Multiplication — Grade 5 Mathematics
In Grade 5, we use long multiplication for 3-digit × 2-digit and 4-digit × 1-digit numbers, multiply decimals by whole numbers, and apply efficient mental strategies including factorising multipliers.
Long Multiplication: 3-Digit × 2-Digit
Split the 2-digit number into tens and units. Multiply by units first, then by tens (shift one place left). Add the partial products.
3 4 7
× 2 6
4 4
2 0 8 2 ← 347 × 6
6 9 4 0 ← 347 × 20
9 0 2 2
Multiplying Decimals
Method: Ignore the decimal point, multiply as whole numbers, then replace the decimal point.
Count the total decimal places in both numbers — put that many in the answer.
Example: 4.7 × 8 → 47 × 8 = 376 → one decimal place → 37.6
Example: 3.4 × 2.5 → 34 × 25 = 850 → two decimal places → 8.50
Count the total decimal places in both numbers — put that many in the answer.
Example: 4.7 × 8 → 47 × 8 = 376 → one decimal place → 37.6
Example: 3.4 × 2.5 → 34 × 25 = 850 → two decimal places → 8.50
Worked Examples
Example 1 — Long Multiplication
Calculate 463 × 38.
- 463 × 8 = 3 704
- 463 × 30 = 13 890
- 3 704 + 13 890 = 17 594
- Check: 463 × 38 ≈ 460 × 40 = 18 400 — close ✓
Example 2 — Multiply a Decimal
Calculate 6.45 × 7.
- 645 × 7 = 4 515
- 6.45 has 2 decimal places → 45.15
Example 3 — Tile Cost 🏗️
A room needs 324 tiles. Each tile costs £4.75. What is the total cost?
- 324 × 475 = 153 900
- £4.75 has 2 decimal places → £1 539.00
- Total cost: £1 539.00
Practice Questions
1. Calculate 256 × 34.
✅ 256×4=1024; 256×30=7680; 1024+7680=8 704
2. Calculate 3.8 × 9.
✅ 38 × 9 = 342 → 1 decimal place → 34.2
3. Calculate 1.25 × 4.
✅ 125 × 4 = 500 → 2 decimal places → 5.00
4. Calculate 524 × 47.
✅ 524×7=3668; 524×40=20960; 3668+20960=24 628
5. 48 people each pay £12.50 entry. What is the total collected?
✅ 48 × 1250 = 60 000 → 2 decimal places → £600.00
Key Points to Remember
- Long multiplication: multiply by units first, then tens (shift left by one).
- For decimals: multiply as whole numbers, then count and place decimal places.
- Factorising: × 24 = × 8 × 3 (easier in two steps).
- Always estimate first to check your answer is in the right range.
- Check with the inverse: answer ÷ multiplier should equal original number.