Add $ \dfrac{2}{5} $ and $ 3y $ to get $ \dfrac{ \color{purple}{ 15y+2 } }{ 5 }$.

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 second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{2}{5} +3y & \xlongequal{\text{Step 1}} \frac{2}{5} + \frac{3y}{\color{red}{1}} = \frac{ 2 }{ 5 } + \frac{ 3y \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2 } }{ 5 } + \frac{ \color{purple}{ 15y } }{ 5 }=\frac{ \color{purple}{ 15y+2 } }{ 5 } \end{aligned} $$

Multiply $10$ by $ \dfrac{15y+2}{5} $ to get $ \dfrac{ 150y+20 }{ 5 } $.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 10 \cdot \frac{15y+2}{5} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{15y+2}{5} \xlongequal{\text{Step 2}} \frac{ 10 \cdot \left( 15y+2 \right) }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 150y+20 }{ 5 } \end{aligned} $$