Multiply $107$ by $ \dfrac{i}{13} $ to get $ \dfrac{ 107i }{ 13 } $.

Step 1: Write $ 107 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 107 \cdot \frac{i}{13} & \xlongequal{\text{Step 1}} \frac{107}{\color{red}{1}} \cdot \frac{i}{13} \xlongequal{\text{Step 2}} \frac{ 107 \cdot i }{ 1 \cdot 13 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 107i }{ 13 } \end{aligned} $$

Add $36$ and $ \dfrac{107i}{13} $ to get $ \dfrac{ \color{purple}{ 107i+468 } }{ 13 }$.

Step 1: Write $ 36 $ 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 $\color{blue}{ 13 }$.

$$ \begin{aligned} 36+ \frac{107i}{13} & \xlongequal{\text{Step 1}} \frac{36}{\color{red}{1}} + \frac{107i}{13} = \frac{ 36 \cdot \color{blue}{ 13 }}{ 1 \cdot \color{blue}{ 13 }} + \frac{ 107i }{ 13 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 468 } }{ 13 } + \frac{ \color{purple}{ 107i } }{ 13 }=\frac{ \color{purple}{ 107i+468 } }{ 13 } \end{aligned} $$

Add $ \dfrac{107i+468}{13} $ and $ 6i $ to get $ \dfrac{ \color{purple}{ 185i+468 } }{ 13 }$.

Step 1: Write $ 6i $ 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 $\color{blue}{13}$.

$$ \begin{aligned} \frac{107i+468}{13} +6i & \xlongequal{\text{Step 1}} \frac{107i+468}{13} + \frac{6i}{\color{red}{1}} = \frac{ 107i+468 }{ 13 } + \frac{ 6i \cdot \color{blue}{ 13 }}{ 1 \cdot \color{blue}{ 13 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 107i+468 } }{ 13 } + \frac{ \color{purple}{ 78i } }{ 13 }=\frac{ \color{purple}{ 185i+468 } }{ 13 } \end{aligned} $$