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# 3.18 Practical examples of negative numbers

Negative numbers occur in financial matters, in temperature or height measurements and many other practical situations.

## Example 26

• (a) If the value of a painting increases by £20 a year and it is worth £200 today, how much will it be worth in a year’s time? How much was it worth a year ago?

• (b) Describe in words how to calculate the value of an object like a picture one year in the future or one year ago, given a constant annual increase.

• (c) If the value of a washing machine decreases by £20 a year and it is worth £200 today, how much will it be worth in a year’s time? How much was it worth a year ago?

• (d) If you regard a decrease as a negative increase, does your answer to (b) apply to the washing machine in (c)?

### Answer

• (a) The value of the painting in a year’s time is £200 + £20 = £220. The value of the painting a year ago was £200 − £20 = £180.

• (b) To work out the value a year in the future, add the annual increase to the current value. To work out the value a year in the past, subtract the annual increase from its current value.

• (c) The value of the washing machine in a year’s time is £200 − £20 = £180.

The value of the washing machine a year ago was £200 + £20 = £220.

• (d) Yes. Thinking about the annual decrease as a negative increase, apply the rules in part (b) to carry out the calculation. The value of the washing machine in a year’s time is current value + annual increase, i.e. £200 + £20 = £180.

The value of the washing machine a year ago is current value − annual increase, i.e. £200 − £20 = 200 + 20 = £220.

So adding a negative increase is the same as subtracting the decrease.

Subtracting a negative increase is the same as adding the decrease.