ARITHMETIC. 
reduce it to a whole or mixed number (by Prob. V.) If 
there be any wliole numbers in the queftion, add their fum 
to tire fum of the fractions, for the required fum. 
Ex. i. Add f, 9f, and 7-f, into one fum. The frac¬ 
tions reduced to a common denominator, become f-fg, §•£-§, 
Wo, m- 
Then — toct? — 3^ the fum of 
SCO 
the fractions; then 92*o> the fum required. 
Ex. 2. Add 
3 b 8-> and 6- 
into one fum. 
Tt 
it and Ei. refpedlively ; which, reduced to a common 
denominator (by Prob. XIV. rule 3), will be ff, if, gf, 
and gg, which being added together make — the 
fum of the fractions ; then, 3+S -|-6 -}-2|-|-= 194 the fum 
required. 
If many fractions are to be added, the belt way is, firft 
to add two of them together; to that fum add a third, to 
that a fourth, and fo on. 
Ex. 3. What is the fum of sf, iJ 5 , 3^, 8^y, and y-A- > 
Firlt fg-'l’o—IaJ> and l^+TT—fS'’ and 'H> 
and 144-^—the fum ot the fractions ; then, 
5 + I +3+ 8 +74“ I i-o'5= 2 ,5^ anfwer. 
Ex. 4. Add 37, 3^, By,,4, -f, 94, 194, 154* and 
-i-, into one firm; and obferve, that fuch of the given 
fradlions as have the fame denominator may be added with¬ 
out any previous reduction. 
Thus, 44*y“ = *y ) and -g-T-i 1 ” 1 '3-3 and ig-f-^-—--2> and 44" 
4= if, and 44-4=i I then, 44-^—if, and 
and TH-H=yW — and I 77§+ I + 2 + I + I = 4 f& 
the lum ot all the fractions. Therefore, 37+3+8+9+ 
^-f 194-154-6f|4=i034f4, the fum required. 
In fradtions of different denominations reduce them to 
one denomination (by Prob. XL) then add then together 
as before diredled. Or you may reduce them to theft- pro¬ 
per quantities (by Prob. IX.) and add them together as in 
Compound Addition. 
Ex. Add f- of a pound, f- of a (hilling, and -f of a pen¬ 
ny, into one fum. Firft fd.= 4 yS. and fl. — 8 i*s. then 
e 7° + -I = Vs 5 s • and +-&=* 
ad. o-J^qrs. the anfwer. 
1 s. d. 
’f- of a pound =211 5 
|- of a fliilling z= o j 
_ 4 of a penny —00 
Anfwer 
's. — s. = 12s. 
Or thus 
(i 
of “) Reduced to their 
2 I proper values by 
if J Prob. IX. 
the fame as above. 
°Ti 
SUBTRACTION of VULGAR FRACTIONS. 
The fractions are to be prepared in all refpedtsas before 
diretted in Addition. Then fubtradt one numerator from 
the other, and under their difference write the common 
denominator. In mixed numbers, fubtradt the fradtions 
from the fradtions, and the whole numbers from the whole 
numbers, borrowing at the denominator when occafion 
requires. 
Ex. 1. From f take 4, reduced to and gf. 
Then ——the remainder. 
63 
Ex. 2. From fof f of f- of 3 take 4 of 4 of 3, reduced 
to 2 f and g, and again to and f|. 
16 a—6 t. 
Then --—=f4=if- 4 , the remainder. 
Ex. 3. What is the difference between fl. and |- of a 
fhilling f Firft, gl. 2= then 8 y and f- are reduced to 
S+° and 44 - 
6 4-0—3 < 
Then - 7 —1044s. the anfwer. 
5 6 
Ex. 4. From g of a pound troy 
Take g of an ounce 
oz. dwt. gr. 
= 9 6 16 
=OII IOy 
Remainder, 8 15 54 
Ex. 5. What is the difference between of a year, and 
-/j of a month, reckoning 13 months to the year ? 
Anfwer, 4111011. i vv. 2d. 14I1.15m. 56-j^jfcc. 
MULTIPLICATION of VULGAR FRACTIONS 1 
Reduce whole numbers to the form of fradlions by 
Prob. II. mixed numbers to improper fradtions by Prob. IV. 
complex fradlions to fimple ones by Prob. VII. and frac¬ 
tions'of different denominations to the fame denomination 
by Prob. X. and XI. then multiply all the numerators to¬ 
gether for a numerator of the produdt, and all the deno¬ 
minators together for a denominator of the produdt. Firft 
let the produdt be expreffed by the tign x between the fi¬ 
gures, then throw out the figures common to both nume¬ 
rator and denominator, or divide both by any figures you 
can, in order to reduce it, by the rules in Prob. VI. 
Ex. 1. Multiply 4, 4, 4, and gof 4 -of 9 together. 
Thus 
3 X 4 X 5 X 7 X 2 X 3 X 9 
7 X 5 X 9 XSX 3 X 4 XI 
=4 the produdt by Prob.6. 
Ex. 2. Multiply —-, 17-4, 44 and — of g of to-- 
gether. Thefe reduced to fimple fradtions, and placed as the 
will Hand thus 
11X190X18X1X4X7. 
i 2 XiiX 95 X 4 X 7 X.ii' 
rule diredts, 
-—— —fr, the produdt. 
2X i X 1 r 11 r 
Ex.3. Multiply 17I. 17s. 6d. into 4I. 13s. 4d. a pound 
the integer. 
Firft 17I. 17s. 6d. =2 1 -| 3 1 . and 4I. 13s. 4d. — <^ 1 . 
I 43 XI 4 _ 143 X 7 — I00I j. — 83l.8s.4d. produfl. 
Then 
8 X 3 4 X 3 42 
Ex. 4. Multiply 7I. 9s. 4d. into ns. iogd. one pound 
the integer. Firft 7I. 9s. 4d. — y#l. and'ns. 10-id. ~ 
ggl. by Prob. X. 
112X19 14X19 7 Xi 9 ,,, , „ OJ 
--—--—-— t-SJ 22:4k 8s. 8d. the 
15X32 i 5 X 4 15X2 
Then 
produdt. 
DIVISION of VULGAR FRACTIONS. 
Prepare the fradlions as diredted for multiplication, then 
multiply the dividend into the divifor inverted, and that 
fradlion will be the quotient. 
Ex. 1. Divide by g. Here the divifor inverted is 4. 
5 ■=§-, the quotient. 
Then 
i 4 X 4 4 X 2 
Ex. 2. Divide g by 8. Thus 
Ex. 3. Divide 56 by 4. Thus 
- - = A-quotient. 
9X8 9x2 
56X9 7 X 9 
=-= 63, the 
quotient. 
Ex. 4. Divide 94 by 44. 
Then 8 fx&— 
43 Xi 43 
1X8 
Firft 9-4= and 4 f= V- 
— iff, the quotient. 
3 X 7 
Ex. 5. Divide 4I. 8s. 8d. by 11s. iogd. one pound the 
integer. Firft 4I. 8s. 8d. =2 266 groats for a numerator, 
and 11. 2= 60 groats for a denominator; therefore, 4l.8s.8d. 
= —*^ 1 . the dividend. Alfo, 11 s. logd. — 95 
three-halfpenc«s, and il. — 160 three-halfpences; there¬ 
fore, ns. iogd. — ^q 1. 22. -§gl. f h e divifor. 
133X32 7X32 224 
Then -—22————- 1 . = 7I. 9s. 4d. the quo- 
30x19 30X1—3° 
tient. This is a proof of Ex. 4, in Multiplication, and 
in this manner may any compound quality be divided by 
another. 
Ex. 6. What is the quotient of 98 yds. 4 ft. 4744 inches, 
by 7 yds. 1 ft. 1 of- inches ? Anfwer, 12 yds, 2 ft. Sgin. 
DECIMAL FRACTIONS. 
A decimal fradlion is one vvhofe denominator is unify, 
with one or more cyphers annexed, as -J-, 44, sJ 
See. The integer, or any thing which‘is called one* 
3 whether 
Vol. II. No. 65. 
