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 (email@example.com) 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.