Order the fractions from least to greatest: \( \frac{4}{3}, \frac{2}{6}, \frac{3}{6}, \frac{4}{5}, 1 \frac{2}{3^{\prime}}, \frac{1}{6} \)
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To order the fractions from least to greatest, we first convert mixed numbers and simplify fractions when necessary. 1. Convert \(1 \frac{2}{3}\) to an improper fraction: \[ 1 \frac{2}{3} = \frac{3 \cdot 1 + 2}{3} = \frac{5}{3}. \] 2. Rewrite the fractions: \[ \frac{4}{3}, \frac{1}{6}, \frac{2}{6} = \frac{1}{3}, \frac{3}{6} = \frac{1}{2}, \frac{4}{5}, \frac{5}{3}. \] 3. Convert them to decimals (optional), or simply find a common denominator to compare: - \( \frac{1}{6} \approx 0.1667 \) - \( \frac{1}{3} \approx 0.3333 \) - \( \frac{1}{2} = 0.5 \) - \( \frac{4}{5} = 0.8 \) - \( \frac{4}{3} \approx 1.3333 \) - \( \frac{5}{3} \approx 1.6667 \) Now ordering these: \( \frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{4}{5}, \frac{4}{3}, \frac{5}{3} \). So, the order from least to greatest is: \[ \frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{4}{5}, \frac{4}{3}, \frac{5}{3}. \]
