Teacher2Teacher 
Q&A #221 
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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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