Using inverse operations
Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations
What a learner can do afterwards
- Use addition and subtraction as inverse operations to check and solve problems
- Use multiplication and division as inverse operations to check and solve problems
- Recognise that squaring and square-rooting are inverse operations
The lesson
An inverse operation undoes another operation. When you add, subtraction is the inverse. When you multiply, division is the inverse. When you square a number, square-rooting is the inverse. If you already know one fact, the inverse gives you a second fact for free.
Zara works out 90 ÷ 9 = 10. Instead of dividing again to check, she uses the inverse: 10 × 9. That gives 90, so her answer is correct.
The same trick works with addition and subtraction. If 156 + 27 = 183, you can check it with the inverse: 183 - 27. That should bring you straight back to 156.
Squaring and square-rooting are inverses too: 8² = 64, and √64 = 8. Whenever you finish a calculation, ask yourself what the inverse operation is. It is often faster than redoing the whole calculation.
Every operation has an inverse that undoes it, so use the inverse to check your answer instead of starting over.
Watch it
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.