# Fractions R Us

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## Fractions R Us

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 In reply to this post by Kirby Urner-5 I believe the means/extremes cross multiplication refers to a proportion and would involve an equation. However, for addition and subtraction of fractions, I also have used the method Paul and Dave describe in every class to all levels of students for many years. Fractions seem to trouble them at all levels. Each time I have demonstrated this easy procedure, students ask why no one has ever shown them this? And that is a very good question!
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 Why? Well, I'd surmise that most text books would shun this procedure because it is not very transparent to the student new to adding fractions. I'd guess that most books would show that adding fractions with common denominators can be simulated with manipulatives - and then concentrate on creating the common denominator. I'd further guess that teachers often do show your method to students who show difficulty in finding common denominators. The issue is likely further clouded by a common desire to find the lowest common denominator (for ease of arithmetic I suppose) Gary Tupper Terrace BC vlm217 wrote: > I believe the means/extremes cross multiplication refers to a proportion and would involve an equation. However, for addition and subtraction of fractions, I also have used the method Paul and Dave describe in every class to all levels of students for many years. Fractions seem to trouble them at all levels. Each time I have demonstrated this easy procedure, students ask why no one has ever shown them this? And that is a very good question!
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 In reply to this post by Kirby Urner-5 Dave Renfro wrote (in part): http://mathforum.org/kb/message.jspa?messageID=6137437>> Now we're not going to get rid of calculators, >> so the issue comes down to a trade-off of how >> much additional practice with fractions should >> we include elsewhere in the curriculum to offset >> this decreased practice, if any. Kirby Urner wrote (in part): http://mathforum.org/kb/message.jspa?messageID=6138734> I agree that calculators will continue to be available, > including as emulated on computer screens, however > some emerging pre-college math curricula displace them > with computers, and introduce a modicum of programming > as a way to learn the underlying concepts. I thought about including something like "(or computers, or whatever)", but decided it would distract too much from the flow of the sentence (which is not to say that I succeeded in doing this in other places, such as this sentence). In 40-60 years we'll probably have voice recognition systems that can answer questions or point the way for finding an answer (as appropriate, such as in a classroom) and automatic math features like how MicroSoft Word can automatically (and usually, but not always) correct misspelled words, with programming at the level you're doing going the way of square root algorithms (still useful for certain people, but not the end user). And perhaps in 100-150 years there will be "math chips" and other kinds as well (likely part organic and part non-organinc) that will be implanted in the brains of children at the appropriate time in their development (like what we do with various vaccinations children get today), and much of education at this time will be learning how to use/adapt to these implants. Also, I suspect sometime between 150 and 200 years these implants will more and more allow us to directly link to whatever the internet evolves into. By the way, these things are hardly much different from where we're at today as compared to some of the things you'll find in stories and novels by Greg Egan (for those interested in some really way way out there thinking). Dave L. Renfro
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 In reply to this post by Paul A. Tanner III On Mar 14, 2008, at 7:06 PM, Paul A. Tanner III wrote: >> > > I'm still not sure that we are talking about the same thing as to what > I was referring to with the phrase "this method." You said, "My main > point was that I don't think this method is as unknown as you said.   > You > later agree that it's very well known . . ." But what I referring to > with the phrase "this method" was not what was I referring to in terms > of "very well known." What I was referring to in terms of "very well > known" is the identity a/b + c/d = (ad + bc)/bd itself, not a method   > of > how to get from a/b + c/d to (ad + bc)/bd. > I'VE NEVER SEEN IN PRINT > ANYWHERE THE METHOD I'M TALKING ABOUT. [emphasis added] Perhaps I'm VERY wrong, but there have been many posts like Dave   Renfro's that indicate that contrary to Paul's opinion, his "theorem,"   "method," "technique," "short-cut," or whatever his preferred   appellation might be, is not quite unknown or original to him. I   strongly believe that we need to collectively lie to Paul, tell him   that indeed he's made an earth-shattering discovery for which he   deserves the world's heartfelt appreciation, and suggest that a Fields   Medal may very well be in his future. Otherwise, we're going to continue to be flooded with posts on this   dead-as-a-doornail topic every time someone raises the issue of   fractions and their teaching. That has been the case for years and   years. It's unbelievable that anyone could be so desperate for kudos,   yet considering the individual in question, it's actually completely   obvious and utterly predictable. I'm not sure that offering him   hosannahs and world-wide acclaim would actually suffice to stem the   flow of these periodic dissertations, but I, for one, would be happy   to give it the old college try.
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