$$(3\frac{4}{7}+2\frac{2}{3})\div11\frac{10}{11}$$
$\frac{11}{21}\approx 0.523809524$
$$\frac{\frac{21+4}{7}+\frac{2\times 3+2}{3}}{\frac{11\times 11+10}{11}}$$
$$\frac{\frac{25}{7}+\frac{2\times 3+2}{3}}{\frac{11\times 11+10}{11}}$$
$$\frac{\frac{25}{7}+\frac{6+2}{3}}{\frac{11\times 11+10}{11}}$$
$$\frac{\frac{25}{7}+\frac{8}{3}}{\frac{11\times 11+10}{11}}$$
$$\frac{\frac{75}{21}+\frac{56}{21}}{\frac{11\times 11+10}{11}}$$
$$\frac{\frac{75+56}{21}}{\frac{11\times 11+10}{11}}$$
$$\frac{\frac{131}{21}}{\frac{11\times 11+10}{11}}$$
$$\frac{\frac{131}{21}}{\frac{121+10}{11}}$$
$$\frac{\frac{131}{21}}{\frac{131}{11}}$$
$$\frac{131}{21}\times \frac{11}{131}$$
$$\frac{131\times 11}{21\times 131}$$
$$\frac{11}{21}$$
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$\frac{11}{3 \cdot 7} = 0.5238095238095238$
