# Algebra I/Content/Working with Numbers/Absolute Value

Back to Table of Contents Algebra I

(Note to contributors: Please use the ^ symbol to designate exponents when you enter them in the wikibook. I will format them on the student-user interface.--HSTutorials 00:42, 17 July 2006 (UTC)

## Vocabulary

- Sign - "+" for numbers more than zero, or "-" for numbers less than zero.
- Absolute Value - The value of a number without its sign.

## Lesson

The absolute value of a number is its value without its sign. For example, the absolute values of -3 and +3 are both 3. (Remember that +3 = 3.) We write "The absolute value of -3" as |-3|.

Variables also have absolute values. Let x be a variable. |x| means that, if x is positive, then |x| = x, but if x is negative, then |x| = -x. (This is because, if x is negative, then -x is positive.)

You can find the absolute value of expressions as well. |-5*3| means the absolute value of -5 multiplied by 3. You can evaluate to find that -5*3 = -15. Thus |-5*3| = |-15| = 15.

You may use the absolute value to find the distance between two numbers on the number line. Let a and b be variables. Then |a-b| is the distance between a and b. For example, if a=3 and b=7, then |3-7| = |-4| = 4. Because you used the absolute value, the distance is the same if you switch the order of the two numbers; if a=7 and b=3, then |7-3|=|4|=4.

## Example Problems

## Practice Games

put links here to games that reinforce these skills

## Practice Problems

(Note: put answer in parentheses after each problem you write)

Solve.

**1.** |-3| (3) **2.** |6| (6) **3.** |-1.8| (1.8)

**4.** |2 - 5| (3) **5.** |-5 + 1| (4) **6.** |9 + 3| (12)

**7.** |-5| - 1 (4) **8.** 3 - |-2| (1) **9.** 9 + |-3| (12)

**10.** |1 - 6| + 5 (10) **11.** -5 - 1 + |6| (0) **12.** -6 + |-5 - 1| (0)