Education > Complete treatise on practical arithmetic and book-keeping

62
REDUCTION OTF VULGAR FRACTIONS.
VI. Ti> reduce fractions of different denominators to equivc
lent fractions of a common one.
Rule I.
If the fractions can be conveniently reduced to a comma
denominator, by multiplying or dividing theif terms,
cording to note 6, page 57, proceed by that method ; bi
if not, multiply each numerator continually into all the d«
nominators, except its own, for each new numerator: an
multiply all the denominators together for the common d*
nominator.
Note. It is evident, that in this and several other operations, wh<
any ef the proposed quantities are integers, mixt numbers, or compoui
fractions, they must be reduced by their proper rules, to the form
simple fractions.
Examples.
Reduce |, f, and ^ to a common denominator.
Thus —» —> and ~=—s—) and
2 3 4 24 24 24
6 8
and -
~ 12 12 12
Reduce 4 and £ to a commoh denominator. •
Reduce •£> r» a:1d 5 j to fractions of a com. denom.
Reduce 2f, and 4 to fractions of a com. denom.
'Rule II.
If the denominators of two given fractions have a con
mon measure, conceive them to be divided by their greate
common measure ; then multiply the terms of each give
fraction by the quotient arising from the other’s deriominato
Examples.
Reduce £ and f to a common denominator.
TT 7 4 7X5 4x3 35 12.
Here and and and ^
Note. In this last example, and those of the two following rules, tl
forms (Iff!? and are printed only to shew which numbe
'9X5 15X3/
or quotients are used in multiplying the terms of the fractions; but
think it quite needless for the pupil to write down his examples in tl-
way; and I would advise him barely to write down such an examp
as the above, thus: and and 11; and so of others.
9 15 45 45