<p>WHY is a negative times a negative a positive?</p>
<p>Why?</p>
<p>The reason that, for example, -5 times -3 is +15 rather than -15 is that the choice of +15 makes arithmetic work the way we think it should. To show you what I mean let me do +5 times -3 first. </p>
<p>Start with the true fact that</p>
<p>-3 + 3 = 0.
Multiply both sides by 5</p>
<p>5(-3 + 3) = 5(0) = 0.
Using the distrubutive law I get</p>
<p>5(-3) + 5(3) = 0
But 5(3) = 15 so</p>
<p>5(-3) + 15 = 0
Thus, whatever the number 5(-3) is, if you add 15 to it you get zero. Thus 5(-3) must be -15. That is 5(-3) = -15. </p>
<p>Now, start again with</p>
<p>-3 + 3 = 0.
This time multiply each side by -5.</p>
<p>-5(-3 + 3) = -5(0) = 0.
Again the distributive law gives</p>
<p>-5(-3) + (-5)(3) = 0.
But we know that (-5)(3) = -15 so</p>
<p>-5(-3) - 15 = 0
Thus, whatever the number -5(-3) is, if you subtract 15 from it you get zero. Thus -5(-3) must be 15. That is -5(-3) = 15. </p>
<p><a href=“http://mathcentral.uregina.ca/QQ/database/QQ.09.01/mary1.html[/url]”>http://mathcentral.uregina.ca/QQ/database/QQ.09.01/mary1.html</a></p>
<p>Basically, if negative times negative = negative
It screws up arithmetic and we have to redo everything :)</p>
<p>wow that was really cool</p>
<p>it’s kind of weird still</p>
<p>i mean subtracting/adding makes sense</p>
<p>if you make a bet, lose 50, you’re at -50, make another bet and lose for 50, and you’ve lost 100</p>
<p>now if you win the second one you’re 0 even</p>
<p>it all makes sense</p>
<p>but if you have “negative” money, and you times it by more, it seems like you should have al lot of “negative” money, not positive!</p>
<p>but I get what you’re saying</p>
<p>Hehe, neat =P. Thanks, michael_pham!</p>
<p>It was one of those things that you accept, but don’t really question, you know? So it’s basically positive because we make it that way. Wow. Cheers!</p>
<p>Like that passage in the SAT on Intelligence. “The conscious excepts things the way they are… They can’t always explain why.” -haha I’m bad at quoting things </p>
<p>But about the money thing, do a search for it.
I found the site earlier, its on Dr. Math’s Forums.</p>
<p>So, how would we use a negative times negative in a word problem? Like, Jane has _ truffles and gives Bill <em>… etc. What type of word problem would require you to use negatives? O</em>o…</p>
<p>Now suppose that, as a bonus, the employer decides to pay the mortgage for one year. The employer removes the mortgage deduction from the monthly paychecks. How much money is gained by the employee in our example? We can represent “removes” by a negative number and figure out the answer by multiplying. </p>
<p>-12 * -$700 = $8,400</p>
<p>This is an illustration of a negative times a negative resulting in a positive. </p>
<p>More at <a href=“Classroom Resources - National Council of Teachers of Mathematics”>Classroom Resources - National Council of Teachers of Mathematics;
<p>Ooh, that’s a really good example =D.</p>
<p>Word problem for subtracting a negative… Jane and Bill go out to eat at a newly-opened Afghan restaurant. After sumptuously dining on dolma and chalau, Jane asks for separate checks. Alas, when the check arrives, Jane discovers she has left her purse at home. Jane borrows $30 from Bill to pay for her dinner. After dinner, Jane smiles so nicely at Bill that he decides to forgive $10 of her debt. How much does Jane now owe Bill? </p>
<p>She started off $30 in the hole. Subtract a debt of $10 that she no longer owes. -$30 - (-$10) = $-20.</p>
<ul>
<li>Ellen</li>
</ul>