Percentages
Calculating percentages of amounts, converting between fractions, decimals and percentages, and percentage increase/decrease.
What is Percentages?
A percentage is a way of expressing a number as a fraction of 100. The word “percent” literally means “per hundred”. So 25% means 25 out of 100, or one quarter.
In the 11+ exam, percentage questions may ask you to find a percentage of an amount, convert between fractions, decimals and percentages, or calculate percentage increase and decrease. These questions are common and often appear in word problems about shopping, discounts and data.
Step-by-Step Method
Find 10% by dividing by 10
This is the most useful shortcut. Once you know 10%, you can find almost any percentage by combining.
Build up the percentage you need
For example, 35% = 10% + 10% + 10% + 5%. Find 10%, then halve it to get 5%, then add them together.
To convert a fraction to a percentage
Divide the numerator by the denominator, then multiply by 100. For example, 3/5 = 0.6 = 60%.
To convert a percentage to a fraction
Write the percentage over 100 and simplify. For example, 45% = 45/100 = 9/20.
For percentage change, use the formula
Percentage change = (difference / original) x 100. Always divide by the ORIGINAL amount.
Worked Examples
Find 35% of 240.
Working
- 10% of 240 = 24.
- 30% = 24 x 3 = 72.
- 5% = 24 / 2 = 12.
- 35% = 72 + 12 = 84.
Convert 3/8 to a percentage.
Working
- Divide 3 by 8 = 0.375.
- Multiply by 100 = 37.5%.
A price increases from 80 to 92. What is the percentage increase?
Working
- Difference = 92 – 80 = 12.
- Percentage increase = (12 / 80) x 100.
- 12 / 80 = 0.15.
- 0.15 x 100 = 15%.
Common Mistakes
Dividing by the new amount instead of the original when finding percentage change.
Always divide by the ORIGINAL value. The original is the starting point.
Thinking 50% off then 20% off is the same as 70% off.
Percentage changes are applied one at a time. 50% off 100 = 50, then 20% off 50 = 40. That is 60% off, not 70%.
Confusing “percentage of” with “percentage increase”.
30% of 200 = 60. A 30% increase on 200 = 200 + 60 = 260.
Top Tips
- Memorise key conversions: 50% = 1/2, 25% = 1/4, 10% = 1/10, 20% = 1/5, 75% = 3/4.
- The 10% method works for almost every percentage question – find 10% first, then build up.
- To find 1%, divide by 100. Then multiply by whatever percentage you need.
- Percentage increase means add the percentage to the original. Percentage decrease means subtract it.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions