$$5\frac{1}{6}+2\frac{3}{5}$$
$\frac{233}{30}\approx 7.766666667$
$$\frac{30+1}{6}+\frac{2\times 5+3}{5}$$
$$\frac{31}{6}+\frac{2\times 5+3}{5}$$
$$\frac{31}{6}+\frac{10+3}{5}$$
$$\frac{31}{6}+\frac{13}{5}$$
$$\frac{155}{30}+\frac{78}{30}$$
$$\frac{155+78}{30}$$
$$\frac{233}{30}$$
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$\frac{233}{2 \cdot 3 \cdot 5} = 7\frac{23}{30} = 7.766666666666667$
