Multiply $35$ by $ \dfrac{i}{8} $ to get $ \dfrac{ 35i }{ 8 } $.

Step 1: Write $ 35 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 35 \cdot \frac{i}{8} & \xlongequal{\text{Step 1}} \frac{35}{\color{red}{1}} \cdot \frac{i}{8} \xlongequal{\text{Step 2}} \frac{ 35 \cdot i }{ 1 \cdot 8 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 35i }{ 8 } \end{aligned} $$

Add $50$ and $ \dfrac{35i}{8} $ to get $ \dfrac{ \color{purple}{ 35i+400 } }{ 8 }$.

Step 1: Write $ 50 $ 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 $\color{blue}{ 8 }$.

$$ \begin{aligned} 50+ \frac{35i}{8} & \xlongequal{\text{Step 1}} \frac{50}{\color{red}{1}} + \frac{35i}{8} = \frac{ 50 \cdot \color{blue}{ 8 }}{ 1 \cdot \color{blue}{ 8 }} + \frac{ 35i }{ 8 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 400 } }{ 8 } + \frac{ \color{purple}{ 35i } }{ 8 }=\frac{ \color{purple}{ 35i+400 } }{ 8 } \end{aligned} $$

Add $ \dfrac{35i+400}{8} $ and $ 5i $ to get $ \dfrac{ \color{purple}{ 75i+400 } }{ 8 }$.

Step 1: Write $ 5i $ 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 $\color{blue}{8}$.

$$ \begin{aligned} \frac{35i+400}{8} +5i & \xlongequal{\text{Step 1}} \frac{35i+400}{8} + \frac{5i}{\color{red}{1}} = \frac{ 35i+400 }{ 8 } + \frac{ 5i \cdot \color{blue}{ 8 }}{ 1 \cdot \color{blue}{ 8 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 35i+400 } }{ 8 } + \frac{ \color{purple}{ 40i } }{ 8 }=\frac{ \color{purple}{ 75i+400 } }{ 8 } \end{aligned} $$