12 Checking your answers
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.
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:
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.
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:
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.
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:
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:
£34 + £6 = £40
To check the percentage calculation you then do:
£6 ÷ 15 × 100 = £40
Don’t forget, sometimes it can also be helpful to use estimation to check your answers, particularly when using decimal or large numbers.
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 showing how to check answers using the inverse operation.