Negative numbers

Foundation and Higher

The idea

On a number line, adding a positive number moves right and subtracting one moves left. Subtracting a negative is the same as adding: $5 - (-3) = 8$ .

Rewrite a double sign first: $-\,-$ becomes $+$ and $+\,-$ becomes $-$ .
For $\times$ and $\div$ : same signs give a positive answer, different signs give a negative one.
Check on a number line or with a temperature: $-4 + 7 = 3$ .

Watch out $(-3)^2 = 9$ , but $-3^2 = -9$ : the power applies before the minus unless there are brackets.

See it worked

Worked exampleNon-calculator1 mark

Write down the smallest of these numbers: $-1.4$ , $-7$ /5, $-1.45$ , $-1.04.$

Convert the fraction to compare like forms: $-7$ /5 = $-1.4.$
For negative numbers, the number furthest below zero is the smallest. The answer is $-1.45.$

Answer $-1.45$

Your turn

Question 1Non-calculator2 marks

Work out $-8$ + 13 $-$ 6.

Question 2Non-calculator5 marks

At 06:00 the temperature is $-9^\circ$ C. It rises by $5^\circ$ C, then falls by $4^\circ$ C.

(a) Work out the final temperature.

(b) How many degrees must the temperature rise to reach $5^\circ$ C?

Question 3Non-calculator6 marks

The mean of six temperatures is $-1.5\,^{\circ}\text{C}$ . Five of the temperatures, in $^{\circ}\text{C}$ , are $-6.5$ , $2$ , $-4$ , $3.5$ and $-1$ .

(a) Work out the sixth temperature.

(b) A seventh temperature is added to the six. The mean of all seven temperatures is a whole number, and the range of all seven is the same as the range of the six.

Find all the possible values of the seventh temperature.

In past papers

96 official questions in 79 papers since 2017. The latest:

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