This document explains how to convert fractions to percentages in 3 main steps: 1) Convert the fraction to a decimal by dividing the numerator by the denominator. Then multiply the decimal by 100 to get the percentage. 2) Think of 100 as the denominator of an equivalent fraction. Find the equivalent fraction by setting 100 as the denominator. 3) Directly convert the fraction to a percentage by multiplying the fraction by 100 and simplifying. This skips converting to a decimal first. Worked examples are provided to demonstrate both converting through decimals and directly to percentages.

1. October 4, 2012
Percentages
1. Converting fractions to
decimals and percentages
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2. Explanation October 4, 2012
Here is the “percent” symbol.
It is made up from a “1” and two “0”s
1 0
0
“Cent” means 100. Percent means “per one hundred”, or
“out of every lot of one hundred”.
Here are 100 matches.
Sort them according to whether they have been struck.
12 out of the total of 100 have been used, so 12%.
88 out of the total of 100 remain unused, so 88%.
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3. Explanation October 4, 2012
You can think of this as a fraction.
12% is the same as 12
100
12 can be simplified as 3
100 25
If you had 25 matches and 3 had been stuck, as a
percentage, this would again be 12%.
3 = 12 = 12%
25 100
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4. Explanation October 4, 2012
To convert a fraction to a percentage you need to find
the equivalent fraction that has 100 as its denominator.
A survey found that
“Seven out of ten students asked,
preferred chocolate to crisps”
7 = 70 = 70%
denominator 10 100
It is not always easy to find the equivalent fraction.
In this case, change the fraction to a decimal, by dividing
the numerator by the denominator.
Then multiply the result by 100.
numerator 7 = 0.7 × 100 = 70%
10
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5. Explanation October 4, 2012
You can skip the stage of converting to a decimal to
convert a fraction straight to a percentage.
To do this you need to think of 100 as a top heavy
fraction.
7 × 100 = 7 × 100 = 700 = 70%
10 10 1 10
Don’t confuse your calculations with the method of using
equivalent fractions!
7 actually means the same as 70%
10
700 is just part of the workings out that gives
10 you the number 70.
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6. Practise October 4, 2012
Show how you would convert each of these fractions to
percentages, first by converting to a decimal, then a
percentage, then by converting directly to a percentage.
Write all numbers to two significant figures.
5 5 = 0.38 0.38 × 100 = 38%
13 13
5 × 100 = 5 × 100 = 500 = 38%
13 13 1 13
4 4 = 0.66 0.66 × 100 = 66%
6 6
4 × 100 = 4 × 100 = 400 = 66%
6 6 1 6
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