Absolute Value Rules

High School

Definition

Absolute value rules tell you how you should go about taking the absolute value of a number. Absolute values always leave you with a postive number, whether or not the output is positive or negative. You will turn any negative numbers into positive ones for absolute values.

Worked examples

\(|{-5}| = 5\)

The absolute value of a negative number is its positive version.

\(|9| = 9\)

The absolute value of a positive number stays positive.

\(|0| = 0\)

Zero is neither positive nor negative, so its absolute value is zero.

Common mistakes

\(|{-8}| = -8\) → \(|{-8}| = 8\) Absolute value always outputs a non-negative number; it removes the negative sign.
\(-|4| = 4\) → \(-|4| = -4\) The negative sign outside the bars is applied after taking the absolute value.
\(|x| = x\) for all \(x\) → \(|x| = x\) only when \(x \ge 0\); \(|x| = -x\) when \(x < 0\) Absolute value returns the positive version, not the original if it was negative.

Where you'll use it next

You'll apply absolute value rules when solving absolute value equations and inequalities, graphing absolute value functions, calculating distance on number lines, and working with error and deviation in algebra and beyond.

Found in 1 StudyPug lesson

Absolute value functions

Grade 11 Math

Absolute value is basically the distance between "number" and "zero" on a number line. We will look into this concept in this lesson. We will also learn how to express absolute value functions as piecewise functions.

11th Grade11th