# How do you solve \frac { z } { 10} = \frac { 45} { 50}?

Apr 3, 2017

See the entire solution process below:

#### Explanation:

Multiply each side of the equation by $\textcolor{red}{10}$ to solve for $z$ while keeping the equation balanced:

$\textcolor{red}{10} \times \frac{z}{10} = \textcolor{red}{10} \times \frac{45}{50}$

$\cancel{\textcolor{red}{10}} \times \frac{z}{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}} = \cancel{\textcolor{red}{10}} \times \frac{45}{\textcolor{red}{\cancel{\textcolor{b l a c k}{50}}} 5}$

$z = \frac{45}{5}$

$z = 9$

Apr 3, 2017

$z = 9$

#### Explanation:

First things first, GET A COMMON DENOMINATOR
(We can multiply $\frac{z}{10}$ by $\frac{5}{5}$ to get the same denominator as $\frac{45}{50}$)

$\frac{z}{10} \cdot \frac{5}{5} = \frac{5 z}{50}$

Now the entire problem looks like:

$\frac{5 z}{50} = \frac{45}{50}$

Now we focus on the numerators. (The denominator stays the same, but I removed it so it is easier to read and doesn't take as long to write down)

Numerator ------> $5 z = 45$

Solve for $z$

$z = \frac{45}{5}$

$z = 9$

Now, put that over the denominator:

$\frac{9}{10} = \frac{45}{50}$