$$4\frac{1}{2}+5\frac{2}{3}$$
$\frac{61}{6}\approx 10.166666667$
$$\frac{8+1}{2}+\frac{5\times 3+2}{3}$$
$$\frac{9}{2}+\frac{5\times 3+2}{3}$$
$$\frac{9}{2}+\frac{15+2}{3}$$
$$\frac{9}{2}+\frac{17}{3}$$
$$\frac{27}{6}+\frac{34}{6}$$
$$\frac{27+34}{6}$$
$$\frac{61}{6}$$
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$\frac{61}{2 \cdot 3} = 10\frac{1}{6} = 10.166666666666666$
