREEHOLD OR REAL ESTATE, IN SUCH AS ARK
BOUGHT TO CONTINUE FOR EVER.
I. When U R are given to find W. %
u >
Rule. =W.
r— 1
EXAMPLES.
47. "What is the worth of a freehold estate of £50 per annum,
allowing 5 per cent, to the buyer ?
50
jins. =£1000.
1,05—1
48. What is an estate of £140 per annum, to continue for ever,
worth in present money, allowing 4 per cent, to the buyer ?
Ans. £3500.
49. If a freehold estate of £75 yearly rent was to be sold, what
is the worth, allowing he buyer C per cent. ?
Ans. £1250.
II, When W R are given to find U.
Rule. wXr — 1=XJ.
EXAMPLES,
50. If a freehold estats is bought for £1000, and the allowanco
of 5 per cent, is made to the buyer, what is the veavly rent?
Ans. 1 ,05-- 1 = ,05, then 1 000 X ^05 = £5 0.
51. If an estate be sold for £3500, and 4 per cent, allowed to
tho buyer, what is the yearly rent 3
per
52. If
and an a
what is tl
III. W
RULE.-
53. If
is the rat(
54. If
£3500, w
55. If
the rate p
v\
To
Rule.
Change
put to int
for the tir
that will 1
56. If
years hen<
5 per ceni
57. W
cominenet
the purch
58. W
ney, to cc
years, allc
Ans. £140.
COMPOUND INTEREST.
165
18 : 2 8d
:ill the qm,
li.'it is the
Ans. 60.
irs, and tlio
7 yeai-s, to
ei42 : 16:
len the les-
[ns. £30.
AS ARE
per annum,
ue for ever,
, £3500.
) sold, what
. £1250.
52. If a freehold estate is bought for £1250 present money,
and an allowance of 6 per cent, made to the buyer for the same,
what is the yearly rent ? ■ j4ns. £75.
III. When W U are given to find R.
w-j-u
Rule. =R.
w
EXAMPLES.
53. If an estate of £50 per annum be bought for £1000, what
Is the rate per cent. ?
Ans.
1000-1-50
1000
; 1,05 = 5 per cent.
54. If a freehold estate of £140 per annum be bought for
£3500, what is the rate per cent, allowed ? Ans. 4 per cent.
55. If an estate of £75 per annum is sold for £1250, what is
the rate per cent, allowed ? Ans. 6 per cent.
PURCHASING FREEHOLD ESTATES IN REVERSION.
To find the worth of a Freehold Eatate in reversion :
u
Rule. Find tlie worth of the yearly rent, thus — =W
Change W into A, and find what principal, being r — 1
piit to interest, will amount to A at the same rate, and
for the time to come, before the estate commences, and a
that will be the worth of the estate in reversion, thus : — =P
rt.
EXAMPLES.
3 allowaiico
rent?
5= £50.
allowed to
'.s. £140.
66. If a freehold estate of £50 per annum, to commence 4
years hence, is to be sold, what is it worth, allowing the purchaser
5 per cent, for the present payment ?
50 1000
Ans. =1000, then =je822 : 14 : 1^.
1,05—1 1,2155
57. What is an estate of £200, to continue for ever, but not to
commence till the end of 2 years, worth in ready money, allowing
the purchaser 4 per cent.? Ans. £4622 : 15 : 7 ,44d.
58. AVhat is an estate of .£240 per annum worth in ready mo-
ney, to continue for ever, but not to commence till the end of 3
years, allowance being made at 6 per cent. ?
Ans. £3358 : 9 : 10 2,24 qrs.
* ■
* I
166
REBATE OR DISCOUNT.
To find the Yearly Rent of an Estate taJcen in reversicm,
liuLR. Find the amount of the worth of the
wr-
-w=U,
estate, at tlie gixon rate, and time before it com- wr*
iiienccs, thus :
Change A into W, and find what yearly rent
being sold will produce U at the same rate, thus :
which will be the yearly rent required.
EXAMPLES.
59. Tf a freehold estate, to commence 4 years hence, is sold
for $822 : 14 : 1^, allowing the purchaser 5 per cent., what is
the yearly income ? Ans. 822,70025 X 1,2155 = 1000,
then 1000X1,05— 1000=£50.
60. A freehold estate is bought for £4622 : 15 : 7 ,44d, which
does not commence till the end of 2 years, the buyer being allow-
ed 4 per cent, for his liioney. I desire to know the yeai-ly in-
come. Ans. £200.
61. There is a freehold estate sold for £3358 : 9 : 10 2,24 qrs.,
but not to commence till the expiration of 3 years, allowing 6
per cent, for present payment ; what is the yearly income ?
Ans 240
REBATE OR DISCOUNT.
A Table shotoing the present ivorth of £l due any number of
years hence^ under 31, rebate at 5 o,nd 6 per cent. *
YEARS.
5 RATES. G
YEARS.
5 RATES. 6
1
,952381
,943390
10
,458111
,393040
2
,907030
,889990
17
,430290
,371304
3
,803838
,839019
IS
,415520
,350343
.1
,822702
,792093
19
,395734
,330513
5
,783520
,747258
20
,370889
,311804
6
,740215
,704900
21
,358942
,294155
7
,710082
,005057
22
,341849
,277505
8
,070839
,027412
23
,325571
,201797
9
,041009
,591898
24
,340008
,240978
10
,013913
,5.jS394
25
,295302
,232995
11
,584079
,520787
20
,281240
,219810
12
,550837
,490909
27
,207848
,207308
13
,.'530321
,408839
28
,255093
,190030
14
,505008
,442301
29
,242940
,184550
15
,481017
,417205
30
,231377
,174110
Note. — The above table is thus vmhIq : 1 ~- 1
first year's present worth; and ,952381 -i- 1,05=
year; and ,90703H-1,05=,8G3838 third year, (fee.
,05 = ,952381,
,90703, second
REBATE OR DISCOUNT.
167
werston,
=A
wr — w=U,
I. When S T R are given to find P.
nee, is sold
nt., what is
= 1000,
I000=£50.
,44d, which
being allow-
e yearly in-
is. je200.
2,24 qrs.,
allowing 6
me ?
dns. 240.
number of
ent,
i. 6
J9304G
ni364
}r)0343
530513
ill804
!94155
^nr•>o'^
!(3l7i.(7
140978
!3-299S
! 198 10
1073ns
90030
84 ^SG
74110
== ,952381,
^03, second
Rule.
:P.
EXAMPLES.
1. What is the present worth of £315 : 12 : 4 ,2d, payable 4
vears hence, at 6 per cent. ?
Ans, 1,06X1,00X1,06X1,06 = 1,26247, then by the table.
315,6175 315,6175
=£250 ,792093
1,26247
249,9984124275
2. If £344 : 14 : 9 1,92 qrs. be payable in 7 years' time, what
is the present worth, rebate being made at 5 ^ er cent. ?
Am. £245.
3. There is a debt of £441 : 17 : 3 1,92 qrs., which is payable
4 yeai-s hence, but it is agreed to be paid in present money ; wliat
sum must the creditor receive, rebate being made at 6 per cent. ?
Ans. £350.
II. When P T R are given to find S.
Rule. pXr*=S.
EXAMPLES.
4. If a sum of money, due 4 years hence, produce £250 for
the present payment, rebate being made at 6 per cent., what waa
the sum due ?
Ans. £250Xl,26247=£315 ; 12 : 42d.
5. If £245 be received for a debt payable 7 years hence, and
an allowance of 5 per cent, to the debtor for present payment,
what was the debt? Ans. £344 : 14 : 9 1,92 qrs.
6. There is a sum of money due at the expiration of 4 years,
but the creditor agrees to take £350 for present payment, allow-
ing 6 per cent., what was the debt ?
Ans. £441 : 17 : 3 1,92 qrs.
III. When S P R are jnven to find T.
s which being continually divided b}' R till nothing
Rule. — =rt remains, the number of those divisions will be
p equal to T.
• li-^'fi
■»l'
168
BEilATE OR DISCOUNT.
EXAMPLES.
1. The present payment of £250 is made for a debt of £315 :
12 : 4 ,2d., rebate at 6 per cent., in what time was the debt pay-
able ? ^ ^
315,6175 which being continually divided, those
Ans. =1,26247 divisions will be equal to 4=the num-
250 ber of years.
8. A person receives £245 now, for a debt of £344 : 14 : 9
1,92 qrs., rebate being made at 5 per cent. I demand in what
time the debt was payable ? Ans, 1 years.
9. There is a debt of £441 : 17 : 3 1,92 qrs. due at a certain
time to come, but per cent, being allowed to the debtor for the
present payment of £350, I desire to know in what time the sum
should have been paid without any rebate ?
Ans. 4 years.
IV. When S P T are giv^n to find R.
s which being extracted by the rules of extraction,
Rule. — =r* (the time given in the question showing the pow-
p er,) will be equal to R.
TU
EXAMPLES.
10. A debt of £315 : 12 : 4,2d. is due 4 years hence, but it is
agreed to take £250 now, what is the rato per cent, that the re-
bate is made at ?
315,6175 4
Ans. = 1,26247 : ^1)26247=1,06 = 6 per cent.
250
11. The present worth of £344 : 14 : 9 1,92 qr..., payable 7
years hence, is £245, at what rate per cent, is the rebate m'ade ?
Ans. 5 per cent.
12. There is a debt of £441 : 17 : 3 1,92 qrs., payable in 4
years time, but it is agreed to take £350 present payment. I de-
sire to know at what rate per cent, the rebate is made at ?
Ans. 6 per cent.
Cross M
1. Und
tions of tl
2. Mult
lowest) bj
retipective
each lovv€i
3. In tl
in the m
more to t]
4. Woi
plio.r, setti
of those i
169
, of £315 :
debt pay-
idcd, those
=the num-
44 : 14 : 9
id in what
7 years.
it a certain
>tor for liiG
le the sum
4 years.
extraction,
g the pow-
e, but it is
lat the re^
ler cent.
payable 1
made?
er cent.
able in 4
nt. I de-
er cent.
THE
TUTOR'S ASSISTANT.
PART IV.
DUODECIMALS,
OR, WHAT 13 GENERALLY CALLED
Cross Multiplication, and Squaring of Dimensions hy Arti-
ficers and Workmen,
RULE FOB MULTIPLYING DUODECIMALLY.
1. Under the multiplicand write the corresponding denomina-
tions of the multiplier.
2. Multiply each term in the multiplicand (beginning at the
lowest) by the feet in the multiplier ; write each result under its
retipective term, observing to carry an unit for every 12, from
each lower denomination to its next superior.
3. In the same manner multiply the multiplicand by the primes
in the multiplier, and write the result of each term one place
more to the rio-ht hand of those in the multiplicand.
4. Work in the same manner with the seconds in the multi-
plier, setting the result of each term two pUices to the right hand
of those iuTihe multiplicand, and so on for thirds, fourths, &c.
* I <*J
lib
H-'
170
DUODECIMALS
EXAMPLES
f. in. f. in.
1. Multiply 7 . 9 by 3 . 6.
Cross Multiplication Practice.
7 9 6^ 7 . 9
3 '^6
3 . 6
Duodecimals.
7 .9
2 . 6
Decimals.
7,75
3,5
21.0.0=7X3
2.3.0=9X3
3.6.0 = 7X6
0.4.6=9X6
23 . 3
3 . 10 . 6
27 . 1.6
23 . 3— X3
3.10.6X6
27 . 1.6
3875
2325
27,125
27.1.6
2. Multiply
3. Multiply
4. Multiply
5. Multiply
6. Multiply
7. Multiply
8. Multiply
9. Multiply
10. Multiply
11. Multiply
12. Multiply
13. Multiply
14. Multiply
15. Multiply
16. Multiply
17. Multiply
18. Multiply
f.in.
8.5
9.8
8.1
7.6
4,7
7.5.9"
10.4.5
75.7
97.8
57.9
75.9
87.5
179.3
259.2
257.9
311.4.7
321.7.3
by
by
by
by
by
by
by
by
by
by
by
by
by
by
by
by
by
f. in
4. 7
7. 6
3. 5
5. 9
3.10
3. 5.3"
8.6
8
9
5
7
8
7.
9.
8.
9.
17.
35.
38.10
48.11
39.11
36. 7.5
9. 3.6
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
f.
38.
72.
27.
43.
17.
25.
79.11.
730. 7.
854. 7.
543. 9.
1331.11.
in.pts.
6.11
6
7. 5
1. 6
6.10,,,,
8. 6.2.3
0.6.6
8
9
3
4
6
3117.10.
6960.10.
12677. 6.10
102S8. 6. 3
11402. 2. 4.11.1
2988. 2.10.4.6
THE APPLICATIO.NT.
Artificers' work is computed by diftereut measures, viz : —
1. Glazing-, and masons' fiat woik, by the foot.
2. Painting, plastering, paving, <fec. by the yard.
3. Partitioning, flooring, roofing, tiling, drc, by the squ;are of
100 feet.
4. Brick work, &c. by the rod of 16^ feet, whose square is
272i feet.
Measurl
ill
10. Tlu
heiu'lit of
and the tl
inches ; w]
Duodecirr
7 . 10 t
6.81
5.4a
19.
10
3 =
59 .
6
3.
178 .
6
54 .
6 .
I
I
%
233 . .
20. Wl:
feet 10 inc
21. Th(
6 inches \
to at 7^d.
22. Wl
7 inches, a
Measun
Note. ]
ber of squ
Decimals.
7,75
3,5
3875
2325
27,125
in.pts.
6.11
C
7. 5
1. 6
8. 6.2.3
11. 0.6.6
7. 8
7.
9. 9
[1. 3
10. 4
10. 6
6.10
6. 3
2. 4.11.1
2.10.4.6
DUODECIMALS.
171
Measuring hj the Foot Square, as Glaziers' and Mason''s' Flat
Work.
EXAMPLES.
10. There is a house with ^ tier of windows, 3 in a tier — tho
hei.u'lit of the first tier 7 feet 10 inches, the second 6 feet 8 inches,
and the third 5 feet 4 inches, the breadtli of each' is 3 feet 11
inches; what will the glazing come to, at 14d. per foot?
Duodecimals.
7.10 the
6 . 8 heights
5 . 4 added.
feet. in. pts.
233 . . 6 at 14d. per ft.
2d.=A 233
19 . 10
3= windows in a tier.
= Is.
38 . 10 == 2d.
. 0^ = 6 parts.
59 . 6
3 . 11 Id breadth.
210)2711 . 10^
£13 . 11 . lOi Ans.
z: —
squrire of
t square is
178 . 6
54 . 6 . o
233 . 0.6
20. What is the worth of 8 squares of glass, each measuring 4
feet 10 inches long, and 2 feet 11 inches broad, at 4^d per toot?
Ans. £1 : 18 : 9.
21. There are 8 windows to be glazed, each measures 1 foot
6 inches wide, and 3 feet in height, how much will they come
to at 7^d. per foot ?
Ans. £1:3:3.
22. What is the price of a marble slab, whose length is 5 feet
7 inches, and the breadth 1 foot 1 inches, at 6s. per fijot ?
Alls. £3:1: 6.
Measuring hy the Yard Square, as Paviers, Painters, Plas-
terers, and Joiners.
Note. Divide the square feet by 9, and it will give the num-
ber of square yards.
-i'
r.
f
it
P2
f
172
DUODECIMALS.
EXAMPLES.
23. A room is to be ceiled, whose length is 74 feet 9 inches,
and width 11 feet 6 inches; what will it come to at 3s. lO^d. per
yard? Ans. £18 : 10 : 1.
24. What will the paving of a court-yard come to at 4§d. per
yard, the length being 58 feet 6 inches, and breadth 54 feet 9
inches ?
Ans. £1:0: 10.
25. A room was painted 97 feet 8 inches about, and 9 feet 10
inches high, what does it come to at 2s. 8^d. per yard ?
Ans. £14 : 11 : 1^.
20. What is the content of a piece of wainscoting in yards
square, that is 8 feet 3 inches long, and 6 feet 6 inches broad,
and what will it come to at 6s. 7^d. per yard ?
Ans. Contents, yards 5.8.7.6 ; comes to £l : 19 : 5.
27. Wliat will the paving of a court-yard come to at 3s. 2d,
per yard, if the length be 27 feet 10 inches, and the breadth 14
feet 9 inches ?
Ans. £7:4:5.
28. A person has paved a court-yard 42 feet 9 inclies in front,
and 68 feet 6 inches in depth, and in this he laid a foot-way the
depth of the court, of 5 feet 6 inches in breadth ; the foot-way is
laid with Purbeck stone, at 3s. 6d. per yard, and the rest with
pebbles, at 3s. per yard ; what will the whole come to ?
Ans. £49 : 17.
29. What will the plastering of a ceiling, at lOd. per yard,
come to, supposing the length 21 feet 8 inches, and the breadth
14 feet 10 inches?
Ans. £1:9:9.
30. What will the wainscoting of a room come to at 6s. per
square yard, supposing the height of the room (takini? in the cor-
nice and moulding) is 12 feet 6 inches, and the conipass 83 feet 8
inches, the three window shutters each 7 feet 8 inches by 3 feet
6 inchoB, and the door 7 feet by 3 feet 6 inches? The shutters
ing worked on both sides, are reckoned work and
Measun
31. In
height of
32. If i
be floored
8 inches, 1
siires are,
5 feet 4 ii
each, and
hole for t
will the w
33. If
length, an
pitch, whi
Note.
the flat ai
of the ro(
t. e. when
the roof ;
one side t
34. W
the lengt
ou the ilia
half work.
Ans. £36 : 12 : 2^.
Note.
brick and
less, it m
DUODECIMALS.
173
Measuring hy the Square of 100 feet, as Flooring^ Partition-
infff Roofing, Tiling, <&c.
EXAMPLES
31. In 173 feet 10 inches in length, and IJ ie't 1 inches in
height of partitioning, how many squares ?
Ans. 18 squares, 39 feet £ 'iiolies, 10 p.
32. If a house of three stories, besides the ground floor, was to
be floored at £6 : 10 per square, and the house niea,sured 20 feet
8 inches, by 16 feet 9 inclies ; there are 1 tire-places, whose mea-
sures jire, two of 6 feet by 4 feet 6 inches each, two of 6 feet by
5 feet 4 inches each, and two of 5 feet 8 inches by 4 feet 8 inches
each, and the seventh of 5 feet 2 inches by 4 feet, and the well
hole for the stairs is 10 feet 6 inches by 8 feet 9 inches: what
will the whole come to ?
Ans. £53 : 13 : 3^.
33. If a house measures within the walls 52 feet 8 inches in
leni^th, and 30 feet G inches in breadth, and the roof be of a true
pitch, what will it come to roofing at 10s. 6d. per square ?
^ Ans. £12: 12 : Hi
Note. In tiling, roofing, and slating, it is customary to reckon
the flat and half of the building within the wall, to be the meiisure
of the roof of that building, when the said roof is of a true i)itch,
i. e. when the rafters are ^ of the breadth of the building ; but if
the roof is more or less than the true pitch, they measure from
one side to the other with a rod or string.
34. What will the tiling of a barn cost, at 25s. 6d. per square ;
the length being 43 feet 10 inches, and breadth 27 feet 5 inches
on the flat, the eave boards projecting 16 inches on each side ?
Ans. £24 : 9 : 5i
■■■'H ]
1 (
i^p-
i^
Measuring hy the Rod.
Note. Bricklayers always value their work at the rate of a
brick and a half thick ; and if the thickness of the wall is more or
less, it must be reduced to that thickness by this.
P3
174
DUODECIMALS.
Rule. Multiply the area of the wall by the number of half
bricks in the thickness of the wall; the product divided by 3,
gives the area.
EXAMPLES.
35. If the area of a v;all be 4085 feet, and the thickness two
bricks and a halt] how many rods doth it contain ?
Ans. 25 rods.
^ 36. If a garden wall be 254 feet round, and 12 feet 1 inches
high, and 3 bricks thick how many rods doth it contain ?
Ans. 23 rods, 136 feet 1 in.
6>
37. How many squared rods are there in a wall 62^ feet lon^
li feet 8 inches high, and 2^ bricks thick ?
Ans. 5 rods, 166 feet 6 in.
38. If the side walls of a house be 28 feet 10 inches in length,
and the height of the roof from the ground 55 feet 8 inches, and
the gable (or triangular part at top) to rise 42 course of bricks,
reckoning 4 course to a foot. Now, 20 feet high is 2^ bricks
thick, 20 feet more at two bricks thick, 15 feet S inches more at
H brick thick, and the gable at 1 brick thick; what will the
whole work come to at £5 16s. per rod?
Ans. £48 : 12 : 7.
Multiplying several figures bg several, and the product to be
produced in one line only.
Rule. Multiply the units of the multiplicand by the units of
the multiplier, setting down the units of the product, and carry the
tens; next multiply the lens in the multiplicand by the unit,s of
the multiplier, to which add the product of the units of the miilti
plicand multiplied by the tens in the multij)lier, and the tens car
riod ; then multiply the hundreds in the multiplicand by the uni(:>
of the multiplier, adding the jjroduct of the tens in the multi})licati(l
multii)li"d by the tens in the multijjlier, and the units of the iniilti-
plicand by the hundreds in the multiplier; and so proceed till you
have multiplied the multiplicand all through, by every figure of
the multiplier.
First, 4)
4 X 2, and
Thirdly, 2;
ry 3. Fou
set down 7
-[-4X5 + ^
+ 5X44
5. Seven il
i'ul carry
1 and carr^
'.ijuied by
:md the wo
iber of half
vided by 3,
lickness two
ds.
3et 7 inches
in?
36 feet 1 in.
2 2 feet long,
06 feet 6 in.
s in length,
inches, and
?e of bricks,
s 2^ bricks
les more at
lat will the
12 : 7.
DUODECIMALS.
EXAMPLES.
175
Multiply 35234
by . . . . . . 52424
Common way,
35234
62424
Product, 1847107216
140936
70468
140936
70468
176170
1847107216
EXPLANATIONS.
First, 4X4=10, that is 6 and carry one. Secondly, 3X4-f
4X2, and 1 that is carried, is 21 — set down 1 and carry 2
Thirdly, 2X44-3X2 + 4X4-|-2 cnrried--=32, that is 2 and car-
ry 3. Fourthly, 5 X 4-f 2 X 2 -f 3 X 4+ 4 X 2+3 carried = 47,
set down 7 and carry 4. Fifthly, 3X4-1-5X2 + 2 X 4 +3X2
MX 5 + 4 carried =60, set down and carry 6. Sixthly, 3X2
+-5X4 + 2X2+3X5+6 carried = 51, set down 1 and carry
5. Sevenihly, 3X4 + 5X2 + 2X5 + 5 carried=37, that is 7
md carry 3. Eighthly, 3X2+5X5+3 carried=34, set down
I and carry 3. Lastly, 3X5 + 3 carried =18, which being mul-
iplied by the last figure in the multiplier, set the whole down,
and the work is finished.
luct to be t
ho units of
id carry the
ho units of
f the multi-
le tens car
3y the units
nultiplicand
f the multi-
eed till you
y figure of
176
THE
TUTOR'S ASSISTANT
PART V.
A COLLKCTION OF QUESTIONS.
1. What, is the vahie of 14 barrels of soap, at 4|d. per lb , each
barrel coiitainiiii^ 254 lb. ? Ans. jCOG : 13 : 6.
2. A and B trade too-ether ; A puts in £320 for 5 months, B
£400 for 3 months, and they ijained £100; what must each man
receive ? Jns. A £o3 : 13 : 9|f a, and B £4G : 6 : 2/^^.
3. How many yards of cloth, at 17s. Gd. }»er yard, can 1 have
for 13 cvvt. 2 qrs. of wool, at 14d. per lb. ?
Ans. 100 yards, 3} qrs.
4. If I buy 1000 ells of Flemish linen for £90, at what may I
sell it per ell in London, to gain £10 l)y the whole ?
Am, 3s. 4d. per ell.
5. A lijus 048 yards of cloth, at 14s. per yard, ready money,
but in barter will have 16s.; B h^us wine at £42 per tun, ready
money : the question is, how much wine must be ^iven for tlio
cloth, and what is the price of a tun of wine in barter ?
Ans. £48 the tun, and 10 tun, 3 hhds. 12f gals, of
wine must be ffiven for tlio clo'
6. A jeweller sold jewels to the value of j£12j j, for which Iie^
received in part 876 French pistoles, at 16s. 6d. each; what sum J
remains unpaid ? o-> # Ans. £477 : G.
7. An oilman bought 417 cvvt 1 qr. 15 lb., gross weight, of
train oil, tare 20 lb, per 112 lb., how many neat gallons H'ere
there, allowing 1^ lb. to a gallon. ? Ans. 5120 gallons.
8. If I buy a yard of cloth for 14s. 6d., and sell it for 10^. 9d|
what do I gain per cent. ? Ans. £15 : 10 : 4f^\.
9. Bought 27 baiys of mnijer, each weischinir sjrross 843 11»., tare
.*t If lb. i»er bag, tret 4 lb. per 104 lb., what do they come to
at SAd. UQt lb.? Ans. £70 : 10 : liV
10. Iff
cost?
11, Iff
12. A jE
and at the
13. A h
times 1 12 I
dilference h
14. A cf
wliich the
divided am
15 At \
in 7^ years
16. A h
£13 a pie
tliey intercl
17. A m
viz. A, B, <
and as IT
15. £10
iicr, that il
must each i
19. A pi
inches broa<
20. If 3
months, bui
'Hi u must c
2\. The
of tlitir jiro^
22. A 1)1
oxen at £1
each, and o
buy?
23. Wk
A COLLECTION OF QUESTIONS.
n7
10. Iff of an ounce cost | of a sliillin"^, what will 4 of a lb.
cost?
An.^. 17s. 6d.
NT
per 11) , each
I : 1.3 : 6.
) months, B
st each man
" • '^ 2 i> 8 •
, can 1 have
,s, 31 qrs.
what may I
(1. per ell.
ady money,
r tun, ready
iven for the
12| gals, of!
■or which he]
; what sum]
£477 : G.
i weight, of!
gallons H'erel
gallons.
for 1 iU. 9d%j
: 4t^x'
84 3 11),, tarej
u\y come toj
. i .-^ . t 3
11. If f of a gallon cost f of a pound, what will | of a tun cost ?
Ans. jElOo.
12. A gentleman spends one day with another, £] : 7 : 10|,
and at the year's end layeth up je340, what is his yearly income ?
Ans. £848 : 14 : 4^.
13. A has 13 fother of lead to send abroad, each being 19^
times 1 12 lb. 13 has 39 ctisks of tin, each 3SS lb., how many ounces
diliercnce is there in the weight of these commodities ?
Ans. 212160 oz.
14. A captain and 160 -ailors took a prize worth £1360, of
which the captain had } for his share, and the rest was equally
divided among the sailors, what was each man's part ?
Aus. The captain had £272, and each sailor £6 : 16.
15. At what rate per cent, will £956 amount to £1314 : 10,
in 7^ years, at simple interest ? Ans. 5 per cent.
16. A hath 24 cows, worth 72s. each, and B 7 horses, worth
£13 a piece, how much Avill make good the difference, in case
they intercliange their said drove of cattle ? Ans. £4 : 12.
17. A man dies and leaves £120 to be given to three |)ersons,
viz. A, B, C ; to A a share unknown ; B twice as much as A,
and C as much as A aiid B ; what was the share of each i
Ans. A £20, B £40, and C £60.
IS. £1000 is to be divided among three men, in such a man-
ner, that if A has £3, B shall have £d, and C £S ; how much
must each man have ?
Am. A£] ~ : 10, B ^2312 : 10, and C £500.
19. A piece of wainscot is S feet 6^ inches long, and 2 feet 9f
indies broad, Avhat is the superficial content ?
Ans. 24 feet : 3" : 4 : 6.
20. If 360 men be in garrison, and have provisions for C
months, but hearing of no relief at the end of 5 rnonths, how many
men must depart tliat the provisions may last so yiuv^'k the longer?
Ans. 2SS men.
2\. The less of 2 numbers is 187, their difference 34, the square
of tiitir j>roduct is required ? jins. 1707920929.
22. A l)utcher send* his man with iE2l6 to v fair to buy cattle;
oxen at Jg 11, cows at 40s., colts at £1 : 5, and hogs at £l : 15
each, and of each a like number, how many of eacli sort did he
buy? Ans. 13 of each sort, and £8 over.
23. What number added to 11^ will produce 363 3| ?
Ans. 24f}-|.
4
:l*
i=i
178
A COLLECTION OF QUESTIONS.
24. AVluit number multiplied by -f will produce llyT-
38. If
Ans. 2644. J 100 more
for 2 sliilli
25. Wliat is the value of 179 hogsheads of tobacco, each weigh-
ing 13 cwt, at £2 : 7 : 1 per cwt. ? Ans. £o478 : 2 : 1 1?
20. ^fy factor sends me word he has bought goods to the va-
lue of £500 : 13 : 6, upon my account, what will his coniinissjon
come to at 3^ per cent. ? Am. £17 : 10 : 5 2 qrs. j%\.
27. If ^ of 6 be three, what will ^ of 20 be ? Ans. 7^
28. What is the decimal of 3 qrs. 14 lb. of a cwt. ?
Ans. ,875
29. ITow many lb. of sugar at 4^d. per lb. must be given in
barter for .GO gross of inkle at 8s. 8d. per gross?
Ans. 138Gf lb.
30. If I buy yarn for 9d. the lb. and sell it again for 13|(1. per
lb., what is the gain per cent. ? Ans. £oO.
31. A tobacconist would mix 20 lb. of tobacco at 9d. per lb.
with GO lb. at 12d. per lb., 40 lb. at 18(1. per lb., and with 12 lb.
at 2s. per lb., what is a pound of this mixture worth ?
Ans. Is. 2^d. j\.
32. What is the difference between twice eight and twenty,
and twice twenty-eight ; as also, between twice five and fifty, and
twice fifty-five ? Ans. 20 and 50.
33. Whereas a noble and a mark just 15 yards did buy ; how
many ells of the same cloth for £oO had I ? Ans. GOo"^ ells.
31. A broker bought for his principal, in the year 1720, ^£400
capital stock in the South-Sea, at £G50 per cent., and sold it
again when it was worth but £130 per cent.; how much was
lost in the whole ? Ans. £2080.
35. C hath candles at 6s. per dozen, ready money, but in bar-
ter will have Gs. 6d. per dozen ; D hath cotton at 9d. per lb. loadyj
money. I demand what price the cotton must be at in barter;
also, how much cotton must be bartered for 100 doz. of cari<lles?
Ans. The cotton at 9(1. 3 qrs. per lb,, and 7 cwt. qrs.
16 lb. of cotton must bo given for 100 doz. candles.
86. If a clerk's salary be ^273 a year, what is that per day ?
Alls, 4s.
37. B hath an estate of £53 per annum, and payeth 5«. lOd.
to the mhHidy, what must C pay whose estate is worth £100 per
a"»"™^ An^, lis. Od. ^3.
A COLLECTIOX OF QUESTIONS.
179
38. If I buy 100 yards of riband at 3 yards for a shilling, and
100 inoro at 2 yards for a shilling, and soil it at the rate of 5 yards
for 2 shillings, whether do I gain or lose, and how much ?
Ans. Lose 3s. 4d.
39. What number is that, from which if you take |, the re-
mainder will be ^ ? Ans. |f .
40. A farmer is willing to make a mixture of rye at 4s, a bushel,
I barley at 3s., and oats at 23. ; how much must he take of each to
I sell it at 2s. 6d. the bushel ?
Ans. 6 of rye, 6 of barley, and 24 of oats.
41. If f of a ship be worth £3740, what is the worth of the
whole ? Ans. £9973 : 6 : 8.
42. Bought a cask of wine for £62 : 8, how many gallons were
ill tlie same, when a gallon was valued at 5s. 4d. ?
Ans. 234.
43. A merry young follow in a short time got the better of | of
his fortune ; by advice of his friends he gave £2200 for an ex-
'^mpL's place in the guards ; his profusion continu^id till he had no
move then 380 guineas left, which he found, by computation, was
/j part of his money after th mmission was bought ; pray M'hat
wius his fortune at first ? Ans-. £10,450.
44. Four men have a sum of money to be divided amongst
theui in such a manner, that the first shall have -J of it, the second
I the third ^, and the fourth the remainder, which i- £28, what
lis the sum? Ans. £112.
45. What is the amount of £1000 for 5| years, at 4| per cent.
[jiniple interest? Ans. £12G1 : 5.
40. Sold goods amounting to the value of £700 at two 4 months,
I what is the present worth, at 5 per cent. sim]-ile interest ?
Ans. £682 : 19 : 5^ jWt-
47. A room 30 feet long, and 18 feet wide, is to be covered with
I painted cloth, liow many yards of f wide will cover it?
Ans. 80 vnrds.
48. Betty told her brother George, that though her fortune, on
her marriage, took £19,312 out of her tamily, it was but | of two
I years' rent, Heaven be praised ! of his yearly income ; i>ray what
was that? Ans, £16,093 : . 8 a yci...
49. A gentleman liaving 50s. to pay among liis labourers for (
day's w<^i"k, would gi\c lo every boy 6d., to every woman 8d
and to every man IGd, ; the num>)er of boys, women, and inei
was the same. I demand tjio number of each ?
180
A COLLECTION OF CiUESTIONS.
^ 60. A stone that measures 4 feet 6 inches long, 2 feet 9 inches
broad, and 3 feet 4 inches deep, how many soHd feet doth it con-
tain ? Ans. 41 feet 3 incites.
51. What does the whole pay of a man-of-war's crew, of 640
sailore, amount to for 32 months' service, each man's pay beino
22s. 6d. per month ? Ans. £23,040. °
62. A traveller would change 500 French crowns, at 4s. 6d.
per crown, into sterh'ig money, but he must pay a halfpenny per
crown for change ; how much must he receive ?
Ans. £111 : 9 :2.
53. B and C traded together, and gained £100 ; B put in £640,
C put in so much that he might receive £60 of the gain. I de-
mand how much C put in ? Ans. £960.
54. Of what principal sum did £20 interest arise in one year,
at the rate of 5 per cent, per annum ? Ans. £400.
55. In 672 Spanish guilders of 2s. each, how many French pis-
toles, at I7s. 6d. per piece? Ans. 76|f.
56. From 7 cheeses, each weighing 1 cwt. 2 qi-s. 5 lb., how
many allowances for seamen may be cut, each weighing 5 oz. 7
drams ? ,; Ans. 3563 ^f
57. If 48 taken from 120 leaves 72, and 72 taken from 91
leaves 19, and 7 taken from thence leaves 12, what number is
that, out of which wh^ you have taken 48, 72, 19, and 7, leaves
1^ ? Ans. 158.
68. A farmer ignorant of numbers, ordered £500 to be dividal
among his five sons, thus :— Give A, says he, ^, B i, C i, D i,
and E | part ; divide this equitably among them, according to
their father's intention.
^ Ans. A £l52f||, B £114iii, C £91^^
D £76ii|, E £65if f .
59 When first the marriage knot was tied
Between my wife and me,
My age did hers as far exceed,
As three times three does three ;
But when ten years, and half ten years,
We man and wife had been,
Her age came then as near to mine,
As eight is to sixteen.
Ques. What was each of our ages when wo were married ?
A71S. 45 years the man, 15 the woman*
I"
1. On j
should be
2. The
from the
is the gre?
3. Afte
33, 58 ; tl
tracted; v
4. Of t
third is s
three nun:
5. The
which is t
6. A si
of age ; v
older ?
7. If 2'
is 21, thei
8. A ir
father's a^
9. Aft(
number tl
10. Th
18 be tal5
will be eq
11. Th
ence and
12. Tl
1 50 from
Is the gre
13. Tl
one and
greater ?
14. W
greatest 1
A COLLECTION OF QUESTIONS.
181
eet 9 inches
cloth it con-
3 inclies.
rew, of 640
8 pay being
£23,040.
s, at 4s. 6d,
ilfpenny per
1:9:2.
mt in £640, \
rmn. I de-
ns. £960.
n one year,,
ns. £400.
French pis-
ns.76^.
5 lb., howj
ing 5 oz. 7
s. 3563if
en from 91
i number is I
nd 7, leaves j
4«s. 158.
) be dividend I
:, Ci,Di,l
ccording to.
irried !
3 womanu
SUPPLEMENTAL QUESTIONS.
1. On goods that cost 412s. there was 25s. profit; how much
should be sold to gain as much more ? Ans. 462s.
2. The less of two numbers is 17, and after having subtracted 23
from the greater, the remainder is eight more than the less ; what
is the greater ? Ans. 4S.
3. After having successively subtracted from a number, 17, 29,
33, 58 ; the remainder is 91 more than the total of the sums sub-
tracted ; what is that number ? Ans. 365.
4. Of three numbers, the fii-st is 215, the second is 519, and the
third is as much as the other two; what is the sum of the
three numbere 3 Ans. 1468.
5. The gmater of two numbers is 56 and the difference is 37 ',
which is the less? Ans. 19.
6. A sister is 8 years younger than her brother who is 27 years
of age ; what will her age be when her brother will be 7 yeara
older ? Ans. 26 years.
7. If 27 be added to the sum of two numbers, the less of which
is 21, their total will be 147 ; which is the greater ? Ans. 99.
8. A man 47 years of age has a son 9 years old ; what will the
father's age be when the son will be the father's present age ?
Ans. 85.
9. After having added successively 17, 29, 33, and 54 to a
number the total is 214 ; what is that number? Ans. 81.
10. The age of the ffither and son together is GO yeai-s : and if
18 be taken from the father's age and added to the son's their age
will be equal ; what is the age of each ?
Ans. 48 and 12.
11. The greater of two numbers is four more than their differ-
ence and their sum is 27 ; determine the numbers?
Ans. 23 and 4.
12. The smaller of two numbers is 160, and after subtracting
150 from one and 48 from the other, the remainder is 244 ; what
is the greater ? Ans. 282.
13. The less of two numbers is 37, and after taking 72 from
one and adding 34 to the other their total is 145; what is tho
greater? Ans. 146.
14. What are the three numbers whose sum is 3291 and th«
greatest 1126 exceeds the smallest hy 79 ?
Ans. The smallest 1,046, the mean 1,120.
P',s
182
A COLLECTION OP QUESTIOIfg.
• , A-t'^'' (dividing a certain sum between 26 persons each re.
C(Mve(l 20 /s. ; what was the sum ? 'aus. 6,682s
16. hroMi a ceilaui f'^uni 152 persons took 8l7 each, and thert
icinainea .^13 ; wh.-it was the sum ? Jns. $'2597
• / ',* ,^^ 1'2^ i' ^^"^ nmnher that beinjr augmented by 56 and di-
v.d. d by 55,the quotient will be 2,854 ? A7is. 156 914
18. What IS the number tlint being divided by 27, 'mves i
quotient equal to the product of 1,091 by 3 ? Am 88 371 '
10. By selling 120 yards of cloth for 3,600s. there was 5s,
p.oiit per yard ; what was the buying price ? Ans. 3,000s
20 [ boucrht 150 yards of cloth for 3,750s. and sold them for
o , Wr'"'^ ' ''^'''^ '^''^ ^ 8^'"" V ^''^ ^'»''?'"n ? Am. 000s
o-n^'.ni i.'"f-''''"''.^ ^'"^ obtained, it; after having multiplied
2o0,o40 by 10 this product should be repeated 2,458 limes?
.,o A 1 «. "'^'^*- 6,158,273,200.
22 A man has 83000 revenue and spends ^5 per day; what
will he hiy up at the end of 1 years ? Am. $1 1,750
23. A class is composed of a certain number of schol'ars • * if
there were 8 more the number would be augmented I ; how many
scnolars were there? * '^^^^ 4^ ^
24 'i'he quarter of the 54th part of a number is 5,454*; wjiat
IS tktt number? Jn.. 1,178,064.
20 On the sale of 150 yards of cloth for 29s. per yard, there
were 600s. protit ; what was the buying price ? Am. 3,750s.
10. What number being divided by 4 gives a quotient such
that, atter subtracting 9, the remainder will be 20 ? Am. 116
27. How many revolutions will the second-hand of a clock
make in a year, the year being 365d. 5h. 48min. ?
oo A , . ^^^*- 525,948 rev.
28. A number is such that in-taking 9 from its fourth part, the
remaindor is 91 ; what is the number? Am. 400.
29. What is the number whose 17th part augmented 54,' is
equal to 602? Am. 9,316.
30. What number added to the product of 185 by 27, gives
115 times 155 for total? Am. 12. SSO.
31. The h , , f two numbers is 187, and their difference is 34
required the »(, uare of their product ? Am. 1 ,707,920,929.
32. AVhat number must be added to the square of 125 to pro-
duce 20,000 for total ? Am. 4 375.
33. The sum of two nurabei-s is 360, and the less is 144 ; re-
quired the result of their product by the square of their difference?
Ans. 161.243.136.
J — J — . .
84. Two
their diffen
ence, their
35. The
double the
what is the
36. Det
power of i:
37. Wh
is 20 and t
38. The
greater ; re
39. Wh
156,970 foi
40. If 2
will be 17£
41. By
42. If y
1,548 ; reo
43. The
by the less,
the two nu
44. The
154; what
45. Req
46. The
150 from c
the two nu
47. A s
his age ; w
48. A f<
tlieir ages
49. 1'he
the son's j
father's; w
50. Fin.
of the othe
ons each re«
y. 6,682s.
1, and thert
s. $'2597.
56 and di-
156,914.
27, gives a
. 88,371.
;re was 5s,
?. 3,000s.
Id tliem for
n,s\ COOs.
multiplied
imes ?
273,200.
day; what
$11,750.
cholars ; if
how many
Ans^ 40.
454 ; what
178,064.
yard, there
3,750s.
)tient such
ns. 116.
3f a clock
948 rev.
h part, the
ns, 400.
ted 54, is
f. 9,316.
/ 27, gives
12.830.
ince is 34
'20,929.
25 to pro-
. 4,375.
s 1 44 ; re-
Jiflfercnce ?
43.136.
\\
A COLLECTION OF QUESTIONS.
183
84. Two numbers are such, that the greater is 37 times 45, and
their difference 19 times 4; required the two numbers, their differ-
ence, their sum and their product ?
ins. The two numbers are 1,665 and 1,5R9;
difi'. 76 ; sum 3,254 ; prod. 2,645,685.
35. The sums of two numbers is 4,517, and by adding 27 to
double the square of 25 you will produce one of the numbers ;
what is the other ? Ans. 3,240.
36. Determine the difference that exists between the fourth
power of 13 and the triple square of 49 ? Ans. 21,358.
37. What is the sum of the cubes of two numbers, whose sura
is 20 and the lest number 9 ? Ans. 2,060.
38. There are two numbers, one is 39 and the other is 27 times
greater ; required their sum and the square of their difference ?
Ans. Sum 1,092, square of their diff. 1,028,196.
39. What is the number that, being multiplied by 55, gives
156,970 for product? Ans. 2,854.
40. If 256 be multipled by an unknown number, the product
will be 1792. ^ Ans. 7.
41. By what number must 54 be multiplied to give 9,990?
Ans. 185.
42. If you multiply a certain number by 7, you will augment it
1,548; required the number? Ans. 258.
43. The sum of two numbers is 13, and their product, divided
. by the less, is equal to the quarter of the same product; required
I the two numbers ? Ans. 9 and 4.
44. The sum of two numbere is 2,45S, and their difference is
154; what are the number*? Ans. 1,152 and 1,306.
45. Required two numbers whose difference is 7, and sum 33 ?
Ans. 20 and 13.
46. The difference between two numbers is 100, and after taking
I 150 from one and 48 from the other, there remains 244 ; required
the two numbers? Ans. 271 and 171.
47. A son is 45 years younger than his father who is four times
his age ; what is the age of each ? Ans. 60 and 15.
48. A father is six times {is old as his son, and tlie sum of both
their ages is 91 ; required their ages? Ans. 78 and 13.
49. 1'he age of tbe father and son together is 80 years, and if
the son's ag»« was doubled, it would be 10 years more than his
father's ; what is each of tlieir ages ? Ans. 50 and 30.
50. Find two numbers whose sum is 108 ; and one the one-fifth
of the other? Ans. 90 and 18.
184
A COLLECTION OF QUESTIONS.
61. 54 years is the aofe of the father and son together; .nnd the
fiftther is 22 years older than the son ; what is the ago of each ?
Ans. 38 and 16.
62. Two numbers are such that by adding 150 to the less, they
are equal, and their sum is 2,400 ; what are the nuinl>ej*s ?
A71S. Greater 1,275, less 1,125.
53. The sum of two numbers is 2,588 and to mako them equal
add 1 7 8 to the less ; what are the numbers ?
Ans. 1,383 and 1,205.
54. The sum and difference of two numbers are 150 and 100;
what is their quotient ? Ans. 5.
55. If I had as many more half dollars as I iiave, after spend-
ing 18, 1 would still have 194; how many have I? Ayis. 106.
56. The sum of two numbers is 2,587, to make them equal sub-
tract 178 from the greater and add 17 to the less; what are the
nurnbci-s? Ans. 1,196 and 1,391.
57. The difference between two numbers is 10, and their quo-
tient is three; what are the numbers? Ans. 5 and 15.
58. Re(|uired to divide 60 into three parts, so that the first may
be 8 more than the second and 16 more than the third ?
Ans. 28, 20 and 12.
59. The divisor and dividend together make 180 and their
quotient is 11; determine the divisor and dividend ?
Ans. 105 and 15.
00. The product of two numbers is 120, and if you add 4 to
the 1g.ss, the product will be 168 ; what are the two numbers?
Ans. 12 and 10.
61. The quotient of two numbers is 18, and their sum 1,121;
find the numbers? Ans. 1,062 and 59.
02. Divide 250 into two such parts, that their quotient will be
31 ? Ans. 248 and 8.
63. The quotient of two numbers is 37 and their difference 684 ;
determine the numbers? Ans. 703 and 19.
64. Divide a number into two such parts that their ditferenco
be 240 and their quotient 31 ? Ans. 248 and 8.
65. With 1,350 shillings I paid 76 labourers who worked during
a week ; how many would I pay with 1,836 shillings. Ans. 102.
66. If I had |350 more ray stock would be tripled ; what do I
possess
Ans. $175.
67. The sum of two numbers is 4,545, and one of them is 4
times greater than the other ; what are the numbere ?
Ans. 3,636 and 900.
68. If y
5,939, the
the two nui
69. Divi
part of the
parts ?
70. Divi
first may b(
24 more tli
71. If I
more, I wo
72. If tl
divided by
73. Wii
give 2,731
74. The
the produc
bers ?
75. I dt
it by 12, a
76. Oi
their prodi
77. The
determine
78. Wh
as 456 by
79. A ]
scribes for
jicome; to ^
ment ?
80. The
second is c
81. TIh
their sum
82. Th(
their differ
83. Div
to the qui]
84. A <
in taking I
A COLLECTION OF QUESTIONS.
165
er ; and the
of each ?
3 and 16.
le less, thej
83 1,125.
them equal
id 1,205.
D and 100;
Ans. 5.
iftcr spend-
i7is. 106.
I equal siib-
vhat are the
id 1,891.
I their quo-
i and 15.
le first may
•
and 12.
' and their
1 and 15,
u add 4 to
mbers 'i
1 and 10.
um 1,121;
1 and 59.
ient ivill be
8 and 8.
■rence 684 ;
i and 19.
r ditferenco
8 and 8.
•ked during
Ins. 102.
what do I
IS. $175.
them Is 4
and 900.
68. Tf you divide by one another two numbers whoso sum is
5,939, the quotient will bo 12 and the remauider 1 1 ; what are
the two numbers? Aiis. 456 and 5,483.
69. Divide 100 into two parts in such sort that the iscventh
part of the sextuple of one of the parts may equal 24 ; what are the
pyrts 8 Ans. 28 and 72.
70. Divide the number 92 into 4 parts, in such sort that the
first may be 10 more than the second, 18 more than th.^ third, and
24 more than the fourth? Ans. 36, 26, 18, 12.
71. If [ had three times more money than 1 have, and $245
more, I would have $2,045 ; what have 1? Ans. $450.
72. If the money 1 have was multiplied by 8 and the jtroduct
divided by 7, I would have $24. Ans. ^21.
73. What number being added to the ninth part of 2,457 would
give 2,731 for totol ? ^n-^- 2,458.
74. The product of two numbers is 144, and ^^^e sixth part of
the product is equal to three times the less ; what are the 2 num-
^rs ? ^^- ^8 and 8.
75. I doubled a number and divided it by 4, then I multiplied
it bv 12, and the third of the result was 48 ; what is the number?
^ Ans. 24.
76. One of the factors of a number is 37, and 5 times
their product is 10,730 ; what is the other? Ans. 58.
77. The sum of two numbei-s is 374, and their quotient is 21 ;
determine the numbers ? Ans. 357 and 1 7.
78. What number multiplied by 12 will give the same product
as 456 by 15? ^^^•'^- ^'^^•
79. A person having 445 shillings per month to si>end, sub-
scribes for 3,150 shillings in effects, that he must pay out of his m
icome ; to what must he reduce his expenses to fulfil his engage-
n^ei^t? -^^*- ^ shillings per day.
80. The total of three numbers is 131, the third is 89, aiid tha
second is quintuple the first; what are the numbers ?
Ans. 7 and 35.
81. The less of two numbers is 7 more than their ditfcivnce, and
their sum is 41 ; what are the numbers ? Ans. 16 and 25.
82. The less of two nun.Oers is 12, and by tripling their sum,
their ditferenco is 51 ; what is the greater? Ans. 29.
83. Divide 20 into two parts in such sort that one part added
to the quintuple of the other will make 84 ? Ans. 1 and 4.
84. A certain person wishing to buy some oranges, finds that
in takino" 24 he would have 7^(3. over, and in taking 30 he would
i ■•
H'.
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IMAGE EVALUATION
TEST TARGET (t4il-2)
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Photographic
Sciences
Corporation
23 WEST MAIN STREET
WEBSTER, NY. 14580
(716) 873-4503
•s?
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186
A COLLECTION OP QVESTTONB.
want lO^d. more; required the price of the oranges and the monei
tJie person had ? • ^
Ans. 8d. each orange ; 6s. 1^3. the money the person had
8o. The sum of two numbers is 450 and the loss is equal to
their difference; what are they? Jns. 150 and 300.
86. A fiither has six sons, there are 4 years difference between
their ages, and the eldest is three times the age of the youno^est
what is the age of each ? Ans. 14, 18, 22 and 26 yeare.
87. Two gsmiblers play a game : the first has 54 shillintrs, the
aecond 41. After the game, the first has four times as much money
as his comrade ; how much did the second loso ?
oo ^Ttri-. , . 1 ^^^- 22 shillings.
88. Which IS the greater of two numbers of which the less is
three, and the sum added to the product is 39 ? Ans. 9.
89. Which are the two numbers whose difference is 6, and of
which 3 times the less and 5 times the greater make 54 ?
Ans. 3 and 9.
90. What two numbers give 116 for sum, and for diffeience
double the less? Ans. 29 and 81.
91. The sixth part of 9 times the sum that I have, divided by
three and sextupled, gives a result such that its fifteenth part is
30 ; what is that sum ? j^n^^ 150.
92. A gambler being asked how many pounds he had, answered :
the quotient of 5 times their number, divided by 1, being muldplied
by 13, gives a product equal to 65 ; how many had he ?
Ans. £1.
93. The seventh part of a number, multiplied by 3, augmented
4, and divided by 13 gives 4 for quotient; what is that number!
Ans. 112.
94. If I add $10 to four times the triple of six times the sura
have, I will have |658 ; how many had I ? Ans, $9.
FRACTIONS.
95. The sum of two fractions is | and their difference is t*,-;!
what are the fractions ? Ans, ^^ and f f .
96. What is the number whose difference between its third and)
its fourth part is 16 ? ^^^ 192,
97. What number will differ eight from its | and its |} ?
Ans. 20. ,
98. With 3i more, the | and the | of a number would be
equal ; what is it ? ^^, 28.
113.
V
of the san:
114.
T
double
th
115.
11
ii ore ;
ho
IIU.
s
what 1 hi
111
1
same sun
A COLLECTION OF QUESTIONS.
187
,'*i
99. There is 125*j difFerance between the fifth and the ninth •
part of a number ; what is it I Ans. 136.
100. The sum of two numbers is 20, and after subtracting |>
from one to add it to the other, they are equal ; what are those
nurnbei-s? Ans. 8 and 12.
101. Find a number whose | will be equal to ^ of 14?
Ans. 5f .
102. There are two towers side'by side, the first is equal to the
^ of the other, which is 156 feet higher ; what is the height of
each ] Ans. 273 and 117 feet.
103. The f and |^ of a ship are under water, and there remains
4 feet over water ; what is its depth ? Ans. 48 feet. ^
104. The ^ and | of a number make 17^ ; what is it?
Ans. 30.
105. If you add the ^ of a number to its half, the total will be
1 , what is the number ? , Ans. ^.
106. A number is such that if you adki ^, ^, ^, of the same
number, the total will be 12 ; find that number? Ans. llf-j.
107. Find a number whose i,'| and ^ ma^e 4 J ?
Ans. mi,
108. Of two numbers one is 17}, and their ^quotient is | ; what
is the other? • ^ws. 15^V
109. The quarter of a number multiplied by f is equal to 1|- ;
tyhat is it ? -Ans. 8.
110. If the triple of | be added to its third, the -^di^will be
115; what is it? IfH. 75-
111. After selling the f of a piece of cloth there rel^lis \ of
the piece plus 6 yards ; how many yards did it contain ? ^
Ans. 18^1 yds.
112. The 4 plus ^ of a number diminished 64 give for result
the I of the same number ; what is the number? Ans. 168.
113. j^ plus I of a number augmented 3, give for result half
of the same number; what is that number ? Ans. 15.
114. The I and f of a number and twelve more make just
double that number ; what is it ? Ans. 32.
115. If I had i, \ and | of what I have, I would have $150
rvore ; how many have I ? -^ws. $360.
11 U. Some body said : if I had the | and | of the double of
what I have, I would 'iave $5 more; how many had he ?
ins. $6.
117. The I plus ^^ of the sum I have, plus $29, exceed that
BAtne sum by $5 ; what is that sum ?
sum
sum
Ans.^lQO,
I''
jl'i
1^ \i
i:<'i
188
A COLLECTION OF QUESTIONS.
M. Ki^^' \'Zi '' ^''^'"^-^^ '*" '"^^ ^^""^ ^^^^ the 1 is white, t Dia
I blue and the remaining 12 feet are red; what is the length
I black,
the rod ?
Am. 49tV ifeet
of
119. 1 bought a property, and paid by account the §■ of a of i
of the pnce, and I owe yet $60,G35 ; what did it cost ? * "
ion Fk- -1 c • . ^ws. $109,143.
Kv T*i '' n u '"/"^ ^"^^ '"^^ P^*"^ t^^t the quotient of greater
f 1,000 more I would acquit myself entirely and ha^-e $200 over
how much have I ? How much do I owe ? '
loo Th. fk- 1 c ■ ^^^- ^400 and $1,200.
I possess r ''^ ™^ ""^"'^ "'^"'^^^^ t^« T^V by $35 ; what do
i.>o a' „ 1 . , , . ^W5. $1,050.
pnfl ; .'^""'"^^^!' '« «"«h that in multiplying its fifth by its sev^
enth ,t IS lessened one-fourt'a ; what is it ? " AnI m
whaf is if? ^""^ '"^^''^'^ ^ ^'°"' ^ """'^'•'' ^^^^ ^^" ^« the rem. ;
whatl.s it? ^ ""^ ^ ""^ ^ """^^^'' augmented ^ of | will make 11 ;
Twiif o-i?.tn"^'"? ' ""'"'''I ^^'^' ^ ^ ^ ^^^" fr<>«^ the't If'its
f mil one unity for remainder. ^„^ ^^j «
♦k-^f V^' '^'■^''^^'' '"^'"^^ ^^t 4,395 shilling, was sold for two-
third ot five tunes what it cost; what was the gain?
19S f^Jf. • , , •^^*- ^^'255 shillings.
A v Ji^termme a number such that, if you multiply it by 4
and divide the product by 4^, the quotient will be'l6 ? ^
. dirifnkh!^ *on^ ^f\i ^^'\'T ^ ^^'^^" ^' ^"^""^^ to the same^L
k diminished $20; what have I? j^^ 125
crivl^fiV.T''''^ "T^^' """'^ ^^ ^^^^^ to the I and the i of 32 to
give 671 for sum? ^«^ ,
T I. 1 ^''f tain person said : I have spent the a of the | of what
I hacl, and 1 have yet $10 ; how many Lad he ? ' H Vl
1a' 1 ', * ^""^'^^ ^ ^^^"'^ payniy debts; $20 less I
woujd^pay but the i ; how much money havj I ? How mucirdo
i^q' wi.n* X , , ^«5. $46 and $75.
Ifi.n Jl m"T """u ^ «"^tracted from the ^ and the i of
>o to reduce thaf, nnmKoi. trt I'fo a 3 - ' . _ ^
j4ns. 64.
168 to reduce that number to its a ? ^„^ jj4
«oi!rf:o !h! T'li^'^f Ir ""'"^'''' ^'' ^''^^^' ^"^ their difte^ence ia
equal to the third of the greater; what are the two numbers ?
Afis. 3,436 ana ^,304*
135. By
136. By
and a half !
137. Of
is f , and tl
13vS. To
part; what
139. Th
their differe
140. Tl]
by the gre
141. '^Di
equal to I
142. Tl
the father
7^ ; what
143. A
while the j
of the grt
leaps must
144. A
on what p
145. It
146. Tl
meet froir
147. 1
148. I
the same
together
^49. I
in 5 houi
would fill
160. 1
empty it
be dry t
A COLLECTION OF QUESTIONS.
189
te, } black,
i length of
)p7 feet.
■ of a of I
109,143.
of greater
and 41.
ebts; with
^200 over;
$1,200.
; what do
$1,050.
by its sev'
IS. 26^.
the rem. ;
. 3,437.
make 11 ;
ins. 12.
le § of its
for two-
lillings.
^ it by f
ns. 96.
atne sum
s. ^^o.
of 32 to
s. 15f
I of what
9. $20.
10 less, I
much do
i\ $15.
the i of
IS. 64.
erence ia
irs?
2,004
135. By what number must you multiply a sum to lessen it |!
1.36. Bv what number must you divide a sum to render it once
^"13^ " Of^three fractions the second is double the first, the third
is I and their sum^s ^ ; what are the two first fractions \
^' ' Ans. jig and j\.
138. To double a number you must multiply its | by its ninth
1 4. • ;t 8 Ans. 27.
part ; what is it f , , . /. ^1 j
139 'Wa a- of one number is equal to the f of another, and
their aifferenci is 6 ; determine those two numbers ? Ans. 18 and 12.
140 The sum of two numbers is 4, and the quotient of the less
by the greater is ^ ; what are they \ Ans. 2i and 1|.
141 ^Divide 60 into two such parts that the 4 of one may be
equal to 1 of the other ? ^^ ^ris. 32 and 28.
142 The father and son together are 70 years old, the age of
the fadicr multiplied by 3 is equal to the son's age multiplied by
. . .1 Arts 9.0 nnfl .'lO.
what are the ages ?
75; wnao lire tuo «j^ca ; 7' ^ . v j
143 A greyhound starts after a hare that is 82 4.aps ahead,
while the crreyhound makes 9 leaps the hare makes 13, but 3 leaps
of the greyhound are equal to 6 leaps of the hare ; how many
leans must the greyhound make to catch the hare ?
. ^ Ans. 369 leaps.
' 144. A watch marks 12, and both hands are together ; required
on what part of the dial the> will next meet ?
Ans. 1 o'clock o^j minutes.
145 It is iust six o clock ; when will the hands meet?
Ans. 32y"V minutes past 6.
146 It ^s just twelve ; required how many times the hands shall
meet from twelve till midnight, and at what o'clock each time?
Ans.
147. The I and i of a number make 39 ; what is that number ?
* Ans. 60.
148 A man can do a piece of work in ^ day, his wife could do
the same in 1 and their son in i day ; what time would tlio three
together take to do it ? ^ ^ ^«^' \fj- .^
149 A sprincr would fill a baain in 3 hours, another would fa I it
in 5 hours : if the two run together, required in what time they
would fill it? . , . , ^ ^n.9.1jhour.
160. A pump would empty a dit«h in ^t <i^^ys» another would
empty it in ^1 ; if both work together, in what time will the ditch
be dry 1 ^^- ^Hf 'iays.
i
hi
'i
190
A COLLECTION OP QUESTIONg.
^ol u ^«^f.«f^^«^^"^en can build a wall 45 yards lonrr in o
8 dap by working 7 hours per day: if both work tocr.ther and
work 8 hours a day, m how many days will the wall be built »
1 ^9 T 1 f'^'e ^^ ^»ours+ AV, or 3 days 3 hours + ^Vo.
152 1 Nvo bands of reapers can reap a field ?i»the first in 4 davs
and the second m 5 days-, if ^ the first and i of the secor.d l^'
employed, m what time will the field be reaped ?
153. A cock gives 8 gallons of water in 1 mlnn^l f Ser
minuteT' '"^ "''''"^'' ' ""^"^ ^^"^"' ^^ ^^^^ ^''^ ^» ^"^
ic^ A ■^^*- IH gallons.
154. A person questioned about his age answered: the a and
wiLVhirayr ''" ' ^""'^^^ "^'^ "^ '^^^^LTo^fr'
stim^n^;/^^'^''"^^' f tf "" augmented i, i andT'ofthe^'^rae
8tim and $5 more make $75 ; what is that sum ? Ans $24
do fff; ^ ^^^^'-Ti^ ""^"'^ ^!' ^ ^^''" ^" i ^^"n another would
do he sam^ m i hour; and a third in 4 hour; in what timo
would the three running together fill it ?
1 f. w T J . , •^^' tV hour or 3 minutes.
♦T.. c -^ , ^ P?^"^ ""^ "^""^^ ^" '* ^ays; ^y brother can do
i? be done?' '^'' ^' ^''^^ ^"'^ '"^^''^^'' ^" "^^'-^^ ^'"^^ ^^'
do^-f?; t T ""^ T^""?" r" '^"^' ^ ^^" ^" 9 dayTallttriaa
do It in days and a third in 12 days; now ifl employ i of the
first baiid 1 of the second, and ^ of the third, in what Ume w^
the well be dug out ? '^^^ 9^^ ^.
159. A basin has three cocks : two destined to fill *it, and a third
to empty It. The first cock would fill the basin alone in 4 hours,
the second m three hours, and the third would empty it in 6 hours
now If the three be opened together, .n what time will it be filled?
1 flA A u ■ L .1 , ^^^- 2f hours.
Tl 1 fiJ f I'l^^i'l^^r' ''?'^' '- *^^ *^ fi"' a"d «"e to empty it.
n^ first would fill ,t alone n 4 hours, the second in 5 hou.^, and
^11 hl'^h''^ "^ r^'^^ '^ '" ^ ^^"••^- '^^^ b^^'n being already
em t ? """** ""^'^ together; in what time will it be
IJ, " A 1 , ■^"'^' 20 hours.
161. A workman can do a piece of work in | day, another can
done?" ' *'''' '^''''' together, in what time will it bo
162. A mother divides a certain numJjer of siigar^pUimt'betweec-
her three d
second ^, a
what was t
163. Th
more, wou
contain ?
164. Th
and |5,00<:
165. Tl
12 ; what
166. Th
If of the sa
167. T^
one alone
it were to
168. I !
to what re
what did i
169.
gallons in
170. A
and leaks
per hour?
171. A
cle, only r
and the |
172. T
gives 18 I
173. T
the same
174. '\
can do it
175. 1
one of th
12 hours
Uio basin
176. 1
V
' long in
build it in
lirf'ther and
uilt»
/I 1 10-
in 4 days,
second be
2*3 days.
2S, another
ive in one
gallons,
the f and
irs lience ;
3 years,
the same
s. $24.
her would
vhat timo
linutes.
er can do
time will
\ days,
other can
' i of the
time will
dp ;,
d a third
4 hours,
6 hours;
be filled?
hours.
BHipty it.
)urs, and
; already
nil it be
hours.
>ther can
vill it bo
r day.
UCbVTSCU
A COLLECTION OF QUESTIONS.
;9i
her three daughters ; the youngest receives the f of the whole, the
second 1, and the third 12 for her part; how many were there, and
wliat was the part of each 3 .
Ans. Total 45 ; 12, 15, 18, resi^ectively.
163. The I and the ^ of what I have in my purse, with $10
more, would make $Q more than I have; what does the pura»
contain ? , /"^- ^^O'
164. The triple of a sum added to the i and \ of the same sum,
and $5,000 more, would make $22,200 ; what is that sum ?
Ans. $4,800.
165. The difference between the f and the | of a number i3
+
12 : what is that number ?
Ans. 216.
166. The total of the f and the f of a number, diminished the
I of the same number gives 14 ; what is the number ?
Ans. 24.
167. Two cocks running together would fill a basin in 2 hours ;
one alone would fill it in 5 : in what time would the other fill it if
it were to run alone ? -'^««- H 1^« ^ t . .
168. I spent the | of what I had in my purse, and if I add ^44
to what remains, the sum it contained fii-st will be augmented \ ;
what did it contain ? •^^^- ^*8.
169. One cock runs 11 gallons in 8 minutes, another runs 7
gallons in 5 minutes ; which runs the most ?
Ans. The second, by ^V S^^- P^^ "^^"•
170. A basin receives 45| gallons of water per hour by a cock,
and leaks by a hole 37f gallons ; how many gallons does it retain
per hour? .1^.9. 7fi gallons. ^
171. A certain person not recollecting what he paid for an arti-
cle, only remembers that there were $14 difference between the f
and the | of the price ; what is it ? -Ans. $40.
172. The -f of a number diminished the | of the same number
gives 18 fur rem. ; what is that number i Ans. 70.
173. The sum of the f and the j\ of a number less one-half of
the same number, gives 24 ; what is that number? Ans. 40.
174. Two workmen can do a piece of work in 3 hours, one alone
can do it in 7 hours ; in what time will the other do it alone ?
Ans. 5^ hours.
175. Three cocks running together would fill a basin in 4 hom-s;
one of them would fill it alone in 10 houre, another would fill it in
12 hours ; what time would the third running alone take to till
Uio basin? -'I'**- iSlionrs
176. The quarter of a field is sown with wheat, the ^ with barley
f
19?
A COLLECTION OP (QUESTIONS.
and the remainder with oats. The portion sown with barley con-
tains 10 acres more than that sown with wheat; required the ex-
tent of tlie whole field and that of each part?
Ans Whole extent 56 acres; U wheat, 24 barley, ^8 oats
177. I have already sold the | of a basket of eggs, and if I add
3y eggs to what remains, the primitive value of the basket will be
augmented one-half, how many eggs were there in the basket?
178. A steam-loom weaves 6 yards of cloth in 3 houiCanother
12 yds. m 7 hours ; which has the greater power?
Ans. The latter weaves Jj- yd. per
, HO A -1 u . ^^^^ ^^^^ *^^»» tbe former.
len tl i " ""^ ''''^ '"'^ ^ ^^'^ ""^ • ^^' ^"^^ ' ^'^'^^ ^^" '^
' AtlS 1 -^ vd
180. A tradesman can do a piece of work in 5| days ; in what
time will he do the i of the work ? Ans 4aa days
181. A ship sails at the rate of 16^ miles an hour; how many
miles will she sail in 3^ hours ? Am. 63^ miles. ^
1 82. A weaver weaves 7 yards of linen in 8 hours ; how many
yards will he weave in 4f hours ? Ans 4ii yds
183. A man weaves 7 yards of linen in 8 hours ; what time will
he take to weave 4| yds. ? Ans. 5X1 houi-s.
184. If o gallons of wine be mixed with 7 gallons of water ; re-
quired what quantity of water in f gallon of the mixture ?
1 Q- T^ .1 « ^ . ^^**- * 8 ^^'^^" ^^ ^^'"*^ H of water.
, mo. It the f ot the | of a number make 120, what is it ?
186. A person being asked the time of day answered ; it is the i
of ^ of f of 24 hours; what o'clock was it? ' Ans. 10 o'clock. '
187. Divide a succession between three heirs in such sort that
the hrst may have the ^ of the whole, and the second the a of
the remainder ; what is the part of each ?
1 Qo A ^ "^^^^' ^^^^ ■^' ^*^^^"^ ^'t' ^^^ ^^^^ t^»'<i 2*r-
188. A sum ot money was employed in four successive pur-
chases. For the first purchase the f of the sum was laid out ; for
the second, ^ of the remainder ; for the third, the § of the second
remainder; and finally, for the fourth the last remainder, which
was $0 ; required the total sum, and the amount of each pur-
cnase f
1 DH^'f ■ ^""^''-^ ^^^ ' ^^'^^ ^' ^^^"^' fV' ^"^^<^ t'ff' fourth yV.
189. A certain person loaves to his nephew a fortune of $80,000,
and orders the } of f of the succession to be given to a servant,
and to his
portion of
190. Tl
the length
191. Tl
that they 1
take each
192. A
travels th(
of the rem
mainder ;
goes 144 1
travelling
193. A
other can
do it togel
3d. What
Ans.
194. A
first day ;
he plays
himself n
fco play ?
195. \
196. r
be woven
197. 1
that per 1
198. ^
the Jyof
the stage
199. .
on sea (3
man bo i
200. 1
A COLLECTION OF QUESTIONS.
193
barley con-
ed the ex-
!8 oats,
id if I add
ket will be
asket?
ins. 30.
•s, another
yd. per
ormer.
lat was its
; in what
f days,
low many
- miles.
»ow many
ri yds.
time will
houi-s.
'ater ; re-
water.
it?
s. 162.
t is the I
)'clock.
sort that
the f of
/r-
Ird
isive pur-
out ; for
le second
er, which
ach pur-
$80,000,
I servant,
and to his nurse ]- of i of i of the same succession; what is the
porUon o eac ^^^ ^^^^ $73 OOO, servt. $6,000, nurse $1,000. ^
190 The SL of 4 of the length of a garden is 48 yards ; what w
the length of ^t I ^ ^ , Jn.. 90 yaixis.
191 Three robbers divide between themselves a sum of money
that th'ey had stolen ; the 6rst takes the | of it and the two others
take each half of what remained; what part fell to each robber?
Ans. First | of the sum, and the two others j\ each. _
192. A stage performs a journey in four days pe first day it
travels the 1 of the whole route ; the second day it travels the \
of the remainder ; the third day it travels the ^ of the second re-
mainder; and lastly, the fourth day it completes the journey and
goes 144 miles; required the length of the journey, and each days
°' Ans. Length 540 miles ; first day 108 miles,
and each of the other days 144 miles.
193 A tradesman can finish a piece of work in | of a day, an-
other can do the same in f day : 1st. What time will they take to
do it tocrether I 2d. What part of the work vvill be done by each !
3d Wlfat will be the gain of each, if the whole be worth 4s. 7d. I
Ans. 1st., ^r day ; 2d., the 1st. j\ of the work the 2d.
the V't; 3d., the 1st. will have 2s. 6d., the 2d. 2s. Id.
194 A little Voy playing marbles augmented his number i the
first day ; on the next day he augmented his last number ^ ; finally,
he plays a third day, and au^-ments his last number | and finds
himself master of 63 murbles ; how many had he when he began
. 1, f 2 Ans. 16 1 »
I9I What number multiplied by 3| will give 1 for product?
Ans. y*j.
196. In 8 hours 5f yards are woven, in what time will 1 yard
be woven 5 ^ ., . 09 1 u * :-
197 A ship sails at the rate of 29| miles m 3f hours, what u
that per hour ? ^«f • «iV m^lf P^'^ ^^\ .
198 While a locomotive runs the whole route, a stage runs but
the -3-of it: how many times does the locomotive go quicker than
,1 ',* 9 Ans. 5h times quicker.
the stage ? , "^ , 2 ^
199 A ship is victualled for 12 days only; and must be kept
on sea during 18 days; to what must the daily rations of each
, J „j « Ans. * 01 one.
man bo reduced i \„ f^
200. Four labourers work together and are paid equally. JNow
the Sr.t who worked the whole day received 4s. 2d. while the
#1
: J
:4
104
A COLLECTION OF QUESTIONS.
second received but 3s. 4d.,the third 2s. 6d., and the fourth Is. 8d.
Required what part of the day the tliree hist hibourers worked ?
Ans. The second f day, 3rd |, 4th f day.
201. A spinning-wlieel takes in 1^ yard of thread every turn it
makes; liow many turns should it make to wmd up 45f yards?
Ans. 401^ turns.
202. An omnibus takes ^ hour to reach its destination, it sta-
tions i hour, and takes i hour to return to its starting place.
Admitting that a trip is composed of going to and from the
station; how many such trips will the omnibus perform from
half-past seven in the morning till 10 o'clock at night?
Ans. 14Jy trips.
203. A traveller having missed the stage, it is already 29 miles
a-head of him. He then takes a calash that goes at the rate of
9 miles an hour, the stage travelling rut 5^ miles per hour. In
what time will the calash overtake the stage ?
Ans. 7 hours 44 minutes.
204. There is 29 miles distance between two towns. Two car-
riages start, one from each town and run towards each other, the
first goes at the rate of 9 miles per hour, and the second 6^ miles
per hour ; in what time will the carriages meet, and what will be
the distance performed by each ?
Ans. 2/y hours. One 18|4 miles, other lOff miles.
205. Two carriages travel at the rate of 9 miles and 5^ miles
respectively, start together from the same town to reach the neigh-
bouring town distant 29 miles. In what time will the former
arrive before the latter? Ans. 2^j\ hours.
206. A saloon requires 8^ pieces of wall-paper f yard wide to
line it. How many pieces | yard wide would do the same ?
Ans. 12f.
207. A spring runs 8f gallons of water in 5 minutes ; in what
time will it run a gallon ? Ans. ± minute.
208. A weaver weaves 9f yards of cloth in 2f days ; how many
yards does he weave per day ? Ans. 3^1.
209. I sold the 4 of a piece of cloth and there remains yet 16
jards ; what was the length of the piece ?
Ans. 35 yards.
210. A bale of merchandise was sold for |75 ; if it liad been
sold for $9 more, the profit would have been just f of the first
cost ; what did it cost ? ^1^5. $60.
211. The rail cars start from New York at noon and arrive at
Philadelphia at 4 o'clock P. M. A stage started with the cafRj and
went but
at Philad
212. >
only travi
than the
213. ^
holds 50
other 4A
214. 1
out f<jr 1
man be i
215. .
minutes :
time ?
210. '
day; no
third 20
217.
and rem
buckets
218.
miles ap
the seco
what wi
219.
leaps a-
after hii
220.
for a ni
miles ai
arrive i
221.
his dep
many I
222.
how m
A COLLECTION OF QUESTIONS.
195
rth Is. 8d.
vorked ?
I f day.
ery turn it
'■ yards ?
^ turns,
ion, it sta-
ging |)lace.
from the
form from
rips.
r 29 miles
le rate of
hour. In
linutes.
Two car-
other, the
i 5^ miles
it will be
■ miles.
5^ miles
he neigh-
le former
hours.
1 wide to
le?
s. 12i
; in what
ninute.
ow many
^- 3|f
ns yet 16
yards,
lad been
the first
s. $60.
arrive at
ottra. and
.
went but the * of the route: at what o'clock v/iU the stage arrive
at Philadelphia ? A. M. Ans. Next day at 2 o clock A. M.
212 While a horseman goes the f of a journey a footman can
only travel the J, ; how many times does the horseman go quicker
than the footman i ^^^' ^ ^^' V^'l^
213. What time will two water-spouts take to hll a basin that
holds 508 gallons, if one runs 5| gallons per minute, and the
other 4A galbns. ^^^- ^8 i»^""tes.
214. A garrison has provisions for 9 days only, and must hold
out for 12 days: to what fraction must the daily rations of each
1 1. J « Ans. to 5 ot usual,
man be reduced { ^ ^i,c... y.j 4
215. A wat<;h is now regular, gets out of order and Jidvances 5 J
minutes in a day ; in how many days will it ag^un inark the exa^t
ti,ne? Ah5. 130fJ days.
210. Three writers equally clever can write 40 pages each per
day: now if the first write but 30 pages, the second 2d, and the
third 20: reauired during what portion of the day each worked?
Ans. 1st. i 2ud. f, 3rd ^ day.
217 If a bucket takes 1^ minute to reach the bottom of a well
and remains i minute below, then If minute ascending, how many
buckets of water may be drawn in 250 muiut£s. . ^ , , ^
Ans. 12 buckets.
218 Two couriers 'start at the same time at a distance of 92^
miles apart, to meet ea<5h other and travel; the first 7 miles an hour
the second 13i miles an hour: in what time will they meet, and
what will bo the distance travelled by each?
Ans. In 44 hours. J he first travelled
3H nicies, the second 60| miles.
219 A fox that makes 2^ leaps in a second is already 30i
leaps a-head, when a dog that makes 4i leaps in a second starta
after him. In what time will the dog overtake the tox i
Ans. 14 2V seconds.
220 Two couriers start at the same time from the same place
for a neighbouring town distant ^ miles, the fii-st trav'els 13^
miles an "hour, the second 7 idem : how many hours will the hrst
arrive before the second ? . A^^- Cff hours^^
221 A courier goes 24 miles in 2 hours. Three hours after
his departure another starts and goes 72 miles in 5 hours, m how
many hours will the latter overtake the former?
•' Ans. 15 hours.
022 With 13^ yards of old silk f wide I can line a vestment:
how many yards | wide will do the same ? Ans, 12if yarda
W
196
A COLLECTION OF QUESTIONS.
223. There is a levy of $800 to be token of three villages in
proportion to their inliabitants, in the fii-st there are 240, second
510, third 450 inhabitants: what share of the impost will each
have to pay? Aiis. 1st. $100, 2nd. $340, 4th. ^300.
224. An uncle on his death-bed bequeathes to his three nephews
a fortune of $07,500 in proportion to their age. The first is 30,
the second 25, tl)e third 20 yeai-s of age : required what will fall
to each? Ans. 1st. $27,000, 2nd. $22,500, 3rd. $1S,000.
225. Divide the number 1,028 into three parts so that they l)e
between themselves as the three fractions, f , ^, | ?
Ans. 320, 420, 288.
220. Divide $450 between three persons so that the second may
have the ^ of the first, and the third the f of what the two first
have together? Ans. $200, $150, $100.
227. Divide 100 shillings between two persons, and give the
second tlie | of the first? Ans. 60, 40 shillings.
228. Divide $180 between two persons, and give the second ^
of the first's part more than the first? Ans. $80, $100.
229. Divide | into tv;o parts so that they be between themselves
as 4 and 7 ? Ans. if, f i.
230. The power of one machine is to that of another as is to
7, while one makes 48 yards of work : how many will the other
make ? * Ans. 56 yards.
231. Distribute $582 between 3 pei-sons so that the part of the
fii-st be to the second as ^ is to |, and that the part of the second
be to that of the third as f is to ^ ? Ans. $168, $252, $162.
232. What is the sui>erficies of a rectangular garden, being 40
yards long by 30 yards in breadth ? Ans. 1,200 yards.
233. What is the area of a meadow in the form a triangle of
60 yards of base and 48 in height? Ans. 1,440 yards.
234. What is the area r f a yf^vd forming a trapezium one of
whose sides is 34 yards and the other 56, its height being 25
yards? ^w*. 1,125 yards.
235. What is the area of a rhombus, whose base is 44-i7j and
height 38a yards? Ans. l,716^f yards.
. 236. V/hat is the superficies of a pillar 17 yards high and 1
yards in circumference? Ans. 119 yards.
237. The circumference of a cone is 12 yards, and the distjince
from the summit to the base is 6 yards ; what would the painting
of it cost at 3 shillings the square yard ?
Ans, 108 shillings.
A Tahle^
num
197
A Tahle for finding the Interest of any sum of Money for oji,
number of months, weeks, or days, at any rate per cent.
Year.
Calen. Month.
Week.
Day.
£
£ s. d.
£ 8. d.
£ !> d.
1
1 8
4i
. Oh
2
3 4
9
u 14
*
3
5
1 a
2
'^
4
6 8
1 6
2i
5
8 4
1 u
34
^
6
10
2 31
4
>
7
11 8
2 84
4i
8
13 4
3 1
54
g
15
3 5i
6
10
16 8
3 104
6i
20
1 13 4
7 84
1 U
30
2 10
11 6i
1 74
40
3 6 8
15 4i
2 24
50
4 3 4
19 2|
2 9
60
5
1 3 1
3 3i
70
5 16 8
1 6 11
3 10
80
6 13 4
1 10 94
4 4i
90
7 10
1 14 74
4 114
100
8 6 8
1 18 5i
5 55
200
16 13 4
3 16 11
10 Hi
300
25
5 15 4i
16 54
400
33 6 8
7 13 10
1 1 11
500
41 13 4
9 12 3h
1 7 4|
GOO
50
11 10 9
1 12 lOi
700
53 6 8
13 9 21
1 IS 44
800
66 13 4
15 7 8|
17 6 U
2 3 10
900
75
2 9 34
1000
83 6 8
19 4 74
2 14 9i
2000
166 13 4
38 9 2|
5 9 7
300r
250
57 13 10
8 4 4i
4000
333 6 8
76 18 5i
10 19 2
5000
416 13 4
96 3 Oi
13 13 Hi
6000
500
115 7 84
16 18 9
7000
583 6 8
134 12 3i
19 3 6|
8000
606 13 4
153 16 11
21 18 44
9000
50
.173 1 64
24 13 n
10,000
833 6 8
192 6 11
27 7 114
20,000
1666 13 4
384 12 34
54 15 lOi
30,000
2500
576 18 5i
82 3 10
-
1/ i
I
198
RuLK. Multiply the principal by the rate per cent,, and the
number of mtniths, weeks, or days, which are required, cut off
two finrures on the right hand side'of the product, and collect from
the table the several sums against the different numbers, which
when added, will make the number remaining. Add the several
sums together, and it will give the interest required.
N. B. For every 10 that is cut off in months, add twopence;
for every 10 cut off' in weeks, add a half-penny; and for every
40 in the days, 1 farthing.
EXAMPLES.,
1. Whr.t is the interest of £24G7 10s. for 10 months, at 4 pei
cent, per annum ?
2467 : 10 900=75 : :
'1 80= 6 : 13 : 4
■ 7= : 11 : 8
9870 :
10
987100
987=82 : 5 :
cent.
2. What is the interest of £2467 10s. for 12 weeks, at 5 per
It.? 2407 : 10 1000 = 19 : 4 : 7^
400= 7 : 13 : 10
80= 1 : 10 : 9i
50= : : 2^
12337 :
10
12
1480150 :
is the interest
2407 : 10
6
14805 :
60
1480150=28 : 9 : 5
3. What is the interest of £2467 10s., 50 days, at 6 per cent!
7000=19 : 3 :
H
400= 1:1:
11
2= 0:0:
u
50= 0:0:
0*
7402)50=20 : 5 : 7
7402150 :
To Jind what an Estate, from me to £60,000 per annum ivill
come to for one day.
Rule 1. Collect the annual rent or income from the table for
1 year, against which take tlie several sums for one day, add
them together, and it will give the answer.
199
An estate of £3*76 per annum, what is that per day f
3G0— : 16 : 5i
70=0 : 3 : 10
6=0 : : 4
376=1 : 0: 1i
To find the amount of any income, salary, or servants^ wages,
for any numhei of months, weeks, or days.
RuiF Multiply the yearly income or salary by the number
What will £270 per annum come to foi 1 1 montns, lor o vy<. ,
and for 6 days^
270
11
2970
270
6
1620
For 11 months,
2000=166 : 13
900= 75 :
70= 5 : 16
4
8
270
3
For 3 weeks.
800=15 : 7 : 8i
10= : 3 : 10^
2970=247 : 10 :
For 6 days.
1000=2 : 14 : 9^
G00 = 1 : 12 : 10^
20=0 : 1 : li
810 = 15 : il : 6^
For the whole time.
247 : 10 :
15 : 11 : 6i
4 : 8 : 9^
1620=4 : 8 : 9^
267 : 10 : 3^
A Tabic showiny the number of days from any day in thi
JnTto the saL day in^nyoth^^r^^
FROM
January . ■
February .
March . .
April . . . .
May
June . . •
July
August. .
September
October .
November
ecember
El!
200
A COMPENDIUM OF BOOK-KEEPING.
BY SINGLE ENTRY.
Book-keeping ,s tlie art of recording the transactions of persons
m business so as to exibit a state of their aflairs in 1 n^^
and satisfactory manner. ^" ^ ^^^'^'^^
Books^may be kept either by Single or by DouMp JPnh.. i »
Single Entry is the method difly ufed in rLflh^Ll ""' ^"*
The books found most expedient in Sino-le Entrv s.^^ ♦!.« n
Book, the Cash-Eook, the Z V, and theK^^ '^' ^"^
debts &c. ; and are entered in the order of their occu JrcT he'
daily transactions of goods bought and sold. "^'^""ePce, the
The Cash-Book is a register of all money transactions. On the
left-hand page^ Cash is made Debt<y, to i\\ s«ms received and
on the right, Cash is made Creditor by all sums paid '
1^ '^^ I^J^If collects together Ihe scattered accounts in the Lav-
Book and Cash-Book, and places the Debtors and Credito^ uZ
opposite pages of the san.e folio; and a reference is madtto^the
folio of the lx>oks from wliich the respective accounts are extrat
ted, by figures placed in a column against the smns. Keferencet
are also made m the Day-Book ancf a-.h-Bcok, to the S in
the Ledger, where the amounts are collected. This r^r^Z s
Jr^y n' ^''""J' ''^T '"^^^^^^ ^'^ transferring the reSsSr
of mercantile proceedings from the previous books to the ui^^
The person from whom you purchase goocfo, or from whom
rJCJ" "'^f^' ^\(^-ditor; ind, on thf conC, th^ pet"
to whom you sell goods, or to whom yon pay mon,y;L Dehtor
In the Bill-Book are inserted the particulars of all Bills of Ej,
change; and jt is sometimes found expedient to keep for tht f r-
^t^^r " i^tnthe^^-ett::,^s
tWu!;fhirer ^ '''' ''' ^*^^ "^- -' ^^tdt
201
DAY BOOK.
(folio 1.)
W -a
January Ist, 1837.
f;
1 commenced business with a capital of Five Hun-
dred Pounds in Cash
2d.
Bennett and Sons, London,*
By 2 hhds. of sugar
cwt. qr. II.
13 1 4
12 3 16
Cr.
cwt.qr.lb.
12
1 1 6
gross wt. 26 20
tare 2 3 6
neat wt. 23 1 14 at 633. per cwt.
2 chests of tea
cwt. qr. lb.
1 15
1 12
2 27
1 22
lb.
25
25
1 3 5 at 6s. per lb.
£
500-
s.
73
3d.
Ha/l and Scott, Liverpool,
By soqp, 1 cwt. at 68s. . . .
candles, 10 dozen at 7s. 9d,
Cr.
60
133
6th.
Ward, William
To 1 cwt. of sugar,
14 lbs. of tea,
4 cwt. of soap,
J}r.
at 703.
at 83. .
at 749.
6lh.
Cooper, William
To 1 sugar hogshead.
Dr.
10
d.
12
18
8
17
5
10
12
18
6
• The sT'.Jdfint mav be directed to fill on this and similar blanks in thif
book and the Ledger with the names of pi;\(;es familiar to him
m
202
DAY BOOK.
(folio
2.)
2
1
2
1
2
o
January 9th
. 1837.
" £
1
1
4
17
17
1
6
1
1
s.
16
17
15
8
5
5
9
8
4
8
10
16
13
16
10
9
4
13
IS
8
G
1
d.
6
6
6
9
3
6
10
6
4
2
2
3
n
Johnson, Richard
To 2 dozen of candles,
i cwt. of soap,
i cwt. of sugar.
at 8s. 3d. . .
JJr.
at 74s
at 70s
10th.
Ward, William
To sugar, 1 cask
cwt. qrs. lb.
gross wt. 5 2 10 cask
tare 2 10
Dr.
neat 5
at 68s
12th.
Smith, John
To 14 lb. of sugar
Dr.
12 lb. of candles
7 lb. of soap *
1 lb. of tea
14th.
Hall and Scott, Liverpool,
By 2 cwt. soap,
at 6Ss ....
Cr.
17th.
JVewton, John
To 21 lb. of soap,
2 dozen of candles,
Dr.
at 74s. per cwt....
at 8s. 3d
19th.
Smith i John
To 14 lb. of sugar
Dr.
i lb. of tea ....'.'.'.'.
21st.
Smith, John
To 28 lb. of sugar
Dr.
12 lb. of candles , .'
2
203
;
DAY BOOK
(t
oho
3.)
2
3
2
2
2
3
3
3
3
January, 23d., 1837.
£
A
d.
G
6
Vates Sc Lane, Bradford, ^*''
By 4 pieces of superfine cloth, each 36 yards,
at 243. per yard. . .
172
2
3
5
9
145
2
148
50
172
4C
5f
C
I or
16
8
9
16
14
5
23d.
Edwards, Benj. Manchester, ^r.
By 2 pieces of calico, each 24 yards, at Is. per yard
23d.
Smith, John ^'
To 14 lb. of soap »
24th.
Johnson, Richard ^^-
1 2 dozen 01 canuies, ^.t oa. ou, • • • • •
1 cwt. 01 soap, o\. /'is. •
1 1 o\k\ r\i alicrnr at 70s
15
8
16
16
12
8
16
17
> 7
! 19
) 15
> 19
6
3
1
6
6
24th.
Smith, John ^' •
To 1 lb. of lea
26th.
Mason, Edward f^-
To 3 pieces of superfine cloth, each 36 yards,
at 278. per yard ....
2 pieces of calico, each 24 yards,
et Is. 2d. per yard..
27th.
Parker, Thomas £»'•
To 1 piece of superfine cloth, 36 yards, at 28s.. .
3 1 St.
Bills Payable, , , ^ C-r
By Yates & Lane's Bill at 2 months, due April 2
Inventory, January 31, lb37.
cwt. qr. lb.
Kaw sugar, i'* o i'* ai u.jo. ........••
Tea, 1 2 16i at 6s. per lb
o^„.» n ^ 1 4. at fiSs
soap, " o it <ti ^los
Candles, z aozen» <*>- '»• «'»j
m
204
CASH BOOK.
o
o
o
a
y
o
*'o
«^
o
oo
o o
00 \fi
CO o
CO
«ooo«oooo«o
«o
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00
I— I
I— I
»-< tH CO
CO CI
a
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o
CITS
V
, -^ > —
■"^"
1 = 1
Oca;
», <u c
<u a o
W g 6
. CO
^pq
' 'V3
a
c?
:o:h'
cask
and
arch
f5?S
A sug
Bernai
due
! t3
«o
0)
:^ S
SW =«J g-c
:«
3
O
•-g
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« «j S -s "^ -G :
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:5 rt .9 o - rt .;5 -'^ c» g
So
c
G^3-S s = i i
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00 a
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C
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Herna
Benn*
Bills
Coop<
E
F
G
H
Edw;
Hall
K
M
Ma
205
INDEX TO THE LEDGER.
NewtoD: Tohn
A ' N
. 2
Hprnnrrl & Co 1
T> Bennett & Sons, London ... 1 |
XJ Bills payable 3
Cooper, William 2
C
Parker, Thomas
P
. 3
)-
D
Q
Edwards, B. Manchester ... 3
E
R
F
Stock account
C^ <5mil-h Tohn
.. 1
.. 2
D
G
T
Hall & Scott, Liverpool 1
H
V
Johnson, Richard 2
I
Ward, William
W
. . A
K
X
L
Yates & Lane, Bradford.
Y
. .. i<
I
Mason, Edward
M
3
z
206
LEDGER.
C
^.
Wo
O O r-i I ,^
00 o o
! CO
I F-l
Oi
o
o
'JO
n
t^ to
I -
o
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eo
• 0) •
: o -
.*; CO a) *j
I -
I -^et
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<u,
o
s ?^ 3
° s tS
pq
C3
a
o
3
^
OB a)
•>— S o
c!5
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"So o
So*-*
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d
pq
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OJ o
Tf -I
. CM
* s
. CO "*
00 2
CO CO
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00 2
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00 (M
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05
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00 2
♦* I— » *-»
to o
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CM
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;^ o O
CO
-o o
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to
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w
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LEU6RR.
207
208
LEDGER.
CO
o
CO
* 2
o
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o
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o o
O 00
o o
on
o
I -co
<o
wl
d o —
f o c-
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to
at
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4j en
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1-1 <«
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=3
0)
pq
PC
c
rt
m
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P4
.«; o o
-. CM TH
•* •
Ci •
D, •
< :
Dec
T3 3 a>
(U
fiq
^ 6 a)
^ ^ _ o
PQJJ
pa
•^' ^ '•o
«s 00
o o
a 00
(JO r-l
o
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o
00
o
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(M
CO ,-t
CO
CO
1-1 o •-< «o CV ^ o
»-< «0 O «0 t- O 00
0> O "^ OS o o o
'V (M r- rf
.-• CO
o
tH rt (N CI CO CO
«9
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v.
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to
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