Why is a negative times a negative a positive?

Anatoray · 06-01-2009, 11:43 PM

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.

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06-01-2009, 11:43 PM	#6 (permalink)
Anatoray Track Member Join Date: Mar 2009 Location: Kentucky Posts: 794 Drives: 09 BLK 370Z Rep Power: 18	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.