1. The problem is to find the common denominator (common denominator) for the fractions $\frac{1}{3}$ and $\frac{3}{5a}$. 2. To add or compare fractions, they must have the same denominator. The common denominator is usually the least common multiple (LCM) of the denominators. 3. The denominators here are $3$ and $5a$. Since $3$ and $5$ are prime to each other and $a$ is a variable, the LCM is their product: $3 \times 5a = 15a$. 4. Convert each fraction to have denominator $15a$: $$\frac{1}{3} = \frac{1 \times 5a}{3 \times 5a} = \frac{5a}{15a}$$ $$\frac{3}{5a} = \frac{3 \times 3}{5a \times 3} = \frac{9}{15a}$$ 5. Now both fractions have the common denominator $15a$. The fractions are $\frac{5a}{15a}$ and $\frac{9}{15a}$.