$$1 \frac{ 1 }{ 7 } \times 1 \frac{ 1 }{ 8 } \times 1 \frac{ 1 }{ 9 } \times 1 \frac{ 1 }{ 10 } \times 1 \frac{ 1 }{ 11 } \times 1 \frac{ 1 }{ 12 } \times 1 \frac{ 1 }{ 13 }$$
$2$
$$\frac{7+1}{7}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{8}{7}\times \frac{1\times 8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{8}{7}\times \frac{8+1}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{8}{7}\times \frac{9}{8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{8\times 9}{7\times 8}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{9}{7}\times \frac{1\times 9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{9}{7}\times \frac{9+1}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{9}{7}\times \frac{10}{9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{9\times 10}{7\times 9}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{10}{7}\times \frac{1\times 10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{10}{7}\times \frac{10+1}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{10}{7}\times \frac{11}{10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{10\times 11}{7\times 10}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{11}{7}\times \frac{1\times 11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{11}{7}\times \frac{11+1}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{11}{7}\times \frac{12}{11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{11\times 12}{7\times 11}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{12}{7}\times \frac{1\times 12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{12}{7}\times \frac{12+1}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{12}{7}\times \frac{13}{12}\times \frac{1\times 13+1}{13}$$
$$\frac{12\times 13}{7\times 12}\times \frac{1\times 13+1}{13}$$
$$\frac{13}{7}\times \frac{1\times 13+1}{13}$$
$$\frac{13}{7}\times \frac{13+1}{13}$$
$$\frac{13}{7}\times \frac{14}{13}$$
$$\frac{13\times 14}{7\times 13}$$
$$\frac{14}{7}$$
$$2$$
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