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Q&A #12679


Language - "reduce" fractions

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Jul 24, 2005 at 15:27:29
Subject: Re: Language - "reduce" fractions

Over the last year since this question was asked (and answered) I have
researched the background of our use of reduce or reduction in mathematics.
I think this might help lots of teachers who can't imagine how such a
potentially confusing term ever came about....

From Reduction of Fractions at:
http://www.pballew.net/arithme1.html#reduce


Many modern elementary teachers get upset by the use of the term "reduce a
fraction". I think this is mostly because they are not familiar with the
origin of the term and only understand the word "reduce" to mean "make
smaller", which is certainly one of the most common definitions of the word
in modern dictionaries. I hope the the following will make them more
understanding of those of us who are VERY old, and still remember when the
term had a broader meaning. Reduction is defined in Milne's Progressive
Arithmetic (1906, William J Milne) thusly, "The process of changing the form
of any number without changing its value is called reduction." An almost
identiacl definition appears in Davies and Peck's Complete Arithmetic,
Theoretical and Practical(page 84, art. 66). Both books include reduction of
fractions to higher terms as well as lower terms, and reduction of "decimals
to common fractions". By 1964, however, The Universal Encyclopedia of
Mathematics by Simon and Schuster contains "A fraction is reduced, or
cancelled, by dividing numerator and denominator by the same number." (pg
364) Later on the same page they note, "a fraction cannot be reduced if
numerator and denominator are mutually prime" indicating that when they
said "the same number" in the first statement, they meant a positive
integer. This definition leads to "reduction" of fractions as making the
numerator and denominator both smaller.

The roots of the word reduce are from the Latin re for back or again, and
dicere which means "to lead". The latter root is also found in the word
educare which is literally, to lead out, and is the source of our modern
English word, educate.

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Hope that is some help in clearing up the mystery.


 -Pat Ballew, for the T2T service

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