How to explain equivalent fractions to your child
Teach equivalent fractions with equal-sized paper strips, clear examples and a short activity that helps your child explain why fractions match.
Your child recognises halves and quarters of a whole.
To explain equivalent fractions, show your child the same amount divided into different numbers of equal pieces. Half a paper strip is still half when you divide that shaded section into two quarters. The pieces change size; the amount you have stays the same.
You need three equal-sized strips of paper and a pencil. Begin with the paper before introducing a rule about multiplying numbers.
Understand the idea
A fraction tells us how many equal parts we have compared with the number of equal parts in one whole. In 2/4, the bottom number says the whole has four equal parts. The top number says we have two of them.
Equivalent fractions have the same value. They might look different when written, but they mark the same point on a number line or cover the same amount of an equal-sized whole.
Say: "We are changing how we name the amount. We are not adding more paper."
Keep the wholes the same size while you demonstrate. Half of a long strip and half of a short strip are both one-half of their own wholes, but they are different lengths. That can distract from the idea you are teaching.
See it worked through
One amount, three equal strips
Fold the first strip into two equal parts and shade one. Label it 1/2.
Fold the second strip into four equal parts and shade two. Label it 2/4. Fold the third into eight equal parts and shade four. Label it 4/8.
Put the strips underneath each other with their left edges aligned. Their shaded sections end in the same place. That shows 1/2 = 2/4 = 4/8.
Ask: "When we changed from halves to quarters, what happened to each piece? What happened to the total shaded amount?"
Each piece became smaller. We needed twice as many pieces to show the same amount. In the written fraction, both numbers doubled: 1 became 2, and 2 became 4.
The numerical rule follows that picture. Multiplying the numerator and denominator by the same non-zero number gives an equivalent fraction. Dividing both by the same common factor works too. For example, dividing both numbers in 4/8 by four gives 1/2.
Try it together
Fold, shade and compare
Draw two equal-length rectangles. Divide one into three equal parts and shade two. Divide the other into six equal parts.
Ask your child to shade the second rectangle so it shows the same amount. Then ask them to complete 2/3 = ?/6 and explain their choice using the picture.
Pause before offering help. If they are unsure, draw a line through the middle of each third to split it into two equal pieces.
Check the answer
Shade four of the six parts. Each shaded third has become two shaded sixths, so two thirds become four sixths. The answer is 2/3 = 4/6. Both numbers were multiplied by two; the shaded amount did not change.
Check their understanding
Ask whether 1/2 and 2/3 are equivalent. A child who only notices that both numbers increased by one may say yes. Return to equal-sized strips and compare their lengths.
Then ask: "Can you find another name for three quarters?" Six eighths is one answer. Let your child draw it, describe it or write 3/4 = 6/8.
Make it easier or harder
Make it easier by using halves and quarters only. Fold together and use the words "one half" before adding symbols.
Make it harder by placing 1/2, 2/4 and 4/8 at the same point on a number line from zero to one. Then ask for an equivalent fraction to 3/5 with denominator 20. It is 12/20 because both numbers multiply by four.
Teaching notes
NSW Education's parent numeracy guidance explains equal parts, the size of the whole and fraction equivalence. The paper-strip examples here are original home activities built around those concepts.
Numeracy practice
Help your child apply their maths understanding with practice questions and explanations.
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