Multiplying NegativesDate: 13 Jan 1995 19:15:37 -0500 From: Nathan Burg Subject: (none) Dear Dr.Math In pondering a question about math. I've gone back to my elementary school lessons of multiplication and negative numbers. When we multiply 2 * 3 it could also be written as 2 + 2 + 2 or as 3 + 3 and they all equal 6. When we multiply -2 * 3 we could also write it as -2 + -2 + -2 and they both equal -6 but how would we re-write -2 * -3? Nathan Burg nburg@walrus.mvhs.edu Date: 14 Jan 1995 10:36:06 -0500 From: Dr. Ken Subject: Re: Nathan Burg's addition question Hello there! As I've said to a few of your schoolmates, we think it's great that you're thinking about the foundations of mathematics. I'll see what I can do with this one. You're right that this is how multiplication is defined. As far as -2 * 3 goes, sure, you could write it as -2 + -2 + -2, but you could also write it as (-)3 + (-)3. It's just like before, when there were three -2's, but now there are negative two 3's. So how could we write -2 * -3? Well, we can either think of it as negative two -3's, in which case we'd get (-)-3 + (-)-3, or we can think of it as negative three -2's, in which case we get (-)-2 + (-)-2 + (-)-2. It's similar to positive number multiplication. In that last figure, if we count up the negative twos, we'll find that there are negative three of them. I hope this helps your intuition a little bit. -Ken "Dr." Math |
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