Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $.

Multiply $ \dfrac{1}{2} $ by $ n $ to get $ \dfrac{ n }{ 2 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $6$ from $ \dfrac{n}{2} $ to get $ \dfrac{ \color{purple}{ n-12 } }{ 2 }$.

Step 1: Write $ 6 $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{n}{2} -6 & \xlongequal{\text{Step 1}} \frac{n}{2} - \frac{6}{\color{red}{1}} = \frac{ n }{ 2 } - \frac{ 6 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ n } }{ 2 } - \frac{ \color{purple}{ 12 } }{ 2 }=\frac{ \color{purple}{ n-12 } }{ 2 } \end{aligned} $$

Subtract $ \dfrac{3}{2} $ from $ \dfrac{n-12}{2} $ to get $ \dfrac{n-15}{2} $.

To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{n-12}{2} - \frac{3}{2} & = \frac{n-12}{\color{blue}{2}} - \frac{3}{\color{blue}{2}} =\frac{ n-12 - 3 }{ \color{blue}{ 2 }} = \\[1ex] &= \frac{n-15}{2} \end{aligned} $$