Addition and subtraction undo each other, and so do multiplication and division. Three numbers make a fact family: 34 + 25 = 59 also tells you 59 − 25 = 34 and 59 − 34 = 25. To find a missing number, undo what was done: for ? − 38 = 45, add 38 back. For a puzzle with two steps, work backwards and undo the last step first.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- inverse
- the operation that undoes another one
- fact family
- the related facts made from the same three numbers
- work backwards
- start from the answer and undo each step in reverse order
Worked examples
Use 34 + 25 = 59. What is 59 − 25?
- 1.The whole is 59, made of 34 and 25.
- 2.Take away the part 25 and the other part is left.
= 34
? − 38 = 45
- 1.Undo taking away 38 by adding it back: 45 + 38 = 83.
- 2.Check: 83 − 38 = 45.
= 83
I think of a number. I multiply it by 4, then add 7. The answer is 43. What was my number?
- 1.Undo the last step first: 43 − 7 = 36.
- 2.Undo multiplying by 4: 36 ÷ 4 = 9.
= 9
For parents
Method: Fact families and undoing
What to say: Which fact do you already know? What would undo that step?
Common mistakes:
- Answers with the number being taken away or divided by, instead of the other part of the fact family.
- Uses the operation in the question again instead of its inverse (or does a think-of-a-number puzzle forwards).
- Uses the right inverse operation but does not regroup (no carry when adding, smaller-from-larger when subtracting).
- Undoes the steps of a two-step puzzle in the order they were done, instead of last step first.
- Undoes only one of the two steps of a think-of-a-number puzzle.