1. **State the problem:** We need to solve the multiplication of two fractions: $\frac{13}{52} \times \frac{12}{52}$. 2. **Formula used:** To multiply fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Apply the formula:** $$\frac{13}{52} \times \frac{12}{52} = \frac{13 \times 12}{52 \times 52} = \frac{156}{2704}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 156 and 2704. - Prime factors of 156: $2 \times 2 \times 3 \times 13$ - Prime factors of 2704: $2 \times 2 \times 2 \times 2 \times 13 \times 13$ The common factors are $2 \times 2 \times 13 = 52$. 5. **Divide numerator and denominator by 52:** $$\frac{\cancel{52} \times 3}{\cancel{52} \times 52} = \frac{3}{52}$$ 6. **Final answer:** $$\frac{13}{52} \times \frac{12}{52} = \frac{3}{52}$$