Absolute Value

What is Absolute Value?

The absolute value, sometimes called the modulus, of a number is the number’s distance from the point of origin. In simpler terms, it is the value of the number regardless whether it’s negative or positive. For example, the absolute value of -8 is simply 8.

The absolute value of a number x is denoted by delim{|}{x}{|}.

To better understand this concept, take a look at the figure below.

Ask yourself, how far is -4 (on the x-axis) from 0? The answer is 4 units, and that is the absolute value of -4.

Sample Problems

Simplify the following expressions.

  1. delim{|}{7 - 2}{|}
  2. delim{|}{{-8} - 3}{|}
  3. delim{|}{- (-3)}{|}
  4. delim{|}{10^2}{|}
  5. - {delim{|}{9}{|}}

Solutions:

  1. delim{|}{7 - 2}{|}
    delim{|}{5}{|}
    delim{|}{5}{|} = 5
  2. delim{|}{{-8} - 3}{|}
    delim{|}{-11}{|}
    delim{|}{-11}{|} = 11
  3. delim{|}{- (-3)}{|}
    delim{|}{3}{|}
    delim{|}{3}{|} = 3
  4. delim{|}{10^2}{|}
    delim{|}{100}{|}
    delim{|}{100}{|} = 100
  5. - {delim{|}{9}{|}}
    - {delim{|}{9}{|}} = -9

    Note: Since the negative sign is outside the “bars”, then this expression means “the NEGATIVE of the absolute value of 9.”