Why is a negative times a negative a positive?

Cypress

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?

fly yellow

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.

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Cypress

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

AK370Z

YouTube - Math: Negative Times Negative Equals Positive

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Anatoray

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.

Cjanik

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.

CBRich

How did we ever live without YouTube?

xiven

i wonder if that is true w/ relationships

2theextreme

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

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Cypress

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.