Negative numbers: plus and minus
You learn to add and subtract with negative numbers by moving along the number line.
How to work it out
- Put your finger on the first number on the number line.
- Plus is to the right, minus is to the left.
- If the second number is negative, turn the direction around.
- Count the steps, and go on past zero.
A worked example
3 − 7
- Start at 3.
- Subtracting moves you left: go 7 steps.
- After 3 steps you are at 0, and after 4 more you are at −4.
More examples
−3 + 7
- Start at −3.
- Adding moves you right: go 7 steps.
- After 3 steps you are at 0, and after 4 more you are at 4.
2 + (−5)
- Start at 2.
- Adding a negative number moves you left: go 5 steps.
- After 2 steps you are at 0, and after 3 more you are at −3.
5 − (−2)
- Start at 5.
- Subtracting a negative number moves you right: go 2 steps.
- You end up at 7.
Try it yourself
5 − 9 =
−5 + 5 =
Watch out
You stop at 0 or turn round: for 3 − 7 you say 4.
Keep going left, past 0. If you end up to the left of 0, the answer has a minus sign.
Tips
- Adding moves you right, subtracting moves you left.
- Do not stop at 0: the number line carries on.
Exceptions
- If you subtract a negative number, like 5 − (−2), you move right: 5 + 2 = 7.
Why it works
To the left of 0 the number line just carries on: −1, −2, −3. Adding moves you to the right, subtracting moves you to the left. If you add a negative number you move left, and if you subtract a negative number you move right.