<< is there any "mathematical convention" as
>to which of the following are "simplified"? >>
Campbell's Law of Algebraic Simplification states, generally, that for the
beginning algebra student, the "simplified" expression is the one possessing
fewer operations left undone. Every operation is an action, and a chance to
screw up the calculation; therefore, the fewer chances to screw up, the
simpler the expression.
After "simplifying" an expression, I will often provide the class with values
for the variables and ask them to calculate the value of the expression,
choosing for themselves whether they want to use the original expression or
the allegedly simplified one. Their choice tells them which is the simplified
one, because the human spirit, Great Thing that it is, always looks for the
easy way among equivalent paths.
:Phil Campbell
College of the Desert, et. al., CA
p.s.: in general, i agree with the posts that state that "simplified" is also
contextually based, and so teach my kids... sometimes, you actually *want* a
fraction to be (even temporarily) in larger terms...
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