Temperatures and real-world negatives
Most schools introduce negative numbers using temperatures, because every child knows what cold weather feels like and a thermometer is a natural number line.
A thermometer is a vertical number line
A thermometer looks like a number line standing up. Bigger numbers go up; smaller numbers go down. 0 sits at the freezing point of water.
- +15 °C is a cool spring afternoon.
- 0 °C is freezing point — ice melts here.
- −10 °C is a cold winter night.
- −40 °C is properly Arctic.
The lower you go below zero, the colder it gets.
Temperature changes
When a temperature rises, the number goes up. When it falls, the number goes down. That's just addition and subtraction in disguise.
The temperature was 5 °C. It rose by 7 degrees. New temperature?
5 + 7 = +12 °C.
The temperature was 3 °C. It fell by 8 degrees. New temperature?
3 − 8 = −5 °C.
The temperature was −2 °C. It rose by 5 degrees. New temperature?
Going up from −2 on the number line, 5 steps: −1, 0, 1, 2, 3. Answer: +3 °C.
The temperature was −4 °C in the morning and −10 °C at night. How much did it fall?
From −4 to −10 you go 6 steps to the left (cooler). Fall = 6 degrees.
Difference between two temperatures
A really useful question: how far apart are two temperatures? On a number line, the distance is just the number of steps between them.
What's the difference between −3 °C and +5 °C?
From −3 you go up 3 steps to 0, then up 5 more to +5. Total: 8 degrees.
Quick rule: add the two "sizes" (3 and 5) when one is positive and the other negative. When both have the same sign, subtract the sizes.
Difference between −2 °C and −9 °C: both negative, sizes 2 and 9. 9 − 2 = 7 degrees.
Depth below sea level
Sea level is the 0 of altitude. Mountains stick up into positive numbers; valleys and ocean floors stretch into negative ones.
- Mount Everest: +8849 m.
- The Dead Sea: about −430 m.
- The Mariana Trench: about −10 994 m (the deepest point in the ocean).
A submarine at "depth 500 m" sits at altitude −500 m.
Money in the red
Banks talk about being "in the red" when an account has less than zero. −£50 means you owe the bank £50.
You have £20. A bill takes out £35. New balance?
20 − 35 = −£15. You're £15 overdrawn.
Your account is at −£40. You deposit £100. New balance?
−40 + 100 = +£60. (Climbed back through zero into the positive.)
A puzzle
Two cities. London is +12 °C. Bratislava is −5 °C. By how many degrees is London warmer?
| 12 | + | −5 |