CASE IV.

55. To reduce fractions having different denominators to equivalent fractions having a common denominator.

RULE.

Multiply each numerator into all the denominators except its own, for the new numerators, and all the denominators together for a common denominator.

EXAMPLES.

1. Reduce,, and, to a common denominator.

1x3x5=15 the new numerator of the 1st.

Therefore, 15, 38, and 34, are the equivalent fractions.

30 30

NOTE. It is plain that this reduction does not alter the values of the several fractions, since the numerator and denominator of each are multiplied by the same number.

QUEST.-55. How do you reduce fractions to a common denominator ?

CASE V.

56. To add fractional quantities together.

RULE.

Reduce the fractions, if necessary, to a common denominator; then add the numerators together, and place their sum over the common denominator.

EXAMPLES.

1. Add,, and together.

By reducing to a common denominator, we havė

And

Hence,

d

me 4.

e

cxbxf=cbf the new numerators.
exbxd=ebd

bxdxf=bdf the common denominator.

adf cbf ebd adf+cbf+ebd
+ +
bdf bdf
bdf bdf

the sum.

bdf

QUEST.-56. How do you add fractions.

9. It is required to add 4, 7, and 2+ together.

7x 9

5

CASE VI.

57. To subtract one fractional quantity from another.

RULE.

1. Reduce the fractions to a common denominator.

II. Subtract the numerator of the fraction to be subtracted from the numerator of the other fraction, and place the difference over the common denominator.