Concept 2 of 8
Add & Subtract Fractions
Today's big idea
To add/subtract fractions, make the bottoms match first (LCD).
Fractions add or subtract only once their bottoms match; rename, then work the tops.
How it works
👀 What's going on?
One quarter of a cake plus two thirds of a cake. You cannot just add the tops, because a quarter and a third are different sizes. The slices have to match first.
💡 Here's the trick
Look at the rows above. Each fraction is renamed so that both sit over 12, the smallest bottom that suits them both. Once the slices are the same size, you simply add the tops.
🪄 How to do it
- 1.Check the two bottoms in the rows above.
- 2.If they differ, find the smallest number both divide into.
- 3.Rename each fraction, then add or subtract the tops only.
✍️ Try it
Work out 2/5 + 1/2. Then work out 7/10 minus 2/5.
Both bottoms divide into 10, so the first becomes 4/10 + 5/10, which is 9/10. For the second, 2/5 is 4/10, and 7/10 minus 4/10 leaves 3/10.
⚠️ Watch out
You might be thinking the bottoms get added too. They do not. That habit turns 1/2 + 1/2 into 2/4, which is a half, yet two halves clearly make one whole.
🌟 Why this matters
Splitting a bill, sharing a pizza or timing a journey all add parts of different sizes. The common bottom is what makes them fair to compare.
Exam tip: Write both fractions over the same bottom first, before you touch the tops.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find: 2/3 + 1/6.”
- 1
Different bottoms — find the LCM
LCM(3, 6) = 6. 🧩
- 2
Build equal fractions
2/3 = 4/6; 1/6 stays 1/6.
- 3
Add the tops
4/6 + 1/6 = 5/6
- 4
Answer ✓
2/3 + 1/6 = 5/6
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Same bottom? Add/subtract tops directly. Different bottoms? Use the LCM.
EXPRESSION · ROUND 1 OF 3
2/7 + 3/7
Quick check
✅ VERIFICATION
What is 3/8 + 1/6?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Multiplying Fractions
Tops × tops · bottoms × bottoms.