Year 4 maths · Key Stage 2 · Number – fractions (including decimals)

Year 4 equivalent fractions, hundredths and fractions of amounts

In Year 4 children learn that one amount can be written as many different fractions, such as 1/2, 2/4 and 5/10. They meet hundredths for the first time, work out fractions of amounts like 3/8 of 24, and add and subtract fractions that have the same denominator, sometimes going past one whole.

Equivalent fractions and hundredths, explained

A fraction describes equal parts of a whole. The bottom number, the denominator, says how many equal parts the whole is cut into. The top number, the numerator, says how many of those parts you have. So 3/4 means “cut into 4 equal parts and take 3 of them”.

Equivalent fractions are different names for the same amount. Cut a pizza in half and take one half, or cut it into quarters and take two: you get the same amount of pizza. To make an equivalent fraction you multiply (or divide) the top and the bottom by the same number. 2/3 becomes 8/12 by multiplying both by 4. Children in Year 4 learn to show this with diagrams and to spot “families” such as 1/2 = 2/4 = 3/6 = 4/8 = 5/10.

Hundredths come from cutting one whole into 100 equal parts, or cutting a tenth into 10. Everyday examples help: a penny is a hundredth of a pound, and a centimetre is a hundredth of a metre. Children count up and down in hundredths and learn that 10/100 is the same as 1/10. This sets up decimals, which come next in Year 4.

To find a fraction of an amount, divide by the denominator to find one part, then multiply by the numerator. For 3/8 of 24, one eighth is 24 ÷ 8 = 3, so three eighths is 3 × 3 = 9. Adding and subtracting fractions with the same denominator works like counting objects: 3 fifths + 4 fifths = 7 fifths, which is more than one whole (7/5).

Words your child will hear

Numerator: The top number of a fraction: how many parts you have.
Denominator: The bottom number: how many equal parts the whole is split into.
Unit fraction: A fraction with 1 on top, such as 1/3 or 1/10.
Non-unit fraction: A fraction with more than 1 on top, such as 2/3 or 7/10.
Equivalent fractions: Fractions that are worth the same, like 1/2 and 4/8.
Hundredth: One of 100 equal parts of a whole, written 1/100.
Simplify: Write a fraction with the smallest possible numbers, so 6/9 becomes 2/3.

What the National Curriculum says

In Year 4, pupils should be taught to:

Recognise and show, using diagrams, families of common equivalent fractions
Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10
Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
Add and subtract fractions with the same denominator

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

A worked example

Fill in the missing number: 2/3 = ?/12

Look at the denominators. Thirds have become twelfths. What do you multiply 3 by to get 12? 3 × 4 = 12.
Do the same to the numerator, because the fraction must stay worth the same amount: 2 × 4 = 8.
Check with a bar. Split a bar into thirds and shade two. Now split each third into 4 smaller pieces: the bar has 12 pieces and 8 of them are shaded.
2/3
8/12

2/3 = 8/12

Common mistakes and how to help

Thinking a bigger denominator means a bigger fraction

In whole numbers 8 is bigger than 4, so it seems that 1/8 must be bigger than 1/4.

What helps: Ask whether they would rather share a cake with 3 friends or with 7. The more pieces a whole is cut into, the smaller each piece.

Adding the denominators: 2/5 + 1/5 = 3/10

Children add “top and top, bottom and bottom” because that’s how adding usually looks.

What helps: Say the fractions as words: 2 fifths plus 1 fifth is 3 fifths, just as 2 apples plus 1 apple is 3 apples. The fifths are the thing being counted, so they don’t change.

Changing only one number to make an equivalent fraction

A child multiplies the denominator but forgets the numerator, so 2/3 turns into 2/12, which is much smaller.

What helps: Draw the bar. If each third is cut into 4 pieces, the shaded part is cut up too, so both numbers grow by the same amount.

Dividing by the numerator when finding a fraction of an amount

For 3/4 of 20 a child works out 20 ÷ 3, because 3 is the first number they see.

What helps: Remind them the denominator tells you how many equal groups to make: split 20 into 4 groups of 5, then take 3 of the groups to get 15.

How to help at home

Fold paper strips. Fold one strip in half, another into quarters and another into eighths, then line them up. Your child can see that 1/2, 2/4 and 4/8 are the same length.
Share food fairly. “Can you give me 1/4 of these 12 grapes? Now 3/4?” Sharing real things into equal groups is exactly how fractions of amounts are taught.
Use money and a tape measure for hundredths. There are 100 pennies in a pound and 100 centimetres in a metre. Ask what fraction of a pound 25p is (25/100, which is the same as 1/4).
Ask “which would you rather have?”. Would you rather have 1/3 or 1/4 of a pizza? 2/4 or 1/2? Explaining the choice builds understanding faster than calculating.

Builds on

Year 3: Tenths and equivalent fractions

Leads on to

Year 5: Mixed numbers and fraction calculations
Year 5: Decimals, thousandths and percentages