$$2\frac{1}{2}+\frac{2}{3}$$
$\frac{19}{6}\approx 3.166666667$
$$\frac{4+1}{2}+\frac{2}{3}$$
$$\frac{5}{2}+\frac{2}{3}$$
$$\frac{15}{6}+\frac{4}{6}$$
$$\frac{15+4}{6}$$
$$\frac{19}{6}$$
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$\frac{19}{2 \cdot 3} = 3\frac{1}{6} = 3.1666666666666665$