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8. Reduce 2ab-3c+ to the form of a fraction.

4αx 5y

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(82.) To reduce fractions to a common denomina

tor.

RULE.

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

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We have seen in Art. 79, that if both numerator and denominator are multiplied by the same number, the value of the fraction will not be altered. If we multiply both the numerator and denominator of the first fraction by 7, and those of the second by 5, the frac

QUEST.-How may we reduce fractions to a common denominator?

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Here it will be seen that the numerator and denominator of the first fraction are both multiplied by d, and in the second fraction they are both multiplied by b. The value of the fractions, therefore, is not changed by this operation.

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QUEST.-How does it appear that the value of fractions is not changed

by reducing them to a common denominator?

E

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PROBLEM V.

(83.) Tc add fractional quantities together.

RULE.

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

The fractions must first be reduced to a common denominator to render them like parts of unity. Before this reduction, they must be considered as unlike quantities.

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QUEST.-How do we add fractions together? Why must the frac

tions be reduced to a common denominator?

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