Addition — Grade 5 Mathematics
In Grade 5, we add large whole numbers (up to millions), decimals with up to 3 decimal places, and use efficient mental strategies including compensation and rearranging to make addition faster and more accurate.
Adding Decimals: Align the Decimal Point
The golden rule: always align the decimal points vertically. Pad shorter numbers with zeros if needed.
1 1
4 7 . 3 8
+ 8 . 9 4
5 6 . 3 2
💡 Zeros as placeholders: 8.94 can be written as 08.94 so both numbers have two digits before the decimal point.
Mental Strategies
Compensation3 847 + 1 998 → 3 847 + 2 000 − 2 = 5 845
Partitioning46.7 + 28.5 → (40+20) + (6+8) + (0.7+0.5) = 60+14+1.2 = 75.2
Rearranging6 + 57 + 94 → (6 + 94) + 57 = 100 + 57 = 157
Near doubles3.4 + 3.6 → double 3.5 = 7.0
Worked Examples
Example 1 — Column Addition with Decimals
Calculate 134.67 + 89.48
1 1 . 1 1
1 3 4 . 6 7
+ 8 9 . 4 8
2 2 4 . 1 5
Answer: 224.15
Example 2 — Three Numbers
Calculate 4 728 + 3 956 + 1 847
- 4 728 + 3 956 = 8 684
- 8 684 + 1 847 = 10 531
Example 3 — Budget Planning 💰
Three items cost £47.35, £129.90, and £8.75. What is the total cost?
- Pair the easy ones: £47.35 + £8.75 = £56.10 (since 0.35 + 0.75 = 1.10)
- £56.10 + £129.90 = £186.00
Practice Questions
1. Calculate 56.84 + 37.29.
✅ 94.13
2. Calculate 2 846 + 5 973 + 1 208.
✅ 2 846 + 5 973 = 8 819; 8 819 + 1 208 = 10 027
3. Use compensation: 7 654 + 2 999.
✅ 7 654 + 3 000 − 1 = 10 653
4. Calculate 5.374 + 8.629.
✅ 14.003
5. A relay team runs legs of 4.85 km, 3.7 km, and 5.48 km. What is the total distance?
✅ 4.85 + 3.7 + 5.48 = 4.85 + 3.70 + 5.48 = 14.03 km
Key Points to Remember
- Always align decimal points before adding; pad with zeros if needed.
- Add from right to left (smallest place value first) to carry correctly.
- Compensation: round to a round number, add, then adjust.
- Rearranging: find pairs that sum to 10, 100, or 1 000 first.
- Estimate first to check your answer is reasonable.