Divide both the top and bottom numbers by $ \color{orangered}{ 15 } $.

Add $3y$ and $ \dfrac{1}{3} $ to get $ \dfrac{ \color{purple}{ 9y+1 } }{ 3 }$.

Step 1: Write $ 3y $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} 3y+ \frac{1}{3} & \xlongequal{\text{Step 1}} \frac{3y}{\color{red}{1}} + \frac{1}{3} = \frac{ 3y \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} + \frac{ 1 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9y } }{ 3 } + \frac{ \color{purple}{ 1 } }{ 3 }=\frac{ \color{purple}{ 9y+1 } }{ 3 } \end{aligned} $$