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From: DOG <firstname.lastname@example.org> To: Teacher2Teacher Public Discussion Date: 2004021802:53:29 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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