Multiply $ \dfrac{1}{11} $ by $ r $ to get $ \dfrac{ r }{ 11 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{11} \cdot r & \xlongequal{\text{Step 1}} \frac{1}{11} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot r }{ 11 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ r }{ 11 } \end{aligned} $$

Add $44r^2+7r$ and $ \dfrac{r}{11} $ to get $ \dfrac{ \color{purple}{ 484r^2+78r } }{ 11 }$.

Step 1: Write $ 44r^2+7r $ 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 first fraction by $\color{blue}{ 11 }$.

$$ \begin{aligned} 44r^2+7r+ \frac{r}{11} & \xlongequal{\text{Step 1}} \frac{44r^2+7r}{\color{red}{1}} + \frac{r}{11} = \frac{ \left( 44r^2+7r \right) \cdot \color{blue}{ 11 }}{ 1 \cdot \color{blue}{ 11 }} + \frac{ r }{ 11 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 484r^2+77r } }{ 11 } + \frac{ \color{purple}{ r } }{ 11 }=\frac{ \color{purple}{ 484r^2+78r } }{ 11 } \end{aligned} $$

Subtract $1$ from $ \dfrac{484r^2+78r}{11} $ to get $ \dfrac{ \color{purple}{ 484r^2+78r-11 } }{ 11 }$.

Step 1: Write $ 1 $ 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 $\color{blue}{11}$.

$$ \begin{aligned} \frac{484r^2+78r}{11} -1 & \xlongequal{\text{Step 1}} \frac{484r^2+78r}{11} - \frac{1}{\color{red}{1}} = \frac{ 484r^2+78r }{ 11 } - \frac{ 1 \cdot \color{blue}{ 11 }}{ 1 \cdot \color{blue}{ 11 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 484r^2+78r } }{ 11 } - \frac{ \color{purple}{ 11 } }{ 11 }=\frac{ \color{purple}{ 484r^2+78r-11 } }{ 11 } \end{aligned} $$