Multiply $7$ by $ \dfrac{i}{9} $ to get $ \dfrac{ 7i }{ 9 } $.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 7 \cdot \frac{i}{9} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{i}{9} \xlongequal{\text{Step 2}} \frac{ 7 \cdot i }{ 1 \cdot 9 } \xlongequal{\text{Step 3}} \frac{ 7i }{ 9 } \end{aligned} $$

Subtract $10i$ from $ \dfrac{7i}{9} $ to get $ \dfrac{ \color{purple}{ -83i } }{ 9 }$.

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

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{9}$.

$$ \begin{aligned} \frac{7i}{9} -10i & \xlongequal{\text{Step 1}} \frac{7i}{9} - \frac{10i}{\color{red}{1}} = \frac{ 7i }{ 9 } - \frac{ 10i \cdot \color{blue}{ 9 }}{ 1 \cdot \color{blue}{ 9 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7i } }{ 9 } - \frac{ \color{purple}{ 90i } }{ 9 }=\frac{ \color{purple}{ -83i } }{ 9 } \end{aligned} $$