Means and ExtremesDate: 06/20/2001 at 07:38:14 From: Jill Ilyes Subject: Means and extremes in proportions My class is currently learning about proportions, and has asked the question, "Why are certain parts of the proportion called the means and the other parts called the extremes?" Can you assist us in clarifying why these particular terms are used and how they apply to the ratios in a proportion? Thanks, Jill Date: 06/20/2001 at 12:20:06 From: Doctor Peterson Subject: Re: Means and extremes in proportions Hi, Jill. As you know, the "means" are the inside terms, b and c, and the "extremes" are the outside terms, a and d, in the proportion we might write in any of these ways: a : b :: c : d a : b = c : d a/b = c/d a c --- = --- b d Whichever way we write it, except the last, b and c are on the inside, and a and d are on the outside. The word "mean" comes through French from Latin "medius," meaing "middle." (It is used in several ways in math, all related to the middle.) The word "extreme" comes from Latin "extremus," the superlative form of "exterus," meaning "outside"; so it means "outermost." Now it should make sense! - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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