Divide both the top and bottom numbers by $ \color{orangered}{ 5 } $.

Multiply $20$ by $ \dfrac{g}{6} $ to get $ \dfrac{ 20g }{ 6 } $.

Step 1: Write $ 20 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 20 \cdot \frac{g}{6} & \xlongequal{\text{Step 1}} \frac{20}{\color{red}{1}} \cdot \frac{g}{6} \xlongequal{\text{Step 2}} \frac{ 20 \cdot g }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20g }{ 6 } \end{aligned} $$

Multiply $20$ by $ \dfrac{g}{6} $ to get $ \dfrac{ 20g }{ 6 } $.

Step 1: Write $ 20 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 20 \cdot \frac{g}{6} & \xlongequal{\text{Step 1}} \frac{20}{\color{red}{1}} \cdot \frac{g}{6} \xlongequal{\text{Step 2}} \frac{ 20 \cdot g }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20g }{ 6 } \end{aligned} $$

Multiply $ \dfrac{1}{3} $ by $ g^2 $ to get $ \dfrac{ g^2 }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $20$ by $ \dfrac{g}{6} $ to get $ \dfrac{ 20g }{ 6 } $.

Step 1: Write $ 20 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 20 \cdot \frac{g}{6} & \xlongequal{\text{Step 1}} \frac{20}{\color{red}{1}} \cdot \frac{g}{6} \xlongequal{\text{Step 2}} \frac{ 20 \cdot g }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20g }{ 6 } \end{aligned} $$

Subtract $ \dfrac{g^2}{3} $ from $ 3g $ to get $ \dfrac{ \color{purple}{ -g^2+9g } }{ 3 }$.

Step 1: Write $ 3g $ 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 first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} 3g- \frac{g^2}{3} & \xlongequal{\text{Step 1}} \frac{3g}{\color{red}{1}} - \frac{g^2}{3} = \frac{ 3g \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} - \frac{ g^2 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9g } }{ 3 } - \frac{ \color{purple}{ g^2 } }{ 3 }=\frac{ \color{purple}{ -g^2+9g } }{ 3 } \end{aligned} $$

Multiply $20$ by $ \dfrac{g}{6} $ to get $ \dfrac{ 20g }{ 6 } $.

Step 1: Write $ 20 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 20 \cdot \frac{g}{6} & \xlongequal{\text{Step 1}} \frac{20}{\color{red}{1}} \cdot \frac{g}{6} \xlongequal{\text{Step 2}} \frac{ 20 \cdot g }{ 1 \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20g }{ 6 } \end{aligned} $$

Add $ \dfrac{-g^2+9g}{3} $ and $ \dfrac{20g}{6} $ to get $ \dfrac{ \color{purple}{ -2g^2+38g } }{ 6 }$.

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

$$ \begin{aligned} \frac{-g^2+9g}{3} + \frac{20g}{6} & = \frac{ \left( -g^2+9g \right) \cdot \color{blue}{ 2 }}{ 3 \cdot \color{blue}{ 2 }} + \frac{ 20g }{ 6 } = \\[1ex] &=\frac{ \color{purple}{ -2g^2+18g } }{ 6 } + \frac{ \color{purple}{ 20g } }{ 6 }=\frac{ \color{purple}{ -2g^2+38g } }{ 6 } \end{aligned} $$