The idea, step by step
Division finds a missing factor
If 8 × 6 = 48, then 48 ÷ 6 = 8 and 48 ÷ 8 = 6. The multiplication total becomes the starting amount in division. A division fact can ask for the number of groups or the number in each group.
Read the context to give the answer its meaning. Sharing 48 counters among 6 pupils gives 8 counters each. Making groups of 6 from 48 counters gives 8 groups. The number is the same, but its unit is different.
Check with the inverse operation
For 63 ÷ 7, ask: seven multiplied by what gives 63? Since 7 × 9 = 63, the quotient is 9. Multiplying the divisor by the quotient checks the original amount.
Zero shared among a positive number of groups gives zero in each: 0 ÷ 5 = 0. Division by zero is not allowed. There is no useful equal-group answer to a question such as 12 ÷ 0. Keep those two situations separate.
A common trap
Writing 6 ÷ 48 = 8 because 6 × 8 = 48.
Instead: Start with the whole amount in division: 48 ÷ 6 = 8. The order cannot be swapped as it can in multiplication.
See the thinking
Find how many in each group
56 stickers are shared equally among 8 pupils. How many does each receive?
- The number statement is 56 ÷ 8.
- Use the related fact 8 × 7 = 56.
- Check that 8 groups of 7 rebuild 56.
Find how many groups
Put 72 tennis balls into tubes of 9. How many tubes are needed?
- The number statement is 72 ÷ 9.
- 9 × 8 = 72, so there are 8 groups.
- The quotient counts tubes, not balls in each tube.
Check your understanding
Use 7 × 8 = 56 to find 56 ÷ 7.
Show answer
8.
Eight groups of seven make the starting total of 56.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Find 54 ÷ 6.1 mark
- Find 64 ÷ 8.1 mark
- Write both division facts related to 4 × 9 = 36.2 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 0 ÷ 7 = 0 does not mean that 7 ÷ 0 is allowed.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find 54 ÷ 6.1 mark
6 × 9 = 54.
9. - Find 64 ÷ 8.1 mark
8 × 8 = 64.
8. - Write both division facts related to 4 × 9 = 36.2 marks
Start each division with the product 36.
36 ÷ 4 = 9 and 36 ÷ 9 = 4. - 45 cards are packed in groups of 5. How many groups are there?1 mark
45 ÷ 5 = 9 because 5 × 9 = 45.
9 groups. - Thirty counters are shared among 6 pupils. A learner answers '5 pupils'. Correct the answer and its unit.2 marks
30 ÷ 6 = 5.
The six pupils are given; the quotient counts counters each.
5 counters per pupil. - Explain why 0 ÷ 7 = 0 does not mean that 7 ÷ 0 is allowed.2 marks
7 × 0 = 0 checks 0 ÷ 7.
No number multiplied by 0 gives 7, so 7 ÷ 0 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 ↗