**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?**

-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.