Subtract $1$ from $ \dfrac{-10}{3} $ to get $ \dfrac{ \color{purple}{ -13 } }{ 3 }$.

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

Step 2: To subtract fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{3}$.

$$ \begin{aligned} \frac{-10}{3} -1 & \xlongequal{\text{Step 1}} \frac{-10}{3} - \frac{1}{\color{red}{1}} = \frac{ -10 }{ 3 } - \frac{ 1 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -10 } }{ 3 } - \frac{ \color{purple}{ 3 } }{ 3 }=\frac{ \color{purple}{ -13 } }{ 3 } \end{aligned} $$

Multiply $10$ by $ \dfrac{i}{6} $ to get $ \dfrac{ 10i }{ 6 } $.

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.

$$ \begin{aligned} 10 \cdot \frac{i}{6} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{i}{6} \xlongequal{\text{Step 2}} \frac{ 10 \cdot i }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10i }{ 6 } \end{aligned} $$

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.

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

Subtract $ \dfrac{10i}{6} $ from $ \dfrac{-13}{3} $ to get $ \dfrac{ \color{purple}{ -10i-26 } }{ 6 }$.

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

$$ \begin{aligned} \frac{-13}{3} - \frac{10i}{6} & = \frac{ \left( -13 \right) \cdot \color{blue}{ 2 }}{ 3 \cdot \color{blue}{ 2 }} - \frac{ 10i }{ 6 } = \\[1ex] &=\frac{ \color{purple}{ -26 } }{ 6 } - \frac{ \color{purple}{ 10i } }{ 6 }=\frac{ \color{purple}{ -10i-26 } }{ 6 } \end{aligned} $$

Subtract $5$ from $ \dfrac{-2i}{3} $ to get $ \dfrac{ \color{purple}{ -2i-15 } }{ 3 }$.

Step 1: Write $ 5 $ 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 $\color{blue}{3}$.

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

Subtract $ \dfrac{-2i-15}{3} $ from $ \dfrac{-10i-26}{6} $ to get $ \dfrac{ \color{purple}{ -6i+4 } }{ 6 }$.

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

$$ \begin{aligned} \frac{-10i-26}{6} - \frac{-2i-15}{3} & = \frac{ -10i-26 }{ 6 } - \frac{ \left( -2i-15 \right) \cdot \color{blue}{ 2 }}{ 3 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ -10i-26 } }{ 6 } - \frac{ \color{purple}{ -4i-30 } }{ 6 }=\frac{ \color{purple}{ -10i-26 - \left( -4i-30 \right) } }{ 6 } = \\[1ex] &=\frac{ \color{purple}{ -6i+4 } }{ 6 } \end{aligned} $$