What Is Absolute Value in Mathematics

The absolute value is always a positive number except for zero, as zero is neither positive or negative. Absolute value refers to the distance of a number from zero, regardless of direction. The distance is always positive, as absolute value of a number cannot be negative. Use this term to refer to the distance of a point or number from the origin (zero) of a number line. Examples The symbol to show the absolute value is two vertical lines: | -5 | 5. This means that the absolute value of -5 is 5 because -5 is five units away from zero. Put another way: |5| shows that the absolute value of 5 is 5.|-5| shows that the absolute value of -5 is 5 Sample Problems Find the absolute value for the following problem. |3x| 9 To solve this problem, divide each side by 3, yielding: x 3 The absolute value of 3 is either -3 or 3 because the number 3 or -3 is three spaces from zero. So, the answer is: (3, −3)Â   Or, try the following problem. |−3r| 9 To find the answer, divide each side by 3 to isolate the variable r, yielding: |−r| 3 As with the previous problem, r can be either 3 or -3 because three is three spaces or units from zero. So, the answer is: (−3, 3)