1. **State the problem:** Simplify the expression $$\frac{7}{8} - \frac{1}{4} - \frac{2}{5}$$. 2. **Find a common denominator:** The denominators are 8, 4, and 5. The least common denominator (LCD) is 40. 3. **Convert each fraction:** $$\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40}$$ $$\frac{1}{4} = \frac{1 \times 10}{4 \times 10} = \frac{10}{40}$$ $$\frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40}$$ 4. **Rewrite the expression:** $$\frac{35}{40} - \frac{10}{40} - \frac{16}{40}$$ 5. **Combine the fractions:** $$\frac{35 - 10 - 16}{40} = \frac{9}{40}$$ 6. **Final answer:** $$\boxed{\frac{9}{40}}$$