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The Ups and Downs of Percent (and Some Interesting Connections)
Author(s) -
Parker Melanie
Publication year - 1997
Publication title -
school science and mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.135
H-Index - 2
eISSN - 1949-8594
pISSN - 0036-6803
DOI - 10.1111/j.1949-8594.1997.tb17385.x
Subject(s) - harmonic mean , representation (politics) , simple (philosophy) , curriculum , mathematics , function (biology) , connection (principal bundle) , geometric mean , arithmetic , mathematics education , statistics , pure mathematics , psychology , epistemology , geometry , philosophy , pedagogy , evolutionary biology , politics , political science , law , biology
Percent is a standardized ratio comparison that is often used to describe relative amounts of increase and decrease. In this paper, the nonsymmetric relationship between percent of increase and percent of decrease is explored in several ways. Beginning with a simple graphical representation of the relationship, the functional relationship is developed, with relative decrease expressed as a function of relative increase. Once expressed in the form f(x) = 100x/(100 + x), an immediate connection is made to two other topics commonly found within the study of rates—the work problem and the harmonic mean. Finally, successive percents of increase or decrease are shown to be everyday applications of the geometric mean. This deeper look at a common mathematical concept has uncovered rich structural relationships between topics that are often isolated in the curriculum.