CASE I.

To reduce a fraction to its simplest terms.

52. The rule for reducing a monomial fraction to its lowest terms has already been given (Art. 44).

With respect to polynomial fractions, the following are cases which are easily reduced.

1. Take, for example, the expression

a2-b2

a2-2ab+b2

This fraction can take the form

(a+b) (a−b)
(a-b)2

(Art. 39 and 40). Suppressing the factor a-b, which is common to the two terms, we obtain

QUEST.-52. How do you reduce a fraction to its simplest terms?

Suppressing the common factors a(a-b), the result is

5(a—b)

8a

Hence, to reduce any fraction to its simplest terms, we suppress or cancel every factor common to the numerator and denominator.

NOTE. Find the factors of the numerator and denominator as explained in (Art. 41).

CASE II.

53. To reduce a mixed quantity to the form of a fraction.

RULE.

Multiply the entire part by the denominator of the fraction; then connect this product with the terms of the numerator by the rules for addition, and under the result place the given denominator.

QUEST-53. How do you reduce a mixed quantity to the form of a

fraction?

54. To reduce a fraction to an entire or mixed quantity.

RULE.

Divide the numerator by the denominator for the entire part, and place the remainder, if any, over the denominator for the fractional part.

QUEST.-54. How do you reduce a fraction to an entire or mixed quantity 1