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.
Try some yourself
Activity 58
Answer the following questions:
(a) If you had £3 in your bank account and drew out £10, how much would you have left?
(b) The temperature was ^{−}5 °C on Monday and dropped overnight by 6 °C. What was the temperature on Tuesday morning?
Answer
(a) 3 − 10 = ^{−}7,
so you would have ^{−}£7 left, i.e. you would have a £7 overdraft.
(b) ^{−}5 − 6 = ^{−}11,
so the temperature was ^{−}11 °C.
Activity 59
Evaluate each of the following:
(a) ^{−}3 + ^{−}12
(b) ^{−}4 − ^{−}11
Think of a financial context where each might be an appropriate calculation (bear in mind that negative numbers can represent debts).
Answer
(a) ^{−}3 + ^{−}12 = ^{−}15 (a debt of £3 plus a debt of £12 gives a debt of £15).
(b) ^{−}4 − ^{−}11 = ^{−}4 + 11 = 7 (incurring a debt of £4 and being let off a debt of £11 results in being £7 better off).
Activity 60
Kim was walking in Israel. She started at 37 metres below sea level and ended up at 42 metres above sea level. How far had she climbed up?
Answer
3 Kim started at ^{−}37 m and ended at 42 m. You want 42 − ^{−}37 = 42 + 37 = 79. So Kim climbed 79 m.