Lesson 4: Absolute Value

Property

The absolute value $|a|$ of a rational number $a$ is the distance from the point on the line to $0$.
A number and its opposite have the same absolute value.
Every rational number has an opposite, or additive inverse. $0$ is its own opposite.

Examples

• The absolute value of $-15$ is its distance from $0$, so $|-15| = 15$.

• The opposite of $9.5$ is $-9.5$. Both numbers are $9.5$ units from $0$, so $|9.5| = |-9.5| = 9.5$.

Property

For any number $x$, it is always true that $x \leq |x|$ because absolute value represents the distance from zero on the number line.
When comparing absolute values of different numbers, we are comparing their distances from zero, which may not preserve the original ordering of the numbers.

Examples