Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Proof of Absolute Value, Division


Date: 7/16/96 at 18:42:40
From: Alfred T Chu
Subject: Proof of Abs. Value, Division

Hello, I have this problem:

Can you prove...
If y does not equal to 0, then
   |x / y| = |x|/|y|

I can't type it on the computer so I am going to say it.
Prove that:  Absolute value of x over y equals absolute value of x 
over absolute value of y.

Please help me out. Thanks a whole lot!

Alfred


Date: 7/23/96 at 15:25:36
From: Doctor Erich
Subject: Re: Proof of Abs. Value, Division

Alfred,

I not completely sure of your exact question but I'm guessing you want 
to prove that |x/y| = |x|/|y| as long as y doesn't equal zero, 
correct?  

Assuming this is the case there are several helpful things to remember 
when dealing with absolute values. First, sometimes absolute value 
problems can be greatly simplified by dealing with them in two parts -
in this case seeing what happens for y<0 and then seeing what happens 
for y>0.  

In this case, if you could prove the theorem for both these simpler 
cases, you could conclude the theorem held for all y not equal to 
zero.  Another helpful thing to remember when dealing with absolute 
values is that |x|*|y|=|x*y|. For example 

  |2|*|-3|= 6 = |-6| = |2 *(-3)|

You can even do this with powers of x and y.  Unfortunately, these 
manipulations don't work as nicely when you're adding or subtracting 
absolute values.  Anyway, I hope that helps you out some... and I hope 
I guessed the right problem.  Write back if you have any other 
questions.

-Doctor Erich,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Calculus

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/