DIRECTED NUMBERS The positive and negative numbers are
DIRECTED NUMBERS
The positive and negative numbers are called integers. They can be shown on a number line. NEGATIVE NUMBERS − 6 − 5 − 4 − 3 − 2 POSITIVE NUMBERS − 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 − 6 − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 6 − 3 + 5 = 2 2 Use a number line to work out − 1 − 4 − 6 − 5 − 4 − 3 − 2 − 1 0 1 2 3 4 5 6 − 1 − 4 = − 5
Adding and subtracting directed numbers The rules for adding and subtracting directed numbers are:
Examples 1 Work out − 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 − 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
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