# How do you simplify 2/(3/11)?

Oct 30, 2016

$\frac{22}{3} = 7 \frac{1}{3}$

#### Explanation:

In order to know how to calculate this, first decide what it means...

This is another way of writing $2 \div \frac{3}{11}$

We could also write $\frac{2}{1} \div \frac{3}{11}$ to have both as fractions.

Dividing by a fraction is the same as "X by the reciprocal"

$\frac{2}{1} \times \frac{11}{3} = \frac{22}{3} \text{ } \leftarrow$ multiply straight across.

But compare the two ways of writing this:

$\frac{\frac{2}{1}}{\frac{3}{11}} = \frac{2 \times 11}{1 \times 3} \text{ } \leftarrow$ can you see a short cut?

$\frac{\frac{\textcolor{red}{2}}{\textcolor{b l u e}{1}}}{\frac{\textcolor{b l u e}{3}}{\textcolor{red}{11}}} = \frac{\textcolor{red}{\left(2 \times 11\right)}}{\textcolor{b l u e}{\left(1 \times 3\right)}} = \frac{22}{3}$

As a general rule note that: $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \times d}{b \times c}$