1. The problem is to find the product of the fractions $\frac{13}{52}$ and $\frac{12}{51}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$\n\n3. Applying the formula, we get:\n$$\frac{13}{52} \times \frac{12}{51} = \frac{13 \times 12}{52 \times 51}$$\n\n4. Calculate the numerator and denominator:\n$$\frac{156}{2652}$$\n\n5. Simplify the fraction by finding the greatest common divisor (GCD) of 156 and 2652. The GCD is 12.\n\n6. Cancel the common factor 12:\n$$\frac{\cancel{12} \times 13}{\cancel{12} \times 221} = \frac{13}{221}$$\n\n7. Therefore, the simplified product is $\frac{13}{221}$.