IGCSE Maths / Ratios and percentages
Percentage of an amount
Edexcel International GCSE Maths (4MA1), chapter 2: Ratios and percentages, specification point 1.6a-f. Free lesson.
Read the revision notes · IGCSE Maths past papers
A percentage is a number of parts per hundred, so you can find a percentage of an amount by multiplying by its decimal multiplier. You can also build percentages from 10%, 5% and 1%, which is useful without a calculator.
Turn a percentage into a decimal multiplier
Percent means per hundred. For example, 35% is 35 parts out of 100, so 35% = 35/100 = 0.35. To find a percentage of an amount, multiply the amount by this decimal multiplier. Divide the percentage by 100 to get the decimal multiplier. The multiplier method is quick and is used in later percentage topics.
Find a percentage with one multiplication
Once you have the multiplier, multiply it by the amount. Check that your answer is a sensible size: 35% is about a third, so 35% of 240 should be close to a third of 240.
Build a percentage without a calculator
You can find 10% by dividing an amount by 10. Then 5% is half of 10%, and 1% is the amount divided by 100. Add the parts that make the percentage you need. For example, 15% = 10% + 5%. You can build many percentages from 10%, 5% and 1%.
Check the decimal place and the answer's size
Dividing by 100 moves the digits two places, not one. So 5% = 0.05, while 0.5 is 50%. Using 0.5 instead of 0.05 gives an answer ten times too large. Also, a percentage of an amount does not always make it smaller. A percentage below 100% gives an answer smaller than the original amount. 100% leaves the amount unchanged. A percentage above 100% gives an answer larger than the original amount.
Practise and remember the method
For a calculator question, use the multiplier. Without a calculator, split the percentage into parts you can find easily. In both cases, check whether the answer's size makes sense. 60% of 450 = 270. For 12% of 200, use 10% and 2 × 1%.