Multiplying and Dividing NegativesDate: 07/20/98 at 15:51:13 From: Brittany Subject: Multiplying and dividing integers Dear Dr. Math, I need to figure out how to multiply and divide integers. We learned it last year, but I never got it. The negative sign always confuses me, and when integers are in fractions, I get lost. For example: -1/2 times +2/3 = ? Please help me. Thanks a lot, Brittany Date: 07/20/98 at 19:12:57 From: Doctor White Subject: Re: Multiplying and dividing integers Brittany: Let's talk about a few things before we get started: 1) Integers are positive and negative whole numbers (... -3, -2, -1, 0, 1, 2, 3, ...) 2) Other numbers like fractions and decimals can have a positive value or a negative value and are called positive or negative numbers, but they are not considered integers. 3) Regardless of whether they are integers or not, there is a quick way to find the correct sign for your answer. First, if the problem contains just multiplication, just division, or just multiplication and division, then the correct sign can be determined rather simply. Just count up how many negative (-) signs there are in the problem. If there is an even number of negative signs then the answer will be positive. If there is an odd number of negative signs then the answer will be negative. Then work the problem as if it had no signs and put the correct sign on the answer. Example 1: (-2)(-3)(4)(-1). Note that there are 3 negatives, so the answer is negative. Then 2 x 3 x 4 x 1 = 24 so (-2)(-3)(4)(-1) = -24 Example 2: (-1/3)(1/2)(-1/5). Note that there 2 negatives, so the answer is positive. Then 1/3 x 1/2 x 1/5 = 1/30 so (-1/3)(1/2)(-1/5) = 1/30 Example 3: [(-2)(1/2)(-.4)]/[(-1)(-4)(-.5)]. Note that there are 5 negatives, so the answer is negative. Then [2 x 1/2 x .4]/[1 x 4 x .5] = .4/2 = .2 Since there is an odd number of negatives (5), the final answer is -.2. This works only if the problem contains just multiplication and division. If it has addition or subtraction in it, then we have another situation to deal with. You might want to look at the Dr. Math Archives and search for integers. You will find some neat discussions on signed numbers. http://mathforum.org/mathgrepform.html Hope this has helped. Let me know if you need more info. Come back soon, and good luck with Algebra next year. - Doctor White, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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