Learn · comparing fractions
Comparing Fractions
Four ways to tell which fraction is bigger, from the quickest to the one that always works.
Same bottom? The bigger top wins. Same top? The smaller bottom wins. If neither matches, check each fraction against 1/2, or rewrite both with the same bottom number.
1. Same bottom: compare the tops
The slices are the same size, so more slices means more pie. 3/5 > 2/5.
2. Same top: the smaller bottom wins
You have the same number of slices, but cutting into fewer parts makes each slice bigger. 1/3 > 1/4, and 2/5 > 2/8. This is the one that feels backwards at first.
3. Nothing matches: use 1/2 as a benchmark
Is each fraction under or over a half? 3/8 is under half (half of 8 is 4). 4/6 is over half (half of 6 is 3). So 4/6 > 3/8, with no calculating at all.
4. The one that always works: make the bottoms match
- Compare 2/3 and 3/5. Find a number both bottoms go into: 15.
- Rewrite 2/3: multiply top and bottom by 5 to get 10/15.
- Rewrite 3/5: multiply top and bottom by 3 to get 9/15.
- Now the slices match: 10/15 > 9/15, so 2/3 > 3/5.
Which method should you use?
| You see | Example | Do this |
|---|---|---|
| Same bottom | 5/8 and 3/8 | Bigger top wins: 5/8 > 3/8 |
| Same top | 2/3 and 2/7 | Smaller bottom wins: 2/3 > 2/7 |
| One over half, one under | 3/5 and 1/4 | Over half wins: 3/5 > 1/4 |
| Both near 1 | 7/8 and 5/6 | Look at what's missing: 1/8 is less than 1/6, so 7/8 > 5/6 |
| Anything else | 3/4 and 5/7 | Make the bottoms match: 21/28 > 20/28, so 3/4 > 5/7 |
“8 is bigger than 4, so 1/8 is bigger than 1/4.” Whole-number thinking is the big trap here. Ask: would you rather share a pie with 3 friends or with 7? Then look at the fraction wall.
Practice against the bakery cat
Bigger Slice starts with pairs you can see and works up to pairs with nothing in common.
Free to play · no signup · works on phones, tablets and computers
Comparing fractions FAQ
How do you compare fractions with different denominators?
Check whether each is above or below 1/2 first. If that doesn't settle it, rewrite both with a common denominator and compare the tops.
What is the butterfly method?
A cross-multiplying shortcut. It's quick but it hides the reason it works. We explain it, and when to use it, in the butterfly method guide.
Where are comparing fractions worksheets?
Here: free comparing fractions worksheets with pictures and 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