Division — Grade 5 Mathematics
In Grade 5, we extend division to 4-digit ÷ 2-digit numbers, express remainders as decimals by continuing to divide, and divide decimals by whole numbers.
Long Division: 4-Digit ÷ 2-Digit
Use the chunk-and-subtract method for 2-digit divisors:
1. Estimate: how many times does the divisor fit into the first 2 (or 3) digits?
2. Multiply and subtract.
3. Bring down the next digit. Repeat.
1. Estimate: how many times does the divisor fit into the first 2 (or 3) digits?
2. Multiply and subtract.
3. Bring down the next digit. Repeat.
0 8 7
13 ⟌1 1 3 1
13 into 11 = 0; 13 into 113 = 8 r9; 13 into 91 = 7 → Answer: 87
Expressing Remainders as Decimals
After getting a remainder, add a decimal point and zeros to the dividend and keep dividing.
Example: 37 ÷ 4 = 9 r1 → add .0 → 10 ÷ 4 = 2 r2 → 20 ÷ 4 = 5 → 9.25
Example: 37 ÷ 4 = 9 r1 → add .0 → 10 ÷ 4 = 2 r2 → 20 ÷ 4 = 5 → 9.25
As remainder:37 ÷ 4 = 9 r1
As fraction:37 ÷ 4 = 9¼
As decimal:37 ÷ 4 = 9.25
Worked Examples
Example 1 — 4-Digit ÷ 2-Digit
Calculate 5 772 ÷ 12
- 12 into 57 = 4 r9 (48)
- 12 into 97 = 8 r1 (96)
- 12 into 12 = 1
- Answer: 481. Check: 481 × 12 = 5 772 ✓
Example 2 — Decimal Remainder
Calculate 58 ÷ 8, giving the answer as a decimal.
- 58 ÷ 8 = 7 r2
- Continue: 20 ÷ 8 = 2 r4; 40 ÷ 8 = 5
- Answer: 7.25
Example 3 — Dividing a Decimal 🎨
4 friends share 13.2 m of ribbon equally. How much each?
- 13.2 ÷ 4
- Treat as 132 ÷ 4 = 33; reintroduce decimal: 3.3 m
- Check: 3.3 × 4 = 13.2 ✓
Practice Questions
1. Calculate 7 392 ÷ 16.
✅ 462 (16 × 462 = 7 392 ✓)
2. Calculate 95 ÷ 4 as a decimal.
✅ 95 ÷ 4 = 23 r3 → 30 ÷ 4 = 7 r2 → 20 ÷ 4 = 5 → 23.75
3. Calculate 18.6 ÷ 6.
✅ 186 ÷ 6 = 31 → 1 decimal place → 3.1
4. Calculate 4 248 ÷ 24.
✅ 177
5. 5 children share a prize of £73. How much each (as a decimal)?
✅ 73 ÷ 5 = 14 r3 → 30 ÷ 5 = 6 → £14.60 each
Key Points to Remember
- Long division: estimate, multiply, subtract, bring down — repeat.
- To express remainder as decimal: add .0 after the dividend and continue dividing.
- Dividing a decimal: ignore the decimal, divide as whole number, then reposition the decimal.
- Always check: quotient × divisor (+ remainder) = dividend.
- Estimation helps: 5 772 ÷ 12 ≈ 6 000 ÷ 12 = 500 — expect answer near 500.