A pumping lemma for invalid reductions of fractions

Michael N. Fried; Mayer Goldberg

doi:10.4169/074683410X521955

A pumping lemma for invalid reductions of fractions

Michael N. Fried, Mayer Goldberg

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	357-364
Number of pages	8
Journal	College Mathematics Journal
Volume	41
Issue number	5
DOIs	https://doi.org/10.4169/074683410X521955
State	Published - 1 Nov 2010

ASJC Scopus subject areas

General Mathematics
Education

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10.4169/074683410X521955

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title = "A pumping lemma for invalid reductions of fractions",

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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AB - 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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JO - College Mathematics Journal

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A pumping lemma for invalid reductions of fractions

Abstract

ASJC Scopus subject areas

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