$$\frac{3}{5}\times1\frac{1}{9}+3\frac{1}{2}$$
$\frac{25}{6}\approx 4.166666667$
$$\frac{3}{5}\times \frac{9+1}{9}+\frac{3\times 2+1}{2}$$
$$\frac{3}{5}\times \frac{10}{9}+\frac{3\times 2+1}{2}$$
$$\frac{3\times 10}{5\times 9}+\frac{3\times 2+1}{2}$$
$$\frac{30}{45}+\frac{3\times 2+1}{2}$$
$$\frac{2}{3}+\frac{3\times 2+1}{2}$$
$$\frac{2}{3}+\frac{6+1}{2}$$
$$\frac{2}{3}+\frac{7}{2}$$
$$\frac{4}{6}+\frac{21}{6}$$
$$\frac{4+21}{6}$$
$$\frac{25}{6}$$
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$\frac{5 ^ {2}}{2 \cdot 3} = 4\frac{1}{6} = 4.166666666666667$
