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. --------- Hope that is some help in clearing up the mystery. -Pat Ballew, for the T2T service

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