$$2\frac{2}{3}+(2\frac{3}{8}+1\frac{5}{6})$$
$\frac{55}{8}=6.875$
$$\frac{6+2}{3}+\frac{2\times 8+3}{8}+\frac{1\times 6+5}{6}$$
$$\frac{8}{3}+\frac{2\times 8+3}{8}+\frac{1\times 6+5}{6}$$
$$\frac{8}{3}+\frac{16+3}{8}+\frac{1\times 6+5}{6}$$
$$\frac{8}{3}+\frac{19}{8}+\frac{1\times 6+5}{6}$$
$$\frac{64}{24}+\frac{57}{24}+\frac{1\times 6+5}{6}$$
$$\frac{64+57}{24}+\frac{1\times 6+5}{6}$$
$$\frac{121}{24}+\frac{1\times 6+5}{6}$$
$$\frac{121}{24}+\frac{6+5}{6}$$
$$\frac{121}{24}+\frac{11}{6}$$
$$\frac{121}{24}+\frac{44}{24}$$
$$\frac{121+44}{24}$$
$$\frac{165}{24}$$
$$\frac{55}{8}$$
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$\frac{5 \cdot 11}{2 ^ {3}} = 6\frac{7}{8} = 6.875$
