<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

2.12: Absolute Value

Difficulty Level: Advanced Created by: CK-12
Atoms Practice
Estimated4 minsto complete
%
Progress
Practice Absolute Value
Practice
Progress
Estimated4 minsto complete
%
Practice Now

What is the absolute value represented by the number line below?

Watch This

Khan Academy Absolute Value Equations

Guidance

Absolute value in the real number system is the distance from zero on the number line. It is always a positive number.

Absolute value is always written as \begin{align*}|x|\end{align*}. Using this notation can be translated as “the positive value of \begin{align*}x\end{align*}”.

Example A

\begin{align*}|-7|=?\end{align*}

Solution:

\begin{align*}|-7|=7\end{align*}

Example B

\begin{align*}|7-15|=?\end{align*}

Solution:

\begin{align*}|7-15|&=?\\ |-8|&=?\end{align*}

\begin{align*}|-8|=8\end{align*}

Example C

\begin{align*}|-9|-|-2| = ?\end{align*}

Solution:

\begin{align*}|-9|-|-2| &= ?\\ |-9|-|-2| &= 9-2\\ |-9|-|-2| &= 7\end{align*}

Concept Problem Revisited

What is the absolute value represented by the number line below?

Remember the definition of absolute value in the real number system is the distance from zero on the number line. Let’s look at the distance from the -6 to zero.

Therefore \begin{align*}|-6|=6\end{align*}.

Vocabulary

Absolute Value
Absolute value in the real number system is the distance from zero on the number line. It is always a positive number and is represented using the symbol \begin{align*}|x|\end{align*}.

Guided Practice

1. \begin{align*}|-50|=?\end{align*}

2. \begin{align*}\big |- \frac{4}{5} \big |=?\end{align*}

3. \begin{align*}|-3|-|-4|=?\end{align*}

Answers:

1. \begin{align*}|-50|=?\end{align*}

\begin{align*}|-50|=50\end{align*}

2. \begin{align*}\big | -\frac{4}{5} \big |=?\end{align*}

\begin{align*}\big | - \frac{4}{5}\big |=\frac{4}{5}\end{align*}

3.

\begin{align*}|-3|-|-4| &=?\\ |-3|-|-4| &=3-4\\ |-3|-|-4| &= -1\end{align*}

Practice

Evaluate each of the following using a number line:

  1. \begin{align*}|-4.5|=?\end{align*}
  2. \begin{align*}|-1|=?\end{align*}
  3. \begin{align*}\big | -\frac{1}{3} \big |=?\end{align*}
  4. \begin{align*}|4|=?\end{align*}
  5. \begin{align*}|-2|=?\end{align*}

Evaluate each of the following:

  1. \begin{align*}|-1|+|3|=?\end{align*}
  2. \begin{align*}|5|-|-2|=?\end{align*}
  3. \begin{align*}\big | -\frac{1}{2}\big |+ \big | - \frac{2}{3} \big |=?\end{align*}
  4. \begin{align*}|-2.4|-|-1.6|=?\end{align*}
  5. \begin{align*}|-3|-|-2.4|=?\end{align*}

Evaluate each of the following:

  1. \begin{align*}|2-4|=?\end{align*}
  2. \begin{align*}|5-6|=?\end{align*}
  3. \begin{align*}\big | -\frac{1}{2} - \frac{5}{6}\big |=?\end{align*}
  4. \begin{align*}|2.3-3.7|=?\end{align*}
  5. \begin{align*}|7.8 - 9.4|=?\end{align*}

Vocabulary

Absolute Value

Absolute Value

The absolute value of a number is the distance the number is from zero. Absolute values are never negative.

Image Attributions

Show Hide Details
Description
Difficulty Level:
Advanced
Search Keywords:
Grades:
Date Created:
Jan 16, 2013
Last Modified:
Apr 14, 2016
Files can only be attached to the latest version of Modality
Reviews
Help us create better content by rating and reviewing this modality.
Loading reviews...
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
MAT.ALG.156.2.L.3

Original text