Learn · equivalent fractions
Equivalent Fractions
Different numbers, same amount of cake.
Equivalent fractions are different fractions for the same amount. 1/2, 2/4 and 4/8 all name the same amount. To make one, multiply the top and bottom by the same number. To check two, simplify both or compare them with a picture.
See it
Take half a pie. Cut every slice in two. Nothing was added or eaten, so it's still the same amount, but now it's 2 of 4. Cut again and it's 4 of 8.
Why the rule works
Cutting every slice into 2 doubles the number of slices in the whole, so the bottom number doubles. It also doubles the slices you have, so the top number doubles too. Cut every slice into 3 and both numbers triple. That's all the rule is: top and bottom are multiplied by the same number because every slice gets cut the same way.
This is why you can't just add the same number to both. 1/2 is not (1 + 2)/(2 + 2) = 3/4: three quarters is plainly more than a half. Adding isn't cutting.
How to find an equivalent fraction
- Pick a number to multiply by, like 3.
- Multiply the top: 2 × 3 = 6.
- Multiply the bottom: 5 × 3 = 15.
- So 2/5 = 6/15. It's the same amount, cut smaller.
Equivalent fractions chart
| Fraction | × 2 | × 3 | × 4 | × 5 | × 6 |
|---|---|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 | 5/10 | 6/12 |
| 1/3 | 2/6 | 3/9 | 4/12 | 5/15 | 6/18 |
| 2/3 | 4/6 | 6/9 | 8/12 | 10/15 | 12/18 |
| 1/4 | 2/8 | 3/12 | 4/16 | 5/20 | 6/24 |
| 3/4 | 6/8 | 9/12 | 12/16 | 15/20 | 18/24 |
| 1/5 | 2/10 | 3/15 | 4/20 | 5/25 | 6/30 |
| 2/5 | 4/10 | 6/15 | 8/20 | 10/25 | 12/30 |
| 3/5 | 6/10 | 9/15 | 12/20 | 15/25 | 18/30 |
| 4/5 | 8/10 | 12/15 | 16/20 | 20/25 | 24/30 |
| 1/6 | 2/12 | 3/18 | 4/24 | 5/30 | 6/36 |
| 5/6 | 10/12 | 15/18 | 20/24 | 25/30 | 30/36 |
| 1/8 | 2/16 | 3/24 | 4/32 | 5/40 | 6/48 |
| 3/8 | 6/16 | 9/24 | 12/32 | 15/40 | 18/48 |
| 5/8 | 10/16 | 15/24 | 20/32 | 25/40 | 30/48 |
| 7/8 | 14/16 | 21/24 | 28/32 | 35/40 | 42/48 |
How to check if two fractions are equal
Divide each top and bottom by the biggest number that goes into both. 6/8 becomes 3/4 and 9/12 becomes 3/4, so they're equal.
2/3 and 8/12: 2 × 4 = 8 and 3 × 4 = 12. Same multiplier on top and bottom means they're equal.
For 2/3 and 8/12, 2 × 12 = 24 and 3 × 8 = 24. The two products match, so they're equal. This one's fast, but it doesn't show why, so teach it last.
Now watch it happen
In Magic Knife, one tap cuts every slice in half so kids see the rule in action. It's the fastest way we know to make this idea stick.
Free to play · no signup · works on phones, tablets and computers
Equivalent fractions FAQ
What are 3 fractions equivalent to 1/2?
3/6, 4/8, 5/10. In each, the top is half of the bottom.
What are equivalent fractions in simple words?
Fractions that look different but mean the same amount, like two quarters of a pie and one half of a pie.
Where can I get an equivalent fractions worksheet?
Right here: free equivalent fractions worksheets with answer keys.
Is the fraction game really free?
Yes. The whole game plays free in your browser, with no signup, no ads and no time limit. A Fraction Bakery app for iPhone is coming later, but the web game stays free.
Take the bakery with you, soon
A Fraction Bakery app for iPhone is on the way. The plan: offline play for the car, a parent report of which fractions have stuck, and the full bakery shelf of prizes. Until then, the whole game is free right here.
Coming soon on theApp Store