To order the given fractions and mixed numbers (1 3/6, 2 3/5, 7/9, 1 7/8) from smallest to largest, we'll first convert everything to improper fractions or decimals for easier comparison.
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Convert Mixed Numbers to Improper Fractions:
- \(1 \frac{3}{6} = \frac{6+3}{6} = \frac{9}{6} = \frac{3}{2}\)
- \(2 \frac{3}{5} = \frac{10+3}{5} = \frac{13}{5}\)
- \(1 \frac{7}{8} = \frac{8+7}{8} = \frac{15}{8}\)
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List the fractions:
- \(7/9\) (as it is)
- \(\frac{3}{2} = \frac{9}{6}\)
- \(\frac{13}{5}\) (as it is)
- \(\frac{15}{8}\) (as it is)
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Convert to a common denominator to compare or find decimal equivalents:
- \(7/9 \approx 0.777\)
- \(\frac{3}{2} = 1.5\)
- \(\frac{13}{5} = 2.6\)
- \(\frac{15}{8} = 1.875\)
Now in decimal form:
- \(7/9 \approx 0.777\)
- \(1 \frac{7}{8} \approx 1.875\)
- \(1 \frac{3}{6} \approx 1.5\)
- \(2 \frac{3}{5} \approx 2.6\)
- Ordering the numbers by value:
- \(7/9\) (≈ 0.777)
- \(1 \frac{3}{6}\) (1.5)
- \(1 \frac{7}{8}\) (1.875)
- \(2 \frac{3}{5}\) (2.6)
Now, rewriting in ordered form:
- \(7/9\)
- \(1 \frac{3}{6}\)
- \(1 \frac{7}{8}\)
- \(2 \frac{3}{5}\)
The correct order from smallest to largest is: 7/9, 1 3/6, 1 7/8, 2 3/5
Thus, the correct response from the options would be: 7/9, 1 3/6, 1 7/8, 2 3/5