Why is a negative times a negative a positive?
 

We got into this big discussion at lunch last Friday. Apart from saying "because it just is" or "those are the rules", no one at work could really explain this. I have to mention that I work in a Computer company with a lot of smart engineers. We also had some statisticians at the table as well as some Business Intelligence Data Analyst types.

So anyone have a good way to explain why this is?

It just keeps the natural progression of numbers in mathmetics. Here is the best example I can come up with:

5 x -4 = -20
4 x -4 = -16
3 x -4 = -12
2 x -4 = -8
1 x -4 = -4
0 x -4 = 0
-1 x -4 = 4
-2 x -4 = 8
-3 x -4 = 12
-4 x -4 = 16
-5 x -4 = 20

In that example the first factor is continuously reduced by 1. The second factor is consistently -4. The product will continue to increase by 4.

I don't know if that helps, but I really don't think there is a decent way to explain it without making yourself retarded.

Thanks for the attempt, but this was the type of conversation we had at lunch. What I want to know is why when you go - * - all of a sudden it goes +. I like your approach though by holding one number constant. I think you may have stumbled on to something on your example of crossing over at zero though. That gives me something to think about.

And BTW - how do you know I am not already retarded!! Hahaha :icon17:

YouTube - Math: Negative Times Negative Equals Positive

I guess you can try to rationalize it by explaining how multiplication works in the same way you do to a child.

I tutored kids by explaining multiplication takes 0, and adds the first number to it the 2nd number of times. So, 3x5 is like 0+3+3+3+3+3=15. With that example, logically, -3x-5 is adding -3 to 0 -5 times. We understand that adding a negative number is the same as subtracting. So you are subtracting 3 from 0 negative 5 times. In this case, I explained negative is like the word opposite in math, so you are doing the opposite of subtracting 3, adding, 5 times, and it becomes 0+3+3+3+3+3=15.

Also, there is a common factor to -3 and -5, which is -1. So you can divide -3x-5 by -1, which changes the equation to 3x5.

i like to explain it this way:

you spend 5 dollars in two turns, so in all you spent 10 dollars , so thats -5x2 = -10

before you spent 5 dollars two turns ago, you had 10 dollars, -5x-2 = 10

when you spend money, its negative, so thats where - is from.

How did we ever live without YouTube?

i wonder if that is true w/ relationships

I was good until that last example and mah head asplode!

Anatoray - I really liked your example. I still could not get my head wrapped around it. The YouTube video really helped. But I kept yelling at the screen saying "No, I never accepted that example".. then he proved it. So now I understand.