To divide \( \frac{5}{6} \) by \( \frac{2}{1} \frac{1}{5} \), you first need to convert the mixed number \( 2 \frac{1}{5} \) into an improper fraction.
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Convert \( 2 \frac{1}{5} \):
- Multiply the whole number (2) by the denominator (5): \( 2 \times 5 = 10 \).
- Add the numerator (1): \( 10 + 1 = 11 \).
- So, \( 2 \frac{1}{5} = \frac{11}{5} \).
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Now, perform the division: \[ \frac{5}{6} \div \frac{11}{5} \]
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To divide by a fraction, multiply by its reciprocal: \[ \frac{5}{6} \times \frac{5}{11} \]
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Multiply the numerators and the denominators: \[ \frac{5 \times 5}{6 \times 11} = \frac{25}{66} \]
So, \( \frac{5}{6} \div 2 \frac{1}{5} = \frac{25}{66} \).