# When $\LaTeX$-ifying, please use stacked fractions

When editing the contents of a question to "$\LaTeX$-ify" it, especially if the question is of a pre-college (or non-math-major) level, please consider using stacked fractions ($\frac{a}{b}$ $\implies$ $\frac{a}{b}$, as opposed to the "slash" fraction $a/b$ $\implies$ $a/b$). Issues of recognizing slash fractions as fractions and issues of grouping often lead to extra difficulty for students in interpreting what they are reading. I think it's fair to assume that, for most questions at the level I'm describing, the text was entered with slash fractions only for lack of knowledge of a way to use stacked fractions.

• The problem with non-displaymode stacked fractions is that they often end up using fonts too small to be legible. For example, your stacked fraction above is barely legible to me even on my 30" 2560x1600 monitor. This leaves no room for further font size reductions, e.g. subscripts or exponents on the fraction would be illegible. Contrast this to the non-stacked version, which uses much larger fonts. – Bill Dubuque Feb 9 '11 at 23:58
• @Bill: While that's true, if you're doing the $\LaTeX$-ifying, you can make them display-style if sizing is an issue. Also, browser-based page-zoom is pretty ubiquitous nowadays. – Isaac Feb 10 '11 at 0:45
• @Isaac: Magnifying glasses were ubiquitous before computers, but books were not typeset so to require their use. – Bill Dubuque Feb 10 '11 at 1:18
• @Bill: "Require" is quite subjective—I find the stacked fraction $\frac{a}{b}$ quite readable on a 12" 1400x1050 display and I know people who would find it unreadably small on a 65" 1080p TV. – Isaac Feb 10 '11 at 1:23
• Yes, obviously it depends on many factors, visual acuity, distance from the screen, default fonts, etc. I too can read the stacked fraction - but not as easily as the slashed one. But very few people would be able to easily read subscripts on such. So one needs to exercise caution before unconditionally applying your suggestion. I too prefer stacked fractions in certain contexts where they better reflect structure (e.g. cancellations). But I am usually careful to make sure they are legible when I employ them. – Bill Dubuque Feb 10 '11 at 3:05
• @All: I for one have several times changed in-line equations to displayed equations precisely because the in-line display seemed too small. (And: @Bill: some books are typeset to require the use of magnifying glasses; amazon.com/… – Arturo Magidin Feb 10 '11 at 5:29
• I think MathJax supports \dfrac, let me try: $\dfrac{a}{b}$. Yep. @Bill: would you be happier if the suggestion above is changed to use \dfrac instead of \frac? – Willie Wong Feb 10 '11 at 12:25
• @Arturo: To be fair, the compact OED includes a magnifying glass and isn't exactly typeset that way (it's the typeset plates of the full OED reduced to fit like 9 to a page). :) – Isaac Feb 10 '11 at 16:37
• @willie: I think it would be wise to expand Isaac's suggestions into general advice on how to choose among the various ways to typeset fractions. The reason mentioned by Isaac is just one of many that may factor into the decision making process. I'd be happy to do this were it not for the fact that I'm sure there are others here who have much more (recent) experience than I with $\LaTeX$ and MathJax. So I defer to them, – Bill Dubuque Feb 10 '11 at 18:01
• For simple things, I find non $LaTeX$ slash fractions acceptable, easier to type, and faster to display. For example, if you are saying " the sum should run up to n/2 because" before you actually display the sum. But generally I like the stacked ones. There are may kinds of $LaTeX$ that cause me to hit Ctrl+ to zoom in, not just fractions. – Ross Millikan Feb 12 '11 at 0:59
• FWIW I'm in the slash-fraction camp. That way I get a reasonable size font without the IMHO very disturbing change in line spacing. As an alternative I would consider using the exponent $-1$. That has the benefit of working also when the product is non-commutative. – Jyrki Lahtonen Apr 7 '12 at 6:41
• @JyrkiLahtonen: I can understand making that decision based on size and spacing when it does not affect the readability or interpretability of the question, but it has been my experience that—specifically at a pre-calculus or non-math-major level—using slash fractions is very likely to lead to misreading or misinterpretation. – Isaac Apr 7 '12 at 18:04

I usually prefer $a^{b/c}$ to $a^\frac{b}{c}$. But I am also acutely aware of undergraduates of the sort who take math courses only because they are required confusing $a/b+c$ with $a/(b+c)$, etc. In some contexts I avoid those for that reason. But recently in a comment I referred to $1/2+1/3+1/5+1/7+1/11+\cdots$, expecting that to be understood as the sum of the reciprocals of the primes, and I don't worry about that because the sort of person who would have been reading it would not be confused by such things.

In $\LaTeX$ one has \dfrac, which looks like this: $\dfrac 23$ and \frac, which looks like this: $\frac23$ in an "inline" setting, but identical to \dfrac in a "displayed" setting, except that with fractions within fractions, it looks like this: $$\frac{\frac12 + 3}{4 + \frac56}.$$ One can use \dfrac in fractions-within-fractions, and get this: $$\frac{\dfrac12 + 3}{4 + \dfrac56}.$$ One also has \cfrac, which looks like this $$1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1}}}}$$

I think common sense is a better approach than rigid guidelines. Clearly $\dfrac{a}{b}$ is clearer (and looks nicer!) than $a/b$ in many situations and should be used when reasonable, but I'd much rather read $$\sum_{j=1}^n e^{2\pi i j/n} = 0$$ than $$\sum_{j=1}^n e^\frac{2\pi i j}{n} = 0$$ or $$\sum_{j=1}^n \exp\left(\frac{2\pi i j}{n}\right) = 0.$$

• Actually, if I could pick, I like the third one myself... – J. M. isn't a mathematician Oct 21 '11 at 11:54
• It does have the advantage of being a nice and big, but I think $e^x$ is much more common notation that $\exp(x)$ especially pre-college. – user7530 Oct 21 '11 at 14:18
• Yeah, and that presents some pedagogical problems, in that students tend to forget that it has to be established that $\exp$ is indeed an exponential function (depending on the definition of course) and they just can't do things like $\exp(x+y)=\exp(x)\exp(y)$ willy-nilly. – J. M. isn't a mathematician Oct 21 '11 at 14:41

One thing I find helpful is to use the \displaystyle command. This fixes problems with the size of the fonts in \frac, and also rendering of integral and summation signs. For example $\frac{a}{b}$ was typeset without this command but $\displaystyle\frac{a}{b}$ was typeset with this command. Compare also $\int_a^b$ and $\displaystyle \int_a^b$.

• Well, \dfrac doesn't need \displaystyle, so if only fractions appear in the post, you can get away with not using \displaystyle... – J. M. isn't a mathematician Oct 20 '11 at 22:09
• Agreed.$\hspace{1em}$ – Cheerful Parsnip Oct 20 '11 at 23:20

I disagree with using this as a general recommendation.

It is especially strange to argue that students will not understand it when we are talking about editing the question.