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(a+b)(a−b)

This fraction may be written

Rejecting the common factor a+b, we obtain

(a+b)2

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(a+b)(a−b)'

Rejecting the common factor a-b, we obtain

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PROBLEM II.

(80.) 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.

27

Thus, is equal to 27÷5, which equals 53. 5

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QUEST.-How may we reduce a fraction to an entire or mixed quan

ity 1

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(81.) To reduce a mixed quantity to the form of a fraction.

RULE.

Multiply the entire part by the denominator of the fraction; to the product add the numerator, with its proper sign, and place the result over the given denominator.

3x5+2 15+2 17

Thus, 3 is equal to

5

5

5:

This result may be proved by the preceding rule.

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QUEST.-HOW may we reduce a mixed quantity to the form of a

fraction?

Examples.

1. Reduce 7 to the form of a fraction.

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a-b

x

7. Reduce a+b+· to the form of a fraction.

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