Comments on Intuitively, what does the 1 mean in $\dfrac{a}{b} = \dfrac{1}{\frac{b}{a}}$?
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Intuitively, what does the 1 mean in $\dfrac{a}{b} = \dfrac{1}{\frac{b}{a}}$?
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For intuition, I instantiate variables with fruits: $a$ as apple and $b$ as berry (pick whatever berry you like).
In terms of apples and/or berries, what does the red $\color{red}{1}$ below mean? What's the unit of $\color{red}{1}$?
$\dfrac{a}{b} \quad = \quad\dfrac{\color{red}{1}}{\dfrac{b}{a}}$.
Unmistakably, I know $\dfrac{a}{b}$ means $\dfrac{\text{apple}}{\text{1 berry}}$, and $b/a$ means $\dfrac{\text{berry}}{\text{1 apple}}$.
I ask only for intuition. Please pretermit formal arguments and proofs. E.g. please don't rely on rationalizing the denominator .
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