1. **State the problem:** Calculate the product of the fractions $\frac{9}{2} \cdot \frac{5}{2} \cdot \frac{3}{2}$.\n\n2. **Formula and rules:** When multiplying fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$$\n\n3. **Apply the formula:** Multiply the numerators: $9 \times 5 \times 3 = 135$.\nMultiply the denominators: $2 \times 2 \times 2 = 8$.\nSo, $$\frac{9}{2} \cdot \frac{5}{2} \cdot \frac{3}{2} = \frac{135}{8}$$\n\n4. **Simplify or convert:** $\frac{135}{8}$ is an improper fraction. To convert to a mixed number, divide 135 by 8:\n$135 \div 8 = 16$ remainder $7$, so $$\frac{135}{8} = 16 \frac{7}{8}$$\n\n**Final answer:** $$\frac{135}{8} \text{ or } 16 \frac{7}{8}$$