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Converting Percentages to Fractions


Rule

Converting Percentages to Fractions

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

Example 1

50% = 50 × 1 100 = 50 100 = 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, 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?

25 50 = 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 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 521 743, it’s smart to use a calculator.

Example 3

5 7 0.714. You can convert this into a percentage by moving the decimal mark two places to the right.

Answer: 5 7 0.714 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 15 25. If you use a calculator, you get

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%.

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

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