✖ Fraction Multiply & Divide: The Power Methods ➗

Multiplying fractions is actually easier than adding them — no common denominator needed! And dividing? Just flip the second fraction and multiply. Let's master both!

✖ Multiply: Top × Top, Bottom × Bottom
23 × 35 = 2×33×5 = 615 = 25
➗ Divide: Keep · Change · Flip (KCF)
34 ÷ 2  →  34 × 12 = 38
🔢 Mixed Numbers: Convert First!
112 × 2 = 32 × 2 = 62 = 3    Always convert to improper first!

The KCF Method for Division:

🔒 KEEP

Keep the first fraction exactly as it is
→

🔄 CHANGE

Change ÷ to ×
→

🙃 FLIP

Flip the second fraction (write its reciprocal)

Example: 23 ÷ 45 → Keep 23, Change ÷ to ×, Flip to 54 → 23 × 54 = 1012 = 56

The Golden Rules:

📝 Worked Examples

Study each method carefully!

Example 1: Multiply Two Fractions

Question: 34 × 25

Multiply numerators: 3 × 2 = 6
Multiply denominators: 4 × 5 = 20
Result: 6/20. Simplify using HCF of 6 and 20 = 2 → 6÷2 = 3, 20÷2 = 10

Answer: 310

Example 2: Multiply a Fraction by a Whole Number

Question: 37 × 4

Write 4 as a fraction: 41
Multiply: 3×47×1 = 127
Convert improper fraction: 12 ÷ 7 = 1 remainder 5

Answer: 157

Example 3: Divide a Fraction by a Whole Number (KCF)

Question: 56 ÷ 3

Keep: 56
Change: ÷ → ×
Flip: 3 = 31 → flipped = 13
Multiply: 56 × 13 = 518

Answer: 518

Example 4: Multiply Mixed Numbers

Question: 123 × 214

Convert to improper fractions: 1⅔ = 53   2¼ = 94
Multiply: 5×93×4 = 4512
Simplify: HCF of 45 and 12 = 3 → 154
Convert: 15 ÷ 4 = 3 remainder 3

Answer: 334

🔬 Multiply & Divide Visualizer

Enter two fractions and choose × or ÷ to see the full working!

×

Click × to switch to division

🧩 Drag 1: Multiply Top × Top, Bottom × Bottom

Complete: 25 × 34

6
20
5
8
25 × 34 =

🧩 Drag 2: Simplify After Multiplying

We got 620 from the last question. Now simplify it!

2
3
10
4
12
HCF of 6 and 20 =
620 ÷
2
=

🧩 Drag 3: KCF — Keep, Change, Flip

Use KCF to set up: 45 ÷ 3

4/5
1/3
4/15
3/1
5/4
KEEP:
FLIP 3 to:
Answer =

🧩 Drag 4: Convert Mixed Number First

Convert 234 to an improper fraction, then multiply by 23.

11
11/6
22
12
9
2 × 4 + 3 =
so 2¾ =
11
4
114 × 23 =
=

🧩 Drag 5: Divide Fraction ÷ Fraction

Use KCF to solve: 35 ÷ 27

7/2
21
10
2/7
6
Flip 27 →
35 × 72 =

🧩 Drag 6: Fraction × Whole Number

Calculate 56 × 4, then simplify.

20
6
10/3
3⅓
24
2
56 × 41 =
Simplify →
=

📝 Practice Questions

Simplify all answers. Convert improper fractions to mixed numbers.

  1. 12 × 13
  2. 23 × 34
  3. 45 × 58
  4. 37 × 5
  5. 29 × 6
  6. 56 × 310
  7. 34 ÷ 2
  8. 56 ÷ 3
  9. 23 ÷ 14
  10. 35 ÷ 310
  11. 112 × 4
  12. 213 × 37
  13. 123 × 112
  14. 214 ÷ 3
  15. 78 ÷ 716
  16. What is 23 of 15?
  17. What is 34 of 20?
  18. A rope is 56 m. It is cut into 5 equal pieces. How long is each piece?
  19. Multiply 78 by 47 and simplify.
  20. Which is greater: 34 × 23 or 23 ÷ 34?
  1. 1/6
  2. 6/12 = 1/2
  3. 20/40 = 1/2
  4. 15/7 = 2 1/7
  5. 12/9 = 4/3 = 1 1/3
  6. 15/60 = 1/4
  7. 3/4 × 1/2 = 3/8
  8. 5/6 × 1/3 = 5/18
  9. 2/3 × 4/1 = 8/3 = 2 2/3
  10. 3/5 × 10/3 = 30/15 = 2
  11. 3/2 × 4 = 12/2 = 6
  12. 7/3 × 3/7 = 21/21 = 1
  13. 5/3 × 3/2 = 15/6 = 2 1/2
  14. 9/4 × 1/3 = 9/12 = 3/4
  15. 7/8 × 16/7 = 112/56 = 2
  16. 2/3 × 15 = 30/3 = 10
  17. 3/4 × 20 = 60/4 = 15
  18. 5/6 ÷ 5 = 5/6 × 1/5 = 1/6 m
  19. 28/56 = 1/2
  20. 3/4 × 2/3 = 1/2.   2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.   8/9 > 1/2 so the division is greater.

🔥 Challenge: Multiply & Divide Word Problems

Show all working. Simplify all answers!

  1. A recipe uses 34 cup of sugar. If you make 112 batches, how much sugar do you need?
  2. A piece of ribbon is 412 m long. It is cut into pieces each 34 m long. How many pieces are cut?
  3. A field is 213 km long and 112 km wide. What is its area?
  4. A car uses 38 of a tank of petrol per hour. How much petrol does it use in 223 hours?
  5. Six friends share 34 of a pizza equally. What fraction does each person get?
  6. Josh walks 56 km every day. How far does he walk in 5 days? Give your answer as a mixed number.
  7. A bottle holds 114 litres. How many full glasses of 516 litre can be filled from the bottle?
  8. A tank is 56 full. It holds 60 litres when full. If 25 of the water is removed, how many litres remain?
  9. A rectangle has area 58 m² and width 512 m. Find the length. (Hint: length = area ÷ width)
  10. Three sisters each inherit 13 of an estate worth £2,400,000. Each sister then gives 14 of her share to charity. How much does each sister give to charity?
  1. 3/4 × 3/2 = 9/8 = 1 1/8 cups
  2. 9/2 ÷ 3/4 = 9/2 × 4/3 = 36/6 = 6 pieces
  3. 7/3 × 3/2 = 21/6 = 7/2 = 3 1/2 km²
  4. 3/8 × 8/3 = 24/24 = 1 tank
  5. 3/4 ÷ 6 = 3/4 × 1/6 = 3/24 = 1/8 of the pizza
  6. 5/6 × 5 = 25/6 = 4 1/6 km
  7. 5/4 ÷ 5/16 = 5/4 × 16/5 = 80/20 = 4 glasses
  8. Full = 60 L. 5/6 full = 50 L. Remove 2/5 of 50 = 20 L. Remaining: 30 litres
  9. 5/8 ÷ 5/12 = 5/8 × 12/5 = 60/40 = 3/2 = 1 1/2 m
  10. Each sister: 1/3 × £2,400,000 = £800,000. Charity: 1/4 × £800,000 = £200,000
Created by Mr Josh ✨ FractionRush