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.

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.