Absolute Value

Definition of Absolute Value

• The absolute value of a number is defined as the distance of that number from zero on a number line.

  • This distance is measured in units and is always a non-negative value.

• The absolute value is symbolized by two vertical bars surrounding the number or expression.

  • Example: The absolute value of x is written as |x|.

Characteristics of Absolute Value

• Absolute value is never negative.

  • It can either be a positive number or zero (|x| ≥ 0).

Calculation of Absolute Value

• To find the absolute value of a given number, follow these steps:

  1. Visualize a number line.

  2. Determine how many units the number is away from zero.

Examples:

Example 1: Absolute Value of Positive Number

• To find the absolute value of positive four (4):

  • Picture a number line and find the distance from zero.

  • Positive four is four units away from zero.

  • Therefore, the absolute value of four is:

  • |4| = 4

Example 2: Absolute Value of Negative Number

• To find the absolute value of negative nine (-9):

  • Visualize a number line and calculate the distance from zero.

  • Negative nine is nine units away from zero.

  • Hence, the absolute value of negative nine is:

  • |-9| = 9

Evaluating Absolute Value of Mathematical Problems

• To evaluate the absolute value of a mathematical expression, the following steps should be performed:

  1. Solve the mathematical problem first.

  2. Find the absolute value of the result from step 1.

Example:

• To find the absolute value of the expression seven plus two (7 + 2):

  1. Calculate the sum: 7 + 2 = 9.

  2. Then, find the absolute value of the result:

  • |9| = 9.