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 .

$\frac{a}{c}÷\frac{e}{m}=\frac{a}{c}×\frac{m}{e}$

Example 1:

Find the quotient.

$\frac{2}{3}÷\frac{7}{9}$

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 $\frac{7}{9}$ , $\frac{9}{7}$ .

$\frac{2}{3}÷\frac{7}{9}=\frac{2}{3}×\frac{9}{7}$

Divide by the GCF , $3$ .

$=\frac{2}{\underset{1}{\overline{)3}}}×\frac{\stackrel{3}{\overline{)9}}}{7}$

Simplify.

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

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 $3\frac{3}{5}÷2\frac{5}{8}$ .

First rewrite the mixed numbers as an improper fraction.

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

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

$=\frac{18}{5}×\frac{8}{21}$

Divide out the common factor.

$=\frac{\stackrel{6}{\overline{)18}}}{5}×\frac{8}{\underset{7}{\overline{)21}}}$

Simplify.

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

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