Negative Numbers

Numbers less than zero are negative. You should be able to add, subtract, multiply and divide with them.

Use the number line for addition and subtraction involving negative numbers:

numbers get lower in this direction numbers get higher in this direction

move this way to subtract move this way to add

EXAMPLES
What is -4 + 7? Start at -4 and move 7 places in the positive direction. So -4 + 7 = 3

Work out 5 - 8 Start at 5 and move 8 places in the negative direction. So 5 - 8 = -3.

Find -2 - 4 Start at -2 and move 4 places in the negative direction. Therefore, -2 - 4 = -6.

+ + makes +

+ - makes -

-+ makes -

-- makes +

These rules are only to be used when.

1) Multiplying or dividing

EXAMPLES
Find: a) -2 × 3 - + makes - so -2 × 3 = -6.

b) -8/-2 -- makes + so -8/-2 = 4.

2) Two signs appear next to each other.

EXAMPLES
Work out: a) 5 - -4 -- makes + so 5 - -4 = 5 + 4 = 9

b) 4 + -6 - -7 + - makes - and - - makes + so 4 + -6 = - -7 = 4 - 6 + 7 = 5

Be careful when squaring or cubing. Squaring a negative number gives a positive number (e.g. -2 x -2 = 4) but cubing a negative number gives a negative number (e.g. -3 x -3 x -3 = -27. Remember that the negative sign affects the overall product when multiplying odd amounts of negative numbers.

Number lines are handy for adding or subtracting negative numbers.

Don’t just learn the rules in that burgundy box - make sure you know when you can use them too.

Q1) The temperature in Mathchester at 9am on Monday was 4 degrees Celsius. At 9am on Tuesday the temperature was -2 degrees Celsius.

a) What was the change in temperature from Monday to Tuesday? 4 - 2 = 2

b) The temperature at 9am on Wednesday was 3 degrees Celsius lower than on Tuesday. What was the temperature on Wednesday? 6 degrees Celsius.