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

[show answer]

Flip second fraction and change divison to multiplication

[show answer]

Multiply across

[show answer]

Simplify: reduce and rename

[show answer]

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]