Q&A #12679

Language - "reduce" fractions

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Dec 09, 2003 at 02:59:15
Subject: Re: Language - "reduce" fractions

I don't know if it is possible for language to be mathematically incorrect,
but it certainly can make certain concepts more difficult to understand if
we use language which is imprecise or misleading.

The problem that many people have with using the word "reduce" when we work
with fractions is that it gives the idea we are making the fraction smaller,
when in fact we are keeping it the same.  What is being reduced, in a sense,
is the  values of numerator and denominator to the smallest values which
make an equivalent proportion to the original.  The fear is that when you
tell a student to "reduce 4/8" he/she may somehow come to believe that 1/2
is smaller than 4/8 because it has been "reduced".  I have seen no real
evidence that this is true, but I also see no reason to preserve the
historical use of a term that can be replaced so simply with more
appropriate terms.  "Simplify" seems to be a good, short replacement, and
for test directions or when we wish to be very exact, we might actually say
something like "Express each fraction as an equivalent fraction using the
smallest possible denominator."  I just wouldn't think that would make it in
typical conversation.

It may be that teachers who use "reduce" are doing no real harm, or are only
slightly delaying an understanding of what is happening in the re-expression
of rational fractions, but with the myriad misunderstandings students have
about fractions, their order and size, it would seem worth the effort to
make this minor adjustment in language.

Hope some of this is of benefit.

Good luck.

 -Pat Ballew, for the T2T service

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