# How do you solve 2/G=8/36?

May 2, 2018

$G = 9$

#### Explanation:

$\frac{2}{G} = \frac{8}{36}$

First, simplify the right side of the equation by dividing it by $4$:
$\frac{2}{G} = \frac{8}{36} \textcolor{b l u e}{\div \frac{4}{4}}$

$\frac{2}{G} = \frac{2}{9}$

Now multiply both sides by $\textcolor{b l u e}{\frac{1}{2}}$:
$\frac{2}{G} \textcolor{b l u e}{\times \frac{1}{2}} = \frac{2}{9} \textcolor{b l u e}{\times \frac{1}{2}}$

$\frac{1}{G} = \frac{2}{18}$

Simplify :
$\frac{1}{G} = \frac{1}{9}$

Since the reciprocal of $G$ or $\left(\frac{1}{G}\right)$ is $\frac{1}{9}$, then we know that $G = 9$.

Hope this helps!

May 2, 2018

$G = 9$

#### Explanation:

The biggest issue is that $G$ is in the denominator. There are two ways to rectify that.

Invert both sides

This is possible because there is only one fraction on each side.

$\frac{2}{G} = \frac{8}{36}$

$\frac{G}{2} = \frac{36}{8}$

Now multiply both sides by $2$ and simplify

$\frac{\cancel{2} \times G}{\cancel{2}} = \frac{\cancel{2} \times {\cancel{36}}^{9}}{\cancel{8}} _ \cancel{2}$

$G = 9$

Cross Multiply

$8 G = 2 \times 36 \text{ } \leftarrow$ no fractions.

$G = \frac{\cancel{2} \times {\cancel{36}}^{9}}{\cancel{8}} _ \cancel{2}$

$G = 9$