Absolute Value (Modulus) of a Number
The absolute value (also called modulus) of a number tells us how far that number is from zero on the number line, without caring about which direction.
1. What is Absolute Value?
Absolute value measures the distance from a number to zero on the number line.
- It is always positive or zero
- It ignores direction — only measures distance
- Distance cannot be negative!
Key Examples:
|−5| = 5 |+5| = 5 |0| = 0
|−5| = 5 |+5| = 5 |0| = 0
2. Notation
We write absolute value using vertical bars: |a|
|−7| reads as:
- "absolute value of negative seven"
- "modulus of negative seven"
The result is 7
The vertical bars look like this: | number |
3. Geometric Meaning — Distance on the Number Line
The absolute value shows the distance from a point to zero (the origin) on the number line.
Interactive visualization — available in the full lesson
|−4| = 4
Point −4 is 4 units away from zero
Point −4 is 4 units away from zero
|3| = 3
Point 3 is 3 units away from zero
Point 3 is 3 units away from zero