Calculating percentages
Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison
What a learner can do afterwards
- Calculate 15% of 360 by finding 10% and 5% and combining
- Calculate and compare discount amounts from different original prices; subtract a discount from its original price to calculate a sale price and compare sale prices
- Explain a strategy for finding any percentage of an amount using known percentage facts
1 · Read
Percent means out of one hundred. Find 1% by dividing an amount by 100. Any whole-number percentage is that many copies of the 1% amount. Useful shortcuts are 10% by dividing by 10, 5% by halving the 10% amount, 50% by halving the whole, and 25% by dividing the whole by 4.
To find 15%, combine 10% and 5% of the same starting amount. For 180, divide by 10 to get 18. Half of 18 is 9, so that is 5%. Add 18 + 9 = 27. Doubling the 10% amount would give 20%, not 15%.
Compare discounts by calculating the money saved from each original price. Bag A costs £70 with 10% off, saving £7. Bag B costs £25 with 20% off: 10% is £2.50, so twice that is £5. Bag A saves more money despite its smaller percentage. To find how much more, subtract the smaller saving from the larger one.
A sale price is the original price minus the discount amount. A £120 item with 25% off has a discount of £120 ÷ 4 = £30. Subtract it: £120 − £30 = £90. When comparing shops, calculate both sale prices before choosing the cheaper one.
Build a percentage by counting known parts. For 45%, use four 10% parts and one 5% part. Add four copies of the 10% amount and one copy of the 5% amount. You can also subtract known parts: 50% minus 5% gives 45%. Check that your chosen percentages add or subtract to the requested percentage.
Build any percentage from 10% and other known facts, and always calculate the actual amount before comparing discounts.
Questions written for this learning dataset. Linked percentage videos by Khan Academy.
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