Key ideas
Finding a percentage
Per cent means out of 100.
15% of £40 = 15100 × 40 = £6
Without a calculator: 10% is ÷ 10, 1% is ÷ 100, 50% is half, 25% is a quarter.
Increase and decrease
1. Find the percentage.
2. Add it for an increase, take it away for a decrease.
Always answer the question: the new amount.
Words to look for
Increase: pay rise, VAT added, interest, grows, price goes up.
Decrease: discount, sale, % off, loses value, reduced.
Percentage change
changeoriginal × 100
Always divide by the original (starting) amount.
Finding a percentage
Find 35% of £60.(2 marks)
Build it from 10% and 5%.10% of £60 = £630% = 3 × £6 = £185% = £3 half of 10%✓1
In plain English35% is 30% plus 5%. Find 10% by dividing by 10, then build up.
Add.35% = £18 + £3 = £21✓2
In plain EnglishAdd the 30% and the 5% to make 35%.
Find 17% of £84.(1 mark)
Out of 100.17100 × 84 = £14.28✓1
In plain EnglishPer cent means out of 100, so 17% is 17 hundredths. On a calculator: 17 ÷ 100 × 84.
Percentage increase
Jo earns £420 a week. She gets a 5% pay rise. How much does she earn now?(3 marks)
Find 5%.5100 × 420 = £21✓1
In plain EnglishFind the size of the pay rise first.
Increase: add it on.£420 + £21✓2= £441 a week✓3
In plain EnglishA pay rise is an increase, so add it to the original amount. The question asks what she earns now, so give the new total.
⚠ A common mistake: stopping at £21. That is the rise, not what she earns now.
Percentage decrease
A jacket costs £75. In a sale it is reduced by 30%. Find the sale price.(3 marks)
Find 30%.10% = £7.5030% = 3 × £7.50 = £22.50✓1
In plain EnglishWithout a calculator, find 10% then multiply by 3.
Decrease: take it away.£75 − £22.50✓2= £52.50✓3
In plain EnglishA sale reduction is a decrease, so subtract it from the original price.
Using percentages in real life
A TV costs £350 before VAT. VAT of 20% is added. What is the total price?(3 marks)
Find 20%.10% = £3520% = £70✓1
In plain EnglishVAT is a tax added on, so this is an increase.
Add it on.£350 + £70✓2= £420✓3
In plain EnglishAdd the VAT to the price before VAT to get the total price.
Shop A sells a bike for £240 with 15% off. Shop B sells the same bike for £230 with 10% off. Which shop is cheaper, and by how much?(4 marks)
Shop A.15100 × 240 = £36£240 − £36 = £204✓1
In plain EnglishWork out the sale price at each shop.
Shop B.10100 × 230 = £23£230 − £23 = £207✓2
In plain EnglishDo the same for Shop B: find 10%, then take it away.
Compare, quoting the prices.Shop A is cheaper, because £204 < £207 by £3✓4
In plain EnglishSay which is cheaper and quote both prices. £207 − £204 = £3.
Finding the percentage change
A game's price rises from £40 to £46. Find the percentage increase.(2 marks)
Find the change.£46 − £40 = £6✓1
In plain EnglishFirst find how much the price went up.
Change over original.640 × 100 = 15%✓2
In plain EnglishDivide the change by the original price (£40, not £46), then multiply by 100.
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Your turn
Questions marked non-calculator should be done without one. Give money answers in pounds, like 52.50. Stuck? Tap Need a hint?