Checking with the Inverse

What does inverse mean?

Inverse is a maths word for opposite. Addition and subtraction are inverses of each other: one undoes the other. If you add 5 to a number and then subtract 5, you land back exactly where you began, as if nothing happened.

This opposite relationship gives you a brilliant superpower: you can check your own answers. After working out a sum, you undo it. If you return to your starting number, your answer is right. If you do not, there is a mistake to find.

This idea grows naturally out of fact families. If that is new, our lesson on fact families: addition and subtraction shows the same three numbers making opposite facts.

The golden rule

To check an addition, use subtraction. To check a subtraction, use addition.

Here is why it works. Suppose 27 + 15 = 42. The 42 is made of 27 and 15 stuck together. If you peel the 15 back off (42 − 15), only the 27 should remain. If something else remains, the sum was wrong.

A table of checks

Calculation	To check	Should equal	Correct?
27 + 15 = 42	42 − 15	27	✅
34 + 12 = 46	46 − 12	34	✅
50 − 16 = 34	34 + 16	50	✅
63 − 28 = 35	35 + 28	63	✅
45 + 19 = 65	65 − 19	45?	❌ (really 46)

Look at the last row. The check does not return 45, which warns us the answer 65 is wrong — 45 + 19 is actually 64.

Worked example 1: checking an addition

You work out 38 + 24 = 62. Is it right?

Undo the addition by subtracting the number you added: 62 − 24.

62 − 24 = 38. You are back at your starting number, so 38 + 24 = 62 is correct.

Worked example 2: checking a subtraction

You work out 71 − 26 = 45. Is it right?

Undo the subtraction by adding back the number you took away: 45 + 26.

45 + 26 = 71. You are back at the starting number, so 71 − 26 = 45 is correct.

Worked example 3: catching a mistake

You work out 53 − 18 = 25. Check it.

Add back: 25 + 18 = 43. But you started at 53, not 43! So 25 is wrong. Work it out again carefully: 53 − 18 = 35. Now check: 35 + 18 = 53. Fixed.

Why this strategy matters

Checking with the inverse turns you into your own teacher. Instead of waiting to be told an answer is wrong, you spot it yourself and put it right. The habit builds accuracy and confidence, and the same inverse thinking becomes essential later in algebra, where solving an equation means undoing operations one at a time.

Try it yourself

You will need paper and a pencil.

1. Write any two-digit addition, like 46 + 27, and solve it.
2. Now undo it with the inverse: take away the number you added.
3. Did you return to your first number? If yes, tick it.
4. Repeat with a subtraction, checking it by adding back.
5. Challenge: Ask a partner to make a deliberate mistake. Can your inverse check catch it?

What's next?

Checking is a habit worth keeping for life. Use it alongside written methods in column addition with carrying and column subtraction with borrowing.