The idea, step by step
Division does not always finish exactly
Twenty-nine divided by four gives seven whole groups with one left over: 29 = 4 × 7 + 1. The remainder must be smaller than the divisor, or another whole group could be made.
What happens next depends on the question. Twenty-nine counters shared into four equal groups can give seven counters to each group and leave one counter. Twenty-nine people travelling in four-seat cars need eight cars because the extra person still needs a seat.
| Situation | Interpretation of 29 ÷ 4 |
|---|---|
| Counters shared among four groups | 7 each, 1 left |
| Cars with four seats | 8 cars are needed |
| Four equal pieces of a 29 m ribbon | 7 and one-quarter metres each |
Read the question before deciding
If the question asks for complete packs, count only full groups. If it asks for enough containers for every item, include an extra container when something remains. If the amount can be cut or shared, the remainder may become a fraction.
Always state what the answer counts. Writing '7 remainder 1' is a useful calculation, but it is not a complete answer to 'How many cars are needed?' Explain why your final answer keeps every person or item in the situation.
A common trap
Always rounding a quotient with a remainder up.
Instead: Round up only when the situation needs room for all the items. For complete packs, report the full packs and leftovers instead.
See the thinking
Enough boats for everyone
A club has 38 people. Each boat holds six people. How many boats are needed?
- 38 ÷ 6 = 6 remainder 2.
- Six boats hold only thirty-six people.
- Use one more boat for the two people left.
Count only complete packs
A baker has 50 biscuits. A sale pack needs eight biscuits. How many complete packs can be made, and how many biscuits remain?
- 8 × 6 = 48.
- Fifty minus forty-eight leaves two.
- Two biscuits cannot make another complete pack.
Check your understanding
Twenty-three students need tables seating four. How many tables are needed?
Show answer
6 tables.
Five tables seat only twenty students. The three remaining students need one more table.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Divide 35 by 6. State the whole quotient and remainder.1 mark
- Forty-three apples are packed six to a bag. How many full bags can be made, and how many apples remain?2 marks
- Fifty-three passengers need vans holding eight passengers each. How many vans are needed?2 marks
- A 19-metre ribbon is cut into four equal pieces. What is the length of each piece?2 marks
- A game needs teams of five. There are 37 players. How many complete teams can be made and how many people will not be in a complete team?2 marks
- A school has 41 students and buses with ten student seats. A learner says four buses are enough because 41 ÷ 10 gives four remainder one. Explain the mistake.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Divide 35 by 6. State the whole quotient and remainder.1 mark
6 × 5 = 30 and 35 − 30 = 5.
5 remainder 5. - Forty-three apples are packed six to a bag. How many full bags can be made, and how many apples remain?2 marks
6 × 7 = 42, leaving one.
7 full bags, 1 apple left. - Fifty-three passengers need vans holding eight passengers each. How many vans are needed?2 marks
Eight times six is forty-eight, leaving five passengers.
A seventh van is needed.
7 vans. - A 19-metre ribbon is cut into four equal pieces. What is the length of each piece?2 marks
Four complete metres for each piece use sixteen metres.
Share the remaining three metres equally among four pieces.
4 and three-quarter metres. - A game needs teams of five. There are 37 players. How many complete teams can be made and how many people will not be in a complete team?2 marks
5 × 7 = 35, leaving two.
7 teams, 2 players left. - A school has 41 students and buses with ten student seats. A learner says four buses are enough because 41 ÷ 10 gives four remainder one. Explain the mistake.3 marks
Four buses seat forty students only.
The one remaining student must also have a seat, so include a fifth bus.
Five buses are needed.
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 ↗