$$3\frac{1}{6}+4\frac{3}{6}=$$
$\frac{23}{3}\approx 7.666666667$
$$\frac{18+1}{6}+\frac{4\times 6+3}{6}$$
$$\frac{19}{6}+\frac{4\times 6+3}{6}$$
$$\frac{19}{6}+\frac{24+3}{6}$$
$$\frac{19}{6}+\frac{27}{6}$$
$$\frac{19+27}{6}$$
$$\frac{46}{6}$$
$$\frac{23}{3}$$
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$\frac{23}{3} = 7\frac{2}{3} = 7.666666666666667$
