I need to write a paper and it's not clear which is correct: $\frac{x/y}{z}$ or $\frac{\frac{x}{y}}{z}$, or possibly some other alternative.
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3Usually the 2nd one is used, to my knowledge. – Colbi Jun 13 '16 at 00:19
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4Whichever is more readable in context. If the expression is in-line, $\frac{x/y}z$ is almost certainly preferable, and this may well also be tha case if it’s part of a more compicated displayed expression. If it’s a displayed expression by itself, the choice is up to you; for me it would depend on the audience and on what I was saying about the expression, but ceteris paribus I’d tend to prefer the first version. I do not agree with @Colbi. – Brian M. Scott Jun 13 '16 at 00:22
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Perhaps one could also say something like $\dfrac{5}{6}\div \dfrac{6}{5}$ – Colbi Jun 13 '16 at 00:32
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1Why not $\frac{1}{z}\frac{x}{y}$? – Neal Jun 13 '16 at 00:56
2 Answers
The "of" can be symbolically replaced by multiplication.
$\dfrac{x}{y} $ of $\dfrac{1}{z} $ , like half of one third is one sixth.
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3Definitely not, except possibly in a discussion of how to teach fractional arithmetic to elementary school students. – Brian M. Scott Jun 13 '16 at 00:27
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Both are 'correct', at least in the sense that nobody will argue that either is somehow 'mathematically wrong'.
However, the latter, $\frac{x/y}{z}$, definitely looks a lot nicer in most circumstances, especially if you're typesetting it in-line like I just did.
If you don't typeset it in-line, then you can perhaps play around. To me, $$\frac{\frac{x}{y}}{z}$$ is not too bad, particularly if the numerator is long and involves more than one term, like $$\frac{g(x)+\frac{f(x+h)-f(x)}{h}}{h}.$$ But you can also play around: you can use \dfrac in the numerator: \frac{g(x)+\dfrac{f(x+h)-f(x)}{h}}{h}, which gives
$$\frac{g(x)+\dfrac{f(x+h)-f(x)}{h}}{h}.$$
The result may be more readable. However, \frac{\dfrac{x}{y}}{z} produces
$$\frac{\dfrac{x}{y}}{z}$$ which certainly looks horrible.
The point stands: use what looks best. Of your two choices, $\frac{x/y}{z}$ is the answer.
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Footnote: this reminds me of a funny story about Barry Mazur annoying Serge Lang. See this MathOverflow post for details. – Will R Jun 13 '16 at 01:34