$$\frac { 10 } { 12 } - \frac { 7 } { 10 } + \frac { 4 } { 11 } \times \frac { 22 } { 20 } \div \frac { 44 } { 40 }$$
$\frac{82}{165}\approx 0.496969697$
$$\frac{5}{6}-\frac{7}{10}+\frac{\frac{4}{11}\times \frac{22}{20}}{\frac{44}{40}}$$
$$\frac{25}{30}-\frac{21}{30}+\frac{\frac{4}{11}\times \frac{22}{20}}{\frac{44}{40}}$$
$$\frac{25-21}{30}+\frac{\frac{4}{11}\times \frac{22}{20}}{\frac{44}{40}}$$
$$\frac{4}{30}+\frac{\frac{4}{11}\times \frac{22}{20}}{\frac{44}{40}}$$
$$\frac{2}{15}+\frac{\frac{4}{11}\times \frac{22}{20}}{\frac{44}{40}}$$
$$\frac{2}{15}+\frac{\frac{4}{11}\times \frac{11}{10}}{\frac{44}{40}}$$
$$\frac{2}{15}+\frac{\frac{4\times 11}{11\times 10}}{\frac{44}{40}}$$
$$\frac{2}{15}+\frac{\frac{4}{10}}{\frac{44}{40}}$$
$$\frac{2}{15}+\frac{\frac{2}{5}}{\frac{44}{40}}$$
$$\frac{2}{15}+\frac{\frac{2}{5}}{\frac{11}{10}}$$
$$\frac{2}{15}+\frac{2}{5}\times \frac{10}{11}$$
$$\frac{2}{15}+\frac{2\times 10}{5\times 11}$$
$$\frac{2}{15}+\frac{20}{55}$$
$$\frac{2}{15}+\frac{4}{11}$$
$$\frac{22}{165}+\frac{60}{165}$$
$$\frac{22+60}{165}$$
$$\frac{82}{165}$$
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$\frac{2 \cdot 41}{3 \cdot 5 \cdot 11} = 0.49696969696969695$
