Negative Numbers 1
Negative Numbers

We extend our number system now to include negative numbers. It is useful to use a number line to illustrate this concept.

Note: Inequality Signs

The sign   <   means 'less than' as in, for example, 4 < 7,
whilst   >   means 'greater than'; so 8 > 4 .

Using inequality signs you can see, for example, that

–2 < 4
–6 < –3
5 > –4
–1 > –7

You can check all these by looking at their positions on the number line.

Worked Examples

1

Make each statement below true by using the symbols < or > .

(a)
–54
 Show me
(b)
37
 Show me
(c)
–6–9
 Show me
(d)
2–2
 Show me

Exercises

What temperature is:

(a)
3°C warmer than –1°C °C
(b)
6°C colder than –3°C °C
(c)
5°C warmer than –5°C °C
(d)
8°C warmer than –7°C °C
(e)
5°C colder than –2°C °C
(f)
3°C colder than 1°C °C
(g)
6°C colder than 2°C °C
(h)
8°C warmer than –12°C °C
(i)
10°C colder than –2°C °C
(j)
20°C warmer than –12°C? °C

What number is;

(a)
3 more than –2
(b)
6 less than 1
(c)
5 more than –7
(d)
6 more than –10
(e)
5 less than –4
(f)
16 less than 3
(g)
5 more than –20
(h)
6 more than 5
(i)
12 less than 10
(j)
20 more than –8?

Write each set of numbers in order with the smallest first.

(a)

6, –7, 8, –2, –5, –10, 3

(b)

3, –2, 8, 0, –1, 1, –3

(c)

5, –7, –20, 100, –50, –90, 60

Put either a < or > sign between each pair of numbers to give a true statement.

(a)
4 2
(b)
–6 –2
(c)
–3 4
(d)
2 –4
(e)
–6 –7
(f)
–6 –5
(g)
0 1
(h)
–1 0

Is each statement below true or false?

(a)
6 < 7
(b)
4 < 3
(c)
8 < –1
(d)
5 < –6
(e)
–6 > –7
(f)
–1 < 0
(g)
–3 > 2
(h)
–7 > 6
(i)
–4 < –3
(j)
–5 > –2

Write down any integer that could go in the boxes below.

(a)
5 < < 7
(b)
–5 < < –3
(c)
–3 > > –7
(d)
–6 < < 0
(e)
–1 < < 2