Division by a Negative and a Definition of DivisionDate: 09/18/2006 at 03:04:18 From: saravanakumar Subject: what does a number divided by a negative number signify If 6 is divided by 3 it means that 6 is being divided into 3 equal parts. But what does 6 divided by -3 mean? Date: 09/19/2006 at 12:03:25 From: Doctor Ian Subject: Re: what does a number divided by a negative number signify Hi, You can do yourself a big favor by letting go of the definition of division you're using now. It's one that is often used to help young students think about division, but it's not ideal, as you've brought up in your question. So, what 6 / 3 = 2 really MEANS is simply that 6 = 2 * 3 That is, division is just the inversion of a multiplication. Using that definition, we can think about all sorts of cases that don't make sense using your definition. For example, if pi ------- = x sqrt(2) then pi = x * sqrt(2) and we don't have to think about what it might mean to break something like pi into "the square root of two equal parts", which kind of gives me a headache just thinking about it! And it extends to your example, too: 6 / -3 = x means the same as 6 = -3 * x which is true only if x = -2, so 6 / -3 = -2 Try playing with variations on this, e.g., -6 / 3 = x -6 = x * 3 -6 = -2 * 3 -6 / 3 = -2 which means that 6 / -3 = -6 / 3 i.e., it doesn't matter where the sign is. Does that make sense? Let me know if you need more help. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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