Associated Topics || Dr. Math Home || Search Dr. Math

### Negative Times Negative

```
Date: 10/17/98 at 13:54:25
From: Julia Alaniz
Subject: Negative values

Could you provide an example for comprehending how a negative times a
negative is a positive? - maybe on the number line. I would like to
understand it rather than just take it as fact.
```

```
Date: 10/23/98 at 20:45:57
From: Doctor Gail
Subject: Re: Negative values

Dear Julia,

Here are a couple of examples for you:

If you are convinced that a positive times a negative is negative, then
one way to look at negative times negative is to observe a pattern.
Consider the following:

3x(-3) = -9
2x(-3) = -6
1x(-3) = -3
0x(-3) =  0

so what comes next in the pattern?  Notice that in each case we are
multiplying 3 by a number 1 smaller than the previous number. Also
observe the pattern that is being created with the products. So the
next logical multiplication sentence is

(-1)x(-3) = 3

Note that negative times negative was positive.

One of the best realistic interpretations that I have found concerns
videotaping. Consider videotaping two students, Julia who is walking
forward in the tape and holds a sign saying "I am walking forward."
Also consider her friend who is walking backward in the tape and holds
a sign saying "I am walking backward."  Now playing the tapes in the
normal fashion would be forward times forward or positive times
positive and Julia looks like she is walking forward (the result is
positive). Similarly, the meaning of negative times negative might be
interpreted as viewing "rewind" times "the friend" or backward times
backward. What would it look like the friend was actually doing?
Walking forward! So one can visualize backward times backward is
forward or negative times negative equals positive.

I hope this explanations begin to convince you that negative times
negative equals positive.

Doctor Gail, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 10/23/98 at 21:52:48
From: Julia Alaniz
Subject: Thanks to Docter Gail

What a most unusual example for visualizing a negative times a negative
- the videotaped example.

I am actually going to try it since I do video training tapes. Thanks
ever so much.

Julia Alaniz
```
Associated Topics:
Middle School Negative Numbers

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search