A Pumping Lemma for Invalid Reductions of Fractions

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...

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Published inThe College mathematics journal Vol. 41; no. 5; pp. 357 - 364
Main Authors Fried, Michael N., Goldberg, Mayer
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.11.2010
Mathematical Association of America
Subjects
Children
College Mathematics
Computer science
Computer Uses in Education
Educational Technology
Elementary School Mathematics
Fractions
Learning Strategies
Mathematics
Mathematics Education
Numbers
Preservice Teacher Education
Pumping
Teaching Methods
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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.
AbstractList 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.
Audience Higher Education
Elementary Education
Author Fried, Michael N.
Goldberg, Mayer
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References Boas R. P. (CIT0001) 1979
Carman R. A. (CIT0002) 1971; 64
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    fullname: Carman R. A.
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  volume-title: Mathematical Plums
  year: 1979
  ident: CIT0001
  doi: 10.1090/dol/004/06
  contributor:
    fullname: Boas R. P.
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  year: 1966
  ident: CIT0005
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    fullname: Ogilvy C. S.
– volume-title: Introduction to the Theory of Computation
  year: 1996
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Snippet Children often incorrectly reduce fractions by canceling common digits instead of common factors. There are cases, however, in which this incorrect method...
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SubjectTerms Children
College Mathematics
Computer science
Computer Uses in Education
Educational Technology
Elementary School Mathematics
Fractions
Learning Strategies
Mathematics
Mathematics Education
Numbers
Preservice Teacher Education
Pumping
Teaching Methods
Title A Pumping Lemma for Invalid Reductions of Fractions
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