To compare the fractions \( \frac{5}{11} \) and \( \frac{4}{5} \) using the benchmark fraction \( \frac{1}{2} \), we can first convert each fraction to a decimal or compare them directly.
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Comparing \( \frac{5}{11} \) with \( \frac{1}{2} \):
- To convert \( \frac{5}{11} \): \[ \frac{5}{11} \approx 0.4545 \]
- Since \( 0.4545 < 0.5 \), we can say: \[ \frac{5}{11} \text{ is less than the benchmark } \frac{1}{2}. \]
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Comparing \( \frac{4}{5} \) with \( \frac{1}{2} \):
- To convert \( \frac{4}{5} \): \[ \frac{4}{5} = 0.8 \]
- Since \( 0.8 > 0.5 \), we can say: \[ \frac{4}{5} \text{ is greater than the benchmark } \frac{1}{2}. \]
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Comparing \( \frac{5}{11} \) and \( \frac{4}{5} \):
- To compare directly, we can convert both fractions to a common denominator or cross-multiply:
- Cross-multiplying: \[ 5 \times 5 = 25 \] \[ 11 \times 4 = 44 \]
- Since \( 25 < 44 \), it follows that: \[ \frac{5}{11} < \frac{4}{5}. \]
Putting it all together:
- The fraction \( \frac{5}{11} \) is less than the benchmark \( \frac{1}{2} \).
- The fraction \( \frac{4}{5} \) is greater than the benchmark \( \frac{1}{2} \).
- \( \frac{5}{11} \) is less than \( \frac{4}{5} \).
Final answers:
- The fraction 5/11 is less than the benchmark 1/2.
- The fraction 4/5 is greater than the benchmark 1/2.
- 5/11 is less than 4/5.
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