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Fractions and mixed numbers

Divide mixed numbers

To divide mixed numbers:

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

Divide $2\frac{1}{3}\div1\frac{2}{3}\;$. Simplify your answer and write it as a proper fraction or as a whole or mixed number.

Write $2\frac{1}{3}\;$ as an improper fraction:

$2\frac{1}{3}=\frac{(2\cdot3)+1}{3}=\frac{7}{3}$

Write $1\frac{2}{3}\;$ as an improper fraction:

$1\frac{2}{3}=\frac{(1\cdot3)+2}{3}=\frac{5}{3}$

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

$2\frac{1}{3}\div1\frac{2}{3}=\frac{7}{3}\div\frac{5}{3}$

$=\frac{7}{3}\cdot\frac{3}{5}$

Cancel common factors, then multiply.

$\frac{7}{3}\cdot\frac{3}{5}=\frac{7}{1}\cdot\frac{1}{5}$

$\frac{7\cdot1}{1\cdot5}=\frac{7}{5}$

$\frac{7}{5}=1\frac{2}{5}$
Divide 5$\frac{3}{8}\div{1}\frac{3}{2}$