## Dividing Fractions

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

1. Convert mixed numbers to impropers
2. Flip second fraction and change divison to multiplication
3. Multiply across
4. 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 divison 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 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 $\frac{8}{3}\div~\frac{6}{5}\,=$ Flip second fraction and change divison to multiplication $\frac{8}{3}\times~\frac{5}{6}\,=$ Multiply across $\frac{40}{18}\,=$ Simplify: reduce and rename $\frac{40}{18}\,=\,\frac{20}{9}\,=\,2\frac{2}{9}$

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]

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

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