Multiply $7$ by $ \dfrac{y}{6} $ to get $ \dfrac{ 7y }{ 6 } $.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 7 \cdot \frac{y}{6} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{y}{6} \xlongequal{\text{Step 2}} \frac{ 7 \cdot y }{ 1 \cdot 6 } \xlongequal{\text{Step 3}} \frac{ 7y }{ 6 } \end{aligned} $$

Multiply $2$ by $ \dfrac{y}{9} $ to get $ \dfrac{ 2y }{ 9 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{y}{9} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{y}{9} \xlongequal{\text{Step 2}} \frac{ 2 \cdot y }{ 1 \cdot 9 } \xlongequal{\text{Step 3}} \frac{ 2y }{ 9 } \end{aligned} $$

Subtract $ \dfrac{y}{2} $ from $ \dfrac{7y}{6} $ to get $ \dfrac{ \color{purple}{ 4y } }{ 6 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{3}$.

$$ \begin{aligned} \frac{7y}{6} - \frac{y}{2} & = \frac{ 7y }{ 6 } - \frac{ y \cdot \color{blue}{ 3 }}{ 2 \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 7y } }{ 6 } - \frac{ \color{purple}{ 3y } }{ 6 }=\frac{ \color{purple}{ 4y } }{ 6 } \end{aligned} $$

Multiply $2$ by $ \dfrac{y}{9} $ to get $ \dfrac{ 2y }{ 9 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{y}{9} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{y}{9} \xlongequal{\text{Step 2}} \frac{ 2 \cdot y }{ 1 \cdot 9 } \xlongequal{\text{Step 3}} \frac{ 2y }{ 9 } \end{aligned} $$

Add $ \dfrac{4y}{6} $ and $ \dfrac{2y}{9} $ to get $ \dfrac{ \color{purple}{ 16y } }{ 18 }$.

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

$$ \begin{aligned} \frac{4y}{6} + \frac{2y}{9} & = \frac{ 4y \cdot \color{blue}{ 3 }}{ 6 \cdot \color{blue}{ 3 }} + \frac{ 2y \cdot \color{blue}{ 2 }}{ 9 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 12y } }{ 18 } + \frac{ \color{purple}{ 4y } }{ 18 }=\frac{ \color{purple}{ 16y } }{ 18 } \end{aligned} $$