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Inverse operations are really important in maths.

For example, when you have to solve equations (which is a huge topic), you can't do it without these inverse operations.


Inverse operations require us to understand the opposite operation of what is shown.


The opposite of + is -

The opposite of - is +

The opposite of x is ÷

The opposite of ÷ is x


e.g. What is the opposite of +7?



e.g. What is the opposite of dividing by 2?

Multiplying by 2



Let's put an inverse operation into context now...

I add 7 and then multiply by 2.

If my answer is 18, what was my original number?


This one is a bit more challenging.

We have two operations: + 7 and x 2.

The inverse operations for these would be - 7 and ÷ 2.


But which operation do we use first?

If we are doing the opposite, we are moving backwards through the sum.

In the question, we added 7 first then multiplied by 2.

When we are doing the inverse, we swap this order as well.


So to solve this we divide by 2 first, then subtract 7:

18 ÷ 2 = 9

9 - 7 = 2

The original starting number was 2. 




Now it's your turn to have a go!

In this activity, you will find inverse operations and use these to work backwards from outcomes to starting points. 

10 questions