Definition: The absolute value of a number is its distance from zero on the number line, so it is never negative and is written with vertical bars.
What is absolute value?
Absolute value measures how far a number sits from 0 on a number line, no matter which direction. We write the absolute value of a number n as |n|.
How do you read it?
The number 9 is 9 units from zero, so |9| = 9. The number -9 is also 9 units from zero, so |-9| = 9. A distance cannot be negative, and |0| = 0.
How is it used in real life?
Absolute value ignores direction. A diver at -34 feet and a drone at 34 feet are both 34 feet from sea level. Their absolute values match, but their positions do not.
How do you compare with it?
To order values, compute each absolute value first. Compare -12 and 7. Since |-12| = 12 and |7| = 7, the number -12 is farther from zero. But -12 is still less than 7, because -12 lies to the left of 7. Distance and size are different ideas.
What is the usual trap?
The bars do not simply remove a minus sign inside a sum. For |3 – 8|, first compute 3 – 8 = -5, and then the absolute value is 5.