Comparing and Ordering Fractions

\begin{array}{cccc}
5\dfrac{5}{6}& \:\:\dotso\:\: &\:\:5\dfrac{2}{3}\:\:\\\\
\color{green}\left(\dfrac{30}{6} + \dfrac{5}{6}\right) & \:\:\dotso\:\: & \color{green}\:\:\dfrac{15}{3} + \dfrac{2}{3}\:\:\\\\
\color{green}\dfrac{35}{6} & \:\:\dotso\:\: & \color{green}\:\:\dfrac{17}{3}\:\:\\\\
\color{green}\dfrac{35}{6} &\:\:\dotso\:\: &\color{green} \:\: \dfrac{17\times \color{red} 2}{3 \times \color{red} 2}\:\:\\\\
\color{green}\dfrac{35}{6} & \:\:>\:\: & \color{green}\:\:\dfrac{34}{6}\:\:\\\\
\end{array}