B How do you multiply fractions again? My brain just froze šŸ˜…

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I was helping my younger sibling with homework and totally blanked—how exactly do you multiply fractions again? I feel like I knew this once upon a time but it's just… gone. 😭
 
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##\dfrac{a}{b}\cdot \dfrac{c}{d}=\dfrac{a\cdot c}{b\cdot d}.##
 
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For the record:

##\dfrac{a}{b} \, : \,\dfrac{c}{d}=\dfrac{a\cdot d}{b\cdot c}##

##\dfrac{a}{b}+ \dfrac{c}{d}=\dfrac{a\cdot d+b\cdot c}{b\cdot d}##

##\dfrac{a}{b}- \dfrac{c}{d}=\dfrac{a\cdot d-b\cdot c}{b\cdot d}##
 
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I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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