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Divide fractions

Divide fractions and mixed numbers

To divide mixed numbers by fractions:

1. Write mixed numbers and whole numbers as improper fractions.
2. Multiply by the reciprocal of the divisor.

Divide $1\frac{1}{2}\div\frac{4}{5}\;$. Simplify your answer and write it as a proper fraction or as a whole or mixed number.

Write $1\frac{1}{2}$ as an improper fraction:

$1\frac{1}{2}=\frac{(1\cdot2)+1}{2}=\frac{3}{2}$

Turn this from a division problem into a multiplication problem by multiplying by the reciprocal.

$1\frac{1}{2}\div\frac{4}{5}=\frac{3}{2}\div\frac{4}{5}$

$=\frac{3}{2}\cdot\frac{5}{4}$

Now multiply.

$\frac{3}{2}\cdot\frac{5}{4}=\frac{3\cdot5}{2\cdot4}=\frac{15}{8}$
$\frac{15}{8}=1\frac{7}{8}$
Divide $\frac{5}{8}\div{4}\frac{2}{7}$