5. Order the following set of numbers from the least to the greatest. \( 2 \frac{5}{7},-1.2,2.8,-1 \frac{3}{8}, 2 \frac{7}{9} \)
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To order these numbers from least to greatest, let's first convert the mixed numbers into improper fractions or decimals for easier comparison. - \( -1.2 \) remains as it is. - \( -1 \frac{3}{8} = -1 - \frac{3}{8} = -\frac{8}{8} - \frac{3}{8} = -\frac{11}{8} \approx -1.375 \) - \( 2 \frac{5}{7} = 2 + \frac{5}{7} = \frac{14}{7} + \frac{5}{7} = \frac{19}{7} \approx 2.714 \) - \( 2 \frac{7}{9} = 2 + \frac{7}{9} = \frac{18}{9} + \frac{7}{9} = \frac{25}{9} \approx 2.778 \) - \( 2.8 \) remains as it is. Now we have: - \( -1.2 \) - \( -1.375 \) - \( 2.714 \) - \( 2.778 \) - \( 2.8 \) Ordering these gives us: 1. \( -1.375 \) or \( -1 \frac{3}{8} \) 2. \( -1.2 \) 3. \( 2.714 \) or \( 2 \frac{5}{7} \) 4. \( 2.8 \) 5. \( 2.778 \) or \( 2 \frac{7}{9} \) Thus, from least to greatest, the numbers are: \( -1 \frac{3}{8}, -1.2, 2 \frac{5}{7}, 2.8, 2 \frac{7}{9} \)