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a'—2ab+b? · Ex. 20. Reduce

to its lowest terms.

(a-6) This fraction may be written

(a+b)(a-6) Rejecting the common factor a-b, we obtain

a-b

atā Ans.

27

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.

Thus, is equal to 27:5, which equals 53.
Also, asta? =(ax+a*)==a+

Ecamples.
1. Reduce 0079 to an entire quantity.

Ans. 954. 2. Reduce a**** to an entire quantity.

Ans. A-X.

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3. Reduce ~

e to a mixed quantity.

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

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PROBLEM III. (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, 31 is equal to 5 5 This result may be proved by the preceding rule.

For 7 is equal to 17:5=33.

Also, at is equal to axetb_actos

QUEST.-How may we reduce a mixed quantity to the form of a fraction ?

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Examples. 1. Reduce 7to the form of a fraction.

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as-c* 2. Reduce x+ to the form of a fraction.

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3. Reduce 2+-
M , axtar,

- to the form of a fraction

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2x–7 4. Reduce 5+ - to the form of a fraction.

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