Why is it that a negative * by a negative equals a positive. Especially given that if I add to negatives I get a negative. Multiplication being addition and all.....

This is basic algebra and a question answered by a simple web search. A thread on such a topic is hardly necessary unless you first searched and didn't understand. In that case you need to cite your source, quote from it, and be specific about your misunderstanding.

 

Ask Dr. Math: FAQ Negative x Negative = Positive

You can look at multiplying negatives as subtracting the result the sum of your additions from zero.

 

ie.

-3 * -2 = 0 - (-2 + - 2 + -2) = 6

 

 

Multiplication of a negative by a positive is equivalent of adding the same negative number to itself.

 

ie.

3 * -4 = -4 + - 4 + -4 = -12

This seems a very odd question given the other threads...

 

Anyway, the question boils down to asking what is (-1)*(-1). What are the natural candidates for this? I suggest 1 and -1. See if either of these choices is consistent with the axioms of the real numbers. Think about distributivity in particular. Doing this should enlighten you.

 

Why is it that a negative * by a negative equals a positive

 

Symmetry

 

You have four choices

 

(negative ) * (negative)

(positive ) * (positive)

 

(positive ) * (negative)

(negative ) * (positive)

 

Two outcomes are positve and two are negative.

 

Note that the integers allow another four possible choices

 

(neutral ) * (negative)

(negative ) * (neutral)

(neutral ) * (positive)

(positive ) * (neutral)

 

All of these outcomes are neutral.

You can look at multiplying negatives as subtracting the result the sum of your additions from zero.

 

You can also think of multiplying by -1 as rotation by 180° (which reverses the direction along the number line). This answers this question and also nicely leads on to an understanding of complex numbers.

 

You can also think of multiplying by -1 as rotation by 180° (which reverses the direction along the number line). This answers this question and also nicely leads on to an understanding of complex numbers.

+1.

See here (the whole thread is similar)

 

http://www.scienceforums.net/topic/88018-proof-a-negative-times-a-negative-equals-a-positive/?p=856454

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Enhancing a little bit:

 

It is like there were 2 KINDS OF POSITIVE, but mathematics don't care.

Endy 0186

 

Awesome!......thanks for the reply quick, simple, no insults!

 

+1

 

 

 

Strange

 

Aren't you supposed to be ignoring me? Id prefer it that way. Get your kicks on route 66.

 

 

 

Acme

 

 

Please take note of Endy0816 reply. This is how to be helpful. In the future either answer a question here (provide links only for support), or don't reply at all. You might as well tell me to go read a text book every time I ask a question.

Edited July 25, 201510 yr by conway

 

You might as well tell me to go read a text book every time I ask a question.

Did it occur to you that the reason for that is that you should go an read a text book?

John

 

I came to a forum for a reason. Endy's, Ajb's, answers were far quicker and more efficient than a text book. Do you tell everyone who asks you a question in chemistry to go read a text book? Did it occur to you John that if you don't have anything nice to post, then don't post anything at all. In fact I know of a great kids movie about a deer that teaches that very lesson. You might benefit from it.

Endy's, Ajb's, answers were far quicker and more efficient than a text book.

Okay, but you should probably get hold of and use a textbook in basic algebra. I am sure people here have some recommendations.

 

Conway post#9

 

Endy 0186

 

Awesome!......thanks for the reply quick, simple, no insults!

 

I agree that some have jumped on you rather than take this as a genuine effort on your part to learn.

 

Which makes it all the more suprising that you ignore genuine answers from those who didn't jump.

 

 

I had thought that you could benefit from seeing some of the very simply but far reaching ideas underlying the modern approach to mathematics in general and arithmetic in particular.but I left post#5 as it was to start with.