Concept 4 of 8
Dividing Fractions
Today's big idea
Divide fractions with KCF: Keep the first, Change ÷ to ×, Flip the second.
Dividing by a fraction is the same as multiplying by its flip.
How it works
👀 What's going on?
A jug holds 2 litres and each glass takes half a litre. That fills four glasses. Dividing by a fraction made the answer bigger, not smaller.
💡 Here's the trick
Look at the boxes above. You keep the first fraction, change the sign to times, then flip the second one over. That flipped fraction has a name: it is the reciprocal.
🪄 How to do it
- 1.Keep the left fraction exactly as the boxes above show.
- 2.Change the divide sign into a times sign.
- 3.Flip the second fraction over, then multiply and simplify.
✍️ Try it
Work out 5/6 divided by 10/9. Then work out 4/7 divided by 3.
Flip 10/9 to 9/10, so 5/6 times 9/10 is 45/60, which is 3/4. For the second, 3 becomes 3/1 and flips to 1/3, giving 4/21.
⚠️ Watch out
You might be thinking that either fraction can be flipped. Only the second one flips. Flipping the first turns 6 divided by 1/2 into 1/12, when the real answer is 12.
🌟 Why this matters
Cutting ribbon into equal lengths, or filling bottles from a jug, is division by a fraction. The answer counts how many pieces you get.
Exam tip: Say keep, change, flip out loud, and only then start multiplying.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find: 5/6 ÷ 2/3.”
- 1
KEEP the first fraction
Keep 5/6. 🔄
- 2
CHANGE ÷ to ×
The sign flips.
- 3
FLIP the second
2/3 becomes 3/2.
- 4
Multiply ✓
5/6 × 3/2 = 15/12 = 5/4
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
KCF: Keep the first, Change ÷ to ×, Flip the second.
DIVISION · ROUND 1 OF 3
2/5 ÷ 3/4
Quick check
✅ VERIFICATION
What is 6/7 ÷ 3/14?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Decimal Place Value
Tenths · hundredths · thousandths.