# One day, 32 of 80 people wore a red shirt to school. What percent of the 80 people did not wear a red shirt to school?

Apr 3, 2018

60 percent

#### Explanation:

Let me start with finding number of people who wore other colored shirt:

$= 80 - 32 = 48$

Therefore, 48 out of 80 people wore other colored shirt.

As percentage this is:

$= 100 \times \frac{48}{80} = 60$ percent

Apr 3, 2018

60%

A lot of detail given to help understanding. Normally a calculation of this type would only take a few lines.

#### Explanation:

Percentage is basically just another fraction. Although, it is a special fraction in that the bottom number (denominator) is fixed at 100.

If the count of red shirts is 32 then the non red shirt count is
$80 - 32 = 48$

So this count as a fraction of the whole is $\frac{48}{80}$

But for this to be a percentage we need the bottom number (denominator) to be 100. So we write as an 'equivalent fraction'.

Let the unknown count be $x$ giving:

$\textcolor{g r e e n}{\frac{48}{80} \equiv \frac{x}{100}}$

To find the value of the top number (numerator) of $x$ we need to get it on its own. So we need to 'get rid' of the 100. We do this by changing it into 1

Multiply both sides by color(red)(100)

$\textcolor{g r e e n}{\frac{48}{80} \equiv \frac{x}{100} \textcolor{w h i t e}{\text{dddd")->color(white)("dddd") 48/80color(red)(xx100) color(white)("d") =color(white)("d}} \frac{x}{100} \textcolor{red}{\times 100}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddddddd.d") ->color(white)("dddd") 48color(red)(xxcancel(100)^(10)/color(green)(cancel(80)^8)) color(white)("d") =color(white)("d}} x \textcolor{red}{\times \frac{\cancel{100}}{\textcolor{g r e e n}{\cancel{100}}}}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddddddd.d") ->color(white)("ddddddd") cancel(48)^6xx10/cancel(8)^1 color(white)("d") =color(white)("d}} x}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddddddd.d") ->color(white)("ddddddddddd") 60color(white)("dddd") =color(white)("d}} x}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$x = 60 \to \frac{x}{100} = \frac{60}{100}$

$\frac{60}{100}$ is the same thing as $60 \times \frac{1}{100}$ and $\times \frac{1}{100}$ is the same thing as %

So 60/100=60%