$$(\frac{5}{9}-1\frac{1}{6}\cdot\frac{1}{2}):\frac{5}{9}+\frac{17}{60}$$
$\frac{7}{30}\approx 0.233333333$
$$\frac{\frac{5}{9}-\frac{6+1}{6}\times \frac{1}{2}}{\frac{5}{9}}+\frac{17}{60}$$
$$\frac{\frac{5}{9}-\frac{7}{6}\times \frac{1}{2}}{\frac{5}{9}}+\frac{17}{60}$$
$$\frac{\frac{5}{9}-\frac{7\times 1}{6\times 2}}{\frac{5}{9}}+\frac{17}{60}$$
$$\frac{\frac{5}{9}-\frac{7}{12}}{\frac{5}{9}}+\frac{17}{60}$$
$$\frac{\frac{20}{36}-\frac{21}{36}}{\frac{5}{9}}+\frac{17}{60}$$
$$\frac{\frac{20-21}{36}}{\frac{5}{9}}+\frac{17}{60}$$
$$\frac{-\frac{1}{36}}{\frac{5}{9}}+\frac{17}{60}$$
$$-\frac{1}{36}\times \frac{9}{5}+\frac{17}{60}$$
$$\frac{-9}{36\times 5}+\frac{17}{60}$$
$$\frac{-9}{180}+\frac{17}{60}$$
$$-\frac{1}{20}+\frac{17}{60}$$
$$-\frac{3}{60}+\frac{17}{60}$$
$$\frac{-3+17}{60}$$
$$\frac{14}{60}$$
$$\frac{7}{30}$$
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$\frac{7}{2 \cdot 3 \cdot 5} = 0.23333333333333334$
