Distance on the Number Line

Liam, a college student, is studying temperature data from an automated backyard weather station for his class. On a winter day, the temperature drops to a minimum of negative 15 degrees Celsius. On a number line, this value is placed to the left of zero, showing a temperature below freezing.

Later that day, the temperature rises to a maximum of 5 degrees Celsius. This value is placed to the right of zero, showing a temperature above freezing.

Liam wants to find the temperature range for that day, which is the difference between the maximum and minimum temperatures. On a number line, this range is the distance between negative 15 and 5. Distance tells us how far apart two numbers are. Since distance measures a gap, not a direction, it is zero or positive.

To find this distance, we subtract one temperature from the other. If we subtract negative 15 from 5, we get 20. But if we subtract in the opposite order, we get negative 20. Since distance cannot be negative, we take the absolute value.

That’s why the distance between any two numbers, a and b, is the absolute value of b minus a or a minus b.