Teacher2Teacher 
Q&A #12670 
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From: dog To: Teacher2Teacher Public Discussion Date: 2006100303:13:03 Subject: Re: Re: Re: Re: Re: Re: Re: Re: you can ALWAYS divide across! If Loyd is still out there, he's not going to like this....the algorithm works because it is the algebraic solution for finding the factor that makes the statement true. In other words, division is defined by the operation of multiplication, so what you are trying to find when you are asking "what is 1/6 divided by 1/5" is: what is the factor that is used with 1/5 to produce 1/6? Think about how this works with whole numbers....12 divided by 3 is asking for the factor that makes the statement 3 x ___ = 12 true. With fractions, when you solve the problem algebraically, you will end up with using the reciprocal to solve your equation. HOWEVER, my main point in THIS discussion is that division should be CONSTRUCTED in young minds as a question of "how many" so that they may evolve algebraically. In other words, you are asking "how many 1/5's are there in 1/6?" To answer this, put the fractions in their equivalent forms using common denominators so that the question is "how many 6/30's are in 5/30's?" Since the deonominators are now common, the question is, "how many 6's are in 5?" which is the same as the notation 5/6. At all costs, I avoid the "gazinta" (aka "goes into") operation that students learn in middle school. A successful student does not have this internal dialogue. They will ask themselves, "how many of these are in there?"
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