Multiplying Two Negative Numbers
Date: 01/16/97 at 12:25:15 From: InnisArt Subject: Integers Dear Dr. Math: I know that when you multiply two negative numbers you get a positive answer. I want to know why the answer is positive. Can you give me a written example why it is that when you multiply two negative numbers you get a positive number? Thanks! -Sunny.
Date: 01/16/97 at 17:22:52 From: Doctor Tom Subject: Re: Integers Hi Sunny, Here's a way to think of it. Suppose you're standing on a road, and you measure mileage to the east as positive, and to the west as negative. So you are at zero, and a town one mile east is at +1 mile, while a town two miles to the west is at -2 miles. So far, so good? A car travelling east will have a positive velocity, and a car travelling west will have a negative one. So a car going east at 60 mph goes at +60 mph, and a car going west at the same speed goes at -60 mph. This makes sense, since if they go for an hour (+1 hour), the east-going car will be at (+1)(+60) = 60 miles, and the car going west will be at (+1)(-60) = -60 miles (= 60 miles west). Still okay? Now suppose a car passes you going east at 60 mph. Where was it one hour ago? Or at -1 hour? Just multiply: (-1)(60) = -60 = 60 miles west. How about a car going west at 60 - where was it an hour ago? Its velocity is -60, the time is -1, so it was at (-1)(-60), and the answer should be 60 miles east, or +60. So (-1)(-60) = +60. I hope this helps. Try making up a similar example with money - money you earn is positive, and money you spend is negative; if you earn or spend at a constant rate, multiply to find out your change in worth. But negative time refers to the past, et cetera. -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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