$$3\frac{2}{3}\div4\frac{4}{5}=$$
$\frac{55}{72}\approx 0.763888889$
$$\frac{\left(3\times 3+2\right)\times 5}{3\left(4\times 5+4\right)}$$
$$\frac{\left(9+2\right)\times 5}{3\left(4\times 5+4\right)}$$
$$\frac{11\times 5}{3\left(4\times 5+4\right)}$$
$$\frac{55}{3\left(4\times 5+4\right)}$$
$$\frac{55}{3\left(20+4\right)}$$
$$\frac{55}{3\times 24}$$
$$\frac{55}{72}$$
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$\frac{5 \cdot 11}{2 ^ {3} \cdot 3 ^ {2}} = 0.7638888888888888$
