Question
Write the ratio as a fraction in lowest terms.
1one fifth
to 2one sixth
1one fifth
to 2one sixth
Answers
GPT-4o mini
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.
1. **Convert the mixed numbers to improper fractions:**
- \(1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}\)
- \(2 \frac{1}{6} = 2 + \frac{1}{6} = \frac{12}{6} + \frac{1}{6} = \frac{13}{6}\)
2. **Set up the ratio:**
\[
\frac{6/5}{13/6}
\]
3. **To divide by a fraction, multiply by its reciprocal:**
\[
\frac{6}{5} \times \frac{6}{13} = \frac{36}{65}
\]
4. **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:
\[
\frac{36}{65}
\]
1. **Convert the mixed numbers to improper fractions:**
- \(1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}\)
- \(2 \frac{1}{6} = 2 + \frac{1}{6} = \frac{12}{6} + \frac{1}{6} = \frac{13}{6}\)
2. **Set up the ratio:**
\[
\frac{6/5}{13/6}
\]
3. **To divide by a fraction, multiply by its reciprocal:**
\[
\frac{6}{5} \times \frac{6}{13} = \frac{36}{65}
\]
4. **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:
\[
\frac{36}{65}
\]