GCSE Maths: Percentages of an amount (Foundation)
Part of the GCSE Maths percentages chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Percentages of an amount
“Find 35% of £240.” Here 35% works like an instruction: take 35 hundredths of the number. Mathematicians call a fraction or a percentage used in this way an operator, because it operates on a number and changes it. You already know that “35 of 40” means “divide by 5, then multiply by 3”. A percentage of an amount works in exactly the same way, and the word of means multiply.
Without a calculator: build up from 10% and 1%
Some percentages are very easy to find. 10% is one tenth, so divide by 10. 1% is one hundredth, so divide by 100. 50% is a half, and 25% is a quarter. To find any other percentage, split it into pieces that you can do. For example 35% = 10% + 10% + 10% + 5%, and 5% is half of 10%.
With a calculator: use a decimal
Write the percentage as a decimal (divide by 100) and multiply. So 35% of 240 is 0.35 × 240 = 84. This is quick, but you must be careful to divide by 100 first: 8% is 0.08 (not 0.8). When the answer is money, round to the nearest penny, which means two decimal places.
It is a good habit to estimate first. For example, 48% of £603 is close to 50% of £600, which is £300. If your calculator says £2,894, you know you have made a slip.
Key ideas
- “Of” means multiply; a percentage can be used as an operator on an amount.
- 10% = divide by 10. 1% = divide by 100. 50% = divide by 2. 25% = divide by 4.
- 5% = half of 10%. 2.5% = a quarter of 10%.
- Build any percentage from these: 35% = 10% + 10% + 10% + 5%.
- Calculator: decimal × amount, e.g. 17.5% of 64 = 0.175 × 64.
- Round money to 2 decimal places (the nearest penny).
Key words. Per cent means “out of 100”. A percentage is a fraction whose denominator is 100, written with the % sign. A multiplier is the number you multiply by to get the new amount in one step.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of £240 = £240 ÷ 10 = £24
- Work out each part. Multiply to build up to the percentage you want.30% = 3 × 10% = 3 × £24 = £72
- Write the answer. Include the units.30% of £240 = £72
Check. Another way: 30% = 0.3 as a decimal, and 0.3 × £240 = £72. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.7% = 5% + 2%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 450 g = 450 g ÷ 10 = 45 g
- Find 1%. 1% is one hundredth, so divide the amount by 100 (each digit moves two places to the right).1% of 450 g = 450 g ÷ 100 = 4.5 g
- Work out each part. Use the 10% or 1% you found.5% = half of 10% = 45 g ÷ 2 = 22.5 g
2% = 2 × 1% = 2 × 4.5 g = 9 g - Add the parts together. The parts together make up the whole percentage.22.5 g + 9 g = 31.5 g
Check. Another way: 7% = 0.07 as a decimal, and 0.07 × 450 g = 31.5 g. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.17.5% = 10% + 5% + 2.5%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of £360 = £360 ÷ 10 = £36
- Work out each part. Use the 10% or 1% you found.10% = £36
5% = half of 10% = £36 ÷ 2 = £18
2.5% = a quarter of 10% = £36 ÷ 4 = £9 - Add the parts together. The parts together make up the whole percentage.£36 + £18 + £9 = £63
Check. Another way: 17.5% = 0.175 as a decimal, and 0.175 × £360 = £63. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.23% = 23 ÷ 100 = 0.23
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).23% of 85 kg = 0.23 × 85 kg
- Work it out on the calculator. Type the multiplication in carefully.0.23 × 85 kg = 19.55 kg
Check. Estimate: 10% of 85 is 8.5, so 23% is 2.3 lots of that: about 19.55. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Watch out
10% is not “divide by 10 and then by 10 again”. You divide by 10 once. And finding the percentage is often only part of the job: read the question to see whether it wants the percentage itself, or what is left after taking it away.Exercise 5B Percentages of an amount (non-calculator)
Non-calculatorMethod. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 80 = 80 ÷ 10 = 8
- Write the answer. Include the units.10% of 80 = 8
Check. Another way: 10% = 0.1 as a decimal, and 0.1 × 80 = 8. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 150 = 150 ÷ 10 = 15
- Work out each part. Multiply to build up to the percentage you want.20% = 2 × 10% = 2 × 15 = 30
- Write the answer. Include the units.20% of 150 = 30
Check. Another way: 20% = 0.2 as a decimal, and 0.2 × 150 = 30. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 240 = 240 ÷ 10 = 24
- Work out each part. Multiply to build up to the percentage you want.30% = 3 × 10% = 3 × 24 = 72
- Write the answer. Include the units.30% of 240 = 72
Check. Another way: 30% = 0.3 as a decimal, and 0.3 × 240 = 72. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Spot that 50% is a half. 50 out of 100 is the same as 1 out of 2.50% = 12
- Halve the amount. To find a half, divide by 2.64 ÷ 2 = 32
Check. Another way: 50% = 0.5 as a decimal, and 0.5 × 64 = 32. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Spot that 25% is a quarter. 25 out of 100 is the same as 1 out of 4.25% = 14
- Find a quarter of the amount. To find a quarter, divide by 4 (or halve twice).120 ÷ 4 = 30
Check. Another way: 25% = 0.25 as a decimal, and 0.25 × 120 = 30. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 200 = 200 ÷ 10 = 20
- Work out each part. Multiply to build up to the percentage you want.5% = half of 10% = 20 ÷ 2 = 10
- Write the answer. Include the units.5% of 200 = 10
Check. Another way: 5% = 0.05 as a decimal, and 0.05 × 200 = 10. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of £50 = £50 ÷ 10 = £5
- Write the answer. Include the units.10% of £50 = £5
Check. Another way: 10% = 0.1 as a decimal, and 0.1 × £50 = £5. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 340 g = 340 g ÷ 10 = 34 g
- Write the answer. Include the units.10% of 340 g = 34 g
Check. Another way: 10% = 0.1 as a decimal, and 0.1 × 340 g = 34 g. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 8.5 m = 8.5 m ÷ 10 = 0.85 m
- Write the answer. Include the units.10% of 8.5 m = 0.85 m
Check. Another way: 10% = 0.1 as a decimal, and 0.1 × 8.5 m = 0.85 m. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 120 ml = 120 ml ÷ 10 = 12 ml
- Write the answer. Include the units.10% of 120 ml = 12 ml
Check. Another way: 10% = 0.1 as a decimal, and 0.1 × 120 ml = 12 ml. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.15% = 10% + 5%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of £360 = £360 ÷ 10 = £36
- Work out each part. Use the 10% or 1% you found.10% = £36
5% = half of 10% = £36 ÷ 2 = £18 - Add the parts together. The parts together make up the whole percentage.£36 + £18 = £54
Check. Another way: 15% = 0.15 as a decimal, and 0.15 × £360 = £54. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.35% = 30% + 5%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of £80 = £80 ÷ 10 = £8
- Work out each part. Use the 10% or 1% you found.30% = 3 × 10% = 3 × £8 = £24
5% = half of 10% = £8 ÷ 2 = £4 - Add the parts together. The parts together make up the whole percentage.£24 + £4 = £28
Check. Another way: 35% = 0.35 as a decimal, and 0.35 × £80 = £28. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Spot that 75% is three quarters. 75 out of 100 is the same as 3 out of 4.75% = 34
- Find one quarter. Divide by 4.£48 ÷ 4 = £12
- Multiply by 3. Three quarters is three lots of one quarter.3 × £12 = £36
Check. Another way: 75% = 0.75 as a decimal, and 0.75 × £48 = £36. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.12% = 10% + 2%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of £250 = £250 ÷ 10 = £25
- Find 1%. 1% is one hundredth, so divide the amount by 100 (each digit moves two places to the right).1% of £250 = £250 ÷ 100 = £2.50
- Work out each part. Use the 10% or 1% you found.10% = £25
2% = 2 × 1% = 2 × £2.50 = £5 - Add the parts together. The parts together make up the whole percentage.£25 + £5 = £30
Check. Another way: 12% = 0.12 as a decimal, and 0.12 × £250 = £30. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 1%. 1% is one hundredth, so divide the amount by 100 (each digit moves two places to the right).1% of £450 = £450 ÷ 100 = £4.50
- Work out each part. Multiply to build up to the percentage you want.2% = 2 × 1% = 2 × £4.50 = £9
- Write the answer. Include the units.2% of £450 = £9
Check. Another way: 2% = 0.02 as a decimal, and 0.02 × £450 = £9. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 1%. 1% is one hundredth, so divide the amount by 100 (each digit moves two places to the right).1% of £7,600 = £7,600 ÷ 100 = £76
- Write the answer. Include the units.1% of £7,600 = £76
Check. Another way: 1% = 0.01 as a decimal, and 0.01 × £7,600 = £76. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.45% = 40% + 5%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 600 g = 600 g ÷ 10 = 60 g
- Work out each part. Use the 10% or 1% you found.40% = 4 × 10% = 4 × 60 g = 240 g
5% = half of 10% = 60 g ÷ 2 = 30 g - Add the parts together. The parts together make up the whole percentage.240 g + 30 g = 270 g
Check. Another way: 45% = 0.45 as a decimal, and 0.45 × 600 g = 270 g. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 30 m = 30 m ÷ 10 = 3 m
- Work out each part. Multiply to build up to the percentage you want.90% = 9 × 10% = 9 × 3 m = 27 m
- Write the answer. Include the units.90% of 30 m = 27 m
Check. Another way: 90% = 0.9 as a decimal, and 0.9 × 30 m = 27 m. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 250 ml = 250 ml ÷ 10 = 25 ml
- Work out each part. Multiply to build up to the percentage you want.60% = 6 × 10% = 6 × 25 ml = 150 ml
- Write the answer. Include the units.60% of 250 ml = 150 ml
Check. Another way: 60% = 0.6 as a decimal, and 0.6 × 250 ml = 150 ml. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.8% = 5% + 3%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 400 kg = 400 kg ÷ 10 = 40 kg
- Find 1%. 1% is one hundredth, so divide the amount by 100 (each digit moves two places to the right).1% of 400 kg = 400 kg ÷ 100 = 4 kg
- Work out each part. Use the 10% or 1% you found.5% = half of 10% = 40 kg ÷ 2 = 20 kg
3% = 3 × 1% = 3 × 4 kg = 12 kg - Add the parts together. The parts together make up the whole percentage.20 kg + 12 kg = 32 kg
Check. Another way: 8% = 0.08 as a decimal, and 0.08 × 400 kg = 32 kg. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 3 km = 3 km ÷ 10 = 0.3 km
- Work out each part. Multiply to build up to the percentage you want.70% = 7 × 10% = 7 × 0.3 km = 2.1 km
- Write the answer. Include the units.70% of 3 km = 2.1 km
Check. Another way: 70% = 0.7 as a decimal, and 0.7 × 3 km = 2.1 km. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.15% = 10% + 5%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 90 minutes = 90 minutes ÷ 10 = 9 minutes
- Work out each part. Use the 10% or 1% you found.10% = 9 minutes
5% = half of 10% = 9 minutes ÷ 2 = 4.5 minutes - Add the parts together. The parts together make up the whole percentage.9 minutes + 4.5 minutes = 13.5 minutes
Check. Another way: 15% = 0.15 as a decimal, and 0.15 × 90 minutes = 13.5 minutes. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.35% = 30% + 5%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of £80 = £80 ÷ 10 = £8
- Work out each part. Use the 10% or 1% you found.30% = 3 × 10% = 3 × £8 = £24
5% = half of 10% = £8 ÷ 2 = £4 - Add the parts together. The parts together make up the whole percentage.£24 + £4 = £28
Check. Another way: 35% = 0.35 as a decimal, and 0.35 × £80 = £28. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. Take the reduction away from the original price.
- Write down the original price and the reduction. The reduction was found in part (a).£80 and £28
- Subtract. A sale price is lower than the original price.£80 − £28 = £52
Check. A 35% reduction leaves 65% of the price: 65% of £80 = 0.65 × 80 = £52. ✓
Watch out. Part (b) asks for the sale price, not the amount taken off.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.45% = 40% + 5%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of 800 = 800 ÷ 10 = 80
- Work out each part. Use the 10% or 1% you found.40% = 4 × 10% = 4 × 80 = 320
5% = half of 10% = 80 ÷ 2 = 40 - Add the parts together. The parts together make up the whole percentage.320 + 40 = 360
Check. Another way: 45% = 0.45 as a decimal, and 0.45 × 800 = 360. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. The rest of the students are boys.
- Write the number of girls. From part (a).Girls = 360
- Subtract from the total. Everyone is either a girl or a boy.800 − 360 = 440
Check. Boys are 55% of 800 = 440. ✓
Watch out. Check that the two answers add up to the total.
Method. To find a percentage of an amount without a calculator, find 10% (divide by 10) or 1% (divide by 100) first. Then build up to the percentage you need.
- Split the percentage into easy parts. We can find 10% and 1% very quickly, so we build the percentage out of them.15% = 10% + 5%
- Find 10%. 10% is one tenth, so divide the amount by 10 (each digit moves one place to the right).10% of £1,600 = £1,600 ÷ 10 = £160
- Work out each part. Use the 10% or 1% you found.10% = £160
5% = half of 10% = £160 ÷ 2 = £80 - Add the parts together. The parts together make up the whole percentage.£160 + £80 = £240
Check. Another way: 15% = 0.15 as a decimal, and 0.15 × £1,600 = £240. ✓
Watch out. 10% means divide by 10 once. Do not divide by 10 and then by 10 again.
Method. There are 12 months in a year, so multiply the monthly saving by 12.
- Write the monthly saving. From part (a).£240
- Multiply by 12. 12 months in a year.£240 × 12 = £2,880
Check. £240 × 10 = £2,400 and £240 × 2 = £480; £2,400 + £480 = £2,880. ✓
Method. Find the percentage that is red or green, then find what is left.
- Add the percentages of red and green. The sweets are different colours, so no sweet is counted twice.25% + 5% = 30%
- Find the percentage that is neither. The whole bag is 100%.100% − 30% = 70%
- Find 70% of 240. 10% of 240 = 24, so 70% is 7 lots of 24.7 × 24 = 168
Check. 25% of 240 = 60 and 5% of 240 = 12. 240 − 60 − 12 = 168. ✓
Watch out. Make sure you answer the question that is asked: “neither” means the sweets left over.
Method. Work out both amounts, then compare them.
- Work out 20% of 350. 10% of 350 = 35, so 20% is 2 lots.2 × 35 = 70
- Work out 30% of 240. 10% of 240 = 24, so 30% is 3 lots.3 × 24 = 72
- Compare. 72 is greater than 70.30% of 240 is bigger.
Check. 0.2 × 350 = 70 and 0.3 × 240 = 72. ✓
Watch out. Finish with a sentence that says which is bigger.
Method. Work out both amounts and show they are the same.
- Work out 20% of 60. 10% of 60 = 6, so 20% is 2 lots.2 × 6 = 12
- Work out 60% of 20. 10% of 20 = 2, so 60% is 6 lots.6 × 2 = 12
- State the conclusion. A “show that” question needs a final sentence.Both are 12, so 20% of 60 = 60% of 20.
Check. 0.2 × 60 = 12 and 0.6 × 20 = 12. ✓
Watch out. In a “show that” question, show the working for both sides.
Method. Test Ali’s method and compare it with the correct method.
- Try Ali’s method. Dividing by 15 is not the same as finding 15%.80 ÷ 15 = 5.33…
- Find 15% correctly. 15% = 10% + 5%. 10% of 80 = 8, and 5% is half of that, 4.8 + 4 = 12
- Compare and explain. 15% means 15 out of 100, so we divide by 100 and multiply by 15 (or use 10% + 5%). We never divide by the percentage itself.Ali is wrong; 15% of 80 = 12.
Check. 0.15 × 80 = 12. ✓
Watch out. Only 10% is “divide by 10”; 15% is not “divide by 15”.
Method. Write each as a fraction of the other number, then compare.
- Work out 8% of 50. 50 is half of 100, so 8% of 50 is half of 8.8% of 50 = 8 ÷ 2 = 4
- Work out 50% of 8. 50% is one half.8 ÷ 2 = 4
- Explain why. 8% of 50 is 8100 × 50 = 8 × 50100. Both are 8 × one half.Both calculations are “half of 8”, so they are equal.
Check. Both answers are 4. ✓
Watch out. Multiplication can be done in any order, so a% of b = b% of a.
Exercise 5C Percentages of an amount (calculator)
Calculator allowedMethod. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.12% = 12 ÷ 100 = 0.12
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).12% of 650 = 0.12 × 650
- Work it out on the calculator. Type the multiplication in carefully.0.12 × 650 = 78
Check. Estimate: 10% of 650 is 65, so 12% is 1.2 lots of that: about 78.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.35% = 35 ÷ 100 = 0.35
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).35% of 840 = 0.35 × 840
- Work it out on the calculator. Type the multiplication in carefully.0.35 × 840 = 294
Check. Estimate: 10% of 840 is 84, so 35% is 3.5 lots of that: about 294.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.7% = 7 ÷ 100 = 0.07
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).7% of 1,250 = 0.07 × 1,250
- Work it out on the calculator. Type the multiplication in carefully.0.07 × 1,250 = 87.5
Check. Estimate: 10% of 1,250 is 125, so 7% is 0.7 lots of that: about 87.50. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.18% = 18 ÷ 100 = 0.18
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).18% of 2,400 = 0.18 × 2,400
- Work it out on the calculator. Type the multiplication in carefully.0.18 × 2,400 = 432
Check. Estimate: 10% of 2,400 is 240, so 18% is 1.8 lots of that: about 432.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.4.5% = 4.5 ÷ 100 = 0.045
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).4.5% of 360 = 0.045 × 360
- Work it out on the calculator. Type the multiplication in carefully.0.045 × 360 = 16.2
Check. Estimate: 10% of 360 is 36, so 4.5% is 0.45 lots of that: about 16.20. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.62% = 62 ÷ 100 = 0.62
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).62% of 85 = 0.62 × 85
- Work it out on the calculator. Type the multiplication in carefully.0.62 × 85 = 52.7
Check. Estimate: 10% of 85 is 8.5, so 62% is 6.2 lots of that: about 52.70. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.10% = 10 ÷ 100 = 0.1
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).10% of 130 = 0.1 × 130
- Work it out on the calculator. Type the multiplication in carefully.0.1 × 130 = 13
Check. Estimate: 10% of 130 is 13, so 10% is 1 lots of that: about 13.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.25% = 25 ÷ 100 = 0.25
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).25% of 130 = 0.25 × 130
- Work it out on the calculator. Type the multiplication in carefully.0.25 × 130 = 32.5
Check. Estimate: 10% of 130 is 13, so 25% is 2.5 lots of that: about 32.50. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.60% = 60 ÷ 100 = 0.6
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).60% of 130 = 0.6 × 130
- Work it out on the calculator. Type the multiplication in carefully.0.6 × 130 = 78
Check. Estimate: 10% of 130 is 13, so 60% is 6 lots of that: about 78.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.90% = 90 ÷ 100 = 0.9
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).90% of 130 = 0.9 × 130
- Work it out on the calculator. Type the multiplication in carefully.0.9 × 130 = 117
Check. Estimate: 10% of 130 is 13, so 90% is 9 lots of that: about 117.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.17.5% = 17.5 ÷ 100 = 0.175
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).17.5% of £84.60 = 0.175 × £84.60
- Work it out on the calculator. Type the multiplication in carefully.0.175 × £84.60 = £14.805
- Round the answer. Give the answer to 2 decimal places (for money, to the nearest penny).£14.805 = £14.81
Check. Estimate: 10% of 84.6 is 8.46, so 17.5% is 1.75 lots of that: about 14.81. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.23% = 23 ÷ 100 = 0.23
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).23% of £149.99 = 0.23 × £149.99
- Work it out on the calculator. Type the multiplication in carefully.0.23 × £149.99 = £34.4977
- Round the answer. Give the answer to 2 decimal places (for money, to the nearest penny).£34.4977 = £34.50
Check. Estimate: 10% of 149.99 is 15.00, so 23% is 2.3 lots of that: about 34.50. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.6.5% = 6.5 ÷ 100 = 0.065
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).6.5% of £2,450 = 0.065 × £2,450
- Work it out on the calculator. Type the multiplication in carefully.0.065 × £2,450 = £159.25
Check. Estimate: 10% of 2,450 is 245, so 6.5% is 0.65 lots of that: about 159.25. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.3.2% = 3.2 ÷ 100 = 0.032
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).3.2% of £19,500 = 0.032 × £19,500
- Work it out on the calculator. Type the multiplication in carefully.0.032 × £19,500 = £624
Check. Estimate: 10% of 19,500 is 1,950, so 3.2% is 0.32 lots of that: about 624.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.12.5% = 12.5 ÷ 100 = 0.125
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).12.5% of £86.40 = 0.125 × £86.40
- Work it out on the calculator. Type the multiplication in carefully.0.125 × £86.40 = £10.80
Check. Estimate: 10% of 86.4 is 8.64, so 12.5% is 1.25 lots of that: about 10.80. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Find the part of her pay that is taxed, then find 20% of it.
- Work out the amount that is taxed. Tax is only paid on the money over £12,570, so subtract.£28,500 − £12,570 = £15,930
- Find 20% of that amount. 20% as a decimal is 0.2.0.2 × £15,930 = £3,186
Check. 10% of £15,930 = £1,593, and double that is £3,186. ✓
Watch out. Do not take 20% of the whole £28,500.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.14.6% = 14.6 ÷ 100 = 0.146
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).14.6% of 48,500 = 0.146 × 48,500
- Work it out on the calculator. Type the multiplication in carefully.0.146 × 48,500 = 7,081
Check. Estimate: 10% of 48,500 is 4,850, so 14.6% is 1.46 lots of that: about 7,081.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.65% = 65 ÷ 100 = 0.65
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).65% of 180 marks = 0.65 × 180 marks
- Work it out on the calculator. Type the multiplication in carefully.0.65 × 180 marks = 117 marks
Check. Estimate: 10% of 180 is 18, so 65% is 6.5 lots of that: about 117.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Work out 12% of the purchase, then compare with the £25 limit.
- Work out 12% of £250. Use 0.12 as a decimal.0.12 × £250 = £30
- Compare with the limit. The cashback cannot be more than £25.£30 is more than £25.
- Write the cashback she gets. The limit applies.£25
Check. If the limit were not there she would get £30; the rule cuts it to £25. ✓
Watch out. Check any limits in the question before you give your final answer.
Method. Round to numbers that are easy to use.
- Round the numbers. 48% is close to 50% and £603 is close to £600.48% ≈ 50%, £603 ≈ £600
- Work out the estimate. 50% is a half.£600 ÷ 2 = £300
Check. The estimate should be close to the exact value found in part (b). ✓
Watch out. An estimate uses rounded numbers; it is not exact.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.48% = 48 ÷ 100 = 0.48
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).48% of £603 = 0.48 × £603
- Work it out on the calculator. Type the multiplication in carefully.0.48 × £603 = £289.44
Check. Estimate: 10% of 603 is 60.3, so 48% is 4.8 lots of that: about 289.44. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Work out 150% of 40 and compare it with 40.
- Change 150% to a decimal. Divide by 100.150 ÷ 100 = 1.5
- Multiply by 40. Of means multiply.1.5 × 40 = 60
- Compare with 40. 60 is more than 40.Ben is wrong.
Check. 100% of 40 is 40, so 150% must be more than 40: 40 + 20 = 60. ✓
Watch out. A percentage over 100% gives an answer bigger than the amount you started with.
Method. Write the percentage as a decimal, then multiply it by the amount.
- Change the percentage into a decimal. Per cent means “out of 100”, so divide by 100.38.4% = 38.4 ÷ 100 = 0.384
- Write the multiplication. To find a percentage of an amount, multiply the amount by the percentage written as a decimal (“of” means multiply).38.4% of 1,250 = 0.384 × 1,250
- Work it out on the calculator. Type the multiplication in carefully.0.384 × 1,250 = 480
Check. Estimate: 10% of 1,250 is 125, so 38.4% is 3.84 lots of that: about 480.00. ✓
Watch out. Divide the percentage by 100 first. 8% is 0.08, not 0.8.
Method. Find the costs, then take them away from the total raised.
- Find 3.5% of £18,400. 3.5% as a decimal is 0.035.0.035 × £18,400 = £644
- Subtract the costs from the total. What is left goes to the cause.£18,400 − £644 = £17,756
Check. The cause gets 96.5% of the total: 0.965 × £18,400 = £17,756. ✓
Watch out. The question asks what goes to the cause, not the costs.
Method. Work out both amounts using the calculator method and compare.
- Work out 15% of 260. 15% = 0.15.0.15 × 260 = 39
- Work out 26% of 150. 26% = 0.26.0.26 × 150 = 39
- Write the conclusion. The two amounts match.Both are 39, so they are equal.
Check. 15 × 260 = 3,900 and 26 × 150 = 3,900, so both give 39 after dividing by 100. ✓
Watch out. Always finish a “show that” question with a conclusion.