1. The problem is to simplify the expression: $$2 \times \frac{3}{2} \times \frac{5}{2} + 2 \times \frac{3}{2} \times \frac{5}{2} + 2 \times \frac{5}{2} \times \frac{5}{2}$$ 2. We use the multiplication and addition rules for fractions. Multiply numerators and denominators separately, then add the results. 3. Calculate each term: - First term: $$2 \times \frac{3}{2} \times \frac{5}{2} = 2 \times \frac{15}{4} = \frac{2 \times 15}{4} = \frac{30}{4} = \frac{15}{2}$$ - Second term is the same as the first: $$\frac{15}{2}$$ - Third term: $$2 \times \frac{5}{2} \times \frac{5}{2} = 2 \times \frac{25}{4} = \frac{2 \times 25}{4} = \frac{50}{4} = \frac{25}{2}$$ 4. Now add all terms: $$\frac{15}{2} + \frac{15}{2} + \frac{25}{2} = \frac{15 + 15 + 25}{2} = \frac{55}{2}$$ 5. The simplified result is $$\frac{55}{2}$$ or 27.5 in decimal form. Therefore, the final answer is $$\boxed{\frac{55}{2}}$$.