$$(\frac{7}{9}\times2\frac{1}{13})\div(1\frac{2}{13}+1\frac{2}{3})$$
$\frac{63}{110}\approx 0.572727273$
$$\frac{\frac{7}{9}\times \frac{26+1}{13}}{\frac{1\times 13+2}{13}+\frac{1\times 3+2}{3}}$$
$$\frac{\frac{7}{9}\times \frac{27}{13}}{\frac{1\times 13+2}{13}+\frac{1\times 3+2}{3}}$$
$$\frac{\frac{7\times 27}{9\times 13}}{\frac{1\times 13+2}{13}+\frac{1\times 3+2}{3}}$$
$$\frac{\frac{189}{117}}{\frac{1\times 13+2}{13}+\frac{1\times 3+2}{3}}$$
$$\frac{\frac{21}{13}}{\frac{1\times 13+2}{13}+\frac{1\times 3+2}{3}}$$
$$\frac{\frac{21}{13}}{\frac{13+2}{13}+\frac{1\times 3+2}{3}}$$
$$\frac{\frac{21}{13}}{\frac{15}{13}+\frac{1\times 3+2}{3}}$$
$$\frac{\frac{21}{13}}{\frac{15}{13}+\frac{3+2}{3}}$$
$$\frac{\frac{21}{13}}{\frac{15}{13}+\frac{5}{3}}$$
$$\frac{\frac{21}{13}}{\frac{45}{39}+\frac{65}{39}}$$
$$\frac{\frac{21}{13}}{\frac{45+65}{39}}$$
$$\frac{\frac{21}{13}}{\frac{110}{39}}$$
$$\frac{21}{13}\times \frac{39}{110}$$
$$\frac{21\times 39}{13\times 110}$$
$$\frac{819}{1430}$$
$$\frac{63}{110}$$
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$\frac{3 ^ {2} \cdot 7}{2 \cdot 5 \cdot 11} = 0.5727272727272728$
