3.18 Practical examples of negative numbers
Negative numbers occur in financial matters, in temperature or height measurements and many other practical situations.
(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)?
(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
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?
(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.
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).
(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).
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?
3 Kim started at −37 m and ended at 42 m. You want 42 − −37 = 42 + 37 = 79. So Kim climbed 79 m.