Complete number sentences (find the unknown) - Using inverse operations
Theory
To find a missing number, undo the operation with its inverse — the operation that reverses it. Addition and subtraction are inverses; multiplication and division are inverses.
An inverse operation reverses another operation.
Addition and subtraction undo each other; multiplication and division undo each other.
If \(\square + 38 = 90\), undo the \(+38\) by subtracting: \(90 - 38 = 52\).
Operations that undo each other
| Sentence | Undo | Answer |
|---|---|---|
| \(\square + 38 = 90\) | \(90 - 38\) | \(52\) |
| \(\square \times 7 = 84\) | \(84 \div 7\) | \(12\) |
| \(\square \div 6 = 15\) | \(15 \times 6\) | \(90\) |
How to use inverse operations
- Find the operation done to the unknown.
- Apply the inverse to the known total.
- Check by putting the answer back in.
Undo the \(+38\) by subtracting.
| \(90 - 38\) | \(=\) | \(52\) |
Divide to undo the \(\times 7\). Check: \(12 \times 7 = 84\).
| \(84 \div 7\) | \(=\) | \(12\) |
Multiply to undo the \(\div 6\). Check: \(90 \div 6 = 15\).
| \(15 \times 6\) | \(=\) | \(90\) |
Add to undo the \(-58\).
| \(26 + 58\) | \(=\) | \(84\) |
Common pitfalls
Frequently asked questions
What is an inverse operation?
It is the operation that reverses another. Subtraction undoes addition, and division undoes multiplication.
How do I undo a multiplication?
Divide by the same number. For \(\square \times 7 = 84\), work out \(84 \div 7 = 12\).
How do I undo a division?
Multiply by the same number. For \(\square \div 6 = 15\), work out \(15 \times 6 = 90\).
Why check by substituting?
Putting your answer back shows both sides are equal, which proves the answer is right.