# How do you solve 7/n=8/7?

Oct 1, 2016

$n = \frac{49}{8}$

#### Explanation:

Given one fraction equal to another fraction we can solve using $\textcolor{b l u e}{\text{cross multiplication}}$

That is : $\frac{\textcolor{red}{7}}{\textcolor{b l u e}{n}} = \frac{\textcolor{b l u e}{8}}{\textcolor{red}{7}}$

Now multiply the terms on the ends of an 'imaginary' cross (X) and equate them.

That is multiply the $\textcolor{b l u e}{\text{blue terms together}}$ and the $\textcolor{red}{\text{red terms together}}$ and equate them.

$\Rightarrow \textcolor{b l u e}{8 \times n} = \textcolor{red}{7 \times 7}$

$\Rightarrow 8 n = 49$

to solve for n divide both sides by 8.

$\frac{\cancel{8} n}{\cancel{8}} = \frac{49}{8}$

$\Rightarrow n = \frac{49}{8} \text{ is the solution}$