To compare the fractions \( \frac{5}{11} \) and \( \frac{4}{5} \) using the benchmark fraction \( \frac{1}{2} \), we will determine if each fraction is less than, greater than, or equal to \( \frac{1}{2} \).
Step 1: Compare \( \frac{5}{11} \) to \( \frac{1}{2} \)
To compare \( \frac{5}{11} \) and \( \frac{1}{2} \), we can cross-multiply:
\[ 5 \times 2 = 10 \] \[ 1 \times 11 = 11 \]
Since \( 10 < 11 \), we have:
\[ \frac{5}{11} < \frac{1}{2} \]
Step 2: Compare \( \frac{4}{5} \) to \( \frac{1}{2} \)
Next, we compare \( \frac{4}{5} \) and \( \frac{1}{2} \) using cross-multiplication again:
\[ 4 \times 2 = 8 \] \[ 1 \times 5 = 5 \]
Since \( 8 > 5 \), we have:
\[ \frac{4}{5} > \frac{1}{2} \]
Conclusion:
Based on our comparisons:
- \( \frac{5}{11} < \frac{1}{2} \)
- \( \frac{4}{5} > \frac{1}{2} \)
This means that \( \frac{5}{11} \) is less than \( \frac{4}{5} \), therefore:
\[ \frac{5}{11} < \frac{4}{5} \]