Lesson 2.17

Intro to Absolute Value

Numbers have two properties: size (magnitude) and direction (sign). Absolute value cares only about size. It asks "How far?" not "Which way?"

Introduction

If you drive 5 miles north (+5) or 5 miles south (-5), you have burned the same amount of gas. Your distance from home is just "5." That is absolute value.

Past Knowledge

Ordering real numbers on a number line.

Today's Goal

Evaluate expressions with absolute value bars: .

Future Success

Needed for evaluating distance on a coordinate plane (Distance Formula).

Key Concepts

Distance from Zero

The symbol for absolute value is two vertical bars: . It turns everything inside POSITIVE.

Negative Input

Positive Input

Zero Input

Distance is NEVER negative.

Worked Examples

Example 1: Basic Evaluation

Basic

Evaluate .

1

Simplify Inside Bars

Example 2: Negative Outside

Intermediate

Evaluate .

1

Absolute Value First

The bars are like parentheses. Evaluate inside first.

2

Apply Outside Negative

Example 3: Operations Inside

Advanced

Evaluate .

1

Subtract Inside

Do NOT turn the -9 into +9. You must finish the math INSIDE first.

Common Pitfalls

Distributing Basics

You CANNOT distribute into absolute value bars. . You must solve inside first.

The Negative Result

Students see and solve it. But absolute value can NEVER be negative. This equation has No Solution.

Real-Life Applications

Error Margins: If a machine cuts a board to 10 inches, and we accept an error of 0.1 inches, we care about the magnitude of the error (). Being long or short by 0.1 is equally acceptable.

Practice Quiz

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