$$5\frac{1}{6}-2\frac{2}{3}$$
$\frac{5}{2}=2.5$
$$\frac{30+1}{6}-\frac{2\times 3+2}{3}$$
$$\frac{31}{6}-\frac{2\times 3+2}{3}$$
$$\frac{31}{6}-\frac{6+2}{3}$$
$$\frac{31}{6}-\frac{8}{3}$$
$$\frac{31}{6}-\frac{16}{6}$$
$$\frac{31-16}{6}$$
$$\frac{15}{6}$$
$$\frac{5}{2}$$
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$\frac{5}{2} = 2\frac{1}{2} = 2.5$