Subtraction — Grade 5 Mathematics
In Grade 5, we subtract large whole numbers and decimals using column subtraction with borrowing across multiple places, and choose efficient mental strategies such as counting up and compensation.
Column Subtraction with Decimals
Align decimal points vertically. Pad shorter decimals with zeros. Borrow across columns as needed.
8 13 . 4 16
9 3 . 5 6
− 4 7 . 8 9
4 5 . 6 7
💡 Counting up (for differences close to each other): 8.003 − 7.996 → jump from 7.996 to 8.000 = 0.004, then to 8.003 = 0.003; total = 0.007.
Mental Strategies
Compensation: 5 000 − 2 997 → 5 000 − 3 000 + 3 = 2 003
Counting up: 4 003 − 1 998 → 1 998 to 2 000 = 2; 2 000 to 4 000 = 2 000; 4 000 to 4 003 = 3; total = 2 005
Partitioning: 73.6 − 28.4 → (70 − 28) + (3.6 − 0.4) = 42 + 3.2 = 45.2
Counting up: 4 003 − 1 998 → 1 998 to 2 000 = 2; 2 000 to 4 000 = 2 000; 4 000 to 4 003 = 3; total = 2 005
Partitioning: 73.6 − 28.4 → (70 − 28) + (3.6 − 0.4) = 42 + 3.2 = 45.2
Worked Examples
Example 1 — Column Subtraction
Calculate 72 405 − 38 167.
- Align and subtract column by column with borrowing.
- 72 405 − 38 167 = 34 238
- Check: 34 238 + 38 167 = 72 405 ✓
Example 2 — Decimal Subtraction
Calculate 50.3 − 18.74
- Write as 50.30 − 18.74 (pad with zero)
- 50.30 − 18.74 = 31.56
Example 3 — Change from a Purchase 🛍️
A customer pays £100 for goods costing £63.47. How much change?
- £100.00 − £63.47
- Count up: £63.47 → £64.00 = £0.53; £64 → £100 = £36
- Change = £0.53 + £36 = £36.53
Practice Questions
1. Calculate 84.5 − 37.86.
✅ 84.50 − 37.86 = 46.64
2. Calculate 63 000 − 27 458.
✅ 35 542
3. Use compensation: 9 000 − 4 995.
✅ 9 000 − 5 000 + 5 = 4 005
4. Calculate 15.003 − 9.847.
✅ 5.156
5. A tank holds 200 L. After use it contains 87.35 L. How much was used?
✅ 200.00 − 87.35 = 112.65 L
Key Points to Remember
- Align decimal points; pad shorter numbers with zeros on the right.
- Borrow from left to right across columns when needed.
- Compensation: round the subtrahend up, subtract, then add back the difference.
- Counting up is efficient when numbers are close together.
- Always check: answer + smaller number should equal the larger number.