Concept 3 of 8
Multiplying Fractions
Today's big idea
Multiply fractions straight across: top × top over bottom × bottom.
Cancel a top against a bottom before multiplying, never two tops.
How it works
👀 What's going on?
Multiplying is the gentlest of the four fraction jobs. No common bottom, no renaming, no swapping the order. Straight across the top and straight across the bottom.
💡 Here's the trick
Look at the fractions above. Tops multiply with tops, and bottoms multiply with bottoms. Cancelling a shared factor across the two fractions first keeps every number small.
🪄 How to do it
- 1.Turn any mixed number in the fractions above into an improper one.
- 2.Cancel a top and a bottom that share a factor.
- 3.Multiply the tops, multiply the bottoms, then simplify.
✍️ Try it
Work out 3/8 times 4/9. Then find 3/5 of 40.
Cancel 4 with 8 and 3 with 9, which leaves 1/2 times 1/3, so the answer is 1/6. For the second, 3 times 40 shared by 5 gives 24.
⚠️ Watch out
You might be thinking that multiplying always makes a number bigger. With fractions below one it does the opposite. Half of a half is a quarter, smaller than either of them.
🌟 Why this matters
Sale prices, half portions and scaled recipes are all one fraction of another. The little word of is your signal to multiply.
Exam tip: Cancel before you multiply, so you never have to simplify a huge answer.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find: 2/3 × 9/10.”
- 1
Cross-cancel where you can
9 and 3 share 3 → cancel. 2 and 10 share 2 → cancel. ✖️
- 2
Now multiply across
(1 × 3) / (1 × 5)
- 3
Read the answer
3/5
- 4
Done ✓
2/3 × 9/10 = 3/5
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Multiply numerators together and denominators together. "Of" = ×.
EXPRESSION · ROUND 1 OF 3
3/5 × 2/7
Quick check
✅ VERIFICATION
What is 5/6 × 3/10 in its lowest terms?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Dividing Fractions
Keep · Change · Flip.