$$2\frac{1}{6}+\frac{5}{12}=$$
$\frac{31}{12}\approx 2.583333333$
$$\frac{12+1}{6}+\frac{5}{12}$$
$$\frac{13}{6}+\frac{5}{12}$$
$$\frac{26}{12}+\frac{5}{12}$$
$$\frac{26+5}{12}$$
$$\frac{31}{12}$$
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$\frac{31}{2 ^ {2} \cdot 3} = 2\frac{7}{12} = 2.5833333333333335$