FRACTIONS. 
with the denominator. y 
feparately taken, into all the denominators b ow 
and the produ Ii} give the new numerators. Then 
multiply all the denominators into one another, and the 
produ will be the common denominator. Thus, 2 and 
4 owes Fs and iz, and 3, Zand ¢ are fede 43, 43, 
and 4$ 
5 ¥. the. Galas of a fration, in the known parts of | 
its integer — Suppo what 
ey é. gr. it were required to know 
is 2 of a pound; multiply the numerator g by 20, the 
“number of known parts in a pound, and divide the produét 
Then 
1oultiply the remainder 4 b 
n the next inferior denomination ; and dividing the pro- 
du& by 16, as before, the a is3d. So that ~3 of a 
pound = 11s. 3d. 
jen value — 
on aa fraction ; an 
the fum 59 = over the former denominator, $2, 
ne the fractio 
. To reduce an es er fradion into its equivalent mixed 
ion $23 divide the nu- 
oti ent is t the in do 
‘part, and the pmannees a ov 
fra€tional art. pad 
uce ae adage nie pe a bald one. — Mul- 
tiply all the petals into each o a new nume- 
rator ; an ll the Genominators for a a new denominator. 
Thus, 3 of 4 of £ reduced will be 
Ts 9 reduce @ vulgar frailion t to & decimal of the fame | 
Pree fee DrecIMAL. 
r ene, 20 ion of vulgar.—t. Lf the given fraGtions 
“have different denominators, reduc 
“Vhen add - Pecgein together, and under the fam 
write the common der nominator. Thus, ¢. gr. } 
12. 22 
1 TF co B= a) had ons are given to be — they 
mutt firft be reduced to fimple ones ; if the ae 
‘be of different rp eeday as £0 ound, and 3 of a 
fhilling, g, they m 
denomination or pound 
dd mixt numbers.—The integers are firft t 
] parts : and if the fum. be a 
d 
the integers, 
17, 9 
sat a= on 
= = 1OZ- 
"satay — 
6 
Fract — raftion of —1. If they have the fame - 
common denominator, fubtra& the leffer cigeniand from 
the greater, and fet the remainder over the on de- 
‘nominator. .Thus, from +2 take +3, and Gee remains 
4o= i, 
we). TF t they have not a common spa they muft 
= reduced to fractions of the fame value, having a com- 
n_ denominator, : ‘and then, - as in ie firft- rule. Thus, 
os e252 tae 
3. "To ‘jubtral a hale —— from a winced oe or 
one mixed number from another.—Reduce the whole, or 
-mixed numbers, to impro ope fra€tions, and then proceed 
‘as in the firft and fecond ru 
FRACTIONS, Multiplication of.—1. Hf the frations | pro- 
firlt be reduced to hradtions oe the Sone 
2 by dividing both. gae and dc by ¢: and- 
pofed be both fimple, sey the numerators one by 
another for a new numerator, and the denominators for a 
new denominator. Thus 2 into "s pr a 
2. If one of them be a mixed, or whole number, it mutt be 
reduced to an improper fraétion 5 and then ei as 
an the Ie rule. Thus, 3 into 5%, gives 34, and ¢ 
eoo36. 
In multiplication of fraétions, obferve that the produ& 
s lefs in valuethan either.the multiplicand, or multipli- 
eine. 3 becaufe i . all multiplications, as unity is te the mut- 
tiplicator, fo is t as unity is 
to either ves fo j is the other factor | to the produ uct. 
unity is bigger than either factor, if the fraCtions be proper 
and therefore either of them muft be greater than ce 
product. 
Thus, in whole numbers, if 5 be multiplied by 8, it 
lay be asi: g:: 8: 403 or I: : 40 WVerelore 
in fractions, alfo, as 1: 22: 3:45; 8 1 
But Tis greater oa either rior 3: ee nies of i 
mutt be bigger than 1. 
Fractrons, Divifion of. —tr. If the fra@tions propofed be 
both fimple, multiply the denominator of the divifor by 
the numerator of the dividend; the produ& is the nu- 
merator of the Rag ieee then multiply the numerator of 
a divifor -by the desominator of the dividend, the pro- 
& i 
if they ce compound frations, reduce them to fimpte 
ones, and proceed as in the firft rule. 
In divifion of fractions obferve, that the quotient is al- 
Ways greater than the dividend; becaufe in all divifion, 
as the divifor is to unity, fo is t e dividend — the sa 
tient: asif 3 divide £2, it will be as 3: 1s: 22: 4. 
3 is greater than 1; wh sea 2 mult be grea —e than # : 
but in fraétions, as 4: 1: 3 where 3 is lefs than 1 
ee 4 bags be lefs then 3 ac. 
eine in fpecies, or algebraic sl aa Tor 
nae feusiuies in otis to their leaft terms.—The comer tot 
d denominators are to be divided by the greatelt com- 
mon divifor, as in numbers. 
Thus the fra@ion — is reduced to a more fimple one 
203 is re- 
667 
7 
- duced to a more fimple one = by ad both 203 ard 
‘2oZaae. 7 — 
667 by 29; and 669 Be is reduced to ~ ae << <_by dividing 
by2g¢. And fo oa - becomes — ~—3e - —“—- by divid- 
, — bb— 
ing by 3a. And — eA u - becomes Lads 
by.dividing by 2—B4. mMon Meafu 
. To reduce frattions in {pecies to a common oe neminator. 
The terms of each are to be multiplied by the denominater 
ther, 
‘ef the o 
Thus, having 2 * ond +; multiply the terms of one — 
bo a’ i 
= d, ae alfo the terms of the other — + by 4, and they 
ad ‘be 
will become 32.2 ha 7 and Fa” whereof the “common denom- 
U2 gator 
