$$5 \frac { 5 } { 6 } \times \frac { 4 } { 5 } \div ( 1 \frac { 2 } { 9 } + \frac { 5 } { 3 } )$$
$\frac{21}{13}\approx 1.615384615$
$$\frac{\frac{30+5}{6}\times \frac{4}{5}}{\frac{1\times 9+2}{9}+\frac{5}{3}}$$
$$\frac{\frac{35}{6}\times \frac{4}{5}}{\frac{1\times 9+2}{9}+\frac{5}{3}}$$
$$\frac{\frac{35\times 4}{6\times 5}}{\frac{1\times 9+2}{9}+\frac{5}{3}}$$
$$\frac{\frac{140}{30}}{\frac{1\times 9+2}{9}+\frac{5}{3}}$$
$$\frac{\frac{14}{3}}{\frac{1\times 9+2}{9}+\frac{5}{3}}$$
$$\frac{\frac{14}{3}}{\frac{9+2}{9}+\frac{5}{3}}$$
$$\frac{\frac{14}{3}}{\frac{11}{9}+\frac{5}{3}}$$
$$\frac{\frac{14}{3}}{\frac{11}{9}+\frac{15}{9}}$$
$$\frac{\frac{14}{3}}{\frac{11+15}{9}}$$
$$\frac{\frac{14}{3}}{\frac{26}{9}}$$
$$\frac{14}{3}\times \frac{9}{26}$$
$$\frac{14\times 9}{3\times 26}$$
$$\frac{126}{78}$$
$$\frac{21}{13}$$
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$\frac{3 \cdot 7}{13} = 1\frac{8}{13} = 1.6153846153846154$