Concept 3 of 9
The Pizza Combiner: Adding/Subtracting Like Fractions
Today's big idea
When the bottoms already match, add the tops and leave the bottom alone.
2/8 + 3/8 = 5/8, because every piece is still an eighth.
How it works
👀 What's going on?
Adding 2/8 + 3/8 is far easier than adding 2/3 + 3/4, and the reason is worth knowing. The bottom numbers already match, so all you are doing is counting.
💡 Here's the trick
Look at the slices above. Every piece is an eighth, so 2 of them plus 3 of them makes 5 of them, and 2/8 + 3/8 = 5/8. The bottom number tells you the size of a piece, and that size has not changed. Only the count did.
🪄 How to do it
- 1.Check the bottoms match, as both are 8 in the picture above, then leave the bottom alone.
- 2.Add or subtract only the top numbers.
✍️ Try it
Work out 2/6 + 3/6, then work out 7/10 minus 4/10. What happens to each bottom number?
2/6 + 3/6 gives 5/6, and 7/10 minus 4/10 gives 3/10. Both bottoms stayed exactly where they were. Subtracting behaves the same as adding, because the size of a slice still has not changed.
⚠️ Watch out
You might be thinking the bottoms should add too, making 2/8 + 3/8 into 5/16. Check that against the picture. 5/16 is smaller than 3/8 on its own, and adding something cannot leave you with less.
🌟 Why this matters
Combining parts of the same thing comes up all the time. Two portions of food, two lengths of ribbon, two chunks of a job already finished.
Exam tip: Look at the bottoms first, because matching bottoms mean the question is much easier than it appears.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“2/9 + 5/9 — same bottom!”
- 1
Check the bottoms
Both are ninths. ✓ Slice sizes match.
- 2
Lock the bottom
The 9 stays — only the count of ninths changes.
- 3
Add the tops
2 + 5 = 7
- 4
Answer ✓
2/9 + 5/9 = 7/9
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Same bottom number? Then just ADD the tops — the bottom never changes. Tap the slices to combine them onto one plate.
Problem 1 of 3
2/8 + 3/8
2/8
3/8
COMBINED PLATE · bottom locked at 8
Tops: 0 + 0 = 0/8
Quick check
✅ VERIFICATION
Work out 5/12 + 4/12.
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Matchmaker
Make the bottoms match, then compare.