Year 5 maths · Key Stage 2 · Number – fractions (including decimals and percentages)

Year 5 fractions: mixed numbers and adding fractions

In Year 5 children compare and order fractions whose denominators are multiples of one another, and write equivalent fractions including tenths and hundredths. They learn that a fraction can be larger than one whole, switching between improper fractions and mixed numbers. They add and subtract fractions with related denominators, and multiply a fraction or mixed number by a whole number using diagrams.

Mixed numbers and fraction calculations, explained

Equivalent fractions are different names for the same amount, made by multiplying or dividing the numerator and denominator by the same number. In Year 5 this is used to compare and order fractions whose denominators are multiples of the same number. To put 1/2, 3/8 and 5/16 in order, rewrite them all in sixteenths: 8/16, 6/16 and 5/16. Now the pieces are the same size, so the order is easy to see: 5/16 is smallest and 1/2 is largest. Children also write equivalent fractions for tenths and hundredths, such as 3/10 = 30/100, which prepares for decimals.

A proper fraction is less than one whole. An improper fraction, such as 7/4, has a numerator bigger than its denominator, and a mixed number, such as 1 3/4, is a whole number plus a fraction. They are two ways of writing the same amount. Children link this to division: 7 ÷ 4 is 1 with 3 left over, and the 3 left over is shared into quarters, giving 1 3/4. Going the other way, 2 2/5 is 2 wholes (10 fifths) plus 2 fifths, which makes 12/5. Number lines marked beyond 1 are used a lot, because they show that 7/4 sits between 1 and 2.

Adding and subtracting fractions works when the pieces are the same size. If the denominators match, add or subtract the numerators and keep the denominator: 2/5 + 4/5 = 6/5, which is 1 1/5. If one denominator is a multiple of the other, change the larger pieces into the smaller ones first, so 7/8 − 1/4 becomes 7/8 − 2/8 = 5/8. Answers that go past one whole are written as mixed numbers, and children subtract from mixed numbers too, such as 1 1/5 − 3/5 = 6/5 − 3/5 = 3/5.

Multiplying a fraction by a whole number is repeated addition. Three lots of 2/5 is 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5, so only the numerator is multiplied. For a mixed number, such as 2 1/3 × 3, children multiply the whole part (2 × 3 = 6) and the fraction part (3 × 1/3 = 1) and add: 7. Diagrams and counters come first, and the rule follows from them. Multiplying one fraction by another is not part of Year 5. Finding a fraction of an amount, such as 3/4 of 20, builds on the same thinking.

Words your child will hear

Proper fraction: A fraction less than one whole, with the numerator smaller than the denominator, such as 3/4.
Improper fraction: A fraction of one whole or more, with the numerator at least as big as the denominator, such as 7/4.
Mixed number: A whole number and a fraction together, such as 1 3/4.
Equivalent fractions: Fractions with the same value, like 3/4 and 6/8.
Common denominator: A denominator shared by two or more fractions after they have been rewritten, so that their pieces are the same size.
Multiple: A number in another number’s times table. 8 is a multiple of 4, so quarters can be changed into eighths.
Denominator: The bottom number of a fraction, showing how many equal parts make one whole.

What the National Curriculum says

In Year 5, pupils should be taught to:

Compare and order fractions whose denominators are all multiples of the same number
Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 1 1/5]
Add and subtract fractions with the same denominator, and denominators that are multiples of the same number
Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Work out 3/4 + 5/8. Write the answer as a mixed number.

The denominators are different, so the pieces are different sizes. But 8 is a multiple of 4 (4 × 2 = 8), so change the quarters into eighths.
Multiply the numerator and denominator of 3/4 by 2. That gives 6/8. The bars show the same amount of shading, cut into smaller pieces.
3/4
6/8
Now both fractions are eighths, so add the numerators and keep the denominator: 6/8 + 5/8 = 11/8. The sum goes past one whole, because it needs more than one bar.
6/8
5/8
Change 11/8 into a mixed number. 8/8 makes one whole, and 11 − 8 = 3 eighths are left over. So 11/8 = 1 3/8.
Check that the answer is sensible: 3/4 + 1/2 is 1 1/4, and 5/8 is a little more than 1/2, so an answer a little over 1 1/4 makes sense.

3/4 + 5/8 = 11/8 = 1 3/8

Common mistakes and how to help

Adding the denominators as well as the numerators

A child writes 3/4 + 5/8 = 8/12. They treat the fraction as two separate whole numbers, adding top to top and bottom to bottom, without picturing what the denominator tells them about the size of the pieces.

What helps: Say the fractions as words: 6 eighths plus 5 eighths is 11 eighths, just as 6 apples plus 5 apples is 11 apples. The name of the piece stays the same.

Thinking the fraction with the bigger numbers is bigger

Comparing 3/4 and 5/8, a child notices that 5 is more than 3 and 8 is more than 4 and decides 5/8 wins. But eighths are smaller pieces than quarters.

What helps: Rewrite both with the same denominator, 6/8 against 5/8, then look at the numerators. A bar or a number line makes this easy to see.

Mixing up the whole number and the remainder

When changing 11/8 to a mixed number, a child writes 3 1/8 or 1 11/8, because the division 11 ÷ 8 gives two numbers and it isn’t clear which job each one does.

What helps: Ask how many whole ones there are (one lot of 8/8), then what is left (3 eighths). Check by converting back: 1 whole is 8/8, plus 3/8 is 11/8.

Multiplying the denominator when multiplying by a whole number

In 3 × 2/5 a child gets 6/15, because multiplying the top and bottom is exactly what they do when making equivalent fractions.

What helps: Remind them what is being counted: 3 lots of 2 fifths is 6 fifths. The fifths stay fifths. Draw three bars each with 2 fifths shaded.

How to help at home

Fill a measuring jug. Add 3/4 of a litre and 1/2 a litre of water and read the total off the jug in millilitres (1,250 ml, which is 1 1/4 litres). Switching between 750 ml, 3/4 and 1 1/4 shows fractions and mixed numbers in use.
Turn a tape measure into a number line. Let 12 cm stand for one whole, so 0 to 36 cm runs from 0 to 3. Ask your child where 7/4 lands (21 cm) and where 2 2/3 lands (32 cm). Seeing improper fractions and mixed numbers land on the same spot makes the two forms feel like one idea.
Fold paper strips into families. Fold identical strips into halves, quarters, eighths and sixteenths and lay them side by side. Ask which is longer, 5/8 or 3/4, and prove it with the strips.
Ask “how many wholes?”. Pizza and cake slices work well: “We have 11 slices and each pizza has 8. How many pizzas is that?” The answer is 1 3/8, and the story fits the maths exactly.

Updated 20 October 2026.