What Sign Do You Use?Date: 10/21/2001 at 18:42:24 From: butterfly Subject: If two negatives equal a positive If two negatives equal a positive, then how do you do it, and what sign do you take? Like -4-(-7): would it be -4 + -7= 11? Thank you, Butterfly Date: 10/22/2001 at 11:33:43 From: Doctor Ian Subject: Re: If two negatives equal a positive Hi Butterfly, When you _multiply_ two negative numbers, you get a positive number: Negative x Negative = Positive - Dr. Math FAQ http://mathforum.org/dr.math/faq/faq.negxneg.html But when you _add_ two negative numbers, you get another negative number. This illustrates one of the problems with trying to rely on 'rules' like 'two negatives equal a positive' without really understanding what the rules mean. The irony in the situation is that once you understand what the rules mean, there is no need to remember them any more! If you owe one friend 4 dollars (i.e., you have '-4 dollars'), and you owe another friend 7 dollars (i.e., you have another '-7 dollars'), how much money do you have altogether? It's not a positive number, is it? If it were, we could all get rich by spending money instead of by earning it. Now, suppose you owe a friend 7 dollars (i.e., you have -7 dollars), and I pay him 4 of those dollars for you (i.e., I've 'taken' -4 dollars away from you). How much money do you have now? -7 - (-4) = ? Here is another way to look at it. I can rewrite a subtraction this way: 7 - 4 = 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 - 1 - 1 - 1 Do you see why? But each of the subtractions cancels out one of the additions, right? = 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 + 1 + 1 \___/ \___/ \___/ \___/ 0 0 0 0 = 1 + 1 + 1 = 3 Well, it works the same way with negative numbers: -7 - (-4) = -1 + -1 + -1 + -1 + -1 + -1 + -1 - (-1) - (-1) - (-1) - (-1) = -1 - (-1) + -1 - (-1) + -1 - (-1) + -1 - (-1) + -1 + -1 + -1 \_______/ \_______/ \_______/ \_______/ 0 0 0 0 = -1 + -1 + -1 = -3 Now, this would be really tedious for something like -298 - (-197) = ? And that's why it's so tempting to make up rules and shortcuts. But applying the wrong rule or shortcut just gets you to the wrong answer more quickly. Does this help? Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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