The idea, step by step
Split the total into useful multiples
To calculate 252 ÷ 6, split 252 into 240 and 12. Both are easy to divide by six: 240 ÷ 6 = 40 and 12 ÷ 6 = 2. The full quotient is 42. The parts can be different sizes as long as they add to the original total.
Another method is to subtract large equal groups. For 252 ÷ 6, forty sixes use 240. There are twelve left, which is two more sixes. Add forty groups and two groups. Both methods describe the same division.
| Part of the total | Groups of 6 |
|---|---|
| 240 | 40 |
| 12 | 2 |
| 252 | 42 |
Check both the number and its meaning
If a quotient is 42 with divisor six, the multiplication check is 42 × 6 = 252. A check should recover the starting total. If a division has a remainder, multiply the whole quotient by the divisor and add the remainder.
Keep the units in a story. If 735 beads are shared equally among five groups, 735 ÷ 5 = 147 means 147 beads in each group. If bags hold five beads each, the same calculation means 147 bags.
A common trap
Dividing only the first part of a partitioned number.
Instead: Every part must be divided. For 248 ÷ 4, divide both 240 and 8: 60 + 2 = 62.
See the thinking
Share a total
Share 735 stickers equally among five classes. How many stickers does each class get?
- Split 735 into 700 and 35.
- 700 ÷ 5 = 140 and 35 ÷ 5 = 7.
- Add 140 and 7, then check 147 × 5 = 735.
Use a nearby multiple
Calculate 364 ÷ 7.
- Fifty sevens make 350.
- 364 − 350 = 14, which is two sevens.
- There are fifty-two groups. Check 52 × 7 = 364.
Check your understanding
Calculate 432 ÷ 8 and give a multiplication check.
Show answer
54; 54 × 8 = 432.
400 ÷ 8 = 50 and 32 ÷ 8 = 4, so the quotient is 54.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Calculate 168 ÷ 4.1 mark
- Calculate 315 ÷ 5.1 mark
- Calculate 456 ÷ 6 using partial quotients.2 marks
- A library packs 288 books equally into eight boxes. How many books are in each box?2 marks
- Calculate 624 ÷ 12 using known multiples of twelve.2 marks
- Zoe says 294 ÷ 7 = 41. Use multiplication to check the claim and then correct it.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Calculate 168 ÷ 4.1 mark
160 ÷ 4 = 40 and 8 ÷ 4 = 2.
42. - Calculate 315 ÷ 5.1 mark
300 ÷ 5 = 60 and 15 ÷ 5 = 3.
63. - Calculate 456 ÷ 6 using partial quotients.2 marks
420 ÷ 6 = 70 and 36 ÷ 6 = 6.
76. - A library packs 288 books equally into eight boxes. How many books are in each box?2 marks
240 ÷ 8 = 30 and 48 ÷ 8 = 6.
There are thirty-six books per box.
36 books. - Calculate 624 ÷ 12 using known multiples of twelve.2 marks
12 × 50 = 600, leaving twenty-four.
12 × 2 = 24, so the quotient is fifty-two.
52. - Zoe says 294 ÷ 7 = 41. Use multiplication to check the claim and then correct it.3 marks
There are seven more in 294, so one more group of seven is needed.
42 × 7 = 294.
41 × 7 = 287, not 294. The correct quotient is 42.
Curriculum reference & lesson scope
Australian Curriculum v9.0; SA Curriculum Mathematics 2026
One-/two-digit multipliers; division strategies; contextual remainders; inverse fact families; unknown factors/dividends/divisors.
Official curriculum source ↗