Q&A #12670

Teachers' Lounge Discussion: Dividing fractions

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From: DOG

To: Teacher2Teacher Public Discussion
Date: 2004021803:53:29
Subject: Re: Re: you can ALWAYS divide across!

Let me start by saying that I am a high school teacher.  I have taught
8th grade through math analysis (precalculus) and division of
fractions is a hurdle that few students have overcome.  I believe that
most students lack a clear understanding of what the operation of
division is really about.  Since fractions are free-standing division
problems, division of fractions is like a double whammy of frustration
for most of my students, regardless of their current curricular level.
I try to get my students to see division using a partitive model: 12/2
is asking "how many 2's are in 12?"  Therefore, division of fractions
like 1/3 divided by 1/4 is asking, "how many 1/4's are in 1/3?"  Since
most students cannot directly "see" their answer, I ask them to rename
each fraction using the common denominator.  Thus, the question can be
restated, "how many 3/12's are in 4/12?"  There is one complete 3/12
and one third of the measuring unit (3/12), so the answer is 1 and
1/3.  Had the problem been written in the standard format:  1 over 3
divided by 1 over 4, then restated as 3 over 12 divided by 4 over 12,
students can simply divide straight across.  The numerators give 4/3
and the denominators result in 12/12.  While this looks like a complex
fraction (a fraction over a fraction), the denominator will always
equal one if you have common denominators.

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