# Why does multiplying two negative numbers result in a positive number?

Asked by jrpowell (40542) October 30th, 2007

This was explained to me in High School.. That was 15 years ago. Could someone explain the reasoning behind it to me? My math is rusty so clarity would be cool.

thanks.

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You can think about it as the same reason why saying “She didn’t not buy 5 apples” means that she bought 5 apples.

If you lost \$5 on a stock and your losses double, that means you lost \$10 (-5×2). If your losses negative-double, that means you gained \$10 (-5×-2).

If this explanation doesn’t make sense, you can read some more (as well as a proof) by Dr. Math.

sferik (6121)

Pick a spot. Know where north is. That’s the plus numbers. South is the negative numbers.
Face north. Walk forwards. You are now walking North or towards higher pluses.
Go back to that spot.
Face north. Turn around (do a 180) and walk forwards.
You’re now walking South, towards higher negative numbers.
No big deal.

Go back to that spot.
Face north.
Walk backwards. Ha! You are walking South again towards the higher negs.

Go back to that spot.
Face north.
Turn around AND walk backwards. Where are you going?

You’re heading North to big positives by doing the equivilant of a negative (turning around) times a negative (walking backwards)

@Modern: I don’t know about johnpowell. but I’ve got severe vertigo and have just fallen to the ground at 0 on the numbers line. Send dramamine asap…POB 73, Spencertown, NY.

gailcalled (54639)

@GailCalled: Sounds like you tripped on an irrational number.

@Mod: Oh, good. My laugh for the day..now I can face my mother’s increasing memory loss w. more equilibrium. What DOES happen to one’s brain if you think about the square root of -1 for too long? I guess the same phenomenon as pondering on what is at the end of the universe’s boundaries..or what was there before the Big Bang. (What was the original question?)

@Sferik: Dr. Math said that (-a + -a) = +2a is a convention…maybe not really provable.

gailcalled (54639)

Without getting too deep into epistemological issues, all math is conventional. It doesn’t exist outside of ourselves. It is a system we created to help us solve problems.

As Dr. Math explains, “this convention has been adopted for the simple reason that any other convention would cause something to break.” That is, the convention was adopted because it was provable.

sferik (6121)

1) condition one is if someone is good (+) or bad (—-)
2) condition two is if someone lives (+) or dies (—-).

+ * + = + (if a good guy lives, that’s good)
+ * —- = —- (if a good guy dies, that’s bad)
—- * + = —- (if a bad guy lives, that’s bad)
—- * —- = + (if a bad guy dies, that’s good)

or

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