To express the ratio of 1 one-fifth to 2 one-sixth as a fraction in lowest terms, we first convert the mixed numbers to improper fractions.
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Convert the mixed numbers to improper fractions:
- \(1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}\)
- \(2 \frac{1}{6} = 2 + \frac{1}{6} = \frac{12}{6} + \frac{1}{6} = \frac{13}{6}\)
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Set up the ratio: \[ \frac{6/5}{13/6} \]
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To divide by a fraction, multiply by its reciprocal: \[ \frac{6}{5} \times \frac{6}{13} = \frac{36}{65} \]
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Check if the fraction can be simplified:
- The numerator \(36\) is \(2^2 \times 3^2\).
- The denominator \(65\) is \(5 \times 13\).
- There are no common factors between \(36\) and \(65\).
Thus, the fraction \( \frac{36}{65} \) is already in its lowest terms.
Therefore, the ratio \(1 \frac{1}{5}\) to \(2 \frac{1}{6}\) as a fraction in lowest terms is:
\[ \frac{36}{65} \]