solution: First, we can use the division rule so that we have an expression with only multiplication of fractions.  We get $$\frac{1}{5}\cdot \frac{8}{7}\div \frac{12}{20}=\frac{1}{5}\cdot \frac{8}{7}\cdot \frac{20}{12}.$$Now, notice that $5$ and $20$ have a common factor of $5$.  We can also see that $8$ and $12$ have a common factor of $4$.  Therefore, we can simplify to get $$\frac{1}{5}\cdot \frac{8}{7}\cdot \frac{20}{12}=\frac{1}{\cancel{5}}\cdot \frac{\cancelto{2}{8}}{7}\cdot \frac{\cancelto{4}{20}}{\cancelto{3}{12}}=\frac{1\cdot 2 \cdot 4}{7\cdot 3}=\boxed{\frac{8}{21}}.$$
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Simplify $\frac{1}{5}\cdot \frac{8}{7}\div \frac{12}{20}$.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: \frac{8}{21}
extra_info.question: Simplify $\frac{1}{5}\cdot \frac{8}{7}\div \frac{12}{20}$.
extra_info.split: test