Putting Fractions in Their Place

Author: Leslie Blackwell Galen

Journal: The American Mathematical Monthly

Volume 111, Number 3, Pages 238—242

Date: March, 2004

Abstract

Mathematicians need fractions, certainly more than fractions need mathematicians. Any respectable book on mathematics, from an elementary primer to the most esoteric monograph, is loaded with fractions carrying out their manual labor of division. But as all these books show plainly, it is not enough to merely think a fraction; the fraction must be enunciated—that is, put on paper—for it to be of any use.

Here we will try to make it easier to understand the fraction, not as a mathematical word, so to speak, but as a typographical entity with many faces and many means of expression. In doing so we hope to help a few authors, whose manuscripts come back bleeding from the copyeditor; a few students, who wonder fleetingly why the same (is it the same?) fraction looks so different from place to place; and a few editors, who gamely fight the good fight to achieve four goals. The first is clarity, that is, clear communication from author to reader. The second is legibility, which entails setting the type so that the myopic reader can read without squinting. The third goal is consistency: every category of fraction should set the same way throughout. The fourth goal is conservation of space.

Though not as important as the first three goals, this last item bears examining. We must swallow our pride and admit that, although worthy, useful, and fascinating, mathematics (especially higher mathematics) is not very popular with the masses. No calculus textbook is likely ever to make the New York Times best-seller list, nor will this MONTHLY sell as many copies as People. The conclusion we must reach, then, is that mathematics is not terribly profitable, either for those who engage in it or for those who publish it. In order to publish as much as can be done under the circumstances, publishers use many methods to conserve: paper, labor, keystrokes, money. The proper use of fractions can be one small weapon in the battle to keep costs down, while not compromising quality.