**High School Number Sense Lesson 23: Absolute Values**

Turn any negative into a positive! :) This type of problem appeared

**12 times**on high school tests this year--on average at

**question # 23**.

**Number Dojo Level: 280**

**What Is It?**

The

**absolute value**of a number is its distance from 0, always represented as a positive number (assuming the number is not 0). Its notation is given as a pair of vertical lines, with the number inside:

**|number|**. So:

**|x| = x when x is positive****|x| = -x when x is negative****|x| = 0 when x = 0**

**How to solve:**

- |x|, when x is positive:
**use x**. - |x|, when x is negative:
**remove the negative sign**. - You will almost always be given a problem with more than one set of absolute value signs. Simply treat them like parentheses and solve from left to right, or from inside out.

**Example 1: |7 - 3|**

- Solve (simplify) what is inside the absolute value sign: ||. 7 - 3 =
**4**. Now you have**|4|**. - Since
**4**is positive, the answer is**4**.

**Example 2: |2 - 8|**

- Solve what's inside. 2 - 8 =
**-6**. Now you have**|-6|**. - Since
**-6**is negative, remove the negative sign to get**6**.

**Example 3: |4 - 6| - |9 - 3|**

- Solve what's inside. 4 - 6 =
**-2**, and 9 - 3 =**6**. Now you have**|-2| - |6|**. - Remove the negative sign on
**-2**to get**2**, and leave the 6 as is. Now you have**2 - 6**. Your answer is**-4**.

**Example 4: 1 - |3 - 6| - |10 - 15| - 21**

- Solve what's inside. 3 - 6 =
**-3**and 10 - 15 =**-5**. Now you have**1 - |-3| - |-5| - 21**. - Remove the negative sign from both.
**-3**becomes**3**and**-5**becomes**5**. Now you have**1 - 3 - 5 - 21**, which is**-28**.

**Example 5: 11 - |10 - |9 + 8||**

- Here we have an embedded absolute value within another absolute value. Solve what's inside (working from the inside out).
**|9 + 8|**=**|17|**=**17**. Now you have**11 - |10 - 17|**. **|10 - 17|**=**|-7|**=**7**.**11 - 7**=**4**.

**Example 6: ||3 + 1| - |4 - 1| - |5 - 9||**

- Here is another example with embedded absolute values. Solve what's inside. |3 + 1| = |4| =
**4**. |4 - 1| = |3| =**3**. |5 - 9| = |-4| =**4**. Now you have**|4 - 3 - 4|**. - |4 - 3 - 4| = |-3| =
**3**.

**Here's a free worksheet to help you practice AbsoluteValue:**

absolutevalue.pdf |

**Up Next for High School: CubesPowers**