Add $ \dfrac{-1}{2} $ and $ 3 $ to get $ \dfrac{ \color{purple}{ 5 } }{ 2 }$.

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

Step 2: To add fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{2}$.

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