# 3.16 Addition of negative numbers

Now think about adding a negative number, by looking at the number line again. Suppose you start at 0. Since 0 + ^{−}3 is the same as ^{−}3, you would expect that adding ^{−}3 to 0 on the number line should take you to the point marked ^{−}3 on the number line. So, 0 + ^{−}3 = ^{−}3.

Suppose Thomas's piggy bank were empty and he added an IOU for £3 to it. The value of the piggy bank would be ^{−}3.

To reach ^{−}3 from 0, move 3 units to the left. In general to add a negative number you move to the left along the number line.

Adding a negative number is the same as subtracting the corresponding positive number.

In terms of Thomas's piggy bank, a negative number is an IOU. Adding an IOU is the same as taking money out (subtracting a positive number).

## Example 25

Evaluate each of the following:

(a) 11 +

^{−}3(b) 2 +

^{−}5

### Answer

(a) In piggy bank terms, this represents contents of £11 plus a £3 IOU. So the overall value is 11 +

^{−}3 = 11 − 3 = 8.

(b) Thomas's piggy bank has £2 in it plus a £5 IOU. So it is worth 2 +

^{−}5 = 2 − 5 =^{−}3.