Dividing Negative Numbers in Real LifeDate: 03/03/2004 at 09:49:33 From: S.Y. Subject: dividing by a negative number Why and when do we divide by a negative number in real life? I can't find a convincing example to make my child happy. Date: 03/03/2004 at 12:34:42 From: Doctor Peterson Subject: Re: dividing by a negative number Hi, S.Y. You can find some examples by turning the multiplication examples given here into divisions: Negative times a negative http://mathforum.org/dr.math/faq/faq.negxneg.html In real life, one common instance is in calculations using variables that can take positive or negative values, such as rates or positions in space. We might define the flow rate through a pipe in gallons per minute, with a positive rate meaning the flow is into a tank, and a negative rate being flow out of the tank. Then a process control computer (which is what I design) might calculate the time it will take to fill the tank by dividing the volume remaining in the tank (its capacity minus the amount of liquid now in it) by the rate. If the resulting time is negative, it means that the tank is emptying and WAS full some time ago. That is a very simple example; in process control there will be all sorts of rates and positions being measured, and positions for valves or speeds of pumps being calculated, and many of these variables can have signs. Because we know how signed numbers work, we can write one equation telling the computer what to do, without having to have separate cases for flow in and flow out, and so on. We don't have to stop and think whether the number is positive or negative. It just happens, hidden inside the computer! I suspect that is typical of how negative numbers are really used today: not in hand calculations, but in automatic calculations or in algebraic equations where negative numbers are nothing special. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 03/04/2004 at 09:11:08 From: S.Y. Subject: Thank you (dividing by a negative number) Dear Dr. Peterson, Thank you for your prompt response. I also looked at the link you provided (negative times negative) and had some ideas about how to make up some examples. As an adult, I can relate to your example in process control (your job sounds cool!), but I still find it difficult to give examples to young kids. Maybe I should have asked for examples on its use in the daily life of ordinary people. Thanks a million! Respectfully, S.Y. Date: 03/04/2004 at 09:32:50 From: Doctor Peterson Subject: Re: Thank you (dividing by a negative number) Hi, S.Y. Since you didn't specify the age of the child involved, I chose not to try to give an age-appropriate example. And I suspect that there are none to give! Negative numbers probably don't arise in ordinary daily lives except in very basic ways. After all, the world got along without them for a very long time. I like introducing the concept of negative numbers to young children using a concrete example (usually a thermometer); but there is no need to introduce multiplication and division by negative numbers at that point, because they don't arise in a child's experience--you don't need to divide by a negative temperature. Only when ideas like coordinates and rates are introduced is it really necessary to raise the question of division. That's not to say that children won't think to ask "if negative numbers are numbers, how do you multiply them?"; but perhaps if they ask that, they are ready for less concrete answers! - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 03/04/2004 at 12:15:19 From: S.Y. Chu Subject: Thank you (dividing by a negative number) Dear Dr. Peterson, Thank you again. I appreciated your insights on this question. Respectfully, S.Y. |
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