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Teachers' Lounge Discussion: Teaching dividing fractions

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From: Mike

To: Teacher2Teacher Public Discussion
Date: 2003041513:17:46
Subject: Re: teaching dividing fractions

In response to those who are wondering about why we flip and multiply
when dividing fractions, I have the following to say.  Division is the
process of finding how many groups of one number "fit" or "go into"
another (usually larger) number.  For example, 10 divided by 2 - means
how many groups of 2 are in 10, which is, of course, 5 groups.  

Similarly, when dividing fractions we are trying to find out how many
groups of one fraction fit into another.  So, 3/4 divided by 1/8 means
how many  groups of 1/8 are in 3/4.  Without calculating, but just
thinking, we could realize that there are 6 groups of 1/8 in 3/4. 
(Hence, 6/8=3/4.)  Likewise, we can get this answer by flipping 1/8 to
get 8/1 and muliplying it by 3/4. (24/4 = 6)  

How does flipping and multiplying get us the right answer?
Generally speaking, when dividing, you are asking yourself by what
number do I multiply this number by to get that number.  For example,
10 divided by 2, could also be stated as 'what do I multiply 2 by in
order to get 10' (the answer is 5).  Similarly, with dividing
fractions, we could say what do I multiply 1/8 by in order to get 3/4.
Well, I am going to multiply 3/4 by the reciprocal of 1/8 and THAT is
what I multiply 1/8 by to get 3/4.

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