1. **Stating the problem:** Calculate the value of the expression: $$120\% - 3 + 2 \times 0.75 + \frac{2}{3}$$ 2. **Formula and rules:** - Percent means per hundred, so $120\% = \frac{120}{100} = 1.2$. - Follow the order of operations: multiplication before addition and subtraction. 3. **Step-by-step calculation:** - Convert percent to decimal: $$120\% = 1.2$$ - Calculate multiplication: $$2 \times 0.75 = 1.5$$ - Substitute values back into the expression: $$1.2 - 3 + 1.5 + \frac{2}{3}$$ - Combine the decimal numbers first: $$1.2 - 3 + 1.5 = (1.2 + 1.5) - 3 = 2.7 - 3 = -0.3$$ - Now add the fraction $\frac{2}{3}$: $$-0.3 + \frac{2}{3}$$ - Convert $-0.3$ to fraction for easier addition: $$-0.3 = -\frac{3}{10}$$ - Find common denominator for $\frac{3}{10}$ and $\frac{2}{3}$: $$\text{LCM of } 10 \text{ and } 3 = 30$$ - Convert fractions: $$-\frac{3}{10} = -\frac{9}{30}, \quad \frac{2}{3} = \frac{20}{30}$$ - Add the fractions: $$-\frac{9}{30} + \frac{20}{30} = \frac{11}{30}$$ 4. **Final answer:** $$\boxed{\frac{11}{30}}$$ This corresponds to option (A).