Pre Algebra Absolute Value
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I'm Positive
Absolute Value

 
 There's a funny looking set of lines that we sometimes use in math:
 

 | (stuff) |

 
 What the lines mean is:
 
 "All right, we know you're in there... Come on out with NO minus sign."
 
 These lines are called:
 

 Absolute Value Notation

 
 If whatever's inside the straight lines doesn't have a minus sign, 
 nothing happens. 
 
 If it does have a "-" sign, it drops it before it comes out 
 (maybe it also raises its hands).
 
 So:
 

| -5 | = 5

 
| 23 | = 23
 
| -3.14 | = 3.14
 
 Example:
 
 So what happens if we have ...
 

| 3 - 7 |

 

 These lines kind of look like parenthesis (  ) don't they?
 Well, they work just like parenthesis too! 
 Do whatever's inside them first. 
 Then lose any minus sign on the way out.
 So:
 

 | 3 - 7 | = | - 4 | = 4

 
 Example:
 
 How about this one ...
 

- | 5 - 8 |

 
 OK, the lines are a type of parenthesis, 
 so you do what's inside them first:
 

- | - 3 |

 
 Then the thing left inside comes out without the minus sign:
 

 - | 3 |

 
 But then the negative sign waiting outside sticks to it:
 

 - 3

 
 Example:
 
 OK, Now let's do ...
 

 - | 5 - 7 |3

 
 Step 1:
 

- | - 2 |3

 
 Step 2:
 

-  23

 
 Step 3:
 

 -  (2 2 2)3

 
 Step 4:
 

 - 8

 
 Example:
 
 OK, Let's go really crazy,
 how about ...
 

 | - | 3 - 7 ||6 - 9| |

 
 Step 1: Do the stuff inside the absolute value lines:
 

 | - | - 4 ||- 3| |

 
 Step 2: Bring the numbers out of their own lines without their "-" signs. 
 Any "-" signs waiting outside then stick to them.
 

 | - 43 |

 
 Step 3: Apply the exponent:
 

 | - (4 4 4) |

 

 | - 64 | 

 
 Step 4: Bring the number out without the "-" sign.
 

64

 

   copyright 2005 Bruce Kirkpatrick

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