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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