document.write( "Question 73583: Why does multiplying two negative numbers equals a positive number? \n" ); document.write( "

Algebra.Com's Answer #52642 by jim_thompson5910(35256) $\"\"$ $\"About$

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It's because a negative number is really the opposite of a positive number. What I'm saying is that -5 is really the opposite of 5. In fact -5 is the additive inverse of 5, which means if we add them together we get 0 (ie 5+(-5)=0). What this means is if I gain $5 and I lose $5 then I'm back at 0. The loss of $5 (translated to -5) is the opposite of the gain of $5 (translated to +5). So if I'm at 5 on the number line and I negate it (make it the opposite sign) then my position is mirrored to -5, the opposite of 5. If I'm at -5 and I negate it (which could look like -(-5)) then I mirror back to 5. Here's a good example to help explain it:
\n" ); document.write( " $\"3-%28-3%29\"$ This problem becomes
\n" ); document.write( " $\"3%2B3\"$ Because the negative undid the (-3). You can think of it as you have $3 and I take 3 I.O.U's from you (you lose I.O.U's and since you have less debt you will have more money) so in a sense you've gained $3. It works the same way with multiplication and division. If I negate a negative number (take the opposite of it), I will have a positive number. Hope this makes sense. Sometimes it takes a while to fully understand the basics of arithmetic, but it's worth it. \n" ); document.write( "

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