# What percent of 180 is 120?

Apr 30, 2017

See the solution process below:

#### Explanation:

First, let's call the percent we are looking for $p$

"Percent" or "%" means "out of 100" or "per 100", Therefore p% can be written as $\frac{p}{100}$.

When dealing with percents the word "of" means "times" or "to multiply".

Putting this altogether we can write this equation and solve for $p$ while keeping the equation balanced:

$\frac{p}{100} \times 180 = 120$

$\frac{\textcolor{red}{100}}{\textcolor{b l u e}{180}} \cdot \frac{p}{100} \times 180 = \frac{\textcolor{red}{100}}{\textcolor{b l u e}{180}} \cdot 120$

$\frac{\cancel{\textcolor{red}{100}}}{\cancel{\textcolor{b l u e}{180}}} \cdot \frac{p}{\textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{180}}} = \frac{12000}{\textcolor{b l u e}{180}}$

$p = 66. \overline{6}$

120 is $66. \overline{6}$% or 66 2/3% of 180.

Apr 30, 2017

66.bar6%

#### Explanation:

You take $120$ over $180$ and times it by 100% to get the percentage.

$\left(\frac{120}{180}\right) = 0. \overline{6}$

0.bar6 xx 100%=66.bar6%