The idea, step by step
Undo a calculation
Addition and subtraction are inverse operations: they undo one another. If 36 + 24 = 60, taking away the 24 returns us to 36.
A part–whole picture shows the connection. The two parts are 36 and 24; the whole is 60. You can find the whole by adding or find either part by subtracting the other part.
Use the inverse as a check
If you calculate 154 − 67 = 87, check by adding 87 + 67. Getting 154 supports your subtraction. If the addition gives another number, return to the working.
A fact family normally has two additions and two subtractions. When the parts are equal, some facts look the same, such as 5 + 5 = 10.
Keep the roles clear
The whole is the starting number for these related subtractions. From 23 + 41 = 64, write 64 − 23 = 41, not 23 − 64 = 41.
A common trap
Checking subtraction by repeating the same subtraction exactly the same way.
Instead: Use addition to rebuild the whole. A different method can reveal an error you repeated.
See the thinking
Build a fact family
Use 28 + 35 = 63 to write the other related facts.
- Swap the two added parts: 35 + 28 = 63.
- Subtract 28 from the whole: 63 − 28 = 35.
- Subtract 35 from the whole: 63 − 35 = 28.
Check subtraction
Levi says 304 − 168 = 136. Check using addition.
- Add the proposed difference to the removed part.
- 136 + 168 = 304.
- This recovers the starting whole.
Check your understanding
Complete the related fact: if 47 + 18 = 65, then 65 − 18 = __.
Show answer
47
Removing one part from the whole leaves the other part.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Use 32 + 19 = 51 to complete 51 − 32 = __.
- Write two subtraction facts for 45 + 27 = 72.
- Check 82 − 36 = 46 with addition.
- Check 250 − 114 = 146 with addition. Is it correct?
- A jar had some marbles. After 26 more are added, it contains 73. Which subtraction finds the starting amount? Find it.
- Write the fact family using the parts 18 and 18 and whole 36. List each different fact once.
Read the worked solutions
- Use 32 + 19 = 51 to complete 51 − 32 = __.
The missing value is the other part.
19 - Write two subtraction facts for 45 + 27 = 72.
Start with the whole, 72, each time.
72 − 45 = 27 and 72 − 27 = 45. - Check 82 − 36 = 46 with addition.
40 + 30 = 70 and 6 + 6 = 12; 70 + 12 = 82.
46 + 36 = 82, so it is correct. - Check 250 − 114 = 146 with addition. Is it correct?
146 + 114 = 260, not 250; 136 + 114 = 250.
No. The correct difference is 136. - A jar had some marbles. After 26 more are added, it contains 73. Which subtraction finds the starting amount? Find it.
Undo adding 26 by subtracting 26 from 73.
73 − 26 = 47 marbles. - Write the fact family using the parts 18 and 18 and whole 36. List each different fact once.
Equal parts make the two addition facts identical and the two subtraction facts identical.
18 + 18 = 36 and 36 − 18 = 18.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Mental strategies; two-/three-digit calculations; regrouping; inverse operations; missing values.
Official curriculum source ↗