Converting Percentages to Fractions

Rule

Converting Percentages to Fractions

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 % = 50 \times \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

Converting Fractions to Percentages

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 %

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 $\frac{1}{2} = 50 %$ .

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: $\frac{5}{7} \approx 0.714 \approx 71.4 %$

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 \div 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: $0.6 = 60 %$ . The answer is that $60$ % of the class are girls.

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Converting Percentages to Decimals Numbers

Activities 2