From: pat ballew
To: Teacher2Teacher Public Discussion
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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