1. Stating the problem: Calculate the product of $\frac{7}{8}$ and $\frac{2}{5}$. 2. Formula: To multiply fractions, multiply the numerators and multiply the denominators: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. Applying the formula: $$\frac{7}{8} \times \frac{2}{5} = \frac{7 \times 2}{8 \times 5} = \frac{14}{40}$$ 4. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD), which is 2: $$\frac{\cancel{14}^{7}}{\cancel{40}^{20}} = \frac{7}{20}$$ 5. Final answer: The product is $\frac{7}{20}$.