Why is negative plus negative positive?

Answer 1

A negative plus a negative is a negative number. It is a larger negative number, that is, it is a smaller number - IOW, it is farther to the left on the number line.

You probably meant to ask why is a negative number TIMES a negative number a positive number.


Think of multiplying m times n as taking m steps, n times. For example, multiplying 3 times 4 means taking three steps - starting at zero and going to the right - four times. When you're done, you will have taken 12 steps to the right.


If you multiply 3 times -4, it is like taking 3 steps backwards. Start at zero, take three steps backwards four times and you end up at -12.


Multiplying -3 times 4 is like taking backwards steps four times. So take three backwards steps, four times, and you end up at -12.


Multiplying -3 times -4 is like taking three backwards steps and going backwards four times. It's like a double reverse.

My answer is a short version of a post on mathforum.org (http://mathforum.org/dr.math/faq/faq.negxneg.html). On that page, see the example titled "On the Road" for a good application of why this is true.