$$1 \frac{ 1 }{ 6 } \times 1 \frac{ 1 }{ 7 } \times 1 \frac{ 1 }{ 8 } \times 1 \frac{ 1 }{ 9 } \times 1 \frac{ 1 }{ 10 } \times 1 \frac{ 1 }{ 11 }$$
$2$
$$\frac{6+1}{6}\times \frac{1\times 7+1}{7}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{7}{6}\times \frac{1\times 7+1}{7}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{7}{6}\times \frac{7+1}{7}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{7}{6}\times \frac{8}{7}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{7\times 8}{6\times 7}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{8}{6}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{4}{3}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{4}{3}\times \frac{8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{4}{3}\times \frac{9}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{4\times 9}{3\times 8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{36}{24}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{3}{2}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{3}{2}\times \frac{9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{3}{2}\times \frac{10}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{3\times 10}{2\times 9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{30}{18}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{5}{3}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{5}{3}\times \frac{10+1}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{5}{3}\times \frac{11}{10}\times \frac{1\times 11+1}{11}$$
$$\frac{5\times 11}{3\times 10}\times \frac{1\times 11+1}{11}$$
$$\frac{55}{30}\times \frac{1\times 11+1}{11}$$
$$\frac{11}{6}\times \frac{1\times 11+1}{11}$$
$$\frac{11}{6}\times \frac{11+1}{11}$$
$$\frac{11}{6}\times \frac{12}{11}$$
$$\frac{11\times 12}{6\times 11}$$
$$\frac{12}{6}$$
$$2$$
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