SECTION V. FRACTIONS.

Multiply all the numerators together for the numerator of the product, and all the denominators together for its denominator.

120. Suppose it required to multiply together ¹⁵/₁₆ and ⁸/₁₀. The product may be written thus:

which reduced to its lowest terms (109) is ¾. This result might have been obtained directly, by observing that 15 and 10 are both measured by 5, and 8 and 16 are both measured by 8, and that the fraction may be written thus:

• 3 × 5 × 8
• 2 × 8 × 2 × 5.

Divide both its numerator and denominator by 5 × 8 (108) and (87), and the result is at once ¾; therefore, before proceeding to multiply any number of fractions together, if there be any numerator and any denominator, whether belonging to the same fraction or not, which have a common measure, divide them both by that common measure, and use the quotients instead of the dividends.

A whole number may be considered as a fraction whose denominator is 1; thus, 16 is ¹⁶/₁ (106); and the same rule will apply when one or more of the quantities are whole numbers.

EXERCISES.