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.
$\begingroup$
$\endgroup$
12
4 Answers
$\begingroup$
$\endgroup$
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 $$ 1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1}}}} $$
$\begingroup$
$\endgroup$
4
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 $$\sum_{j=1}^n \exp\left(\frac{2\pi i j}{n}\right) = 0.$$
-
5$\begingroup$ Actually, if I could pick, I like the third one myself... $\endgroup$ Commented Oct 21, 2011 at 11:54
-
$\begingroup$ 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. $\endgroup$– user7530Commented Oct 21, 2011 at 14:18
-
$\begingroup$ 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. $\endgroup$ Commented Oct 21, 2011 at 14:41
-
$\begingroup$ Note that the third option would probably look better if the size of the brackets of the exponential were set manually, to be either exactly large enough or ever so slightly too small (and the others with \textnormal{e} in place of e). $\endgroup$ Commented Feb 10, 2023 at 23:25
$\begingroup$
$\endgroup$
2
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 $\displaystyle \int_a^b$.
answered Oct 20, 2011 at 19:32
-
$\begingroup$ Well,
\dfracdoesn't need\displaystyle, so if only fractions appear in the post, you can get away with not using\displaystyle... $\endgroup$ Commented Oct 20, 2011 at 22:09 -
$\begingroup$
$\endgroup$
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.
\dfrac, let me try: $\dfrac{a}{b}$. Yep. @Bill: would you be happier if the suggestion above is changed to use\dfracinstead of\frac? $\endgroup$