Ordinals and Denominators

At the moment, what is fascinating about the book are the little interesting nuggets.

And, at the risk of being exposed to a collective raising of readers' eyebrows at its obviousness, I present below one of those nuggets—about fractions—that I came across tonight.

Every third lot wins, every fifth man is Chinese. It seems that this is the origin of the ordinal numbers as a means to indicate denominators of fractions: Counting 1, 2, 3, . . . , 10 to count out the tenth; all these "tenth" people or objects together form a (one, the) tenth of the whole. Thus the tenth part is in fact the last of all of them. In an obsolete terminology nine parts means 9/10, the remainder that is left if the tenth is counted out. "Decimate" originally meant counting out the tenth (to be shot).

At this point in his writing about fractions, Freudenthal is not making teaching suggestions (thankfully, given that last sentence), but simply conducting a survey—a thorough survey, it seems—of the different ways fractions (have) come up in informal contexts. Still, the paragraph above brings up an interesting (to me) perspective and mathematical connection that may be didactically useful.

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