Multiply $8$ by $ \dfrac{k}{4} $ to get $ \dfrac{ 8k }{ 4 } $.

Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 8 \cdot \frac{k}{4} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{k}{4} \xlongequal{\text{Step 2}} \frac{ 8 \cdot k }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 8k }{ 4 } \end{aligned} $$

Multiply $6$ by $ \dfrac{k}{3} $ to get $ \dfrac{ 6k }{ 3 } $.

Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 6 \cdot \frac{k}{3} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{k}{3} \xlongequal{\text{Step 2}} \frac{ 6 \cdot k }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 6k }{ 3 } \end{aligned} $$

Multiply $2$ by $ \dfrac{k}{4} $ to get $ \dfrac{ 2k }{ 4 } $.

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.

$$ \begin{aligned} 2 \cdot \frac{k}{4} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{k}{4} \xlongequal{\text{Step 2}} \frac{ 2 \cdot k }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 2k }{ 4 } \end{aligned} $$

Multiply $6$ by $ \dfrac{k}{3} $ to get $ \dfrac{ 6k }{ 3 } $.

Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 6 \cdot \frac{k}{3} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{k}{3} \xlongequal{\text{Step 2}} \frac{ 6 \cdot k }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 6k }{ 3 } \end{aligned} $$

Subtract $ \dfrac{6k}{3} $ from $ \dfrac{8k}{4} $ to get $ \dfrac{ \color{purple}{ 0 } }{ 12 }$.

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}{ 3 }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{8k}{4} - \frac{6k}{3} & = \frac{ 8k \cdot \color{blue}{ 3 }}{ 4 \cdot \color{blue}{ 3 }} - \frac{ 6k \cdot \color{blue}{ 4 }}{ 3 \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 24k } }{ 12 } - \frac{ \color{purple}{ 24k } }{ 12 }=\frac{ \color{purple}{ 0 } }{ 12 } \end{aligned} $$

Subtract $ \dfrac{6k}{3} $ from $ \dfrac{2k}{4} $ to get $ \dfrac{ \color{purple}{ -18k } }{ 12 }$.

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}{ 3 }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{2k}{4} - \frac{6k}{3} & = \frac{ 2k \cdot \color{blue}{ 3 }}{ 4 \cdot \color{blue}{ 3 }} - \frac{ 6k \cdot \color{blue}{ 4 }}{ 3 \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 6k } }{ 12 } - \frac{ \color{purple}{ 24k } }{ 12 }=\frac{ \color{purple}{ -18k } }{ 12 } \end{aligned} $$

Subtract $1$ from $ \dfrac{-18k}{12} $ to get $ \dfrac{ \color{purple}{ -18k-12 } }{ 12 }$.

Step 1: Write $ 1 $ 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 $\color{blue}{12}$.

$$ \begin{aligned} \frac{-18k}{12} -1 & \xlongequal{\text{Step 1}} \frac{-18k}{12} - \frac{1}{\color{red}{1}} = \frac{ -18k }{ 12 } - \frac{ 1 \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -18k } }{ 12 } - \frac{ \color{purple}{ 12 } }{ 12 }=\frac{ \color{purple}{ -18k-12 } }{ 12 } \end{aligned} $$

Subtract $1$ from $ \dfrac{-18k}{12} $ to get $ \dfrac{ \color{purple}{ -18k-12 } }{ 12 }$.

Step 1: Write $ 1 $ 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 $\color{blue}{12}$.

$$ \begin{aligned} \frac{-18k}{12} -1 & \xlongequal{\text{Step 1}} \frac{-18k}{12} - \frac{1}{\color{red}{1}} = \frac{ -18k }{ 12 } - \frac{ 1 \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -18k } }{ 12 } - \frac{ \color{purple}{ 12 } }{ 12 }=\frac{ \color{purple}{ -18k-12 } }{ 12 } \end{aligned} $$

Subtract $ \dfrac{-18k-12}{12} $ from $ 7 $ to get $ \dfrac{ \color{purple}{ 18k+96 } }{ 12 }$.

Step 1: Write $ 7 $ 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 first fraction by $\color{blue}{ 12 }$.

$$ \begin{aligned} 7- \frac{-18k-12}{12} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} - \frac{-18k-12}{12} = \frac{ 7 \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} - \frac{ -18k-12 }{ 12 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 84 } }{ 12 } - \frac{ \color{purple}{ -18k-12 } }{ 12 }=\frac{ \color{purple}{ 84 - \left( -18k-12 \right) } }{ 12 } = \\[1ex] &=\frac{ \color{purple}{ 18k+96 } }{ 12 } \end{aligned} $$