# 400 is 262 1/2% of what?

Mar 24, 2017

See the entire solution process below:

#### Explanation:

First, rewrite 262 1/2% as 262.5%.

"Percent" or "%" means "out of 100" or "per 100", Therefore 262.5% can be written as $\frac{262.5}{100}$.

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:

$\frac{262.5}{100} \times n = 400$

$\frac{\textcolor{red}{100}}{\textcolor{b l u e}{262.5}} \times \frac{262.5}{100} \times n = \frac{\textcolor{red}{100}}{\textcolor{b l u e}{262.5}} \times 400$

$\frac{\cancel{\textcolor{red}{100}}}{\cancel{\textcolor{b l u e}{262.5}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{262.5}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} \times n = \frac{\textcolor{red}{40000}}{\textcolor{b l u e}{262.5}}$

$n = 152.38$ rounded to the nearest thousandth.

262 1/2% of $\textcolor{red}{152.38}$ (rounded to the nearest thousandth) is 400.