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.
