Concept 5 of 7
Same Bottom: Comparing Like Fractions
Today's big idea
When the bottoms match, every piece is the same size, so just count the pieces.
Same-size pieces are what make counting the tops a fair comparison.
How it works
👀 What's going on?
Two people take slices from the same cake, cut the same way. Working out who got more should not need any thinking at all. It does not, so long as you notice the slices are the same size.
💡 Here's the trick
Look at the two bars above. Both are cut into 8, so every single piece is the same width. That makes the comparison pure counting: 5 pieces beats 3 pieces, so 5/8 is bigger than 3/8. Whenever two fractions share a bottom number, only the tops matter.
🪄 How to do it
- 1.Check that the bottom numbers match, the way the bars above are both cut into 8.
- 2.Compare the top numbers only. The bigger top is the bigger fraction.
✍️ Try it
Which is bigger, 2/7 or 5/7? Then put 1/6, 4/6 and 3/6 in order from smallest to biggest.
Both sevenths, so compare 2 and 5: 5/7 is bigger. For the second, all of them are sixths, so sorting the tops 1, 3, 4 sorts the fractions: 1/6, 3/6, 4/6.
⚠️ Watch out
You might be thinking a bigger top always wins. It only wins when the bottoms match. Compare 5/8 with 3/4 and the bigger top belongs to 5/8, but 3/4 is the same as 6/8, so 3/4 is actually the bigger one.
🌟 Why this matters
Slices of the same pizza, or minutes out of the same hour. Whenever the whole is cut the same way for both, you can just count.
Exam tip: Before comparing tops, always check the bottoms; that check is the question in disguise.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Which is bigger: 5/9 or 2/9?”
- 1
Check the bottoms
Both have 9 at the bottom → LIKE fractions.
- 2
Same bottom = compare tops
Just look at the numerators: 5 vs 2.
- 3
Bigger top wins
5 > 2 → 5/9 > 2/9.
- 4
Answer ✓
5/9 is bigger
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap the bigger fraction — the longer bar.
COMPARE · ROUND 1 OF 3
Quick check
✅ VERIFICATION
Which is bigger: 3/7 or 6/7?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Comparing Unit Fractions
For 1-on-top fractions, the smaller bottom wins.