Lesson 3: Absolute Values of Rational Numbers

Property

The absolute value of a number is its distance from zero on the number line.
The absolute value of a number $n$ is written as $|n|$ and $|n| \geq 0$ for all numbers.
Absolute values are always greater than or equal to zero.

Examples

• The absolute value of $-9$ is $9$, because $-9$ is $9$ units away from $0$. This is written as $|-9| = 9$.
• The absolute value of $25$ is $25$, because $25$ is $25$ units away from $0$. This is written as $|25| = 25$.
• The equation $|x| = -4$ has no solution. Absolute value represents distance, which cannot be a negative number.

Explanation

Think of absolute value as a 'distance-meter' from zero. Since distance can't be negative, the absolute value of any number, positive or negative, will always be a positive result or zero. It simply tells you how far away you are.