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# Absolute Value

## Absolute value is simply the distance from zero of any given number or integer. Check out our modules and lessons below.

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Practice Absolute Value
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Absolute Value

What is the absolute value of the number –6?

### Absolute Value

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

#### Find the absolute value

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

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

#### Find the absolute value

|715|=?\begin{align*}|7-15|=?\end{align*}

|715||8|=?=?\begin{align*}|7-15|&=?\\ |-8|&=?\end{align*}

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

#### Find the absolute value

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

|9||2||9||2||9||2|=?=92=7\begin{align*}|-9|-|-2| &= ?\\ |-9|-|-2| &= 9-2\\ |-9|-|-2| &= 7\end{align*}

### Examples

#### Example 1

Earlier, you were asked to find the absolute value of -6.

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

#### Example 2

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

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

#### Example 3

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

45=45\begin{align*}\big | - \frac{4}{5}\big |=\frac{4}{5}\end{align*}

#### Example 4

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

|3||4|=34=1\begin{align*}|-3|-|-4|=3-4=-1\end{align*}. Remember that just because there is an absolute value in the problem doesn't mean that the answer is automatically positive!

### Review

Evaluate each of the following:

1. |4.5|=?\begin{align*}|-4.5|=?\end{align*}
2. |1|=?\begin{align*}|-1|=?\end{align*}
3. 13=?\begin{align*}\big | -\frac{1}{3} \big |=?\end{align*}
4. |4|=?\begin{align*}|4|=?\end{align*}
5. |2|=?\begin{align*}|-2|=?\end{align*}
6. |1|+|3|=?\begin{align*}|-1|+|3|=?\end{align*}
7. |5||2|=?\begin{align*}|5|-|-2|=?\end{align*}
8. 12+23=?\begin{align*}\big | -\frac{1}{2}\big |+ \big | - \frac{2}{3} \big |=?\end{align*}
9. |2.4||1.6|=?\begin{align*}|-2.4|-|-1.6|=?\end{align*}
10. |3||2.4|=?\begin{align*}|-3|-|-2.4|=?\end{align*}
11. |24|=?\begin{align*}|2-4|=?\end{align*}
12. |56|=?\begin{align*}|5-6|=?\end{align*}
13. 1256=?\begin{align*}\big | -\frac{1}{2} - \frac{5}{6}\big |=?\end{align*}
14. |2.33.7|=?\begin{align*}|2.3-3.7|=?\end{align*}
15. |7.89.4|=?\begin{align*}|7.8 - 9.4|=?\end{align*}

To see the Review answers, open this PDF file and look for section 2.12.

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### Vocabulary Language: English

Absolute Value

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