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 inequalities
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mandm87
New Member

USA
2 Posts

Posted - 08/30/2007 :  18:34:15  Show Profile
I know that when you are solving an inequality that involves multiplying to deviding by a negative you have to flip the inequality sign but I do not understand why. Could someone please help me understand this?
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sahsjing
Advanced Member

USA
2399 Posts

Posted - 08/30/2007 :  18:43:46  Show Profile
3 > -1
Multiply both sides by -1,
-3 < 1

You got it?
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 08/31/2007 :  07:33:40  Show Profile
Another difficult concept involves division by a number between 1 and -1. The beginning math student gets confused. Just when they understand that division results in a smaller number, they find out that is not always the case.
122=6
6015=4
10075=4/3
and so on.
However, look at something like
12.75=16
You end up with a bigger number than you started with.
Think about why and it will help you.

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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 08/31/2007 :  13:36:32  Show Profile
Yes, that is what I was pointing out. I wanted mandm87 not to get frustrated if still did not understand after the explanations that you and sahsjing gave. Many things that seem simple are really more difficult.
quote:
Originally posted by David

12.75 = 16 might cause confusion because the rule for division by a fraction is generally [and necessarily] taught without explanation. That is so since it's basis lies in a more general knowledge of the number system, albeit in fundamental properties, and young people ready to learn by rote are not ready to encompass that just yet. If there is a problem it is in that the basis for the rule for fractions is not taught later on either, for the most part.

It's easier to explain algebraically if the decimal [.75] is seen as a fraction [3/4]..."If this is 3/4 of that, then that is 4/3 of this." It's still not simple to see in terms of physical division of blocks, as in aliquot parts.


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