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# Positive and negative numbers

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

## Multiplying and dividing

When multiplying (or dividing) two numbers with the same signs, the resulting answer is positive. If one is positive and the other negative, the answer will be negative.

e.g.      $^{-}4 \times^{-}5 = 20$   (positive $20$)

e.g.      $^{-}25 \div 5 = ^{-}5$

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

e.g.    $^{-}12 \div ^{-}4 \times^{-}6 =$ to work this out: $^{-}12 \div ^{-}4$ is equal to  $3$ then multiply by $^{-}6$ gives $^{-}18$

Note: division can be shown as a fraction.

e.g.      $\dfrac{^{-}30}{5}=^{-}6$

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.    $3 - 8 = ^{-}5$   Start at $3$ on the number line and move $8$ places down (left). We end at  $^{-}5$.

e.g.    $^{-}2 -5 = ^{-}7$   Start at $^{-}2$ on the number line and move $5$ places down (left). We end at $^{-}7$.

e.g.    $^{-}2 +10 = 8$   Start at $^{-}2$ and move $10$ places up (right) past zero and end at $8$.

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

e.g.    $2 - ^{-}4$   ($2$ subtract negative $4$) and $5 + ^{-}7$  ($5$ plus negative $7$)

Subtracting a negative is the same as adding:

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

Therefore $2 - ^{-}4$   can be written as $2 + 4 = 8$

Adding a negative is the same as subtracting:

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

Therefore $5 + ^{-}7$ can be written as $5 - 7 = ^{-}2$

## Practice using negative numbers

Complete these questions to assess your understanding: