Negative numbers — Mathematics, 11–13 years
Numbers below zero help describe amounts that go in the opposite direction from ordinary counting.
Numbers below zero
Zero is not the end of the number line. Numbers to its left are negative: they can show a temperature below freezing, money owed, or moving backwards from a starting point. The farther left, the smaller the number.
Why we need them
Ordinary counting cannot describe what happens when you lose more than you have, or when a temperature drops below freezing. Negative numbers solve this gap by giving every step in the opposite direction a place on the same number line.
A temperature change
At dawn it is −3 °C. By midday it rises 7 degrees, so calculate −3 + 7. Moving seven places right on a number line lands on 4, so the midday temperature is 4 °C. The sign shows the starting temperature was below zero.
The sign is part of the number
A common mistake is to treat −5 as if it were simply 5 with a decoration, or to think that −8 is larger than −3 because 8 is larger than 3. This feels natural from counting, but on the number line −8 is farther left, so it is smaller.
Where they appear
Negative numbers appear on thermometers, bank statements, lifts below ground level, and game scores with penalties. In each case they record a position or amount below a chosen zero; they do not mean that the object or situation is unreal.
Keep exploring
Other languages
Loading MyLeoNes™…