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Absolute Value

Definition:

The absolute value of a number is a measure of its distance from zero on the number line.

Formula:

The absolute value of a number x is denoted by |x| and is defined as:

|x| = x if x is positive|x| = -x if x is negative|x| = 0 if x is zero

Properties:

  • Absolute value is always non-negative.
  • The absolute value of a sum is less than or equal to the sum of the absolutes.
  • The absolute value of a product is equal to the product of the absolutes.
  • The absolute value of a quotient is equal to the quotient of the absolutes.

Applications:

  • Absolute value is used to find the distance of a number from zero.
  • Absolute value is used to find the magnitude of numbers.
  • Absolute value is used in calculus to find the distance between points.
  • Absolute value is used in mathematics to solve a variety of problems, such as finding the solutions to inequalities.

Examples:

|3| = 3|-5| = 5|0| = 0|-2| = 2

Additional Notes:

  • The absolute value of a complex number is not defined.
  • The absolute value of a vector is not defined.
  • The absolute value of a matrix is not defined.

FAQs

  1. What is the absolute value of 15?

    The absolute value of 15 is 15.

  2. What is the absolute value of -15?

    The absolute value of -15 is 15.

  3. What does |-6 mean in math?

    |-6| means the absolute value of -6, which is 6.

  4. What is the absolute value?

    The absolute value is the distance of a number from 0, always a positive number or zero.

  5. What is the absolute value of 5?

    The absolute value of 5 is 5.

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