1. The problem states that Merly bought 2 \(\frac{1}{2}\) kg of rice and Riza bought 3 \(\frac{3}{4}\) times as much as Merly. 2. Convert Merly's purchase to an improper fraction: 2 \(\frac{1}{2} = \frac{5}{2}\) kg. 3. Convert the multiplier for Riza's purchase to an improper fraction: 3 \(\frac{3}{4} = \frac{15}{4}\). 4. To find how much rice Riza bought, multiply Merly's amount by the multiplier: $$\frac{5}{2} \times \frac{15}{4} = \frac{5 \times 15}{2 \times 4} = \frac{75}{8}.$$ 5. Simplify \(\frac{75}{8}\) to a mixed number: divide 75 by 8. 6. \(75 \div 8 = 9\) remainder 3, so \(\frac{75}{8} = 9 \frac{3}{8}\) kg. 7. Therefore, Riza bought 9 \(\frac{3}{8}\) kg of rice.