What is a percentage?
Percentages are a way of expressing proportion.
Proportion tells you how much of one thing there is in relation to the whole.
'Per cent' means ‘out of 100’ and a percentage is written as a number with the % symbol.
There are some simple techniques to help work out percentages.
One way to find a percentage of an amount is to use 50%, 10% and 1% building blocks.
Activity: How to calculate a percentage
Complete this interactive activity to better understand how to calculate a percentage. Then put your knowledge to the test.
Finding 50%
50% is the same as \( \frac{50}{100} \) or one half.
To work out 50%, simply divide the number by 2.
For example, to find 50% of 80:
80 ÷ 2 = 40
Once you’ve found 50%, you can use this to find other percentages.
To find 25%, divide the value you found for 50% by 2.
For example:
40 ÷ 2 = 20
So, 25% of 80 is 20.
Finding 10%
To work out 10%, divide the number by 10.
For example, to find 10% of 360:
360 ÷ 10 = 36
To find a multiple of 10%, divide by 10 and then multiply by the number of tens you want to find.
For example, to find 30% of 360, multiply the value you found for 10% by 3.
36 × 3 = 108
So, 30% of 360 is 108.
You could also find 5%, by dividing 10% by 2.
36 ÷ 2 = 18
So, 5% of 360 is 18.
Finding 1%
For percentages that aren’t a multiple of 10, divide the number by 100 to find 1%.
Then multiply by the number of percent you need to find.
For example, to find 22% of 1200. First divide 1200 by 100 to find 1%.
1200 ÷ 100 = 12
Then multiply by 22, to find 22%.
12 × 22 = 264
So, 22% of 1200 is 264.
Parts of a whole
Fractions, percentages and decimals are all ways to describe parts of a whole.
The sign % stands for 'per cent' which means 'out of 100'.
Fractions can be expressed as percentages and decimals.
For example, a half is 50%, a quarter is 25%, a tenth is 10% and a fifth is 20%.
Example 1
Rohan got 40 marks out of 80 in his maths test. Maria got 45%. Who did better, Rohan or Maria?
✓Rohan.
40 out of 80 is equivalent to one half.
Half expressed as a percentage is 50%.
50% is greater than 45%, so Rohan has the better maths score.
Example 2
Here is a battery level indicator. It tells you how much power there is in your battery. What is each segment worth as a percentage?
✓20%.
Look at the full battery indicator. There are 5 segments in total.
Percentage are parts out of 100.
Each segment is worth 20 parts out of 100 parts. Expressed as a percentage, each part is 20%
Example 3
Convert the percentage into two equivalent fractions.
✓ 80% is the same as 80 parts out of 100.
It's easier to write 80 parts out of 100 as a fraction \(\frac{80}{100}\)
This fraction can be simplified to \(\frac{8}{10}\) and simplified further to \(\frac{4}{5}\)
Play our fun maths game Guardians: Defenders of Mathematica. game
Use your times tables and more maths skills to defeat monsters and reclaim the Kingdom of Mathematica
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