Absolute Value

Study Sheet

Absolute Value

Distance from zero

Distance Is Never Negative

Concept
The Big Idea
-10-9-8-7-6-5-4-3-2-1012345678910-77

∣x∣|x| is how far xx is from zero, ignoring direction. Distance cannot be negative, so the answer is never negative.

Example
Why ∣−7∣=7|-7| = 7

−7-7 sits seven steps from zero, so its absolute value is 77 — the same distance as +7+7.

In Plain Terms & More Examples

Concept
In plain terms

Absolute value is distance from zero, so it is never negative — just drop the sign.

Example
Finding ∣−12∣|-12|

It is 1212 steps from zero, so ∣−12∣=12|-12| = 12.

Example
Finding ∣8∣|8|

It is already positive: ∣8∣=8|8| = 8.