wut

\(\boxed{\color{red}\dfrac{1}{a}:\dfrac{1}{b}\color{black}=\color{red}b:a}\)

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Here is why

 

\(\begin{align}\frac{1}{7}&:\frac{1}{8}\\~\\ \frac{1}{7}\times \frac{56}{1}&:\frac{1}{8}\times \frac{56}{1}\\~\\ \frac{1}{1}\times \frac{8}{1}&:\frac{1}{1}\times \frac{7}{1}\\~\\ 8&:7 \end{align} \)