Q&A #19701

Division in 7th grade general math

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From: Gail (for Teacher2Teacher Service)
Date: Jul 24, 2008 at 17:49:56
Subject: Re: Division in 7th grade general math

Hi Luann, 

What you are asking about is interesting, because it requires that we put the
math into words, and sometimes that can be tricky.

Before we do the fraction problems you have suggested, let's think about 
dividing in terms of some whole numbers.  If you divide 12 BY 3 (which looks 
like this 12 / 3), for example, you get three piles of 4, or four piles of 
3, right?  Because "divided by 3" means, put the amount you started with 
into a 3 equal piles, or into piles of 3, and 3 x 4 is the same amount as 4 
x 3.  You are asking "how many groups of 3 are in 12?"

If, on the other hand, someone asked you to divide 12 INTO 3, (which looks 
like this 3 / 12), that would be like having 3 cookies, and needing to share 
them with 12 people.  You are asking "how many groups of 12 are in 3?"  You 
know that you can't get even ONE group of 12 from 3; in fact, you would have 
only 1/4 of a cookie for each person.

So, if you started with 1, and divided by 1/2, that would be like trying to 
find out how many groups of 1/2 there are in 1, and the answer would be 2.

If you started with 1 and were dividing it INTO 1/2, that would be like 
saying how many 1s are in 1/2?  There isn't even one 1 in 1/2, is there?  In 
fact, there is only half of a 1 in 1/2.

I hope that helps.  Let us know if you still have questions.  :-)  

 -Gail, for the T2T service

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