Division — Grade 3 Mathematics
In Grade 3, we extend division to 3-digit numbers using the short division (bus stop) method. We also handle remainders and understand when to round up or down based on context.
Short Division (Bus Stop Method)
The "bus stop" layout:
Steps — work from left to right:
1. How many times does the divisor go into the first digit? Write the answer on top.
2. If there is a remainder, carry it to the next digit.
3. Repeat until all digits are processed.
0 4 8
3 ⟌1 4 4
Steps — work from left to right:
1. How many times does the divisor go into the first digit? Write the answer on top.
2. If there is a remainder, carry it to the next digit.
3. Repeat until all digits are processed.
💡 Check: Quotient × divisor + remainder = original number. e.g., 48 × 3 + 0 = 144 ✓
Worked Examples
Example 1 — Short Division, No Remainder
Calculate 252 ÷ 4
0 6 3
4 ⟌2 5 2
- 2 ÷ 4 = 0 remainder 2 → carry 2
- 25 ÷ 4 = 6 remainder 1 → carry 1
- 12 ÷ 4 = 3 remainder 0
- Answer: 63
- Check: 63 × 4 = 252 ✓
Example 2 — Short Division with Remainder
Calculate 175 ÷ 6
0 2 9
6 ⟌1 7 5
Remainder: 1
- 1 ÷ 6 = 0 r1 → carry 1
- 17 ÷ 6 = 2 r5 → carry 5
- 55 ÷ 6 = 9 r1
- Answer: 29 remainder 1
- Check: 29 × 6 + 1 = 174 + 1 = 175 ✓
Example 3 — Real World: Sharing Books 📚
A teacher has 196 books to share equally among 7 classes. How many books per class?
- 196 ÷ 7
- 1 ÷ 7 = 0 r1; 19 ÷ 7 = 2 r5; 56 ÷ 7 = 8 r0
- Answer: 28 books per class.
- Check: 28 × 7 = 196 ✓
Rounding Remainders in Context
When a word problem has a remainder, decide:
Round UP — if you need enough to cover everything (e.g., buses for people — extra people need an extra bus).
Round DOWN — if you can only use complete groups (e.g., how many complete packs of 6 from 25 items → 4 packs, ignore the remainder of 1).
Round UP — if you need enough to cover everything (e.g., buses for people — extra people need an extra bus).
Round DOWN — if you can only use complete groups (e.g., how many complete packs of 6 from 25 items → 4 packs, ignore the remainder of 1).
Practice Questions
1. Calculate 144 ÷ 6.
✅ 24 (Check: 24 × 6 = 144 ✓)
2. Calculate 235 ÷ 5.
✅ 47 (Check: 47 × 5 = 235 ✓)
3. Calculate 200 ÷ 7. What is the remainder?
✅ 200 ÷ 7 = 28 remainder 4 (28 × 7 = 196; 200 − 196 = 4)
4. 135 pupils travel by minibus. Each minibus holds 9. How many minibuses are needed?
✅ 135 ÷ 9 = 15 minibuses
5. 85 stickers are packed into bags of 6. How many complete bags? How many stickers are left over?
✅ 85 ÷ 6 = 14 r1 → 14 complete bags, 1 sticker left over
Key Points to Remember
- Short division works left to right — opposite to long multiplication.
- Carry remainders to the next digit (prepend to it).
- Always check: quotient × divisor + remainder = original number.
- Division and multiplication are inverse operations: 63 × 4 = 252 and 252 ÷ 4 = 63.
- When rounding remainders: think about what makes sense in the real-world context.