# 40 is what percent of 32?

Mar 1, 2017

40 is color(red)(125%) of 32

#### Explanation:

First, lets 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:

$40 = \frac{p}{100} \times 32$

$\frac{\textcolor{red}{100}}{\textcolor{b l u e}{32}} \times 40 = \frac{\textcolor{red}{100}}{\textcolor{b l u e}{32}} \times \frac{p}{100} \times 32$

$\frac{4000}{\textcolor{b l u e}{32}} = \frac{\cancel{\textcolor{red}{100}}}{\cancel{\textcolor{b l u e}{32}}} \times \frac{p}{\textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{32}}}$

$125 = p$

$p = 125$

Mar 1, 2017

125%.

#### Explanation:

Translate from words to math:

$\text{40 is what percent of 32}$

$40 = x \times \frac{1}{100} \times 32$

$40 = \frac{32 x}{100}$

$\frac{40 \times 100}{32} = x$

$125 = x$

You can also think of it as this:

32 is like our whole. It's like our 100%. So 32 is to 100% as 40 is to what percent?

32/(100%)=40/x

32x=40(100%)

x=(40(100%))/32

x=125%