1. DIRECTED NUMBERS

2. The positive and negative numbers are called integers.
They can be shown on a number line.
NEGATIVE NUMBERS
POSITIVE NUMBERS
−6 −5 −4 −3 −2 −
7 ºC
To find the difference between a temperature of 4 ºC and a temperature of
−3 ºC, you find the gap between these two numbers on the number line.
The difference is 7 ºC.

3. The number line can be used for adding and subtracting numbers.
Examples
1 Use a number line to work out −3 + 5
−3 + 5 = 2
−6 −5 −4 −3 −2 −
2 Use a number line to work out −1 − 4
−1 − 4 = −5
−6 −5 −4 −3 −2 −

4. Adding and subtracting directed numbers
The rules for adding and subtracting directed numbers are:

5. Examples 1 Work out 2 Work out −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6 −5 −4 −3 −2 −
2 Work out
−6 −5 −4 −3 −2 −

6. Examples 3 Work out 4 Work out −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6 −5 −4 −3 −2 −
4 Work out
−6 −5 −4 −3 −2 −

7. + × + = + + × − = − − × + = − − × − = + + ÷ + = + + ÷ − = − − ÷ + = −
Multiplying and dividing directed numbers
The rules for multiplying and dividing directed numbers are:
Multiplication
+ × + = +
+ × − = −
− × + = −
− × − = +
Division
+ ÷ + = +
+ ÷ − = −
− ÷ + = −
− ÷ − = +
If the two signs are the same, the answer will be positive.
If the two signs are different, the answer will be negative.

8. Examples
1 Work out
the two signs are the same so the answer is positive
2 Work out
the two signs are different so the answer is negative

9. Examples
3 Work out
the two signs are different so the answer is negative
4 Work out
the two signs are the same so the answer is positive

10. Examples
5 Work out
the two signs are the same so the answer is positive
6 Work out
first work out −2 × −2 = 4
the two signs are different so the answer is negative