9B Absolute Value Study Guide

Key Vocabulary

Absolute Value — the distance a number is from zero on a number line. Always positive or zero. Written with bars: |n|. (valor absoluto)

Distance — how far apart two points are. Distance is always positive. (distancia)

Positive — a number greater than zero (to the right of zero on a number line). (positivo)

Negative — a number less than zero (to the left of zero on a number line). (negativo)

Opposite — a number that is the same distance from zero but on the other side. Example: 5 and −5 are opposites. (opuesto)

Visual Example — Number Line

  |−5| = 5             |5| = 5
  ←———————————————————→
 −5  −4  −3  −2  −1   0   1   2   3   4   5
  ⇐---- 5 units ----⇒     ⇐---- 5 units ----⇒

  Both −5 and 5 are 5 units from zero.
  So |−5| = 5 and |5| = 5.

Think of it this way: Absolute value is like asking "How far?" without caring about direction. Distance is always positive!

Step-by-Step: Finding Absolute Value

1 Look at the number inside the absolute value bars.
2 Ask: "How far is this number from zero?"
3 If positive or zero → the absolute value is the same number.
4 If negative → drop the negative sign to make it positive.

Formula Box

|5| = 5 |−5| = 5 |0| = 0

|n| = distance from 0 = always positive or zero

Watch Out!

Absolute value is NEVER negative. |−3| = 3, NOT −3.
The bars | | mean "absolute value," not parentheses or brackets.
|0| = 0. Zero is zero units from itself.
Opposites have the SAME absolute value. |−8| = |8| = 8, because both are 8 units from zero.

Practice Problems

1. What is |7|?

2. What is |−12|?

3. What is |0|?