Q From Andrew Purkiss: Some fractions were, maybe still are, called vulgar fractions. I cannot think there is anything rude about putting a numerator over a denominator, so why vulgar?
A This bothered me at school and I can’t recall having been given a good answer at the time. The problem lies in the changing meaning of vulgar. It comes from the Latin adjective vulgaris that derives from vulgus, the common people. This is also the origin of Vulgate, the Latin version of the Bible, which comes from the closely related vulgata, meaning “for the public” (it was so, when it was written, in the fourth century AD).
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.
Confusingly, I have come across definitions in which the term vulgar fraction is reserved for an improper fraction; I was taught exactly the reverse at school — that a vulgar fraction had a smaller number on top than below. But the definitions above are the ones in common use and which are in the major dictionaries.
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”.
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