3 Addition and subtraction on the number line
The number line can be used to show how calculations can be carried out with negative numbers. First you’ll have a reminder of how this works with positive numbers by looking at the sum 2 + 4.
Using Figure 7 below you can see that to add 4 onto 2 you need to move 4 places to the right of 2, giving 6.
The same method of moving to the right works if the starting number is negative. For example, suppose an account is overdrawn by £5, the account balance would be recorded as –£5. If the account holder then paid £8 into the account, £5 of this would pay off the debt and £3 would be recorded as the new balance, so (–5) + 8 = 3.
On the number line in Figure 8, the starting number is –5, and moving 8 units to the right verifies the answer as 3.
Now consider subtraction, again first with positive numbers, for example 6 − 4. The starting number is 6 but this time you move 4 units to the left to get to the answer, which is 2 (Figure 9). To subtract, you move to the left on the number line.
Similarly, if an account is overdrawn by £2 (–£2), and then the account holder withdrew another £3, the account would be overdrawn by £5. This is represented on the number line by starting at –2, then moving 3 units to the left to get the answer –5. This is written as (–2) − 3 = –5 (Figure 10).
See how you get on in this next activity.
Activity _unit8.3.1 Activity 4 Working with negative numbers
Try the following examples. Start by drawing your own number line from –10 to + 10.
- a.3 − 7
- a.Start at 3, move 7 units to the left.
Thus, 3 − 7 = –4.
- b.(–2) + 5
- b.Start at –2, move 5 units to the right.
Thus, (–2) + 5 = 3.
- c.(–3) − 6
- c.Start at –3, move 6 units to the left.
Thus, (–3) − 6 = –9.
- d.(–4) + 2
- d.Start at –4, move 2 units to the right.
Thus, (–4) + 2 = –2.
Well done for completing your first calculations using negative numbers. These examples all involved subtracting or adding positive numbers to a negative number. Things become slightly more challenging when looking at adding and subtracting negative numbers but again you’re going to call into help your trusty number line.