# Multiply a number by 4/5 then dividing by 2/5 is the same as multiplying by what number?

Apr 6, 2018

2

#### Explanation:

to divide a fraction you would multiply by it's inverse.

$x \cdot \frac{4}{5} / \frac{2}{5}$ would be rewritten as

$x \cdot \frac{4}{5} \cdot \frac{5}{2}$

cancel the 5s out and you are left with multiplying $x$ by 4 and then dividing it by 2 but you should reduce that as well, making it $2 x$

Apr 6, 2018

$2$

#### Explanation:

Let us assume the unknown number to be $x .$

According to the question, We have:

$\implies x \times \frac{4}{5} \div \frac{2}{5}$

$\implies x \times \frac{{\cancel{4}}^{2}}{\cancel{5}} \times \frac{\cancel{5}}{\cancel{2}}$

$\implies x \times 2$

$\therefore$ Multiplying a number by $\frac{4}{5}$ then dividing it by $\frac{2}{5}$ is the same as multiplying by $2$

Hope this helps! :)