 # Converting Percentages to Fractions

Rule

### ConvertingPercentagestoFractions

You convert from a percentage to a fraction by exchanging the % sign for $\frac{1}{100}$. Then, you can simplify or expand the fraction if needed.

Example 1

 $50\phantom{\rule{0.17em}{0ex}}\text{%}=50×\frac{1}{100}=\frac{50}{100}=\frac{1}{2}$

Next, you will see how to convert the other way around; from fractions to percentages.

Rule

### ConvertingFractionstoPercentages

When you convert a fraction into a percentage, you can always do so via decimal numbers.

Let’s start with a simple example, $\frac{25}{50}$. Remember that a fraction is a ratio between two quantities.

Example 2

There are 25 girls in a group of 50 students. What percentage of the group are girls?

 $\frac{25}{50}=\frac{1}{2}=0.5=0.50=50\phantom{\rule{0.17em}{0ex}}\text{%}$

In the last step, we used the rule about moving the decimal mark two places to the right when converting from decimal numbers to percentages. You can also simply remember that $\frac{1}{2}=50\phantom{\rule{0.17em}{0ex}}\text{%}$.

Remember that you can change a fraction into a decimal number by either doing the division by hand, or by using a calculator. If the numbers are complicated, for example $\frac{521}{743}$, it’s smart to use a calculator.

Example 3

$\frac{5}{7}\approx 0.714$. You can convert this into a percentage by moving the decimal mark two places to the right.

Answer: $\frac{5}{7}\approx 0.714\approx 71.4\phantom{\rule{0.17em}{0ex}}\text{%}$

You might prefer to find the percentage by creating an equation with an unknown $x$. We’ll take a closer look at that later, but right now, let’s use the method shown in the example above.

Example 4

In a class of 25 students, 15 of them are girls. What percentage of the class are girls?

15 out of 25 is a ratio between two quantities that can be expressed as the fraction $\frac{15}{25}$. If you use a calculator, you get

 $\frac{15}{25}=15÷25=0.6$

You can also simplify the fraction and calculate 3 divided by 5, but you will get $0.6$ anyway. You then use the rule about moving decimal marks: $0.6=60\phantom{\rule{0.17em}{0ex}}\text{%}$.

The answer is that $60$ % of the class are girls.