DIRECTED NUMBERS

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 −1 0 1 2 3 4 5 6 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.

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 −1 0 1 2 3 4 5 6 2 Use a number line to work out −1 − 4 −1 − 4 = −5 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

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

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

+ × + = + + × − = − − × + = − − × − = + + ÷ + = + + ÷ − = − − ÷ + = − 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.

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

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

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