Numbers, units and arithmetic

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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)?

• (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

• (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.

### 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).

• (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?

3 Kim started at 37 m and ended at 42 m. You want 42 − 37 = 42 + 37 = 79. So Kim climbed 79 m.

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