$$5\frac{1}{6}+2\frac{2}{3}-4\frac{1}{6}$$
$\frac{11}{3}\approx 3.666666667$
$$\frac{30+1}{6}+\frac{2\times 3+2}{3}-\frac{4\times 6+1}{6}$$
$$\frac{31}{6}+\frac{2\times 3+2}{3}-\frac{4\times 6+1}{6}$$
$$\frac{31}{6}+\frac{6+2}{3}-\frac{4\times 6+1}{6}$$
$$\frac{31}{6}+\frac{8}{3}-\frac{4\times 6+1}{6}$$
$$\frac{31}{6}+\frac{16}{6}-\frac{4\times 6+1}{6}$$
$$\frac{31+16}{6}-\frac{4\times 6+1}{6}$$
$$\frac{47}{6}-\frac{4\times 6+1}{6}$$
$$\frac{47}{6}-\frac{24+1}{6}$$
$$\frac{47}{6}-\frac{25}{6}$$
$$\frac{47-25}{6}$$
$$\frac{22}{6}$$
$$\frac{11}{3}$$
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$\frac{11}{3} = 3\frac{2}{3} = 3.6666666666666665$
