Algebra I/Content/Working with Numbers/Absolute Value

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(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

  1. Sign - "+" for numbers more than zero, or "-" for numbers less than zero.
  2. 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)