# How do you simplify \frac{\frac{8}{5}}{4}?

Sep 25, 2017

See below.

#### Explanation:

There are a few ways to tackle this:

If we look at this as being just like any other fraction, then the same rules will apply:

$\frac{\frac{8}{5}}{4}$ we can multiply top and bottom without changing the relationship so, using $\frac{8}{5} \div 4$

Multiply top and bottom by $5$:

$\frac{\frac{\cancel{5} \left(8\right)}{\cancel{5}}}{5 \left(4\right)}$ = 8/((5)(4) = $\frac{8}{20}$ = $\textcolor{b l u e}{\frac{2}{5}}$

Alternatively:

$\frac{8}{5} \div 4$ is equal to $\frac{8}{5} \times$ the reciprocal of $4$. The reciprocal of a number can be found by putting $1$ over the number. So:

Reciprocal of $4$ is $\frac{1}{4}$

So we have:

$\frac{8}{5} \times \frac{1}{4} = \frac{8 \times 1}{5 \times 4} = \frac{8}{20} = \textcolor{b l u e}{\frac{2}{5}}$

There are even more ways to achieve this, but you can just use the one you find easiest.

Sep 25, 2017

$\frac{\frac{8}{5}}{4} = \textcolor{red}{\frac{2}{5}}$

#### Explanation:

In general $\frac{\textcolor{b l u e}{a}}{\textcolor{m a \ge n t a}{b}} = \textcolor{b l u e}{a} \times \textcolor{m a \ge n t a}{\frac{1}{b}}$

In this case we have
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{a} = \textcolor{b l u e}{\frac{8}{5}}$ and $\textcolor{m a \ge n t a}{b} = \textcolor{m a \ge n t a}{4}$

So
$\textcolor{w h i t e}{\text{XXX}} \frac{\textcolor{b l u e}{\frac{8}{5}}}{\textcolor{m a \ge n t a}{4}} = \textcolor{b l u e}{\frac{8}{5}} \times \textcolor{m a \ge n t a}{\frac{1}{4}}$

$\textcolor{w h i t e}{\text{XXXXX}} = \frac{{\cancel{8}}^{2}}{5} \times \frac{1}{\cancel{4}}$

$\textcolor{w h i t e}{\text{XXXXX}} = \frac{2}{5}$