To evaluate the expression \(\frac{3 \frac{1}{4} \times 1 \frac{3}{5}}{11 \frac{1}{5}-5 \frac{1}{3}}\), we will convert mixed numbers to improper fractions and perform the operations step-by-step.
1. Convert mixed numbers to improper fractions:
- \(3 \frac{1}{4} = 3 + \frac{1}{4} = 3 + 0.25 = 3.25\)
- \(1 \frac{3}{5} = 1 + \frac{3}{5} = 1 + 0.6 = 1.6\)
- \(11 \frac{1}{5} = 11 + \frac{1}{5} = 11 + 0.2 = 11.2\)
- \(5 \frac{1}{3} = 5 + \frac{1}{3} = 5 + 0.3333 \approx 5.3333\)
2. Calculate the numerator:
- The numerator of the expression is \(3 \frac{1}{4} \times 1 \frac{3}{5} = 3.25 \times 1.6\).
- \(3.25 \times 1.6 = 5.2\)
3. Calculate the denominator:
- The denominator of the expression is \(11 \frac{1}{5} - 5 \frac{1}{3} = 11.2 - 5.3333\).
- \(11.2 - 5.3333 = 5.8667\)
4. Compute the fraction:
- The fraction is \(\frac{3 \frac{1}{4} \times 1 \frac{3}{5}}{11 \frac{1}{5}-5 \frac{1}{3}} = \frac{5.2}{5.8667}\).
- Performing the division gives us \( \frac{5.2}{5.8667} \approx 0.8864 \approx \frac{4}{5} \).
Thus, the evaluated result is \(\frac{4}{5}\), which corresponds to:
C. [tex]\(\frac{4}{5}\)[/tex]
