Multiply $3$ by $ \dfrac{m}{5} $ to get $ \dfrac{ 3m }{ 5 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 3 \cdot \frac{m}{5} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{m}{5} \xlongequal{\text{Step 2}} \frac{ 3 \cdot m }{ 1 \cdot 5 } \xlongequal{\text{Step 3}} \frac{ 3m }{ 5 } \end{aligned} $$

Multiply $ \dfrac{3m}{5} $ by $ m^2 $ to get $ \dfrac{ 3m^3 }{ 5 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Add $ \dfrac{11}{2} $ and $ \dfrac{3m^3}{5} $ to get $ \dfrac{ \color{purple}{ 6m^3+55 } }{ 10 }$.

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}{ 5 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{11}{2} + \frac{3m^3}{5} & = \frac{ 11 \cdot \color{blue}{ 5 }}{ 2 \cdot \color{blue}{ 5 }} + \frac{ 3m^3 \cdot \color{blue}{ 2 }}{ 5 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 55 } }{ 10 } + \frac{ \color{purple}{ 6m^3 } }{ 10 }=\frac{ \color{purple}{ 6m^3+55 } }{ 10 } \end{aligned} $$

Add $ \dfrac{6m^3+55}{10} $ and $ 5m $ to get $ \dfrac{ \color{purple}{ 6m^3+50m+55 } }{ 10 }$.

Step 1: Write $ 5m $ 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 $\color{blue}{10}$.

$$ \begin{aligned} \frac{6m^3+55}{10} +5m & \xlongequal{\text{Step 1}} \frac{6m^3+55}{10} + \frac{5m}{\color{red}{1}} = \frac{ 6m^3+55 }{ 10 } + \frac{ 5m \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 6m^3+55 } }{ 10 } + \frac{ \color{purple}{ 50m } }{ 10 }=\frac{ \color{purple}{ 6m^3+50m+55 } }{ 10 } \end{aligned} $$