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.