Basic Technical Mathematics, 11th Edition

6.5 Multiplication and Division of Fractions

• Multiplication of Fractions • Division of Fractions • Using Calculator for Checking Answers

From arithmetic, recall that the product of two fractions is a fraction whose numerator is the product of the numerators and whose denominator is the product of the denominators of the given fractions. Also, the quotient of two fractions is found by inverting the second fraction and then proceeding as in multiplication. Symbolically, these operations are shown below:

Multiplication and Division of Fractions

$$\begin{array}{c}{\displaystyle \frac{a}{b}}\hspace{0.17em}\times \hspace{0.17em}{\displaystyle \frac{c}{d}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{ac}{bd}}\\ {\displaystyle \frac{a}{b}}\hspace{0.17em}÷\hspace{0.17em}{\displaystyle \frac{c}{d}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{{\displaystyle \frac{a}{b}}}{{\displaystyle \frac{c}{d}}}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{a}{b}}\hspace{0.17em}\times \hspace{0.17em}{\displaystyle \frac{d}{c}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{ad}{bc}}\end{array}$$

The first three examples illustrate the multiplication of fractions.

EXAMPLE 1 Multiplying basic fractions

1. ${\displaystyle \frac{3}{5}}\hspace{0.17em}\times \hspace{0.17em}{\displaystyle \frac{2}{7}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{(3)(2)}{(5)(7)}}\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{6}{35}}\begin{array}{l}\leftarrow \hspace{0.17em}\text{multiply numerators ...}\end{array}$