# How do you solve 6/a=3/8?

Jan 3, 2017

$\frac{6}{a} = \frac{3}{8}$

Multiply each side by $a$:
$6 = \frac{3}{8} a$

Isolate $a$ by multiplying each side by the reciprocal of $\frac{3}{8}$:
$6 \cdot \left(\frac{8}{3}\right) = a$

$a = 16$

Jan 3, 2017

Multiply each side of the equation by the lowest common denominator to eliminate the fractions and then solve for $a$. See full solution process below.

#### Explanation:

First, multiply each side of the equation by the lowest common denominator (in this case $\textcolor{red}{8} \textcolor{b l u e}{a}$)to eliminate the fractions and keep the equation balanced:

$\frac{6}{\textcolor{b l u e}{a}} \times \textcolor{red}{8} \textcolor{b l u e}{a} = \frac{3}{\textcolor{red}{8}} \times \textcolor{red}{8} \textcolor{b l u e}{a}$

$\frac{6}{\cancel{\textcolor{b l u e}{a}}} \times \textcolor{red}{8} \cancel{\textcolor{b l u e}{a}} = \frac{3}{\cancel{\textcolor{red}{8}}} \times \cancel{\textcolor{red}{8}} \textcolor{b l u e}{a}$

$6 \times \textcolor{red}{8} = 3 \textcolor{b l u e}{a}$

$48 = 3 \textcolor{b l u e}{a}$

We can now divide each side of the equation by $\textcolor{red}{3}$ to solve for $a$ and keep the equation balanced:

$\frac{48}{\textcolor{red}{3}} = \frac{3 \textcolor{b l u e}{a}}{\textcolor{red}{3}}$

$16 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \textcolor{b l u e}{a}}{\cancel{\textcolor{red}{3}}}$

$16 = a$

or

$a = 16$