Positive and negative numbers

The method for multiplying/dividing positive and negative numbers is different to adding/subtracting positive and negative numbers.

When more integers are involved work the calculations from left to right.

e.g.     to work this out: is equal to   then multiply by  gives

Note: division can be shown as a fraction.

e.g.     

Addition and subtraction

A number line is helpful to visualise what happens when we add and subtract.

When adding we are moving up the number line (to the right), while when we subtract we are moving down the number line (to the left):

e.g.       Start at  on the number line and move  places down (left). We end at  .

e.g.       Start at  on the number line and move places down (left). We end at .

e.g.       Start at  and move  places up (right) past zero and end at .

Things can get a little more complicated when adding or subtracting a negative:

e.g.       ( subtract negative ) and   ( plus negative )

Subtracting a negative is the same as adding:

(think of “taking away a debt” is like “giving” i.e. adding).

 Therefore    can be written as  

Adding a negative is the same as subtracting:

(think of “giving a debt” is like “taking away” i.e. subtracting)

Therefore  can be written as  

Practice using negative numbers

Complete these questions to assess your understanding: