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zxcv_890@hotmail.com
science forum beginner
Joined: 05 Oct 2005
Posts: 15
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 Posted: Fri Jun 23, 2006 1:09 am Post subject:
notation limitation for rational
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I often notice that students get confused how to rewrite an expression
like
(1/3)(pi)(x) into
((pi)(x))/3.
What I do is think of pi and x as being over 1, and then simply apply
the rule for multiplying rationals. Of course, x may already denote a
rational number, so why should I have to think of it that way? If we
were dealing with an actual rational number in for x (e.g., 2/5), we
would not think of it as (2/5)/1, and write ((pi)(2/5))/3; we'd just
leave 2/5 as is and write (2pi)/(3*5). So, isn't the fact that we use
a single variable for rational numbers force us to do the algebra a
little differently than if we were working with actual numbers (even
though, admittedly, the end result is equivalent)? It seems to me that
it's just a notational limitation that there's no way around. |
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William Elliot
science forum Guru
Joined: 24 Mar 2005
Posts: 1906
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| Posted: Fri Jun 23, 2006 3:23 am Post subject:
Re: notation limitation for rational
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On Thu, 22 Jun 2006 zxcv_890@hotmail.com wrote:
| Quote: | I often notice that students get confused how to rewrite an expression
like
(1/3)(pi)(x) into
((pi)(x))/3.
I apply the communitive law of multiplication. |
1/a * b = b * 1/a = b/a
| Quote: | What I do is think of pi and x as being over 1, and then simply apply
the rule for multiplying rationals. Of course, x may already denote a
rational number, so why should I have to think of it that way?
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Because you weren't taught math but only math by cook book rules??
| Quote: | If we were dealing with an actual rational number in for x (e.g., 2/5),
we would not think of it as (2/5)/1, and write ((pi)(2/5))/3; we'd just
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No, I wouldn't think of 2/5 as (2/5)/1 even tho (2/5)/1 = 2/5
| Quote: | leave 2/5 as is and write (2pi)/(3*5). So, isn't the fact that we use a
single variable for rational numbers force us to do the algebra a little
differently than if we were working with actual numbers (even though,
admittedly, the end result is equivalent)? It seems to me that it's
just a notational limitation that there's no way around.
Recall by definition a/b = a * 1/b. Thus |
((pi)(2/5))/3 = (pi)(2/5) * 1/3 = pi * 2 * 1/5 * 1/3 = pi * 2 * 1/15
= 2.pi/15
I think you are wanting to create more rules or to extend the rule book
rules beyond their usual use, instead of understanding the math in algebra
and using that to answer your questions. |
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zxcv_890@hotmail.com
science forum beginner
Joined: 05 Oct 2005
Posts: 15
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| Posted: Fri Jun 23, 2006 11:48 pm Post subject:
Re: notation limitation for rational
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William Elliot wrote:
| Quote: | I think you are wanting to create more rules or to extend the rule book
rules beyond their usual use, instead of understanding the math in algebra
and using that to answer your questions.
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Thanks for the post, but I'm not trying to do anything more than
understand math as it exists. I didn't get that in high school
because, remarkably, math is almost never taught the way it's discussed
in this forum. I thank goodness for this forum and for generous people
like you where I can get answers that I can't seem to get from my
teachers and textbooks. Speaking of books, would you be kind enough to
recommend one or two that present high school level algebra in a more
rigorous manner? |
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William Elliot
science forum Guru
Joined: 24 Mar 2005
Posts: 1906
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| Posted: Sat Jun 24, 2006 5:34 am Post subject:
Re: notation limitation for rational
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On Fri, 23 Jun 2006 zxcv_890@hotmail.com wrote:
| Quote: | William Elliot wrote:
I think you are wanting to create more rules or to extend the rule book
rules beyond their usual use, instead of understanding the math in algebra
and using that to answer your questions.
Thanks for the post, but I'm not trying to do anything more than
understand math as it exists. I didn't get that in high school
because, remarkably, math is almost never taught the way it's discussed
in this forum. I thank goodness for this forum and for generous people
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That's been a problem, teaching rule book math and it's gotten worse now
with the notion that teaching how to use a graphic calculator is teaching
math.
| Quote: | like you where I can get answers that I can't seem to get from my
teachers and textbooks. Speaking of books, would you be kind enough to
recommend one or two that present high school level algebra in a more
rigorous manner?
No I don't. Browse around library or book store and see what you can |
find. Perhaps an old text would be more inclined to teach the basis
like associative, commutative and distributive laws.
Many another reading this thread will offer reference or if not, post
message sci.math, alt.math.undergrad to request references as you want. |
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