Associated Topics || Dr. Math Home || Search Dr. Math

### 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/
```
Associated Topics:
Elementary Fractions
Middle School Fractions

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search