Concept 1 of 8
Mixed ↔ Improper
Today's big idea
Mixed to improper: whole × bottom, plus the top, all over the same bottom.
A mixed number and its improper form name the same amount, whole parts and all.
How it works
👀 What's going on?
You order two and three quarter pizzas. The kitchen counts only in quarter slices, so it needs eleven of them. Both numbers name the same lunch.
💡 Here's the trick
Look at the picture above. Two whole circles plus three quarters is the same as eleven single quarters. A mixed number shows the wholes, an improper fraction counts every slice.
🪄 How to do it
- 1.Read the picture above and find the bottom number.
- 2.Mixed to improper: times the whole by the bottom, then add the top.
- 3.Improper to mixed: divide the top by the bottom, keep the leftover on top.
✍️ Try it
Write 3 2/5 as an improper fraction. Then write 29/6 as a mixed number.
For the first, 3 times 5 is 15, and 15 plus 2 is 17, so it is 17/5. For the second, 29 shared by 6 is 4 with 5 left over, so it is 4 5/6.
⚠️ Watch out
You might be thinking the bottom number changes as well. It never does. Two and three quarters is 11/4, not 11/8, because you are still counting in quarters.
🌟 Why this matters
Recipes, spanner sets and tape measures all mix wholes with parts. A builder reads 5 1/2 inches, but a calculator wants 11/2, and you need both.
Exam tip: Turn everything improper before you multiply or divide, then turn the answer back.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Convert 3¾ to an improper fraction.”
- 1
Multiply whole × bottom
3 × 4 = 12. 🔁
- 2
Add the top
12 + 3 = 15.
- 3
Put over the same bottom
15 / 4
- 4
Improper form ✓
3¾ = 15/4
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Mixed → Improper: × whole, + top, keep bottom. Improper → Mixed: divide top by bottom.
CONVERSION · ROUND 1 OF 3
2 2/5 → improper
Quick check
✅ VERIFICATION
Convert 5 1/3 to an improper fraction.
⚡ Finish the activity above first to answer.
Keep going!
Up next: Add & Subtract Fractions
Match the bottom first.