Science, Maths & Technology

### Become an OU student Everyday maths 2

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available. Figure _unit2.9.1 Figure 23 Inverse operations

An inverse operation is an opposite operation. In a sense, it ‘undoes’ the operation that has just been performed. Let’s look at two simple examples to begin with.

## Case study _unit2.9.1 Example: Check your working 1

6 + 10 = 16

### Method

Since you have done an addition sum, the inverse operation is subtraction. To check this calculation, you can either do:

#### Extract _unit2.9.1

16 − 10 = 6

or

16 − 6 = 10

You will notice here that the same 3 numbers (6, 10 and 16) have been used in all the calculations.

## Case study _unit2.9.2 Example: Check your working 2

5 × 3 = 15

### Method

This time, since you have done a multiplication sum, the inverse operation is division. To check this calculation, you can either do:

#### Extract _unit2.9.2

15 ÷ 5 = 3

or

15 ÷ 3 = 5

Again, you will notice that the same 3 numbers (3, 5 and 15) have been used in all the calculations.

If you have done a more complicated calculation, involving more than one step, you simply ‘undo’ each step.

## Case study _unit2.9.3 Example: Check your working 3

A coat costing £40 has a discount of 15%. How much do you pay?

### Method

Firstly, we find out 15% of £40:

#### Extract _unit2.9.3

40 ÷ 100 × 15 = £6 discount

£40 − £6 = £34 to pay

To check this calculation, firstly you would check the subtraction sum by doing the addition:

#### Extract _unit2.9.4

£34 + £6 = £40

To check the percentage calculation, you then do:

#### Extract _unit2.9.5

£6 ÷ 15 × 100 = £40

You have now completed the number section of the course. Before moving on to the next session, ‘Units of measure’, complete the quiz on the following page to check your knowledge and understanding.

## Summary

In this section you have:

• learned that each of the four operations has an inverse operation (its opposite) and that these can be used to check your answers

• seen examples and practised checking answers using the inverse operation.