# How do you solve 11/10=r/11?

May 24, 2018

$r = \frac{121}{10}$

#### Explanation:

Multiplying by $11$ we get
$\frac{121}{10} = r$

May 24, 2018

Divide both sides by $r$'s coefficient and you have your answer:
$r = \frac{121}{10} = 12.1$

#### Explanation:

Making this easy, we want to know what $r$ is. Currently, we know the value of $\frac{r}{11}$, so it would stand to make sense that we need to divide both sides by $r$'s coefficient $\left(\frac{1}{11}\right)$, which is the same as multiplying by its inverse, 11:

$\frac{11}{10} \times \textcolor{red}{11} = \frac{r}{11} \times \textcolor{red}{11}$

$\frac{11 \times \textcolor{red}{11}}{10} = \frac{\textcolor{red}{\cancel{11}} r}{\cancel{11}}$

$\textcolor{g r e e n}{r = \frac{121}{10} = 12.1}$