Evaluate \(\frac{3\frac{1}{4} \times 1\frac{3}{5}}{11\frac{1}{3} - 5 \frac{1}{3}}\)

To evaluate this expression, we need to follow the order of operations, which is a set of rules for the order in which we perform arithmetic operations. The order of operations is: 1. Parentheses 2. Exponents 3. Multiplication and division (performed from left to right) 4. Addition and subtraction (performed from left to right) In this expression, there are no parentheses or exponents, so we can start by performing the multiplication and division. First, we need to convert the mixed numbers to improper fractions, so that we can easily multiply and divide them. \(\frac{3\frac{1}{4} \times 1\frac{3}{5}}{11\frac{1}{3} - 5 \frac{1}{3}} = \frac{\frac{13}{4} \times \frac{8}{5}}{\frac{32}{3}}\) Next, we can simplify the expression by canceling out common factors. \(\frac{\frac{13}{4} \times \frac{8}{5}}{\frac{32}{3}} = \frac{13 \times 2}{4 \times 5} = \frac{26}{20} = \frac{13}{10}\) Therefore, the answer is \(\frac{13}{10}\), which is equivalent to \(\frac{26}{20}\) and can be simplified to \(\frac{13}{15}\). So the correct option is: \(\frac{13}{15}\).