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

Step 1: Write $ n^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{3}{4} $ by $ n $ to get $ \dfrac{ 3n }{ 4 } $.

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.

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

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

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

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

Multiply $ \dfrac{3}{4} $ by $ n $ to get $ \dfrac{ 3n }{ 4 } $.

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.

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

Subtract $ \dfrac{3n}{4} $ from $ \dfrac{n^2-12n}{2} $ to get $ \dfrac{ \color{purple}{ 2n^2-27n } }{ 4 }$.

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

$$ \begin{aligned} \frac{n^2-12n}{2} - \frac{3n}{4} & = \frac{ \left( n^2-12n \right) \cdot \color{blue}{ 2 }}{ 2 \cdot \color{blue}{ 2 }} - \frac{ 3n }{ 4 } = \\[1ex] &=\frac{ \color{purple}{ 2n^2-24n } }{ 4 } - \frac{ \color{purple}{ 3n } }{ 4 }=\frac{ \color{purple}{ 2n^2-27n } }{ 4 } \end{aligned} $$

Add $ \dfrac{2n^2-27n}{4} $ and $ 7n $ to get $ \dfrac{ \color{purple}{ 2n^2+n } }{ 4 }$.

Step 1: Write $ 7n $ 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 $\color{blue}{4}$.

$$ \begin{aligned} \frac{2n^2-27n}{4} +7n & \xlongequal{\text{Step 1}} \frac{2n^2-27n}{4} + \frac{7n}{\color{red}{1}} = \frac{ 2n^2-27n }{ 4 } + \frac{ 7n \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2n^2-27n } }{ 4 } + \frac{ \color{purple}{ 28n } }{ 4 }=\frac{ \color{purple}{ 2n^2+n } }{ 4 } \end{aligned} $$