Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Identify the problem
We need to divide $$\frac{1}{5}$$ by $$\frac{15}{4}
Step 3:: Recall the division rule for fractions
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction.
Step 4:: Find the reciprocal of \frac{15}{4}
The reciprocal is $$\frac{4}{15}
Step 5:: Multiply \frac{1}{5} by \frac{4}{15}
\frac{1}{5} \div \frac{15}{4} = \frac{1}{5} \times \frac{4}{15}
Step 6:: Multiply the numerators and denominators
= \frac{1 \times 4}{5 \times 15}
Step 7:: Simplify
= \frac{4}{75}
Final Answer
\frac{4}{75}
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