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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{2}{7} $ by $ b $ to get $ \dfrac{ 2b }{ 7 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2}{7} \cdot b & \xlongequal{\text{Step 1}} \frac{2}{7} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot b }{ 7 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 2b }{ 7 } \end{aligned} $$

Subtract $8$ from $ \dfrac{b}{2} $ to get $ \dfrac{ \color{purple}{ b-16 } }{ 2 }$.

Step 1: Write $ 8 $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{b}{2} -8 & \xlongequal{\text{Step 1}} \frac{b}{2} - \frac{8}{\color{red}{1}} = \frac{ b }{ 2 } - \frac{ 8 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ b } }{ 2 } - \frac{ \color{purple}{ 16 } }{ 2 }=\frac{ \color{purple}{ b-16 } }{ 2 } \end{aligned} $$

Multiply $ \dfrac{2}{7} $ by $ b $ to get $ \dfrac{ 2b }{ 7 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2}{7} \cdot b & \xlongequal{\text{Step 1}} \frac{2}{7} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2 \cdot b }{ 7 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 2b }{ 7 } \end{aligned} $$

Subtract $ \dfrac{2b}{7} $ from $ \dfrac{b-16}{2} $ to get $ \dfrac{ \color{purple}{ 3b-112 } }{ 14 }$.

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

$$ \begin{aligned} \frac{b-16}{2} - \frac{2b}{7} & = \frac{ \left( b-16 \right) \cdot \color{blue}{ 7 }}{ 2 \cdot \color{blue}{ 7 }} - \frac{ 2b \cdot \color{blue}{ 2 }}{ 7 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 7b-112 } }{ 14 } - \frac{ \color{purple}{ 4b } }{ 14 }=\frac{ \color{purple}{ 3b-112 } }{ 14 } \end{aligned} $$

Add $ \dfrac{3b-112}{14} $ and $ 4 $ to get $ \dfrac{ \color{purple}{ 3b-56 } }{ 14 }$.

Step 1: Write $ 4 $ 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 $\color{blue}{14}$.

$$ \begin{aligned} \frac{3b-112}{14} +4 & \xlongequal{\text{Step 1}} \frac{3b-112}{14} + \frac{4}{\color{red}{1}} = \frac{ 3b-112 }{ 14 } + \frac{ 4 \cdot \color{blue}{ 14 }}{ 1 \cdot \color{blue}{ 14 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3b-112 } }{ 14 } + \frac{ \color{purple}{ 56 } }{ 14 }=\frac{ \color{purple}{ 3b-56 } }{ 14 } \end{aligned} $$