# How do you solve 8/3 = 12/n?

May 27, 2017

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\frac{\textcolor{red}{3}}{\textcolor{b l u e}{8}}$:

$\frac{\textcolor{red}{3}}{\textcolor{b l u e}{8}} \times \frac{8}{3} = \frac{\textcolor{red}{3}}{\textcolor{b l u e}{8}} \times \frac{12}{n}$

$\frac{\cancel{\textcolor{red}{3}}}{\cancel{\textcolor{b l u e}{8}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{8}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \frac{36}{8 n}$

$1 = \frac{36}{8 n}$

Now, multiply each side of the equation by $\textcolor{red}{n}$ to solve for $n$ while keeping the equation balanced:

$\textcolor{red}{n} \times 1 = \textcolor{red}{n} \times \frac{36}{8 n}$

$n = \cancel{\textcolor{red}{n}} \times \frac{36}{8 \textcolor{red}{\cancel{\textcolor{b l a c k}{n}}}}$

$n = \frac{36}{8}$

$n = \frac{4 \times 9}{4 \times 2}$

$n = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 9}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \times 2}$

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

May 27, 2017

$n = \frac{9}{2} \text{ "->" } 4 \frac{1}{2}$

#### Explanation:

Given: $\frac{8}{3} = \frac{12}{n}$

We need to find $n$ so lets make it the top value (numerator)

Turn everything upside down (yes you can do this!)

$\frac{3}{8} = \frac{n}{12}$

We now need to 'get' $n$ on its own so we need to 'get rid' of the 12. We do this by turning it into 1 as 1 times anything does not change the value.

Multiply both sides by 12

$\textcolor{g r e e n}{\frac{3}{8} \textcolor{red}{\times 12} \text{ "=" } \frac{n}{12} \textcolor{red}{\times 12}}$

color(green)(" "36/8" "=" "ncolor(red)(xx12/(color(green)(12)))#

But $\frac{12}{12} = 1 \text{ }$ and $\text{ } n \times 1 = n$

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

$n = \frac{9}{2} \text{ "->" } 4 \frac{1}{2}$