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### 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
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

- 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.
```
Associated Topics:
High School Negative Numbers
Middle School Division
Middle School Negative Numbers

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