# How do you solve 4/5 x = 2/5?

May 20, 2017

See a solution process below:

#### Explanation:

Multiply each side of the equation by $\frac{\textcolor{red}{5}}{\textcolor{b l u e}{4}}$ to solve for $x$ while keeping the equation balanced:

$\frac{\textcolor{red}{5}}{\textcolor{b l u e}{4}} \times \frac{4}{5} x = \frac{\textcolor{red}{5}}{\textcolor{b l u e}{4}} \times \frac{2}{5}$

$\frac{\cancel{\textcolor{red}{5}}}{\cancel{\textcolor{b l u e}{4}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{4}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} x = \frac{\cancel{\textcolor{red}{5}}}{\textcolor{b l u e}{4}} \times \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}$

$x = \frac{2}{4}$

$x = \frac{2}{2 \times 2}$

$x = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 2}$

$x = \frac{1}{2}$