PipkinPlay with Pipkin

Maths · Years 5–6

Fractions, decimals and percentages explained

By Dave Allen · Updated · 5 min read

Drafted and fact-checked with AI help, against the sources below. Not yet reviewed by a teacher. How we write our guides

What it is

Per cent (%)
Parts per hundred. 25% means 25 out of every 100, so it's the same as 25 hundredths.
Decimal
A number with a decimal point, such as 0.25. The digits after the point are tenths, hundredths and thousandths.
Equivalent
Worth the same amount. One quarter, 0.25 and 25% are equivalent.
Decimal place
A digit after the decimal point. 0.375 has three decimal places.

The national curriculum says children should be taught throughout that percentages, decimals and fractions are different ways of expressing proportions. A good picture for this is a square split into 100 small squares, called a hundred grid. Colour 25 of the squares and you have coloured one quarter of it, 0.25 of it and 25% of it, all at once.

1/2  = 0.5  = 50%
1/4  = 0.25 = 25%
3/4  = 0.75 = 75%
1/5  = 0.2  = 20%
1/10 = 0.1  = 10%
1/100 = 0.01 = 1%
Equivalents worth knowing by heart

100% means the whole amount. So 50% is half of it and 25% is a quarter of it, which links percentages back to finding fractions of amounts.

How it's taught at school

This topic builds up over three years in the national curriculum for England:

  • Year 4: tenths and hundredths as decimals, and the decimal equivalents of one quarter, one half and three quarters.
  • Year 5: decimals with up to three decimal places, the per cent symbol, and writing percentages as a fraction out of 100 and as a decimal. Children also learn the percentage and decimal equivalents of one half, one quarter, one fifth, two fifths and four fifths, and of fractions whose denominator is a multiple of 10 or 25.
  • Year 6: recalling and using the equivalences between simple fractions, decimals and percentages, finding percentages of amounts, and using percentages to compare.

A handy way to find a percentage of an amount is to start from 10%, which is the same as dividing by 10. Then build the percentage you need from 10%, 5% and 1%. The curriculum's own example is 15% of 360:

10% of 360 = 36
 5% of 360 = 18
15% of 360 = 54
Finding 15% of 360

Percentages make comparing easy. Is 17 out of 20 better than 21 out of 25? As percentages, they are 85% and 84%, so 17 out of 20 is slightly better.

In Year 6, children also learn that a fraction is a division. Three eighths means 3 ÷ 8, which is 0.375. For fractions like one third the decimal goes on for ever, so children round it, for example to three decimal places: 0.333.

Tip
Point out percentages when you see them: a sale sign, a battery symbol, a test score. Ask "What fraction is that?" and "Is that more or less than half?" Everyday examples make the links stick.

From Pipkin

Practise maths with Pipkin

Short, calm puzzles that follow the UK curriculum. Free, with no sign-up.

Open Pipkin

Common mistakes (and how to help)

Thinking a decimal with more digits is bigger, so 0.45 is more than 0.5
Compare the tenths first: 0.5 has 5 tenths and 0.45 has only 4. It helps to add a zero so both have the same number of places: 0.50 is clearly more than 0.45. Money helps too: 50p is more than 45p.
Writing 0.5 as 5% instead of 50%
Go back to hundredths. 0.5 is 5 tenths, which is 50 hundredths, so it's 50%. Coloured squares on a hundred grid show this well.
Thinking one fifth is 0.5, because of the 5
One fifth means 1 ÷ 5, which is 0.2, or 20%. Ask "Is one fifth more or less than one half?" If it's less than a half, it must be less than 0.5.
Finding 10% by dividing by 100, or 1% by dividing by 10
Link it back to fractions. 10% is a tenth, so divide by 10. 1% is a hundredth, so divide by 100. Check with a simple amount: 10% of £100 is £10.

Three quick activities at home

Hundred grid colouring

About 10 minutes · You need: Squared paper, or paper with a 10 by 10 grid drawn on it, and some pens

  1. Ask your child to colour 25 squares of the 100.
  2. Ask them to write that amount three ways: as a fraction (one quarter), as a decimal (0.25) and as a percentage (25%).
  3. Try 50, 75, 20 and 10 squares too, and talk about which fractions they match.

Score swap

About 5 minutes · You need: Nothing: this works anywhere

  1. Say a score out of 10, 20, 25 or 50, such as 18 out of 25.
  2. Your child turns it into a percentage. For out of 25, multiply both numbers by 4: 72 out of 100, or 72%.
  3. Compare two scores, such as 7 out of 10 and 18 out of 25, and decide which is better.

Tape measure decimals

About 5 minutes · You need: A tape measure, or a metre ruler

  1. Pull out 1 metre and remind your child that 1 m is 100 cm.
  2. Ask them to show 0.5 m, 0.25 m and 0.75 m. That's 50 cm, 25 cm and 75 cm.
  3. Ask what fraction of the metre each one is, and what percentage.

Try it with your child

Free Pipkin puzzles on this topic. No sign-up. They open on the children's side of Pipkin.

Questions parents ask

Why does my child need three ways of writing the same number?

Each one is handiest in a different place. Fractions are good for sharing, decimals for money and measuring, and percentages for comparing. Moving between them easily is what the Year 6 curriculum asks for.

Does my child need to know one third as a decimal?

In Year 6, children learn that some fractions, like one third, have decimals that go on for ever, and they round them, for example to 0.333. The equivalents to know by heart are the simpler ones, such as halves, quarters, fifths and tenths.

From Pipkin

Practise maths with Pipkin

Short, calm puzzles that follow the UK curriculum. Free, with no sign-up.

Open Pipkin

Related guides

Sources

  1. Department for Education: National curriculum in England: mathematics programmes of study
  2. Department for Education: Teaching mathematics in primary schools (Mathematics guidance: key stages 1 and 2)
  3. BBC Bitesize: Calculating percentages (KS2 Maths, Year 6)