A fact family shows the inverse relationship
If 8 + 5 = 13, then the subtraction facts come from the same three numbers.
The same number family gives 13 - 5 = 8 and 13 - 8 = 5. Addition builds the total and subtraction undoes it.
Year 2
Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
Use addition and subtraction as inverse operations to check answers and solve missing number problems.
Lesson overview
Number - addition and subtraction
Addition and subtraction undo each other. If we know one addition fact, we can use it to write related subtraction facts. This is called the inverse relationship. It helps us check a calculation and find a missing number without starting again.
Use subtraction to check addition
If 24 + 11 = 35, we can check it with subtraction.
Start with the answer. If 35 - 11 = 24, then the addition is correct.
Use the inverse to find a missing number
In 9 + ? = 15, subtraction can help us find the missing part.
Take the known part away from the total. 15 - 9 = 6, so the missing number is 6.
Worked example
Check whether 18 + 7 = 25 is correct, then solve 25 - ? = 18.
- Look at the addition fact: 18 + 7 = 25.
- To check it, use the inverse operation.
- Start from 25 and subtract 7.
- 25 - 7 = 18, so the addition is correct.
- Now solve 25 - ? = 18 by subtracting 18 from 25.
- 25 - 18 = 7, so the missing number is 7.
Try it
Use the opposite operation to check the calculation or find the missing number.
Question 1
Question 2
Question 3
Question 4
Question 5
Common mistakes
These are the slips to watch for when using the inverse relationship.
- Using the same operation again instead of the inverse operation.
- Starting from the wrong number when checking with subtraction.
- Forgetting that the total stays the same in a fact family.
Related topics
These ideas support checking, fact families and missing-number thinking.
- Show that addition of two numbers can be done in any order and subtraction of one number from another cannot.
- Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100.
- Solve missing number problems such as 7 = ? - 9.