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A Pumping Lemma for Invalid Reductions of Fractions

Michael N. Fried and Mayer Goldberg
The College Mathematics Journal
Vol. 41, No. 5 (November 2010), pp. 357-364
DOI: 10.4169/074683410x521955
Stable URL:
Page Count: 8
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A Pumping Lemma for Invalid Reductions of Fractions
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Abstract Children often incorrectly reduce fractions by canceling common digits instead of common factors. There are cases, however, in which this incorrect method leads to correct results. Instances such as 16/64 and 19/95 are well-known. In this paper, we consider such “weird fractions” and show how examples of them can be multiplied ad infinitum and lead to interesting questions.

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