What are equivalent fractions?
Equivalent fractions are fractions with different numbers that describe the same amount. The numbers change, but the value does not: when you cut something into more pieces, each piece is smaller, so you need more of them to make the same amount.
- 1/2 = 2/4 = 4/8 = 8/16
- 1/3 = 2/6 = 4/12
- 2/3 = 4/6 = 8/12
- 3/5 = 6/10 = 9/15
You can check any pair by cross-multiplying: if the two products match, the fractions are equivalent. For 2/4 and 4/8, 2 x 8 = 16 and 4 x 4 = 16, so they are the same amount.
How do you show equivalent fractions with pictures?
Pictures work because a child can see two fractions that look completely different cover exactly the same space. The eye settles the argument before the rule arrives.
Draw two identical bars, one above the other. Split the top bar into 2 equal parts and shade 1. Split the bottom bar into 4 equal parts and shade 2. The shaded areas line up exactly, so 1/2 and 2/4 must be the same amount.
A fraction wall does the same job in a tidier form: a row of halves, a row of quarters and a row of eighths, all the same length. Hold a ruler vertically and it shows which fractions line up, with 1/2 sitting directly above 2/4 and 4/8. For a fuller sequence of models, see how to teach fractions.
Try this: cut two identical strips of paper. Fold one in half and colour one half. Fold the other into quarters and colour two quarters. Hold them together against a window and ask your child what they notice about the coloured parts and the number of sections.
Why do you multiply the top and bottom by the same number?
Because you are changing how the amount is counted, not how much there is. Multiplying the top and bottom by the same number turns each piece into smaller pieces and then counts more of them.
Start with 1/2 and multiply both numbers by 2. The bar is now cut into twice as many pieces. Double the count and halve the size of each piece, and the amount stays the same. So 1 x 2 = 2 and 2 x 2 = 4, which gives 1/2 = 2/4.
Multiply both numbers by 3 and every piece becomes a third of its old size: 1/2 = 3/6. Multiply by 4 and you get 4/8. The multiplier is really a fraction worth one whole, such as 2/2 or 3/3, and multiplying by one never changes a value.
The rule works for any fraction. Take 3/5: multiply top and bottom by 2 to get 6/10, or by 3 to get 9/15. Both are the same amount as 3/5, written in smaller pieces.
Can you divide to find equivalent fractions?
Yes, dividing the top and bottom by the same number gives an equivalent fraction in simpler terms. This is called simplifying or cancelling, and it is the multiply rule running backwards.
Take 12/16 and divide both numbers by 4 to get 3/4. Take 9/12 and divide both by 3 to get 3/4. Both simplify to the same fraction, which shows they were the same amount all along.
A fraction is in its simplest form when no whole number greater than 1 divides both the top and the bottom exactly. Simplifying is also the first step towards converting between fractions, decimals and percentages, which is covered in fractions, decimals and percentages.
What mistakes should you watch for?
The commonest slips come from treating the top and bottom as separate numbers rather than one amount. A quick picture usually clears them up faster than a correction.
- Adding the same number to the top and bottom. 1/2 becomes 2/3, which is a bigger amount, so the fractions are not equivalent. Adding changes the value; multiplying by a fraction such as 2/2 does not.
- Changing only one number. Doubling the top of 1/2 gives 2/2, a whole one. Both numbers need the same treatment.
- Assuming a bigger bottom number means a bigger fraction. 1/8 is smaller than 1/4, because eighths are smaller pieces than quarters.
- Counting pieces without checking their size. Two pieces of very different sizes are not two of the same thing.
Drawing the bar takes ten seconds and settles the question. Visual maths covers more of these models and why they help.
How does Slice practise equivalent fractions?
Slice is a free iPhone maths game for ages 9 and up where the puzzles are built from real objects: pizza, toast, chocolate, spinners and pie charts. Because players fill, cut and share those objects, choosing a fraction that matches another becomes a practical decision about food rather than an abstract rule.
The game covers fractions, decimals, percentages, angles, time, ratio, money and probability across 161 puzzles in 5 learning paths, plus a daily challenge. It supports the ideas in this guide and does not replace teaching. You can read more on the Slice page.
Common questions
What does equivalent mean in fractions?
Equivalent means equal in value. Equivalent fractions are written with different numbers but name the same amount, so 1/2, 2/4 and 4/8 all cover the same half of a shape.
How do you find an equivalent fraction for any fraction?
Multiply the top and bottom by the same whole number. For 2/3, multiply both by 2 to get 4/6, or by 5 to get 10/15. Each version covers exactly the same amount as 2/3.
Why isn't 1/3 equivalent to 1/2?
Because thirds are smaller pieces than halves, and no whole number of thirds makes exactly one half. One half is one and a half thirds, which is not a whole number of pieces, so no equivalent fraction for 1/2 can have 3 on the bottom.
Do equivalent fractions have the same decimal and percentage?
Yes. Equivalent fractions are the same amount, so they share one decimal and one percentage. 1/2, 2/4 and 4/8 are all 0.5 and all 50%.