Negative numbers

The thermometer shows −4 °C, your account slips to −12 €, the parking spot is on level −2 underground. Numbers below zero are all around you. Once you place them on the number line, they lose all their mystery and become perfectly normal numbers to work with.

The number line also goes left

So far you have only looked right on the number line: 0, 1, 2, 3 and so on. Left of zero it continues just the same, only with a minus sign: −1, −2, −3. Zero is the middle, like the ground floor of a building with a basement. Adding still means jumping right, subtracting means jumping left. The only new thing: you may now jump past zero.

Which number is smaller?

On the number line, further left means smaller. That is why −7 is smaller than −2, even though 7 looks bigger than 2. Think of temperatures: −7 °C is colder than −2 °C. Or of your account: at −7 € you owe more than at −2 €.

Calculating across zero

For calculations like 3 − 5, a stopover at zero helps: from 3 you first jump 3 to the left (reaching 0), then 2 more, so you land at −2. The same works the other way: for −4 + 9 you first jump 4 to the right (reaching 0), then 5 more, giving 5. Zero is your reliable anchor point. And if you already start below zero, the rule does not change: for −3 − 4 you move 4 more steps left from −3 and land at −7.