Proof of Absolute Value, DivisionDate: 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/ |
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