Page 11 - Mathematics Coursebook

1.2 Adding and subtracting negative numbers

1.2 Adding and subtracting negative numbers

You have seen how to add or subtract a positive number by thinking of temperatures going up and down.
Examples: −3 + 5 = 2 −3 − 5 = −8
Suppose you want to add or subtract a negative number, for example, −3 + −5 or −3 − −5.
How can you do that? –3 –5
You need to think about these in a di$erent way.
To work out −5 + −3, start at 0 on a number line. –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2

−5 means ‘move 5 to the le&’ and −3 means ‘move 3 to the le&’.
!e result is ‘move 8 to the le&’.
−5 + −3 = −8 –5 + –3 = –8

To work out −3 − −5 you want the difference between −5 and −3. –3 – –5 = 2
To go from −5 to −3 on a number line, move 2 to the right.
−3 − −5 = 2 –6 –5 –4 –3 –2 –1 0 1 2

Worked example 1.2
Work these out. a 2 + −6 b 2 − −6

–6 2 – –6
a 2 + −6 = −4 b 2 − −6 = 8
2

–7 –6 –5 –4 –3 –2 –1 0 1 2 3
–5 –4 –3 –2 –1 0 1 2 3

2 – –6 = 8

) Exercise 1.2

1 Work these out. a −3 + 4 b 3 + −6 c −5 + −5 d −2 + 9
2 Work these out. a 3 − 7 b 4 − −1 c 2 − −4 d −5 − 8

3 Work these out. a 3 + 5 b −3 + 5 c 3 + −5 d −3 + −5
4 Work these out. a 4 − 6 b 4 − −6 c −4 − 6 d −4 − −6

5 a Work these out.

i 3 + −5 ii −5 + 3 iii −2 + −8 iv −8 + −2
b If V and W are two integers, is it always true that V+ W = W+ V?
Give a reason for your answer.
6 a Work these out.
i 5 − −2 ii −2 − 5 iii −4 − −3 iv −3 − −4

b If V and W are two integers, what can you say about V − W and W− V?

10 1 Integers