✖️ Decimal Multiply: Multiply & Divide Decimals 🔢

Multiplying and dividing decimals might look tricky, but they follow the same methods as whole numbers — you just need to track the decimal point carefully! In Grade 6, you'll multiply decimals by whole numbers and by other decimals, divide decimals by whole numbers, and use 10/100/1000 shortcuts.

✖️ Multiply Decimal × Whole Number
3.7 × 4 → treat as 37 × 4 = 148 → 1 decimal place → 14.8
✖️ Decimal × Decimal
2.4 × 1.3 → 24 × 13 = 312 → 2 d.p. total → 3.12
÷ Divide Decimal by Whole
8.4 ÷ 3 → bus stop: 8.4 ÷ 3 = 2.8 · Keep decimal point in same position

📏 Golden Rules

✖️ Multiplying Decimal × Whole Number

Ignore the decimal point, multiply as integers, then count the total decimal places in the original numbers and insert the decimal point that many places from the right.

Example: 4.37 × 6 → ignore decimal → 437 × 6 = 2622 → 2 d.p. → 26.22

✖️ Multiplying Decimal × Decimal

Same process — ignore both decimal points, multiply as whole numbers, then the answer has as many decimal places as the total decimal places in both factors combined.

Example: 2.4 × 1.3 → 24 × 13 = 312 → 1 + 1 = 2 d.p. → 3.12

× / ÷ Powers of 10 Shortcuts

Multiplying by 10: digits move 1 place LEFT  →  0.47 × 10 = 4.7

Multiplying by 100: digits move 2 places LEFT  →  0.47 × 100 = 47

Multiplying by 1000: digits move 3 places LEFT  →  0.47 × 1000 = 470

Dividing by 10: digits move 1 place RIGHT  →  4.7 ÷ 10 = 0.47

Dividing by 100: digits move 2 places RIGHT  →  4.7 ÷ 100 = 0.047

Dividing by 1000: digits move 3 places RIGHT  →  4.7 ÷ 1000 = 0.0047

÷ Dividing Decimal ÷ Whole Number

Use short division (bus stop), keeping the decimal point in the same position in the quotient.

Example: 9.45 ÷ 3 → 9÷3=3, 4÷3=1 r1, 15÷3=5 → Answer: 3.15

÷ Dividing Decimal ÷ Decimal

Multiply both numbers by 10 (or 100) first to make the divisor a whole number, then divide.

Example: 4.8 ÷ 0.6 → ×10 both → 48 ÷ 6 = 8

🔎 Always Estimate First

Round decimals to the nearest whole number and multiply/divide to get a rough answer. Then check your exact answer is close to the estimate!

Example: 4.37 × 6 → estimate: 4 × 6 = 24 → exact answer 26.22 is close ✓
Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

📝 Worked Examples

Example 1: Decimal × Whole Number

Calculate 4.37 × 6

Step 1: Ignore decimal → 437 × 6 = 2,622
Step 2: Count decimal places → 4.37 has 2 decimal places → answer has 2 d.p.
Step 3: Place decimal point → 2622 → 26.22
✅ Estimate check: 4 × 6 = 24 (close to 26.22) ✓

Example 2: Decimal × Decimal

Calculate 3.4 × 2.5

Step 1: Ignore decimals → 34 × 25 = 850
Step 2: Count total decimal places → 1 + 1 = 2 d.p.
Step 3: Place decimal point → 850 → 8.50 = 8.5
✅ Estimate check: 3 × 3 = 9 (close to 8.5) ✓

Example 3: Dividing Decimal by Whole Number

Calculate 9.45 ÷ 3

Step 1: Set up bus stop: 9.45 ÷ 3
Step 2: 9 ÷ 3 = 3
Step 3: 4 ÷ 3 = 1 remainder 1 → bring down → 15
Step 4: 15 ÷ 3 = 5
Step 5: Keep decimal point in same position → Answer: 3.15
✅ Check: 3.15 × 3 = 9.45 ✓

Example 4: Dividing Decimal by Decimal

Calculate 4.8 ÷ 0.6

Step 1: The divisor (0.6) is not a whole number — multiply both by 10
Step 2: 4.8 × 10 = 48  and  0.6 × 10 = 6
Step 3: 48 ÷ 6 = 8
✅ Check: 0.6 × 8 = 4.8 ✓
Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

🔬 Decimal Calculator

Enter two numbers and choose an operation to see the full method step by step!

Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

🎯 Drag 1: Decimal × Whole Number

Calculate 2.4 × 3

2.4 × 3 = ?

Drag the correct answer into the drop zone!

6.2
6.4
7.2
7.4
2.4 × 3 =
?

💡 Hint: 24 × 3 = 72. Now place 1 decimal point: 7.2

Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

🎯 Drag 2: Decimal × 100

Calculate 0.83 × 100

0.83 × 100 = ?

Drag the correct answer into the drop zone!

8.3
83
830
0.083
0.83 × 100 =
?

💡 Hint: × 100 moves digits 2 places LEFT. 0.83 → 83.

Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

🎯 Drag 3: Decimal × Decimal

Calculate 1.5 × 2.4

1.5 × 2.4 = ?

Drag the correct answer into the drop zone!

3.2
3.4
3.6
3.8
1.5 × 2.4 =
?

💡 Hint: 15 × 24 = 360. Total 2 decimal places. 360 → 3.60 = 3.6

Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

🎯 Drag 4: Divide by Whole Number

Calculate 7.2 ÷ 4

7.2 ÷ 4 = ?

Drag the correct answer into the drop zone!

1.6
1.7
1.8
1.9
7.2 ÷ 4 =
?

💡 Hint: Bus stop: 7.2 ÷ 4. 7÷4 = 1 remainder 3, 32÷4 = 8 → 1.8

Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

🎯 Drag 5: Divide Decimal by Decimal

Calculate 3.6 ÷ 0.9

3.6 ÷ 0.9 = ?

Drag the correct answer into the drop zone!

3
4
5
6
3.6 ÷ 0.9 =
?

💡 Hint: Multiply both by 10: 36 ÷ 9 = ?

Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

🎯 Drag 6: Divide by 1000

Calculate 45.6 ÷ 1000

45.6 ÷ 1000 = ?

Drag the correct answer into the drop zone!

4.56
0.456
0.0456
456
45.6 ÷ 1000 =
?

💡 Hint: ÷ 1000 moves digits 3 places RIGHT. 45.6 → 0.0456

Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

✏️ Practice Questions

Work through all 20 questions, then check your answers!

  1. 3.5 × 4 = ______
  2. 6.8 × 3 = ______
  3. 0.7 × 9 = ______
  4. 4.25 × 4 = ______
  5. 2.3 × 1.4 = ______
  6. 5.6 × 2.5 = ______
  7. 0.8 × 0.7 = ______
  8. 3.14 × 100 = ______
  9. 0.065 × 1000 = ______
  10. 4.5 ÷ 3 = ______
  11. 8.4 ÷ 4 = ______
  12. 9.6 ÷ 0.8 = ______
  13. 7.5 ÷ 0.5 = ______
  14. 3.6 ÷ 100 = ______
  15. 1.44 ÷ 1.2 = ______
  16. A piece of ribbon is 4.5 m long. It is cut into 6 equal pieces. How long is each piece? ______
  17. 0.45 × 0.2 = ______
  18. Petrol costs £1.48 per litre. Find the cost of 3.5 litres. ______
  19. 8.64 ÷ 3 = ______
  20. 2.7 × 3.3 = ______

Answers

  1. 3.5 × 4 = 14
  2. 6.8 × 3 = 20.4
  3. 0.7 × 9 = 6.3
  4. 4.25 × 4 = 17
  5. 2.3 × 1.4 = 3.22
  6. 5.6 × 2.5 = 14
  7. 0.8 × 0.7 = 0.56
  8. 3.14 × 100 = 314
  9. 0.065 × 1000 = 65
  10. 4.5 ÷ 3 = 1.5
  11. 8.4 ÷ 4 = 2.1
  12. 9.6 ÷ 0.8 = 12
  13. 7.5 ÷ 0.5 = 15
  14. 3.6 ÷ 100 = 0.036
  15. 1.44 ÷ 1.2 = 1.2
  16. 4.5 ÷ 6 = 0.75 m
  17. 0.45 × 0.2 = 0.09
  18. £1.48 × 3.5 = £5.18
  19. 8.64 ÷ 3 = 2.88
  20. 2.7 × 3.3 = 8.91
Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭

🏆 Challenge Problems

Ten harder problems — show your working!

  1. A room is 4.8 m × 3.5 m. What is the area?
  2. Tom earns £8.45 per hour. He works 6.5 hours. How much does he earn?
  3. A bottle holds 2.4 litres. How much do 8.5 bottles hold?
  4. Calculate 12.6 ÷ 0.07. (Hint: multiply both by 100 first)
  5. A car travels 37.8 km on 4.2 litres of fuel. What is the fuel consumption in km per litre?
  6. If 0.35 kg of cheese costs £2.45, what is the cost per kg?
  7. A square garden has area 32.49 m². Find the side length. (Hint: √32.49)
  8. Calculate 1.2 × 1.2 × 1.2. (Hint: 1.2³)
  9. 4.5 litres of paint covers 18 m². How many litres are needed for 40 m²?
  10. A number multiplied by 0.4 gives 6.8. What is the number?

Answers

  1. 4.8 × 3.5 = 16.8 m²
  2. 8.45 × 6.5 = 54.925 → £54.93 (rounded to nearest penny)
  3. 2.4 × 8.5 = 20.4 litres
  4. 12.6 ÷ 0.07 → × 100 both → 1260 ÷ 7 = 180
  5. 37.8 ÷ 4.2 → × 10 both → 378 ÷ 42 = 9 km per litre
  6. 2.45 ÷ 0.35 → × 100 both → 245 ÷ 35 = £7 per kg
  7. √32.49 = 5.7 m (since 5.7 × 5.7 = 32.49)
  8. 1.2³ = 1.2 × 1.2 × 1.2 = 1.44 × 1.2 = 1.728
  9. 40 ÷ 18 × 4.5 = 10 litres
  10. 6.8 ÷ 0.4 → × 10 both → 68 ÷ 4 = 17
Collins Cambridge Primary Maths · Stage 6 · Units 15 & 16 · FractionRush 🍭