How to work out percentages: 10%, 1% and building up

How percentages are calculated

A percentage is a number of hundredths. Per cent means "out of 100", so 15% means 15 out of every 100, and 100% is the whole amount. Children learn this in Year 5, along with writing a percentage as a fraction out of 100 and as a decimal: 15% is ¹⁵⁄₁₀₀, and it's also 0.15.

That gives two ways to work out any percentage:

• Without a calculator, find an easy percentage, such as 10%, 50% or 1%, and build the one you need from it. This is what children do in Year 6, and it's how most adults do percentages in their heads.
• With a calculator, turn the percentage into a decimal and multiply. This comes later, at secondary school.

How to get a percentage of an amount

To get a percentage of an amount, start from the percentages that are quick to find:

Percentage	Fraction	How to find it
100%	the whole	the amount itself
50%	1⁄2	halve it
25%	1⁄4	halve it, then halve again
10%	1⁄10	divide by 10
5%	1⁄20	find 10%, then halve it
1%	1⁄100	divide by 100

Then add or multiply them to make the percentage you want. 30% is three lots of 10%. 75% is 50% and 25%. 90% is the whole take away 10%. The national curriculum links this to finding fractions of amounts, because 10% of a number is the same as ¹⁄₁₀ of it. Fractions of amounts explains that step.

A bar split into ten equal parts shows why 10% is so useful. Each part is 10% of 360:

Worked example: 15% of 360

The national curriculum uses this one as its example for Year 6.

1. Find 10%. Divide 360 by 10: 360 ÷ 10 = 36.
2. Find 5%. It's half of 10%, so half of 36 is 18.
3. Add them. 15% is 10% and 5%: 36 + 18 = 54.

So 15% of 360 is 54.

Worked example: 35% of 80

1. Find 10%: 80 ÷ 10 = 8.
2. Make 30%. That's three lots of 10%: 8 × 3 = 24.
3. Find 5%. Half of 8 is 4.
4. Add them: 24 + 4 = 28.

So 35% of 80 is 28.

Worked example: 12% of 250

1. Find 10%: 250 ÷ 10 = 25.
2. Find 1%. Divide by 100: 250 ÷ 100 = 2.5.
3. Make 2%. That's two lots of 1%: 2.5 × 2 = 5.
4. Add 10% and 2%: 25 + 5 = 30.

So 12% of 250 is 30. Using 1% means you can build any whole-number percentage, even awkward ones like 37%.

Shortcuts for common percentages

• 50%, 25% and 75%. These are a half, a quarter and three quarters. 75% of 48 is half of 48 and a quarter of 48: 24 + 12 = 36.
• 90%, 95% and 99%. Take a little away from the whole. 90% of 70 is 70 take away 10%: 70 − 7 = 63.
• 20%. Find 10% and double it. 20% of 45 is 4.5 doubled, which is 9.

How to calculate a number as a percentage

To write one number as a percentage of another, make a fraction and change it into hundredths. In Year 6, children do this to compare things, like two test scores out of different totals.

Say your child scores 13 out of 20. As a fraction, that's ¹³⁄₂₀. Multiply the top and bottom by 5 to make the denominator 100: ¹³⁄₂₀ = ⁶⁵⁄₁₀₀. So 13 out of 20 is 65%.

When the total doesn't go into 100, simplify first. 27 out of 30 is ²⁷⁄₃₀, and dividing the top and bottom by 3 gives ⁹⁄₁₀. Then ⁹⁄₁₀ = 90%.

Fractions, decimals and percentages has more examples of changing fractions and decimals into percentages, including ones like ³⁄₈ that need a division.

How to work out percentages on a calculator

To work out a percentage on a calculator, divide the percentage by 100 to make a decimal, then multiply it by the amount. 15% is 0.15, and 0.15 × 360 = 54. 12% is 0.12, and 0.12 × 250 = 30.

To write a number as a percentage, divide it by the total and multiply by 100. For 13 out of 20, 13 ÷ 20 = 0.65, and 0.65 × 100 = 65, so it's 65%.

Calculators are part of maths at secondary school. At primary school, the national curriculum says calculators shouldn't take the place of mental and written methods, so your child will work percentages out with 10% and 1% first. It's worth learning that way even if a calculator is handy, because it lets you check whether a calculator answer makes sense.

At secondary school: how to calculate improvement percentage

Percentage increase and decrease is secondary school maths, in key stage 3. It's included here because many parents search for it. The method is: find the change, divide it by the starting amount, then multiply by 100.

An improvement. A test score goes up from 20 to 23. The change is 23 − 20 = 3. Divide by the starting score: 3 ÷ 20 = 0.15. Then 0.15 × 100 = 15, so that's a 15% improvement.

A drop. A price falls from 80 to 60. The change is 80 − 60 = 20. Divide by the starting price: 20 ÷ 80 = 0.25, so that's a 25% drop.

Always divide by the amount you started with, not the new one. At secondary school, children also meet percentages over 100%: if something goes from 20 to 50, it has risen by 150%.

Common mistakes when working out percentages

• Dividing by 100 for 10%. 10% of 360 is 36, not 3.6. Divide by 10 for 10% and by 100 for 1%.
• Adding percentages of different amounts. 10% of 360 and 5% of 80 don't add up to 15% of anything.
• Forgetting the whole is 100%. If 30% of a class walk to school, 70% don't.
• Treating a percentage as the answer. 15% of 360 is 54, not 15. The percentage tells you how much of the amount to take.
• Dividing by the new amount for a change. For a percentage increase or drop, divide by where you started.
• Not checking. 25% is a quarter, so 25% of 80 should be smaller than half of 80. A quick estimate catches most slips.

How to help at home

• Start with 10%. Pick any number and ask for 10% of it. Then ask for 5%, 20% and 30%, built from the 10%.
• Use money. A pound is 100p, so 1% of £1 is 1p and 15% of £1 is 15p. A "20% off" sign in a shop is a good real question.
• Talk about scores. If your child gets 18 out of 20 on a spelling test, ask what that is as a percentage.
• Keep the times tables sharp. Building percentages uses lots of multiplying and dividing by 10, 2 and 5. The times tables and short multiplication help.

When do children learn percentages?

Percentages start in Year 5 maths, when children learn the % sign, that per cent means parts per hundred, and the percentages for a half, a quarter, a fifth and tenths. In Year 6 maths they work out percentages of amounts, such as 15% of 360, and use percentages to compare. Percentage change and calculator methods come at secondary school. It all builds on decimals and fractions.

Percentage questions to try

1. What is 10% of 450?
2. What is 25% of 64?
3. What is 15% of 80?
4. What is 60% of 35?
5. What is 4% of 300?
6. Write 7 out of 20 as a percentage.

Answers

1. 45 (450 ÷ 10 = 45)
2. 16 (half of 64 is 32, and half of 32 is 16)
3. 12 (10% is 8 and 5% is 4, so 8 + 4 = 12)
4. 21 (10% is 3.5, so 60% is 3.5 × 6 = 21)
5. 12 (1% is 3, so 4% is 3 × 4 = 12)
6. 35% (⁷⁄₂₀ = ³⁵⁄₁₀₀)

For the rest of what children learn in these years, see the KS2 maths guide. The bar model is a good way to draw percentage problems.