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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 , 3, and #, to a common denominator.

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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.

b 2. Reduce + and + to equivalent fractions having

a common denominator.

a × 0–6, $ × b=&”

and bx e-be, the common denominator.

; the new numerators.

QUEst.—55. How do you reduce fractions to a common denominator?

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CASE W.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.

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35+30+30+ 30 which, by reducing to the lowest term me 4}}.

- 0. c e 2. Find the sum of T. d’ and 7.

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- - 5a-2 7. It is required to add 4a, ; , and together.

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10. It is required to add 3.4% and s—o together.

23 Ans. 3.4 .

- 6b c 11. Required the sum of ac-5, and 1–7.

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CASE WI. 57. To subtract one fractional quantity from another.

RULE.

I. 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.

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