$$\{ ( 18 \div 6 \frac { 2 } { 3 } ) + 6 \frac { 1 } { 6 } \} - 2 \frac { 1 } { 8 }$$
$\frac{809}{120}\approx 6.741666667$
$$\frac{18\times 3}{6\times 3+2}+\frac{6\times 6+1}{6}-\frac{2\times 8+1}{8}$$
$$\frac{54}{6\times 3+2}+\frac{6\times 6+1}{6}-\frac{2\times 8+1}{8}$$
$$\frac{54}{18+2}+\frac{6\times 6+1}{6}-\frac{2\times 8+1}{8}$$
$$\frac{54}{20}+\frac{6\times 6+1}{6}-\frac{2\times 8+1}{8}$$
$$\frac{27}{10}+\frac{6\times 6+1}{6}-\frac{2\times 8+1}{8}$$
$$\frac{27}{10}+\frac{36+1}{6}-\frac{2\times 8+1}{8}$$
$$\frac{27}{10}+\frac{37}{6}-\frac{2\times 8+1}{8}$$
$$\frac{81}{30}+\frac{185}{30}-\frac{2\times 8+1}{8}$$
$$\frac{81+185}{30}-\frac{2\times 8+1}{8}$$
$$\frac{266}{30}-\frac{2\times 8+1}{8}$$
$$\frac{133}{15}-\frac{2\times 8+1}{8}$$
$$\frac{133}{15}-\frac{16+1}{8}$$
$$\frac{133}{15}-\frac{17}{8}$$
$$\frac{1064}{120}-\frac{255}{120}$$
$$\frac{1064-255}{120}$$
$$\frac{809}{120}$$
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$\frac{809}{2 ^ {3} \cdot 3 \cdot 5} = 6\frac{89}{120} = 6.741666666666666$
