# How do you multiply 6/7 div 3/2?

Mar 16, 2016

$\frac{4}{7}$ As you become more practiced you will considerably reduce the number of steps. You will be able to do a lot of it in your head.

#### Explanation:

Shortcut method:

Turn the divisor $\left(\frac{3}{2}\right)$ upside down (invert) and then multiply

So we have

$\frac{6}{7} \div \frac{3}{2} \text{ "=" } \frac{6}{7} \times \frac{2}{3}$

But, when multiplying you are allowed to do this:

$\textcolor{b l u e}{\frac{6}{7}} \times \textcolor{red}{\frac{2}{3}} \text{ "=" } \textcolor{b l u e}{\frac{6}{\textcolor{red}{3}} \times \frac{\textcolor{red}{2}}{7}}$

This gives:

$2 \times \frac{2}{7} \text{ " =" " 2/7+2/7" " =" } \frac{4}{7}$