$$1\frac{1}{2}+3\frac{5}{8}-3\frac{7}{12}+3\frac{2}{9}$$
$\frac{343}{72}\approx 4.763888889$
$$\frac{2+1}{2}+\frac{3\times 8+5}{8}-\frac{3\times 12+7}{12}+\frac{3\times 9+2}{9}$$
$$\frac{3}{2}+\frac{3\times 8+5}{8}-\frac{3\times 12+7}{12}+\frac{3\times 9+2}{9}$$
$$\frac{3}{2}+\frac{24+5}{8}-\frac{3\times 12+7}{12}+\frac{3\times 9+2}{9}$$
$$\frac{3}{2}+\frac{29}{8}-\frac{3\times 12+7}{12}+\frac{3\times 9+2}{9}$$
$$\frac{12}{8}+\frac{29}{8}-\frac{3\times 12+7}{12}+\frac{3\times 9+2}{9}$$
$$\frac{12+29}{8}-\frac{3\times 12+7}{12}+\frac{3\times 9+2}{9}$$
$$\frac{41}{8}-\frac{3\times 12+7}{12}+\frac{3\times 9+2}{9}$$
$$\frac{41}{8}-\frac{36+7}{12}+\frac{3\times 9+2}{9}$$
$$\frac{41}{8}-\frac{43}{12}+\frac{3\times 9+2}{9}$$
$$\frac{123}{24}-\frac{86}{24}+\frac{3\times 9+2}{9}$$
$$\frac{123-86}{24}+\frac{3\times 9+2}{9}$$
$$\frac{37}{24}+\frac{3\times 9+2}{9}$$
$$\frac{37}{24}+\frac{27+2}{9}$$
$$\frac{37}{24}+\frac{29}{9}$$
$$\frac{111}{72}+\frac{232}{72}$$
$$\frac{111+232}{72}$$
$$\frac{343}{72}$$
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$\frac{7 ^ {3}}{2 ^ {3} \cdot 3 ^ {2}} = 4\frac{55}{72} = 4.763888888888889$