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$\begingroup$

For example:

$$ \frac{\ \dfrac{3}{5}\ }{\dfrac{7}{8}} $$

I was wondering if such a situation had a name, wherein both the numerator and the denominator of a fraction consist of fractions themselves. I was also wondering if this was something common, or at least in some way useful.

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    I learned the name "compound fraction" for things like this. One way they appear is when you have a fraction $\frac xy$ and substitute $\frac 35$ for $x$ and $\frac 78$ for $y$ (for reasons elsewhere in the problem). then Joe Johnson 126 has shown the next step.2012-02-21
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    Tutoring middle and high schoolers, I've seen these called "complex fractions," a term that I find confusing.2012-02-21
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    $\frac{\ \dfrac{3}{5}\ }{\dfrac{7}{8}}$ is a bit ambiguous. I would have written $\frac{\left(\dfrac 35\right)}{\left(\dfrac 78 \right)}$2016-05-07

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