$$- 3 \frac { 9 } { 24 } \div [ 4 \frac { 3 } { 8 } \times \{ \frac { 1 } { 2 } + ( 5 \frac { 1 } { 2 } - 6 \frac { 1 } { 2 } ) \} ]$$
$\frac{54}{35}\approx 1.542857143$
$$\frac{-\frac{72+9}{24}}{\frac{4\times 8+3}{8}\left(\frac{1}{2}+\frac{5\times 2+1}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{81}{24}}{\frac{4\times 8+3}{8}\left(\frac{1}{2}+\frac{5\times 2+1}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{4\times 8+3}{8}\left(\frac{1}{2}+\frac{5\times 2+1}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{32+3}{8}\left(\frac{1}{2}+\frac{5\times 2+1}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(\frac{1}{2}+\frac{5\times 2+1}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(\frac{1}{2}+\frac{10+1}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(\frac{1}{2}+\frac{11}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(\frac{1+11}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(\frac{12}{2}-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(6-\frac{6\times 2+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(6-\frac{12+1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(6-\frac{13}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(\frac{12}{2}-\frac{13}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\times \frac{12-13}{2}}$$
$$\frac{-\frac{27}{8}}{\frac{35}{8}\left(-\frac{1}{2}\right)}$$
$$\frac{-\frac{27}{8}}{\frac{35\left(-1\right)}{8\times 2}}$$
$$\frac{-\frac{27}{8}}{\frac{-35}{16}}$$
$$\frac{-\frac{27}{8}}{-\frac{35}{16}}$$
$$-\frac{27}{8}\left(-\frac{16}{35}\right)$$
$$\frac{-27\left(-16\right)}{8\times 35}$$
$$\frac{432}{280}$$
$$\frac{54}{35}$$
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$\frac{2 \cdot 3 ^ {3}}{5 \cdot 7} = 1\frac{19}{35} = 1.542857142857143$
