# How do you divide 2/5 div 3/10?

Mar 25, 2018

$\frac{4}{3} = 1 \frac{1}{3}$

#### Explanation:

To divide by a fraction, change to multiply by the reciprocal:

$\frac{2}{5} \div \frac{3}{10}$

$= \frac{2}{5} \times \frac{10}{3}$

$= \frac{2}{\cancel{5}} \times {\cancel{10}}^{2} / 3$

$= \frac{4}{3}$

Mar 25, 2018

See a solution process below:

#### Explanation:

Use this rule for dividing fractions:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

Substituting gives:

$\frac{\frac{\textcolor{red}{2}}{\textcolor{b l u e}{5}}}{\frac{\textcolor{g r e e n}{3}}{\textcolor{p u r p \le}{10}}} \implies \frac{\textcolor{red}{2} \times \textcolor{p u r p \le}{10}}{\textcolor{b l u e}{5} \times \textcolor{g r e e n}{3}} \implies \frac{\textcolor{red}{2} \times \cancel{\textcolor{p u r p \le}{10}} \textcolor{p u r p \le}{2}}{\cancel{\textcolor{b l u e}{5}} \textcolor{b l u e}{1} \times \textcolor{g r e e n}{3}} \implies \frac{4}{3}$