$\begin{aligned} \underbrace{\dfrac23 + \dfrac23 + \cdots + \dfrac23}_{\color{#20A900}{A}\color{#333333} \text{ copies of } \frac23} &= \underbrace{\dfrac45 + \dfrac45 + \cdots + \dfrac45}_{\color{#3D99F6}{B}\color{#333333} \text{ copies of } \frac45} \\\\\\ 20 \leq \color{#20A900}{A}\color{#333333}+\color{#3D99F6}{B}\color{#333333} &\leq 24\\\\ \color{#20A900}{A}\color{#333333}+\color{#3D99F6}{B}\color{#333333} &=\, ? \end{aligned}$

I have $\color{#20A900}{A}\color{#333333}$ copies of $\frac23$ on the left-hand side of the equality, and $\color{#3D99F6}{B}\color{#333333}$ copies of $\frac45$ on the right. In total, I've written down between 20 and 24 fractions. Exactly how many fractions are there?

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