Video and Examples

This video demonstrates how to divide fractions. Sample: $2\frac{1}{5}\,\div~\,5\frac{1}{2}\,=$

It is a four-step process to divide mixed numbers:

Convert mixed numbers to impropers
Flip second fraction and change division to multiplication
Multiply across
Simplify: reduce and rename

$2\frac{1}{5}\,\div~\,5\frac{1}{2}\,=$

Convert mixed numbers to impropers	$\frac{11}{5}\,\div~\,\frac{11}{2}\,=$
Flip second fraction and change division to multiplication	$\frac{11}{5}\,\times~\,\frac{2}{11}\,=$
Multiply across	$\frac{22}{55}$
Simplify: reduce and rename	$\frac{2}{5}$

Example

The problem	$3\frac{1}{2}\div~5\frac{1}{4}\,=$
Convert mixed numbers into fractions	$\frac{7}{2}\div~\frac{21}{4}\,=$
Flip second fraction and change division to multiplication	$\frac{7}{2}\times~\frac{4}{21}\,=$
Multiply across	$\frac{28}{42}\,=$
Simplify: reduce and rename	$\frac{28}{42}\,=\,\frac{2}{3}$

Example

The problem	$2\frac{2}{3}\div~1\frac{1}{5}\,=$
Convert mixed numbers into fractions	[show answer] $\frac{8}{3}\div~\frac{6}{5}\,=$
Flip second fraction and change division to multiplication	[show answer] $\frac{8}{3}\times~\frac{5}{6}\,=$
Multiply across	[show answer] $\frac{40}{18}\,=$
Simplify: reduce and rename	[show answer] $\frac{40}{18}\,=\,\frac{20}{9}\,=\,2\frac{2}{9}$

What if one of the numbers is a whole number instead of a mixed number?

For more practice with fractions, please try this Fraction Calculator.

Self-Check

Q1: $\,\,\,3\frac{1}{3}\,\div~\,2\frac{1}{6}\,=\,\,\,$ [show answer]

$1\frac{7}{13}$

Q2: $\,\,\,1\frac{5}{6}\,\div~\,2\frac{1}{8}\,=\,\,\,$ [show answer]

$\frac{44}{51}$

Q3: $\,\,\,4\frac{1}{5}\,\div~\,3\frac{1}{2}\,=\,\,\,$ [show answer]

$1\frac{1}{5}$

Last modified: Thursday, 16 April 2020, 2:19 PM