What is the value of 1 \frac{1}{2} \times 1 \frac{1}{3} \times 1 \frac{1}{4} \times 1 \frac{1}{5} \times 1 \frac{1}{6} \times 1 \frac{1}{7} \times 1 \frac{1}{8} \times 1 \frac{1}{9}?
1
\frac{1}{5}
5
\frac{5}{9}
10
The problem involves mixed numbers.
We first convert each mixed number to an improper fraction:
1\frac{1}{2} \times 1\frac{1}{3} \times 1\frac{1}{4} \times 1\frac{1}{5} \times 1\frac{1}{6} \times 1\frac{1}{7} \times 1\frac{1}{8} \times 1\frac{1}{9}= \frac{3}{2} \times \frac{4}{3} \times \frac{5}{4} \times \frac{6}{5} \times \frac{7}{6} \times \frac{8}{7} \times \frac{9}{8} \times \frac{10}{9}= \frac{\not{3}}{2} \times \frac{\not{4}}{\not{3}} \times \frac{\not{5}}{\not{4}} \times \frac{\not{6}}{\not{5}} \times \frac{\not{7}}{\not{6}} \times \frac{\not{8}}{\not{7}} \times \frac{\not{9}}{\not{8}} \times \frac{10}{\not{9}}=\frac{1}{2} \times \frac{10}{1} = 5
Final result:\boxed{5}
