The idea, step by step
Keep equality true
An unknown is a value you have not yet found. A box can stand for that value. In box+7=19, both sides must have the same value, so the box is 12. Check it by replacing the box: 12+7=19.
Inverse operations undo each other. Subtraction undoes addition, and division undoes multiplication. Use the relationship rather than guessing a new number each time.
Undo the last step first
If a number is multiplied by 4 and then 3 is added, the added 3 is the final step. To find the original number from a result of 23, first subtract 3, then divide by 4.
For a missing subtracted value or divisor, think about the complete relationship. In 30−box=12, the box is the difference between 30 and 12. Always check in the original order.
A common trap
To solve box−8=15, subtract 8 from 15.
Instead: The original number had 8 removed. Restore it by adding: 15+8=23, and 23−8=15.
See the thinking
Worked example 1
Find the missing number: box×6=42.
- Use the inverse relationship 42÷6.
- 42÷6=7. Check: 7×6=42.
Worked example 2
A number is doubled and then 5 is added. The result is 21. Find the number.
- Undo the final addition: 21−5=16.
- Undo doubling: 16÷2=8. Check: 2×8+5=21.
Check your understanding
Find the missing number: box÷5=9.
Show answer
45.
The inverse relationship is 9×5=45.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- Find the missing number: box+9=25.1 mark
- Find the missing number: box−12=18.1 mark
- Find the missing number: 7×box=56.1 mark
- Find the missing number: box÷4=11.1 mark
- Find the missing number: box×3+4=25.2 marks
- Find the missing number: 50−box=17. Explain the check.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find the missing number: box+9=25.1 mark
25−9=16.
16. - Find the missing number: box−12=18.1 mark
18+12=30.
30. - Find the missing number: 7×box=56.1 mark
56÷7=8.
8. - Find the missing number: box÷4=11.1 mark
11×4=44.
44. - Find the missing number: box×3+4=25.2 marks
25−4=21; 21÷3=7. Check 7×3+4=25.
7. - Find the missing number: 50−box=17. Explain the check.2 marks
50−17=33; replacing the box gives 50−33=17.
33.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Growing rational patterns; rules; brackets/order of operations; unknowns; algorithms.
Official curriculum source ↗