To compare the given fractions and mixed numbers, let's first convert all the mixed numbers to improper fractions (if applicable) and then evaluate their decimal values:
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Responses:
- Start Fraction 13 over 15 End Fraction = \( \frac{13}{15} \) ≈ 0.8667
- Start Fraction 15 over 8 End Fraction = \( \frac{15}{8} = 1.875 \)
- Start Fraction 9 over 6 End Fraction = \( \frac{9}{6} = 1.5 \)
- Start Fraction 7 over 9 End Fraction = \( \frac{7}{9} \) ≈ 0.7778
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Order from smallest to largest:
- \( \frac{7}{9} \) ≈ 0.7778 (smallest)
- \( \frac{13}{15} \) ≈ 0.8667
- \( \frac{9}{6} = 1.5 \)
- \( \frac{15}{8} = 1.875 \) (largest)
So, the order for the first set of responses is:
- Start Fraction 7 over 9 End Fraction
- Start Fraction 13 over 15 End Fraction
- Start Fraction 9 over 6 End Fraction
- Start Fraction 15 over 8 End Fraction
Now, let's check the other options and evaluate their order as well.
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Responses (Option 2):
- 2 Start Fraction 3 over 5 End Fraction = \( 2 + \frac{3}{5} \) = \( \frac{10}{5} + \frac{3}{5} = \frac{13}{5} \) = 2.6
- 1 Start Fraction 7 over 8 End Fraction = \( 1 + \frac{7}{8} \) = \( \frac{8}{8} + \frac{7}{8} = \frac{15}{8} \) = 1.875
- 1 Start Fraction 3 over 6 End Fraction = \( 1 + \frac{1}{2} = 1.5 \)
- Start Fraction 7 over 9 End Fraction = \( \frac{7}{9} \) ≈ 0.7778
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Order for Option 2:
- \( \frac{7}{9} \) ≈ 0.7778
- \( 1 + \frac{3}{6} = 1.5 \)
- \( 1 + \frac{7}{8} = 1.875 \)
- \( 2 + \frac{3}{5} = 2.6 \)
Next for Option 3 and 4:
- Responses (Option 3):
- 79 = 79
- Start Fraction 10 over 6 End Fraction = \( \frac{10}{6} = 1.6667 \)
- 16 over 18 = \( \frac{16}{18} \) = \( \frac{8}{9} \) ≈ 0.8889
- Start Fraction 13 over 5 End Fraction = \( \frac{13}{5} = 2.6 \)
Order for Option 3:
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79
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\( \frac{8}{9} \) ≈ 0.8889
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\( \frac{10}{6} \) = 1.6667
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\( \frac{13}{5} \) = 2.6
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Responses (Option 4):
- 79
- 136
- 178
- 235
Final Numeric Order: After evaluating all options, the order from smallest to largest (using the values given) is:
- Response with fractions:
- 79
- Start Fraction 7 over 9 End Fraction
- Start Fraction 13 over 15 End Fraction
- Start Fraction 9 over 6 End Fraction
- Start Fraction 15 over 8 End Fraction
- 79, 136, 178, 235 directly listed is also correct.
The smallest to largest of the given choices:
- 79, 136, 178, 235