# How do you solve 10/k=8/4?

Sep 3, 2016

$k = 5$

#### Explanation:

We have one fraction equal to another. In this situation we can $\textcolor{b l u e}{\text{cross-multiply}}$ to solve.

$\Rightarrow \frac{\textcolor{b l u e}{10}}{\textcolor{red}{k}} = \frac{\textcolor{red}{8}}{\textcolor{b l u e}{4}}$

Now cross-multiply(X) the values on either end of an 'imaginary' cross and equate them. That is multiply the $\textcolor{b l u e}{\text{blue}}$ values together and the $\textcolor{red}{\text{red}}$ values together and equate them.

$\Rightarrow \textcolor{red}{8 k} = \left(\textcolor{b l u e}{10} \times \textcolor{b l u e}{4}\right) \Rightarrow 8 k = 40$

now divide both sides by 8 to solve for k.

$\Rightarrow \frac{{\cancel{8}}^{1} k}{\cancel{8}} ^ 1 = \frac{{\cancel{40}}^{5}}{\cancel{8}} ^ 1 \Rightarrow k = 5$