$$\frac{3}{5}\div\frac{17}{6}\times\frac{15}{9}$$
$\frac{6}{17}\approx 0.352941176$
$$\frac{3}{5}\times \frac{6}{17}\times \frac{15}{9}$$
$$\frac{3\times 6}{5\times 17}\times \frac{15}{9}$$
$$\frac{18}{85}\times \frac{15}{9}$$
$$\frac{18}{85}\times \frac{5}{3}$$
$$\frac{18\times 5}{85\times 3}$$
$$\frac{90}{255}$$
$$\frac{6}{17}$$
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$\frac{2 \cdot 3}{17} = 0.35294117647058826$
