Equivalent fractions explained for parents

What it is

Fraction

A number of equal parts of a whole. The parts must be the same size.

Denominator

The bottom number. It tells you how many equal parts the whole is split into.

Numerator

The top number. It tells you how many of those parts you have.

Unit fraction

A fraction with 1 as the numerator, such as one half, one third or one quarter. A fraction with any other numerator, such as three quarters, is a non-unit fraction.

Equivalent fractions

Fractions that look different but are worth the same amount, such as one half, two quarters and four eighths.

Imagine folding a sheet of paper in half and colouring one half. Fold it in half again and open it: you now have 4 equal parts, and 2 of them are coloured. The coloured amount hasn't changed, so one half and two quarters are equivalent.

1/2 = 2/4 = 4/8
1/3 = 2/6
1/4 = 2/8

To make an equivalent fraction, you multiply (or divide) the top and bottom numbers by the same number. Two quarters is one half with the top and bottom numbers both doubled: 1 × 2 = 2 and 2 × 2 = 4. In Year 3, though, children see equivalence with diagrams first, and the rule comes later.

How it's taught at school

Fractions build up through primary school. In Year 1 children meet halves and quarters as equal parts. In Year 2 they find one third, one quarter, two quarters and three quarters of shapes and amounts, and see that two quarters is the same as one half.

In Year 3, the national curriculum expects children to recognise and show, using diagrams, equivalent fractions with small denominators. Expect bars, circles and shapes split into equal parts, or fractions on a number line, where equivalent fractions sit in the same spot.

Year 3 children also find fractions of a set of objects. To find a unit fraction, they divide by the denominator. For a non-unit fraction, they then multiply by the numerator. Many schools draw this as a bar model: a long rectangle split into equal parts, with the whole amount written above it.

1/3 of 12 = 4
2/3 of 12 = 8
1/4 of 12 = 3

Year 3 also covers comparing and ordering unit fractions, and fractions with the same denominator. With the same denominator, more parts means more: three fifths is bigger than two fifths. With unit fractions it works the other way round, because more parts means each part is smaller, so one third is bigger than one quarter.

Equivalent fractions keep coming back. In Year 4 children use diagrams to show families of common equivalent fractions. In Year 5 they name and write equivalent fractions of a given fraction, including tenths and hundredths, and in Year 6 they simplify fractions.

Common mistakes (and how to help)

Thinking a bigger denominator means a bigger fraction, so one eighth is more than one quarter

Fold two strips of paper the same length, one into quarters and one into eighths. Put one part of each side by side. Your child can see that sharing between more people gives everyone a smaller piece.

Calling any piece a half or a quarter, even when the parts aren't equal

Cut a paper strip into 2 unequal pieces and ask "Is this a half?" Talk about why not. Then fold it properly so the 2 parts match exactly.

Adding 1 to the top and bottom numbers, such as thinking one half is the same as two thirds

Draw both as bars of the same length and shade them. Your child will see that two thirds covers more. Equivalent fractions come from multiplying or dividing, not adding, and diagrams show this well.

Finding two thirds of 12 but stopping at 4

4 is one third of 12, which is the first step. Ask "How many thirds do we want?" Two thirds means two lots of 4, which is 8. Sharing 12 pasta pieces into 3 groups and taking 2 groups makes it clear.

Three quick activities at home

Questions parents ask

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: Equivalent fractions (KS2 Maths)