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I am just wondering about the origins of the phrase 'vulgar fraction'. It is synonymous with 'common fraction' & 'simple fraction' and simply refers to any fraction of two integers (e.g.: 2/5).

I assume vulgar is used in the 'lack of sophistication or taste' sense of the word, but don't understand why that applies to fractions.

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    Vulgar comes from Latin vulgus, the same word that gave volk in German and folk in English. – Sam Aug 10 '16 at 12:56
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    @vasile, I'm not so sure about that. According to etymonline, folk and vulgus are from entirely different sources. – Joe Aug 10 '16 at 17:55
  • Note also the Vulgate, a bible translation that was certainly not meant to be "vulgar" in the modern, pejorative, sense of the word. – oerkelens Aug 10 '16 at 18:38
  • @vasile - So, it's the people's fraction? I'm going to start throwing some vulgar elbows around. – BruceWayne Aug 10 '16 at 20:47
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The meaning of vulgar is that of "simple, common" not the original offensive one as suggested by World Wide Words:

  • Over time, vulgar went down in the world. It moved from “in ordinary use”, and “relating to the ordinary people”, to “commonplace”; by the seventeenth century it had begun to assume our modern senses of “lacking sophistication or good taste” and “making explicit and offensive reference to sex or bodily functions”.

........

  • Vulgar turned up first in English in the fourteenth century and then referred to something that was in common or general use or something customary or done as a matter of everyday practice. There was nothing disapproving about it.
  • That old usage survived in a few fixed phrases. A couple that are now archaic are vulgar tongue, the language that was spoken by ordinary people, not one full of expletives; another was vulgar name, the common name of a species, as opposed to its scientific one.
  • A vulgar fraction is one based on ordinary or everyday arithmetic as opposed to these highfalutin decimal things, which were at first called decimal fractions. It refers specifically to one in which two whole numbers (the numerator and denominator) are placed above and below a horizontal line. Neither part can be zero.

  • Americans also know vulgar fractions as common fractions; another term sometimes used is simple fraction. Fractions in which the numerator is bigger than the denominator, making the fraction greater than unity, are called improper fractions, the other sort, of course, being proper.

  • From "vulgus", Latin for "common people". – Max Williams Aug 10 '16 at 10:15
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In the expression "vulgar fraction" the adjective "vulgar" does not have its current meaning of "crude" but rather "popular". Evidence that in European languages the root "vulgar" once meant "widely accessible or popular" is that in French a popularisation of, say, science is still called "vulgarisation".

vulgar, from Your Dictionary

Spoken by or expressed in language spoken by the common people; vernacular: the technical and vulgar names for an animal species

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