Fractions made easy: equal parts, step by step

What is a fraction?

A fraction is part of a whole that has been cut into equal parts. The most important word is equal. If you cut a sandwich into 4 pieces and they are all different sizes, you haven’t made quarters.

Every fraction has two numbers, one on top of the other:

A handy way to remember: denominator and down both start with d. So 35 means “the whole is cut into 5 equal parts, and we have 3 of them”.

The fraction wall

A fraction wall shows one whole at the top, then the same length cut into halves, thirds, quarters and so on. The more parts you cut it into, the smaller each part gets.

Fractions are numbers too

Fractions have their own place on the number line. Here the gap between each whole number is cut into quarters. 12 sits halfway between 0 and 1, and fractions keep going past 1.

Fractions of amounts

To find a fraction of a number, remember: divide by the bottom, times by the top. Dividing by the bottom number tells you what one part is worth. Multiplying by the top number counts up the parts you need.

Check it makes sense. 35 is a bit more than a half. Half of 40 is 20, so the answer should be a bit more than 20. 24 looks right.

Equivalent fractions

Equivalent fractions are worth the same amount, even though they look different. On the fraction wall, 12 lines up exactly with 24, 36, 48, 510 and 612. They all cover the same length.

To make an equivalent fraction, multiply the top and the bottom by the same number. You cut every part into the same number of smaller pieces, so the amount doesn’t change.

Only multiply or divide. Adding the same number to the top and bottom does not work: 12 is not the same as 23.

Simplifying fractions

Simplifying means writing a fraction with the smallest numbers you can, without changing its value. Divide the top and the bottom by the same number. When no number bigger than 1 goes into both, the fraction is in its simplest form.

Comparing and ordering fractions

To order fractions, do the same thing with all of them. To put 34, 58 and 12 in order, write them all in eighths: 68, 58 and 48. Smallest first, that’s 12, 58, 34.

Mixed numbers and improper fractions

When the top number is bigger than the bottom number, the fraction is more than 1 whole. 114 is called an improper fraction. You can also write it as a mixed number: a whole number and a fraction, 234.

Adding and subtracting fractions

When the bottom numbers are the same

Add or subtract the top numbers. The bottom number stays the same, because the size of the parts doesn’t change.

When the bottom numbers are different

Change the fractions so they have the same bottom number first, using equivalent fractions. Then add or subtract the tops.

Multiplying and dividing fractions

Children start this in Year 5 and Year 6. Here are the main kinds, with the simplest first.

Multiplying can make things smaller. Multiplying by a fraction less than 1 means taking part of something, so the answer is smaller than you started with. 12 × 10 = 5.

Fractions, decimals and percentages

A fraction is a division. 38 means 3 ÷ 8, which is 0.375. That’s how you turn any fraction into a decimal.

Going the other way, read the decimal’s place value: 0.43 is 43 hundredths, so 0.43 = 43100. 0.6 is 6 tenths, so 0.6 = 610 = 35. A percentage is a fraction out of 100: 43% = 43100.

There’s much more on percentages in our Percentages made easy guide.

Working backwards

Sometimes you know the part and need the whole. Find one part, then multiply by the bottom number.

Tips for teaching fractions

For parents. Real things to share and fold come first: the numbers make much more sense after that.

1. Share food fairly. Pizza, cake and chocolate bars are perfect. “Cut it so we get the same amount” is where fractions begin. A chocolate bar of 12 squares is great for thirds, quarters and sixths.
2. Keep saying “equal”. Ask “Are these really halves? Are the pieces the same size?” It stops the most common early mistake.
3. Fold paper. Fold a strip in half, then half again, and open it up to find quarters. Fold again for eighths. Colour some parts and name the fraction.
4. Build a fraction wall. Cut paper strips of the same length into halves, thirds, quarters and sixths, and line them up. Children can see that 24 and 12 are the same length.
5. Cook together. Measuring jugs and recipes are full of fractions: half a litre, a quarter of a teaspoon. Halving or doubling a recipe is real fraction practice.
6. Use money. A quarter of £1 is 25p and a tenth of £1 is 10p. Sharing pocket money or sweets between brothers and sisters gives fractions of amounts.
7. Read the clock. Half past and quarter to are fractions of an hour. A quarter of an hour is 15 minutes, so three quarters is 45 minutes.
8. Use groups of things, not just shapes. Half of 10 toy cars, a third of 12 grapes. Fractions of a group lead straight into “divide by the bottom, times by the top”.
9. Put them on a number line. Fractions are numbers, not only pieces of pizza. Counting in quarters along a line (0, 14, 24, 34, 1, 114) helps with mixed numbers later.
10. Little and often. Ten minutes twice a week works better than one long session. Roll a fresh worksheet each time.

What do children learn, and when?

In England, the National Curriculum builds fractions up step by step. The examples below are our own.

1. Year 1 (5–6)Find and name a half as one of two equal parts, and a quarter as one of four equal parts, of a shape, an object or an amount.
2. Year 2 (6–7)Find, name and write 13, 14, 24 and 34 of a length, a shape, a group of objects or an amount. Write simple fraction facts such as 12 of 8 = 4, and know that 24 is the same as 12.
3. Year 3 (7–8)Count up and down in tenths, and see that tenths come from dividing by 10. Find fractions of a group of objects, using unit and non-unit fractions with small denominators. Treat fractions as numbers. Use diagrams to find equivalent fractions with small denominators. Add and subtract fractions with the same denominator within one whole, such as 38 + 48 = 78. Compare and order unit fractions, and fractions with the same denominator.
4. Year 4 (8–9)Recognise families of common equivalent fractions. Meet hundredths, which come from dividing by 100 or dividing tenths by 10. Use fractions to find amounts, including non-unit fractions where the answer is a whole number. Add and subtract fractions with the same denominator. Know the decimals for tenths, hundredths, 14, 12 and 34.
5. Year 5 (9–10)Compare and order fractions whose denominators are all multiples of the same number. Find equivalent fractions, including tenths and hundredths. Switch between mixed numbers and improper fractions, as in 47 + 57 = 97 = 127. Add and subtract fractions with the same denominator, and with denominators that are multiples of the same number. Multiply proper fractions and mixed numbers by whole numbers. Read and write decimals as fractions, such as 0.43 = 43100. Percentages start here too.
6. Year 6 (10–11)Simplify fractions using common factors, and use common multiples to give fractions the same denominator. Compare and order fractions, including ones bigger than 1. Add and subtract fractions with different denominators, and mixed numbers. Multiply simple pairs of proper fractions and give the answer in its simplest form, such as 13 × 12 = 16. Divide proper fractions by whole numbers, such as 25 ÷ 2 = 15. See a fraction as a division and work out its decimal, such as 58 = 0.625. Recall the matching fractions, decimals and percentages.The curriculum’s non-statutory guidance also suggests working backwards from a unit fraction to the whole: if a fifth of a rope is 12 m, the whole rope is 60 m.
7. Key Stage 3 (11–14)Change terminating decimals into fractions and back, such as 2.25 and 94, or 0.625 and 58. Add, subtract, multiply and divide proper and improper fractions and mixed numbers, both positive and negative. Write one amount as a fraction of another, with answers less than and greater than 1. Use fractions as operators: finding 34 of something is the same as multiplying it by 34.

Paraphrased from the National Curriculum for England. Schools only have to cover each key stage’s content by the end of that key stage, so the year your child meets each idea can vary.