Multiply $2$ by $ \dfrac{i}{3} $ to get $ \dfrac{ 2i }{ 3 } $.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{i}{3} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{i}{3} \xlongequal{\text{Step 2}} \frac{ 2 \cdot i }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 2i }{ 3 } \end{aligned} $$

Add $1$ and $ \dfrac{2i}{3} $ to get $ \dfrac{ \color{purple}{ 2i+3 } }{ 3 }$.

Step 1: Write $ 1 $ 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 $\color{blue}{ 3 }$.

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

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

Step 1: Write $ i $ 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 $\color{blue}{3}$.

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