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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?

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

#### Example A

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

Solution:

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

#### Example B

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

Solution:

|715||8|=?=?

|8|=8

#### Example C

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

Solution:

|9||2||9||2||9||2|=?=92=7

#### Concept Problem Revisited

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*}.

### 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 |x|\begin{align*}|x|\end{align*}.

### Guided Practice

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

2. 45=?\begin{align*}\big |- \frac{4}{5} \big |=?\end{align*}

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

Answers:

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

2. 45=45\begin{align*}\big | - \frac{4}{5}\big |=\frac{4}{5}\end{align*}

3. |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!

### Practice

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*}

### Vocabulary Language: English

Absolute Value

Absolute Value

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

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