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Topic: dropped topics
Replies: 21   Last Post: Jun 23, 1995 8:15 PM

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Dr. Susan Addington

Posts: 21
Registered: 12/6/04
Re: dropped topics
Posted: Jun 20, 1995 7:50 PM
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Good point! Multiple representations of mathematical ideas is
one of my pet (what's the opposite of a peeve?)s.

An important aspect of fractions is that they are exact.
For example, 1/7 = .142857142857...
If you use the decimal where do you stop?
Most people seem to use the rule that some teacher beat into them
long ago: round to 2 decimal places. (Why?)

If you're doing almost anything in number theory, you do NOT
want to convert to decimals, for the same reason.

Other reasons for teaching operations with fractions:

In algebra, understanding rational expressions builds on
an understanding of how to do arithmetic with fractions.

In discrete probability problems, fractions are often more
intuitive: the probability of getting 3 heads out of 5 coin flips is
10/32, which tells you more about the whole situation than .3125.

Here is a problem to answer the objection "why does anybody need
to divide fractions?"

If you have 12 1/2 cups of lemonade and want to serve 2/3 cup to
each customer, how many servings do you have?

Susan Addington (addington@gallium.csusb.edu)
Math Department, California State University
San Bernardino, CA 92407
phone: (909) 880-5362 fax: (909) 880-7119
World Wide Web: http://www.math.csusb.edu/susan/home.html


On Tue, 20 Jun 1995, Norm Krumpe wrote:

> Another is that they should understand that there are multiple ways of
> representing the same thing. And, depending on the audience with which they
> are communicating, they need to choose the appropriate representation. For
> example, you might not go to a lumber yard and tell them you need a piece of
> wood that is .75 yards long. Instead, you would say you wanted a piece that
> is 27 inches long. Similarly, "forty-five hundredths" may be appropriate in
> some situations, while "point four five" may be better in others.






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