Negative Numbers
Temperatures below zero, bank overdrafts, floors below ground: negative numbers make sense once you can picture them. Here's the picture.
Think of a number line
Negative numbers are numbers below zero. On a number line they sit to the left of zero; the further left, the smaller. So −8 is less than −2, just as −8 °C is colder than −2 °C.
Adding a positive number moves you right. Subtracting moves you left.
- Start at −3
- Move 5 to the right
- 2
- Start at 2
- Move 6 to the left
- −4
Why minus a minus is a plus
Adding a negative is the same as subtracting: 5 + (−3) = 5 − 3 = 2.
Subtracting a negative is the same as adding: 5 − (−3) = 5 + 3 = 8.
Picture it with debt: if someone takes away a $3 debt from you, you're $3 better off. Taking away a negative is a gain.
Multiplying and dividing
| Signs | Answer is | Example |
|---|---|---|
| + × + | positive | 3 × 4 = 12 |
| − × − | positive | −3 × −4 = 12 |
| + × − | negative | 3 × −4 = −12 |
| − × + | negative | −3 × 4 = −12 |
Same signs give a positive; different signs give a negative. The same rule works for division: −20 ÷ −5 = 4, and −20 ÷ 5 = −4.
Counting negatives: with several numbers, an even number of negatives gives a positive answer; an odd number gives a negative one.