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

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

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

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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 divison 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 divison to multiplication	[show answer] $\frac{8}{3}\times~\frac{5}{6}\,=$
Multiply across	[show answer] $\frac{40}{18}\,=$
Simplify: reduce and rename	[show answer] $\frac{40}{18}\,=\,\frac{20}{9}\,=\,2\frac{2}{9}$

Self-Check

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

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

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

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