# Dividing fractions review

CCSS Math: 6.NS.A.1
Review the basics of dividing fractions, and try some practice problems.

## Dividing fractions

Dividing fractions is the same as multiplying by the reciprocal (inverse).
For example:
$\dfrac34\goldD{\div}\dfrac{\blueD2}{\greenD3}$$=\dfrac34\goldD{\times}\dfrac{\greenD3}{\blueD2}$
Once we have a multiplication problem, we multiply the numerators then multiply the denominators.
Example 1: Fractions
$\dfrac{3}{2} \div \dfrac{8}{3} = {?}$
The reciprocal of $\dfrac{8}{3}$ is $\dfrac{3}{8}$.
Therefore:
$\dfrac{3}{2} \div \dfrac{8}{3} = \dfrac{3}{2} \times \dfrac{3}{8}$
$\phantom{\dfrac{3}{2} \times \dfrac{3}{8}} = \dfrac{3 \times 3}{2 \times 8}$
$\phantom{\dfrac{3}{2} \times \dfrac{3}{8}} = \dfrac{9}{16}$
Example 2: Mixed numbers
$3\dfrac{1}{2} \div 1\dfrac{1}{4} =$
Let's start by converting the mixed numbers to fractions.
$\phantom{=}3\dfrac{1}{2} \div 1\dfrac{1}{4}$
$= \dfrac{7}{2}\div\dfrac{5}{4}$
$=\dfrac{7}{2}\cdot\dfrac{4}{5} ~~~~~~~\text{Multiply by the reciprocal.}$
$=\dfrac{7}{\blueD{1}\cancel{2}}\cdot \dfrac{\blueD{2}\cancel{4}}{5} ~~~~~~~\text{Simplify.}$
$=\dfrac{7}{\blueD{1}}\cdot \dfrac{\blueD{2}}{5}$
$=\dfrac{14}{5}\text{ or }2\dfrac45$
$\dfrac{3}{5} \div \dfrac{1}{9} = {?}$