$$\frac { 3 } { 5 } 1 \frac { 3 } { 7 } \div \frac { 2 } { 5 } - \frac { 1 } { 2 } + \frac { 2 } { 3 } \times \frac { 6 } { 7 }$$
$\frac{31}{14}\approx 2.214285714$
$$\frac{\frac{3}{5}\times \frac{7+3}{7}}{\frac{2}{5}}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{\frac{3}{5}\times \frac{10}{7}}{\frac{2}{5}}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{\frac{3\times 10}{5\times 7}}{\frac{2}{5}}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{\frac{30}{35}}{\frac{2}{5}}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{\frac{6}{7}}{\frac{2}{5}}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{6}{7}\times \frac{5}{2}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{6\times 5}{7\times 2}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{30}{14}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{15}{7}-\frac{1}{2}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{30}{14}-\frac{7}{14}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{30-7}{14}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{23}{14}+\frac{2}{3}\times \frac{6}{7}$$
$$\frac{23}{14}+\frac{2\times 6}{3\times 7}$$
$$\frac{23}{14}+\frac{12}{21}$$
$$\frac{23}{14}+\frac{4}{7}$$
$$\frac{23}{14}+\frac{8}{14}$$
$$\frac{23+8}{14}$$
$$\frac{31}{14}$$
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$\frac{31}{2 \cdot 7} = 2\frac{3}{14} = 2.2142857142857144$
