Multiply $ \dfrac{5}{2} $ by $ q^2 $ to get $ \dfrac{ 5q^2 }{ 2 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{2} \cdot q^2 & \xlongequal{\text{Step 1}} \frac{5}{2} \cdot \frac{q^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot q^2 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5q^2 }{ 2 } \end{aligned} $$

Add $2q$ and $ \dfrac{5q^2}{2} $ to get $ \dfrac{ \color{purple}{ 5q^2+4q } }{ 2 }$.

Step 1: Write $ 2q $ 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 first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} 2q+ \frac{5q^2}{2} & \xlongequal{\text{Step 1}} \frac{2q}{\color{red}{1}} + \frac{5q^2}{2} = \frac{ 2q \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 5q^2 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4q } }{ 2 } + \frac{ \color{purple}{ 5q^2 } }{ 2 }=\frac{ \color{purple}{ 5q^2+4q } }{ 2 } \end{aligned} $$

Add $ \dfrac{5q^2+4q}{2} $ and $ 5q $ to get $ \dfrac{ \color{purple}{ 5q^2+14q } }{ 2 }$.

Step 1: Write $ 5q $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{5q^2+4q}{2} +5q & \xlongequal{\text{Step 1}} \frac{5q^2+4q}{2} + \frac{5q}{\color{red}{1}} = \frac{ 5q^2+4q }{ 2 } + \frac{ 5q \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5q^2+4q } }{ 2 } + \frac{ \color{purple}{ 10q } }{ 2 }=\frac{ \color{purple}{ 5q^2+14q } }{ 2 } \end{aligned} $$