Find: `(11)/(4) + 7 (3)/(4) xx (8)/(15) div 2 (1)/(2)`

Answer

To solve the expression \( \frac{11}{4} + 7 \frac{3}{4} \times \frac{8}{15} \div 2 \frac{1}{2} \), we will follow the order of operations: division, multiplication, and then addition.

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions**:
- \( 7 \frac{3}{4} = \frac{7 \times 4 + 3}{4} = \frac{28 + 3}{4} = \frac{31}{4} \)
- \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \)

Now, the expression becomes:
\[ \frac{11}{4} + \frac{31}{4} \times \frac{8}{15} \div \frac{5}{2} \]

2. **Perform Division**:
- To divide by a fraction, multiply by its reciprocal:
\[ \frac{8}{15} \div \frac{5}{2} = \frac{8}{15} \times \frac{2}{5} = \frac{8 \times 2}{15 \times 5} = \frac{16}{75} \]

Now, the expression simplifies to:
\[ \frac{11}{4} + \frac{31}{4} \times \frac{16}{75} \]

3. **Perform Multiplication**:
- Now multiply \( \frac{31}{4} \) by \( \frac{16}{75} \):
\[ \frac{31 \times 16}{4 \times 75} = \frac{496}{300} \]

Now, the expression becomes:
\[ \frac{11}{4} + \frac{496}{300} \]

4. **Convert \( \frac{11}{4} \) to a Common Denominator**:
- The common denominator between 4 and 300 is 300. Convert \( \frac{11}{4} \):
\[ \frac{11}{4} = \frac{11 \times 75}{4 \times 75} = \frac{825}{300} \]

5. **Add the Fractions**:
- Now add \( \frac{825}{300} + \frac{496}{300} \):
\[ \frac{825 + 496}{300} = \frac{1321}{300} \]

### Final Answer:
\[ \frac{1321}{300} \]