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Dividing Fractions

To divide a fraction by another fraction, multiply the first fraction by the multiplicative inverse of the second fraction... that is, its reciprocal .

$\frac{a}{c} \div \frac{e}{m} = \frac{a}{c} \times \frac{m}{e}$

Example 1:

Find the quotient.

$\frac{2}{3} \div \frac{7}{9}$

To divide by a fraction, multiply by its multiplicative inverse.

That is, multiply the first fraction $\frac{2}{3}$ by the reciprocal of the second fraction $\frac{7}{9}$ , $\frac{9}{7}$ .

$\frac{2}{3} \div \frac{7}{9} = \frac{2}{3} \times \frac{9}{7}$

Divide by the GCF , $3$ .

$= \frac{2}{\underset{1}{3}} \times \frac{\overset{3}{9}}{7}$

Simplify.

$\begin{array}{l} = \frac{2}{1} \times \frac{3}{7} \\ = \frac{6}{7} \end{array}$

Dividing Mixed Numbers

To divide by a mixed number , first rewrite the mixed numbers as an improper fraction . Then divide the fractions.

Example 2:

Find $3 \frac{3}{5} \div 2 \frac{5}{8}$ .

First rewrite the mixed numbers as an improper fraction.

$3 \frac{3}{5} \div 2 \frac{5}{8} = \frac{18}{5} \div \frac{21}{8}$

Now multiply by the multiplicative inverse of $\frac{21}{8}$ , $\frac{8}{21}$ .

$= \frac{18}{5} \times \frac{8}{21}$

Divide out the common factor.

$= \frac{\overset{6}{18}}{5} \times \frac{8}{\underset{7}{21}}$

Simplify.

$\begin{array}{l} = \frac{6}{5} \times \frac{8}{7} \\ = \frac{48}{35} \end{array}$

Converting the improper fraction into a mixed number, the answer is $1 \frac{13}{35}$ .