Fractions everywhere

23+23++23A copies of 23=45+45++45B copies of 4520A+B24A+B=?\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 A\color{#20A900}{A}\color{#333333} copies of 23\frac23 on the left-hand side of the equality, and B\color{#3D99F6}{B}\color{#333333} copies of 45\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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