Reduction of Vulgar Fractions.         126

3 A. compound fraction is the fraction of a fraction, and known by the word of, as, £ o/f of | o/T8T o/T\, &c.

4. A mixed number or fraction is composed of a whole number and a fraction, as 8f, 17^, 8^-, &c.

REDUCTION OF VULGAR FRACTIONS.

1.    To reduce fractions to a common denominator.

Rule 1.—Multiply each numerator into all the denominators, except its own, for a new numerator; and all the denominators, for a common denominator.    Or,

2.—Multiply the common denominator by the several given numerators separately, and divide the product by their several denominators ; the quotients will be the new numerators.

EXAMPLES.

(1)  Reduce |- and y to a common denominator.

Ans. ^| and £f.

1st num.      2nd num.

£. x7=U, 4 x4=16, then 4 x7=28 den.=-*-f and |f.

(2)  Reduce $, f, and |, to a common denominator.

Anc    3 2    4 8     4o  Alls, -j^-, ^-, ls-f.

,'8X Reduce ¦§¦, -J, and -^, to a common denominator.

An«     a 7 o     400     3 15 Ans- TT5-) TT^' 4T"B

(4)  Reduce -^y, f, -f, and ^, to a common denominator.

An«    iocs      840       240       P-*^-•"¦"»• -T5To> TTTOI ¦T6T5> Tfi^ff-

(5)  Reduce f, f, f, and J, to a common denominator.

Ans    67 2      5 60      360     105

(6)  Reduce %, ^, f, and -|, to a common denominator.

Ana  7 2Q  1200  540  1296 •""»• ¦st-jw) TT^u') Tr'ffTT» lita

2.    2*o reduce a vulgar fraction to its lowest term.

Rule.—Find a common measure by dividing the lower term by the upper, and that divisor by the remainder following, till nothing remains; the last divisor is the common measure ; then divide both parts of the fraction by the common measure, and the quotient will give the fraction required.

Efg" If the common measure happens to be 1, the fraction is already in its lowest term; and when a fraction lu.t'i cyphers at the right hand, it may be abreviated by cutting them off; as, ^T\%.            y 0    '