Dividing Negative Numbers in Real Life

Date: 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.