Dividing by Zero and Dividing Zero by SomethingDate: 11/14/2006 at 19:43:11 From: Sabrina Subject: Zero principle in division I am trying to understand the difference between dividing by zero and dividing zero by something. One of them is zero and the other is "can't be done". Which is which and why??? Please help! Date: 11/15/2006 at 10:45:16 From: Doctor Ian Subject: Re: Zero principle in division Hi Sabrina, When we 'divide A by B', we're doing this: __ B ) A So if we're 'dividing zero by something', it looks like __ ? ) 0 And if we're 'dividing by zero', it looks like __ 0 ) ? So far, so good? Now, note that 4 3 ___ ___ 3 ) 12 4 ) 12 3 x 4 = 12 are three ways of saying exactly the same thing. In other words, any division problem can be rewritten as a multiplication problem. So if we have something like ? __ 5 ) 0 it means the same thing as 5 * ? = 0 And the only value that makes that true is 0: 0 __ 5 * 0 = 0 ---> 5 ) 0 So if we divide 0 by anything (except 0, as we'll see in a moment), we get 0... BECAUSE if we multiply anything by 0, we get 0. That's just the same fact, stated two different ways. Does that make sense? (Write back if it doesn't.) So, what about dividing BY zero? Well, if we have something like ? __ 0 ) 5 it has to mean the same thing as 0 * ? = 5 right? But there ISN'T ANY POSSIBLE VALUE that can make that true since anything times 0 will still be 0. So we say that division BY zero is 'undefined'. It doesn't make sense, and we just can't do it. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 11/28/2006 at 19:15:31 From: Sabrina Subject: Thank you (Zero principle in division) Thanks so much for clearing that up. It really helped. It is still a bit confusing but your answer explains it all. I just hope I can remember that on my next test!!! |
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