1. **State the problem:** Multiply the fractions $\frac{3}{4}$ and $\frac{1}{5}$.\n\n2. **Formula for multiplying fractions:** To multiply two fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$\n\n3. **Apply the formula:** Multiply the numerators: $3 \times 1 = 3$.\nMultiply the denominators: $4 \times 5 = 20$.\nSo, $$\frac{3}{4} \times \frac{1}{5} = \frac{3}{20}$$\n\n4. **Simplify the fraction if possible:** The numerator 3 and denominator 20 have no common factors other than 1, so the fraction is already in simplest form.\n\n**Final answer:** $$\frac{3}{20}$$