1. The problem is to find an equivalent fraction to $\frac{3}{9}$ with a denominator of 27. 2. Recall that equivalent fractions have the same value but different numerators and denominators. The formula to find an equivalent fraction is: $$\frac{a}{b} = \frac{a \times k}{b \times k}$$ where $k$ is a nonzero number. 3. Here, the original denominator is 9, and we want the new denominator to be 27. So, we find $k$ such that: $$9 \times k = 27$$ 4. Solving for $k$: $$k = \frac{27}{9} = 3$$ 5. Multiply both numerator and denominator of $\frac{3}{9}$ by 3: $$\frac{3 \times 3}{9 \times 3} = \frac{9}{27}$$ 6. Therefore, the equivalent fraction of $\frac{3}{9}$ with denominator 27 is $\frac{9}{27}$.