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Absolute Value

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Absolute Value

What is the absolute value of the number –6?

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Khan Academy Absolute Value

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| . Using this notation can be translated as “the positive value of x ”.

Example A

|-7|=?

Solution:

|-7|=7

Example B

|7-15|=?

Solution:

|7-15|&=?\\|-8|&=?

|-8|=8

Example C

|-9|-|-2| = ?

Solution:

|-9|-|-2| &= ?\\|-9|-|-2| &= 9-2\\|-9|-|-2| &= 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 .

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| .

Guided Practice

1. |-50|=?

2. \big |- \frac{4}{5} \big |=?

3. |-3|-|-4|=?

Answers:

1. |-50|=50

2. \big | - \frac{4}{5}\big |=\frac{4}{5}

3. |-3|-|-4|=3-4=-1 . Remember that just because there is an absolute value in the problem doesn't mean that the answer is automatically positive!

Explore More

Evaluate each of the following:

  1. |-4.5|=?
  2. |-1|=?
  3. \big | -\frac{1}{3} \big |=?
  4. |4|=?
  5. |-2|=?
  6. |-1|+|3|=?
  7. |5|-|-2|=?
  8. \big | -\frac{1}{2}\big |+ \big | - \frac{2}{3} \big |=?
  9. |-2.4|-|-1.6|=?
  10. |-3|-|-2.4|=?
  11. |2-4|=?
  12. |5-6|=?
  13. \big | -\frac{1}{2} - \frac{5}{6}\big |=?
  14. |2.3-3.7|=?
  15. |7.8 - 9.4|=?

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