# 71.5 is 52% of what number?

Feb 25, 2017

71.5 is 52% of 137.5

#### Explanation:

"Percent" or "%" means "out of 100" or "per 100", Therefore 52% can be written as $\frac{52}{100}$.

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

Finally, lets call the number we are looking for "n".

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

$71.5 = \frac{52}{100} \times n$

$\frac{\textcolor{red}{100}}{\textcolor{b l u e}{52}} \times 71.5 = \frac{\textcolor{red}{100}}{\textcolor{b l u e}{52}} \times \frac{52}{100} \times n$

$\frac{7150}{\textcolor{b l u e}{52}} = \frac{\cancel{\textcolor{red}{100}}}{\cancel{\textcolor{b l u e}{52}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{52}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} \times n$

$137.5 = n$

$n = 137.5$