What is the formal way to denote a fraction of a fraction?

Question

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.

Answer 1

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.

Answer 2

The "of" can be symbolically replaced by multiplication.

$\dfrac{x}{y} $ of $\dfrac{1}{z} $ , like half of one third is one sixth.