<s>[INST] Mixed Fractions and Multiplication (with Variables) I stumbled over this expression: $3 \frac{1}{x^3}$.
How should you interpret something like that?
While you could see that as implicitit multiplication ($3 * \frac{1}{x^3}$),
you could also argue that $3 \frac{1}{x^3}$ is a mixed fraction ($3 + \frac{1}{x^3}$).
I think in situations with only numbers or only variables everything should be clear:
$3 \frac{1}{2} = 3 + \frac{1}{2} = 3.5$
$a \frac{b}{c} = a * \frac{b}{c}$
This should also be true: $3 \frac{b}{c} = 3 * \frac{b}{c}$.
But what do our conventions say to something like $3 \frac{1}{x^3}$ or $6 \frac{x}{3}$ or $\frac{1}{x^2}5$? Is there any written standard that you should generally follow? Multiplication or addition?
 [/INST] This can be written as $$\frac{3}{1}\cdot \frac{1}{x^3}=\frac{3\cdot 1}{1\cdot x^3}=\frac{3}{x^3}$$
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