Understand the idea.
Division finds a missing factor
Division finds a missing factor in equal groups. If , then and . Start with the whole amount, then decide which group quantity is already known.
The story gives the quotient its meaning. Sharing counters among pupils asks for counters per pupil. Putting counters into groups of asks for the number of groups. Both calculations give , but the answers have different units.
Check with the inverse operation
For , ask how many sevens make . Since , the quotient is . To check any exact division, multiply the number of groups by the number in each group and recover the original total.
Zero objects shared among five groups gives zero per group: . Division by zero is different and is not defined. No number of zero-sized groups can make , so has no answer.
See the method in action.
Find how many in each group
56 stickers are shared equally among 8 pupils. How many does each receive?
Worked solution
- 1
Write the equal-sharing calculation.
The whole is 56 stickers and the number of pupils is 8.
- 2
Find the matching multiplication fact.
Eight equal shares of seven use all 56 stickers.
- 3
Give the quotient with its meaning.
Each pupil receives seven stickers; the quotient counts stickers per pupil.
7 stickers each.
Find how many groups
Put 72 tennis balls into tubes of 9. How many tubes are needed?
Worked solution
- 1
Divide the total by the size of each tube.
Each tube holds nine balls, so the missing quantity is the number of tubes.
- 2
Use a fact that rebuilds 72.
Eight groups of nine account for all the tennis balls.
- 3
State the required number of tubes.
Eight full tubes hold exactly 72 balls, with none left over.
8 tubes.
Try it yourself.
Check your understanding
Use 7 × 8 = 56 to find 56 ÷ 7.
Show answer & reasoning
8.
The quotient is because . Eight groups of seven rebuild the starting total, checking .
Keep practising
6 worksheet questions · 9 marks
Read the questions online
- Find .1 mark
- Find .1 mark
- Write both division facts related to .2 marks
- 45 cards are packed in groups of 5. How many groups are there?1 mark
- Thirty counters are shared among 6 pupils. A learner answers '5 pupils'. Correct the answer and its unit.2 marks
- Explain why does not mean that is allowed.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find .1 mark
.
9. - Find .1 mark
.
8. - Write both division facts related to .2 marks
Start each division with the product 36.
and . - 45 cards are packed in groups of 5. How many groups are there?1 mark
because .
9 groups. - Thirty counters are shared among 6 pupils. A learner answers '5 pupils'. Correct the answer and its unit.2 marks
.
The six pupils are given; the quotient counts counters each.
5 counters per pupil. - Explain why does not mean that is allowed.2 marks
checks .
No number multiplied by 0 gives 7, so is undefined.
Zero counters shared among seven groups gives zero each. Dividing seven by zero has no valid group size answer.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Facts to 10×10; related division; larger calculations; multiples/powers of ten; efficient strategies.
Official curriculum source ↗