Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Some important demonstrations on negative numbers
Replies: 70   Last Post: Dec 8, 2012 1:28 PM

 Messages: [ Previous | Next ]
 Robert Hansen Posts: 11,345 From: Florida Registered: 6/22/09
Re: Some important demonstrations on negative numbers
Posted: Nov 27, 2012 11:52 AM

It also isn't self-evident that x^(1/3) is the cube root, or that x^(-a) is 1/(x^a), but when you define the exponent operator in this way, it keeps things consistent (they don't break). That is the message I try to drive home. How to recognize convention and the way it is developed.

Bob Hansen

On Nov 27, 2012, at 10:12 AM, Peter Duveen <pduveen@yahoo.com> wrote:

> I have a new student, who was confused about negative numbers, both multiplication and division of the same. I wanted to demonstrate to him that a negative times a negative is a positive, but got flustered because I could not produce the demonstration. I promised to show him the demonstration at our next weekly meeting.
>
> Later, I sat down and derived the following demonstration:
>
> Proof that the multiplication of two negative numbers is a positive number: - 1 + 1 = 0 (Definition of -1); -1(-1 + 1) = 0 (0 times any number is 0); -1x-1 + -1x1 = 0 (distributive law of multiplication); -1x-1 + -1 = 0 (1 x any number is that number itself); -1x-1 = 1 (definition of -1; the same quantity added to equal quantities produce equal quantities).
>
> Main point is, it is not particularly self-evident that a negative number times a negative number yields a positive number. Some will undoubtedly argue that to demonstrate this property rather than to just state it will confuse the student. At the same time, I would argue that to not demonstrate it will confuse the student.
>
> I'm just throwing this out for discussion, but other properties that ought to be demonstrated are that 1/-a = -(1/a), another property that many may feel does not need to be demonstrated. On the contrary, I believe that not demonstrating it will lead to confusion.

Date Subject Author
11/27/12 Peter Duveen
11/27/12 James Elander
11/27/12 Robert Hansen
11/27/12 Joe Niederberger
11/27/12 Clyde Greeno @ MALEI
11/27/12 Robert Hansen
11/27/12 Peter Duveen
11/28/12 Robert Hansen
11/27/12 Joe Niederberger
11/27/12 Robert Hansen
11/27/12 Joe Niederberger
11/28/12 Robert Hansen
11/27/12 Joe Niederberger
11/28/12 GS Chandy
11/28/12 GS Chandy
11/28/12 Robert Hansen
11/28/12 Peter Duveen
11/28/12 Robert Hansen
11/28/12 Robert Hansen
11/29/12 kirby urner
11/28/12 Peter Duveen
11/28/12 syeds
11/28/12 GS Chandy
11/28/12 Joe Niederberger
11/28/12 Paul A. Tanner III
11/28/12 Robert Hansen
11/29/12 kirby urner
11/28/12 Joe Niederberger
11/29/12 Paul A. Tanner III
11/28/12 Jonathan J. Crabtree
11/28/12 Joe Niederberger
11/29/12 Robert Hansen
11/28/12 Joe Niederberger
11/29/12 Peter Duveen
11/29/12 Peter Duveen
11/29/12 Joe Niederberger
11/30/12 Robert Hansen
11/29/12 Joe Niederberger
11/29/12 Joe Niederberger
11/29/12 Peter Duveen
11/29/12 Joe Niederberger
11/29/12 Jonathan J. Crabtree
11/29/12 Robert Hansen
11/29/12 Jonathan J. Crabtree
11/30/12 Robert Hansen
11/29/12 Joe Niederberger
11/30/12 Joe Niederberger
11/30/12 Robert Hansen
11/30/12 Joe Niederberger
11/30/12 Robert Hansen
11/30/12 Joe Niederberger
11/30/12 Robert Hansen
11/30/12 Joe Niederberger
11/30/12 Jonathan J. Crabtree
11/30/12 Robert Hansen
11/30/12 Clyde Greeno @ MALEI
11/30/12 Joe Niederberger
11/30/12 Clyde Greeno @ MALEI
11/30/12 Robert Hansen
12/1/12 Robert Hansen
11/30/12 Robert Hansen
11/30/12 Clyde Greeno
12/1/12 Robert Hansen
11/30/12 Jonathan J. Crabtree
12/1/12 Joe Niederberger
12/1/12 Robert Hansen
12/8/12 Clyde Greeno @ MALEI
12/1/12 Joe Niederberger
12/2/12 Jonathan J. Crabtree
12/2/12 Clyde Greeno @ MALEI
12/3/12 Robert Hansen