Q&A #12670

Teachers' Lounge Discussion: Dividing fractions

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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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