Numerator, Denominator: Etymologies

Date: 03/25/2002 at 20:01:02
From: Faith Baker
Subject: Numerators and denominators

Why are the parts of a fraction called the numerator and the 
denominator?  

Thanks for the help!

Date: 03/26/2002 at 02:51:14
From: Doctor Sarah
Subject: Re: Numerators and denominators

Hi Faith - thanks for writing to Dr. Math.

In a fraction, the numerator tells you the number of things you have, 
and the denominator tells you the kind of thing you're dealing with.

From Steven Schwartzman's _The Words of Mathematics_:

numerator
   the first element is from Latin numeratus, past participle, or 
numerare "to number." The more basic word is the Latin masculine noun 
numerus "number"... A numerator is literally "a numberer." In 
arithmetic, the numerator of a fraction gives the number of parts 
being considered, where each part is an equal fraction of the whole. 
Since the numerator tells you how many parts you have, when you add 
fractions you add only numerators, never denominators...

denominator
   from Latin de and nomen, "name," cognate to the English word with 
the same meaning... In arithmetic the denominator of a fraction names 
the kind of thing you're dealing with. In the fraction 3/5, for 
example, you have three fifths, just the way you could have three 
sheep or three apples or three of any other thing... Since the 
denominator names the sort of a thing you're dealing with, you must 
have a common denominator when you add fractions; otherwise it's like 
trying to add sheep and apples...

- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/