-6 times -6Date: Thu, 03 Nov 1994 12:26:28 -0600 From: Robert Trueblood Subject: Question I really need to know what the answer to this problem is. -6 X -6 ____________ Any clue Doc? Robert Trueblood From: Dr. Ken Date: Thu, 3 Nov 1994 12:55:02 -0500 (EST) Robert- We're not realy sure what you mean to ask. Do you mean x - 6^(-6)? Or -6 times -6? In the former case, it's x - 1/46656. In the latter, it's 36, since the negatives cancel out. -Ken "Dr." Math Date: Thu, 03 Nov 1994 13:16:17 -0600 From: Robert Trueblood I Mean -6 times -6 Since multiplication is repetitive addition and multiplication is impossible without repetitive addition or memorization. -6 + -6 =-12 -12 + -6 = -18 -18 + -6 = -24 -24 + -6 = -30 -30 + -6 = -36 So the answer should be -36 BUT: if you draw a bar graph and start at -6 at 6 6 times you get a positive 30 Hmm can you explain your answer of +36 Thanks Robert Trueblood From: Dr. Ken Date: Thu, 3 Nov 1994 14:28:56 -0500 (EST) Here's how it would work. If you want to use the technique for multiplication where x times y means you add x to itself y times, then what you've found in your example is -6 x 6, because you added negative six to itself six times. To find -6 x -6, we'd have to add negative six to itself negative six times. Kind of a funny concept, but we can make some sense of it. If we add two negative sixes together (-6 x 2), we get -6 + -6 = -12. If we add one negative six together (-6 x 1), we get -6. If we add zero negative sixes together (-6 x 0), we get 0. Notice that we are increasing by sixes each time. If we add -1 negative sixes together (-6 x -1), we get -(-6) = 6. If we add -2 negative sixes together (-6 x -2), we get -(-6) + -(-6) = 12. You can see the pattern then, and how -6 x -6 = 36. -Ken Date: Thu, 3 Nov 1994 14:38:14 -0500 X-Sender: dbonaro1@cc.swarthmore.edu Hi, Robert, this is Demetri. I must admit that I, myself, was puzzled when I read your reasoning and, although I knew that the result is not -36 but +36, I couldn't quite see what was wrong with your approach. I think I have it now, though, so here goes: What you have done above is taken +6 times the number -6 and not -6 times (in other words, you have found the result to 6 times -6, not to -6 times -6). Adding -6 to itself is the same as taking -6 twice. This is exactly what you have described above, all the way until we had -6 taken -6 times. So, one way to think about this is to take 6*(-6) (that is 6 times -6), find the result to this (which is exactly what you have above, ie -36) and then consider what -[6(-6)] is. This is nothing other than the negative of 6(-6) or, if you prefer, its opposite (opposite numbers are two numbers whose sum is 0- you may know this, but I said it just in case you don't know). Clearly, the opposite of -36 is +36, because -36 +36 = 0. Therefore, -6*(-6) = +36 I realise that it is rather hard to explain things like this via email, but I hope that you've understood what I am talking about and that I haven't confused you even more. If I have, though, do write back and we'll have another go at it. Demetri- Dr. of some sort. |
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