$$15\frac{5}{9}\div5\frac{2}{3}$$
$\frac{140}{51}\approx 2.745098039$
$$\frac{\left(15\times 9+5\right)\times 3}{9\left(5\times 3+2\right)}$$
$$\frac{5+9\times 15}{3\left(2+3\times 5\right)}$$
$$\frac{5+135}{3\left(2+3\times 5\right)}$$
$$\frac{140}{3\left(2+3\times 5\right)}$$
$$\frac{140}{3\left(2+15\right)}$$
$$\frac{140}{3\times 17}$$
$$\frac{140}{51}$$
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$\frac{2 ^ {2} \cdot 5 \cdot 7}{3 \cdot 17} = 2\frac{38}{51} = 2.7450980392156863$
