1. **State the problem:** Maurice found $\frac{1}{2}$ of a lemon meringue pie and ate $\frac{3}{5}$ of that portion. We need to find what fraction of the whole pie Maurice ate. 2. **Formula used:** To find the fraction of the whole pie eaten, multiply the fraction of the pie found by the fraction eaten: $$\text{Fraction eaten} = \frac{1}{2} \times \frac{3}{5}$$ 3. **Multiply the fractions:** Multiply the numerators and denominators: $$\frac{1 \times 3}{2 \times 5} = \frac{3}{10}$$ 4. **Interpretation:** Maurice ate $\frac{3}{10}$ of the whole pie. **Final answer:** $$\boxed{\frac{3}{10}}$$