|Absolute Value|

Contributor: Briana Pincherri. Lesson ID: 11134

Are you positive you know about negative numbers? What's the opposite of a negative number? Do you know how to use number lines? You're on your way to learning absolute value!

categories

Integers/Rational Numbers and Operations

subject
Math
learning style
Visual
personality style
Lion
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

You have probably seen some pretty crazy things that are NOT numbers in the math you've learned thus far, but have you ever seen a trapped number like this:

|-3|

  • Why do you think there are bars around that negative three?
  • Is it in number jail?
  • Did it do something wrong?
  • Can positive numbers be trapped, too?

If you're baffled by that little number cage, then you're absolutely in the right place!

There are so many different types of numbers.

complex and real numbers

Most numbers you have learned so far are considered rational numbers.

When you learned to count, you learned whole numbers. Whole numbers do not include fractions or decimals:

0, 1, 2, 3, 4, 5 … on forever

Now that you are older, you have learned about integers. These are whole numbers that also include negative numbers.

Just like whole numbers, there are no fractions or decimals:

… -3, -2, -1, 0, 1, 2, 3 … on forever

Integers are represented on a number line:

number line

You probably also have an understanding of opposite numbers when it comes to positive and negative integers:

How did you know the integers above were opposites of each other?

  • The numbers have opposite signs (+ or -).

  • Both the positive and negative opposites were the same distance away from 0.

  • The number itself stayed the same. For example, +7 and -7 both have 7.

Today, you will learn about absolute value.

This explains why the number stays the same when you have opposite integers.

Absolute value is how far an integer is from 0, regardless of being negative or positive.

You will use a number line to find the absolute value of an integer.

The absolute value symbol looks like two vertical bars around a number, just like this:

|-5 | = 5

number line

You see, the absolute value of -5 is 5 because it is 5 spaces away from 0.

Look at this other example:

number line

The negative integer (-3) and the positive integer (3) both have the same absolute value. Both integers are 3 spaces away from 0.

As you can see, it does not matter if you are asked to find the absolute value of a positive number or a negative number, your answer will always be the positive version of that number:

|-6| = 6

|6| = 6

|-485| = 485

|485| = 485

And, guess what? We actually don't even NEED a number line to find the absolute value!

We KNOW that absolute value represents the distance a number is from 0 on a number line, and we also know we don't have to have a number line to count it. Instead, just remember:

The absolute value of any positive or negative number is just the positive version of that number!

Before you practice on your own, watch Math Shorts Episode 10 - Absolute Value from Planet Nutshell:

  • Easy enough?

Let's put this idea into practice and have you try a few on your own in the Got It? section!

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