The absolute value of a number is the number's distance from zero on the number line.
Since distance is always positive, the absolute value is always positive.
Denoted by two vertical bars around the number, for example, (|x|).
Explanation with Diagram
Consider a scenario where two people exit a building (represented by zero on a number line):
Person 1: Walks 20 meters to the right, located at +20.
Person 2: Walks 20 meters to the left, located at -20.
Both are 20 meters from the building, illustrating that absolute value is about distance, not direction.
Application on a Number Line
Absolute value examples:
Absolute Value of 20:
20 is 20 units from zero.
(|20| = 20).
Absolute Value of -20:
-20 is also 20 units from zero.
(|-20| = 20).
Specific Examples
(|8|) (Absolute Value of 8):
8 is 8 units from zero.
Therefore, (|8| = 8).
(|-5|) (Absolute Value of -5):
-5 is 5 units from zero.
Therefore, (|-5| = 5).
(|0|) (Absolute Value of 0):
0 is 0 units from zero.
Therefore, (|0| = 0).
Common Misconceptions
"Absolute value makes everything positive":
While it's true that absolute values are non-negative, it's crucial to understand that absolute value indicates distance from zero, not merely changing numbers to positive.
Conclusion
Understanding absolute value is fundamental in grasping the concept of distance on a number line.
Absolute value reflects distance, keeping it always non-negative, and is essential for solving distance-related problems.