Add $ \dfrac{1}{1156} $ and $ r $ to get $ \dfrac{ \color{purple}{ 1156r+1 } }{ 1156 }$.

Step 1: Write $ r $ 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 $\color{blue}{1156}$.

$$ \begin{aligned} \frac{1}{1156} +r & \xlongequal{\text{Step 1}} \frac{1}{1156} + \frac{r}{\color{red}{1}} = \frac{ 1 }{ 1156 } + \frac{ r \cdot \color{blue}{ 1156 }}{ 1 \cdot \color{blue}{ 1156 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1 } }{ 1156 } + \frac{ \color{purple}{ 1156r } }{ 1156 }=\frac{ \color{purple}{ 1156r+1 } }{ 1156 } \end{aligned} $$

Subtract $6$ from $ \dfrac{1156r+1}{1156} $ to get $ \dfrac{ \color{purple}{ 1156r-6935 } }{ 1156 }$.

Step 1: Write $ 6 $ 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 $\color{blue}{1156}$.

$$ \begin{aligned} \frac{1156r+1}{1156} -6 & \xlongequal{\text{Step 1}} \frac{1156r+1}{1156} - \frac{6}{\color{red}{1}} = \frac{ 1156r+1 }{ 1156 } - \frac{ 6 \cdot \color{blue}{ 1156 }}{ 1 \cdot \color{blue}{ 1156 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1156r+1 } }{ 1156 } - \frac{ \color{purple}{ 6936 } }{ 1156 }=\frac{ \color{purple}{ 1156r-6935 } }{ 1156 } \end{aligned} $$