$$\frac { 1 } { 2 } - \frac { 1 } { 3 } + \frac { 3 } { 4 } \times \frac { 4 } { 5 } \div \frac { 1 } { 2 } - \frac { 4 } { 5 }$$
$\frac{17}{30}\approx 0.566666667$
$$\frac{3}{6}-\frac{2}{6}+\frac{\frac{3}{4}\times \frac{4}{5}}{\frac{1}{2}}-\frac{4}{5}$$
$$\frac{3-2}{6}+\frac{\frac{3}{4}\times \frac{4}{5}}{\frac{1}{2}}-\frac{4}{5}$$
$$\frac{1}{6}+\frac{\frac{3}{4}\times \frac{4}{5}}{\frac{1}{2}}-\frac{4}{5}$$
$$\frac{1}{6}+\frac{\frac{3\times 4}{4\times 5}}{\frac{1}{2}}-\frac{4}{5}$$
$$\frac{1}{6}+\frac{\frac{3}{5}}{\frac{1}{2}}-\frac{4}{5}$$
$$\frac{1}{6}+\frac{3}{5}\times 2-\frac{4}{5}$$
$$\frac{1}{6}+\frac{3\times 2}{5}-\frac{4}{5}$$
$$\frac{1}{6}+\frac{6}{5}-\frac{4}{5}$$
$$\frac{5}{30}+\frac{36}{30}-\frac{4}{5}$$
$$\frac{5+36}{30}-\frac{4}{5}$$
$$\frac{41}{30}-\frac{4}{5}$$
$$\frac{41}{30}-\frac{24}{30}$$
$$\frac{41-24}{30}$$
$$\frac{17}{30}$$
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$\frac{17}{2 \cdot 3 \cdot 5} = 0.5666666666666667$
