# How do you solve 6/z=3/5?

Apr 17, 2017

$10$

#### Explanation:

$\frac{6}{z} = \frac{3}{5}$
$\frac{6}{3} = \frac{z}{5}$
$2 = \frac{z}{5}$
2×5=z
$z = 10$

Apr 17, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by the common denominator of the two fractions which is $\textcolor{red}{5} \textcolor{b l u e}{z}$. This will eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{5} \textcolor{b l u e}{z} \times \frac{6}{z} = \textcolor{red}{5} \textcolor{b l u e}{z} \times \frac{3}{5}$

$\textcolor{red}{5} \cancel{\textcolor{b l u e}{z}} \times \frac{6}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{z}}}} = \cancel{\textcolor{red}{5}} \textcolor{b l u e}{z} \times \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}$

$30 = 3 z$

Now, divide each side of the equation by $\textcolor{red}{3}$ to solve for $z$ while keeping the equation balanced:

$\frac{30}{\textcolor{red}{3}} = \frac{3 z}{\textcolor{red}{3}}$

$10 = \frac{\textcolor{red}{\cancel{\textcolor{red}{3}}} z}{\cancel{\textcolor{red}{3}}}$

$10 = z$

$z = 10$

Another method to solve an equation of two fractions is to "flip" the fractions and then solve for $z$:

$\frac{z}{6} = \frac{5}{3}$

Now multiply each side of the equation by $\textcolor{red}{6}$ to solve for $z$:

$\textcolor{red}{6} \times \frac{z}{6} = \textcolor{red}{6} \times \frac{5}{3}$

$\cancel{\textcolor{red}{6}} \times \frac{z}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}} = \frac{30}{3}$

$z = 10$