Percentages of amounts

Objective. Calculate familiar and composite percentages mentally.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Finding a percentage of an amount means working out that proportion of a quantity, often by breaking the percentage into easier parts. For instance, to find 15% of 60, find 10% by dividing by 10 to get 6, then find 5% by halving that to get 3, and add them to get 9. Composite percentages combine known pieces: 35% is 25%+10%, or 30%+5%. Using a calculator, multiplying by the decimal equivalent works directly, so 15% of 60 is 0.15×60=9.

Worked example

Calculate 35% of 180 without using a calculator.

1 $Find 10% of 180 by dividing by 10: 18.$
2 $Find 5% of 180 by halving 18: 9.$
3 $Combine to make 35% as 10%+10%+10%+5%: 18+18+18+9.$
4 $Add these parts: 54+9=63.$

Answer: 63

Concept mastery

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Practice

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Common mistake. Pupils sometimes find 10% correctly but then double it for 15% instead of adding half of that 10% value. Build percentages from 10% and 5% blocks carefully rather than guessing a shortcut.

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