From: pat ballew <pat.ballew@eu.dodea.edu>
To: Teacher2Teacher Public Discussion
Date: 2009120207:53:12
Subject: Re: Re: fractions as remainders in long division



I will disagree a little with Loyd about the importance of remainders
in upper level math.   It is, I think, at times very important to
distinguish the quotient and the remainder as seperate entities.  One
big idea where this shows up is the divison of polynomials. If you
divide a polynomial f(x) by a linear term (x-a), the result is a
constant term.  This constant term is important as it represents the
value of f(a) for the function in question.  If this turns out to be
zero, of course, that makes (x-a) a factor of f(x).  I still use the
sythetic division method I learned back in the dark ages of my youth
to evaluate polynomials because it is much easier than raising numbers
to powers repeatedly.  
The situation has lots of applications in modular arithmetic (perhaps
called clock-arithmetic in elementary schools) where the quotient is
often of no interest, and the remainder is the factor of importance.  

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