Percentages: how to find, increase and decrease them
Work out a percentage of an amount, increase or decrease by a percentage and calculate percentage change, with worked examples for KS3 and GCSE.
KS3GCSEMiddle SchoolCurriculum fit: GCSE Maths Ratio, proportion and rates of change (Foundation and Higher). US: Grade 6-7 percent problems.
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What is it?
Per cent means 'out of 100'. So 25% is 25 out of 100, which is the fraction 1/4 or the decimal 0.25. Percentages make it easy to compare amounts.
Most percentage questions fall into three types: finding a percentage of an amount, increasing or decreasing by a percentage, and working out a percentage change.
Key formulas and ideas
- Percentage of an amount = amount × percentage ÷ 100.
- Increase by r%: multiply by 1 + r/100. Decrease by r%: multiply by 1 − r/100.
- Percentage change = (new − old) ÷ old × 100.
- One quantity as a percentage of another = part ÷ whole × 100.
Worked examples
Example 1: Percentage of an amount
Question: Find 20% of 150.
- 20% = 20/100.
- 150 × 20 ÷ 100 = 30.
Answer: 30
Example 2: Increase
Question: Increase 80 by 15%.
- The multiplier is 1.15.
- 80 × 1.15 = 92.
Answer: 92
Example 3: Percentage change
Question: A price rises from 50 to 65. Find the percentage change.
- Change = 65 − 50 = 15.
- 15 ÷ 50 × 100 = 30.
Answer: 30% increase
Common mistakes
- Working out the percentage change using the new value instead of the old value.
- Adding the percentage to the number instead of finding the percentage of the number first.
- Treating 15% off then 15% off as 30% off.
- Forgetting to give units or the percent sign.
Practice questions
Frequently asked questions
Can a percentage be more than 100%?
Yes. 150% means one and a half times the original amount.
How do I find 10% quickly?
Divide by 10. Then 5% is half of that, and 1% is dividing by 100.
Related guides
Reverse percentages and compound interest: step by step
Work backwards from a final price to the original amount, and calculate compound interest, with worked examples and practice questions.
GCSEHigh SchoolFractions, decimals and percentages: how to convert them
Switch between fractions, decimals and percentages, including recurring decimals, with worked examples and practice questions to check your answers.
KS3GCSEMiddle SchoolHigh SchoolExponential growth and decay: formulas and worked examples
Model repeated percentage change with y = a × bˣ, including compound growth, depreciation and doubling, with step-by-step examples.
GCSEA-LevelHigh SchoolSources and review
- DfE: GCSE mathematics subject content and assessment objectives
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.