Bot GPT 4-o mini To compare the fractions and mixed numbers, we can convert all of them to improper fractions or decimal form. Here are the conversions:
- \( 1 \frac{3}{6} = 1 + \frac{3}{6} = \frac{6}{6} + \frac{3}{6} = \frac{9}{6} = \frac{3}{2} \)
- \( 2 \frac{3}{5} = 2 + \frac{3}{5} = \frac{10}{5} + \frac{3}{5} = \frac{13}{5} \)
- \( \frac{7}{9} \) remains as is.
- \( 1 \frac{7}{8} = 1 + \frac{7}{8} = \frac{8}{8} + \frac{7}{8} = \frac{15}{8} \)
Now we have the following fractions to compare:
- \( \frac{3}{2} \)
- \( \frac{13}{5} \)
- \( \frac{7}{9} \)
- \( \frac{15}{8} \)
Next, we need to convert them to a common denominator or decimal values for easier comparison.
- \( \frac{3}{2} = 1.5 \)
- \( \frac{13}{5} = 2.6 \)
- \( \frac{7}{9} \approx 0.777 \)
- \( \frac{15}{8} = 1.875 \)
Now, let's order them from smallest to largest based on their decimal values:
- \( \frac{7}{9} \approx 0.777 \) (smallest)
- \( 1 \frac{3}{6} = \frac{3}{2} = 1.5 \)
- \( 1 \frac{7}{8} = \frac{15}{8} = 1.875 \)
- \( 2 \frac{3}{5} = \frac{13}{5} = 2.6 \) (largest)
Thus, the numeric order from smallest to largest is:
\( \frac{7}{9}, 1 \frac{3}{6}, 1 \frac{7}{8}, 2 \frac{3}{5} \)
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