Kathy Burgis wrote:
>This will probably cause another flood of mail, but I guess I have to
>admit that I do not think simplifying fractions is a worthwhile activity
>either. In fact, I have problems with the concept of "simplified form"
>in general.
>
>Cheers,
>Kathy Burgis
Here are some typical "Simplify" problems. I would be interested in why
you object to them (if you do):
1. Simplify: 3x + 2(x-1) -4(-x+(2(1-x)))
2. Simplify: (x^2 + 2x + 2)(x^2 - 2x + 2)/(4 + x^4)
3. Simplify: (x^(4/5))^(5/16)
4. Simplify: (ln 16)/(ln 4)
As for "simplifying" fractions (i.e., reducing them to lowest terms), I
don't see what the BFD is all about: you find the prime factorization of
the top and the bottom, then cancel common factors. This is hardly rocket
science.
And there *is* a reason to reduce fractions to lowest terms: that makes
the fraction more understandable. If you survey 1309 people and find that
561 believe a certain thing, then that belief is held by 561 out of 1309,
so the fraction of people that believe it is 561/1309. Reducing that to
3/7 means that 3 out of 7 people believe that thing. The latter is much
easier to use and to comprehend. Of course, you could use a calculator to
find the decimal equivalent 0.428571... Depending on the situation, that
might be more useful than 3/7. But I think students should know both how
to reduce a fraction to lowest terms, and know that a/b means a divided by
b. Each has its own uses. If I had 28 people, then I would expect that 12
of them held that belief (using multiplication of fractions--the *reduced*
one times 28, or equality of ratios, but *not* a calculator), whereas if I
had 362 people, then I would expect that about 155 of them would hold that
belief (multiplying 0.428571... times 362, but *not* multiplying fractions
or using ratios).
And, of course, reducing fractions to lowest terms always gives you an
exact result, whereas a calculator only gives you something approximate.
The approximate result might be good enough, or even more desirable than
the reduced fraction, of course, but that depends on the situation.
mark snyder
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************