Every mixed number can be written as the sum of its whole number and fractional parts. So, our mixed number can be written as

\[ 2 \, \dfrac{1}{3} = 2 + \dfrac{1}{3}. \]

Now, substituting ${\color{blue}\dfrac{6}{3}}$ for ${\color{blue}2}$ and adding the fractions, we obtain

\begin{align} {\color{blue}2} + \dfrac{1}{3} = {\color{blue}\dfrac{6}{3}} + \dfrac{1}{3} = \dfrac{7}{3}. \end{align}

Every mixed number can be written as the sum of its whole number and fractional parts. So, our mixed number can be written as

\[ 8 \, \dfrac{4}{7} = 8 + \dfrac{4}{7}. \]

Now, substituting ${\color{blue}\dfrac{56}{7}}$ for ${\color{blue}8}$ and adding the fractions, we obtain

\begin{align} {\color{blue}8} + \dfrac{4}{7} = {\color{blue}\dfrac{56}{7}} + \dfrac{4}{7} = \dfrac{60}{7}. \end{align}

First, we write the whole number part $(1)$ as a fraction with $1$ in the denominator.

\[ 1 = \dfrac{1}{1} \]

We put this over a denominator of $3$ by multiplying the numerator and denominator by $3{:}$

\[ \dfrac{1}{1} = \dfrac{1 \times 3}{1 \times 3} = \dfrac{3}{3} \]

Now, we add the fractions:

\begin{align} 1 \,\dfrac{1}{3} = \dfrac{3}{3} + \dfrac{1}{3} = \dfrac{4}{3} \end{align}

First, we write the whole number part $(19)$ as a fraction with $1$ in the denominator.

\[ 19 = \dfrac{19}{1} \]

We put this over a denominator of $3$ by multiplying the numerator and denominator by $3{:}$

\[ \dfrac{19}{1} = \dfrac{19 \times 3}{1 \times 3} = \dfrac{57}{3} \]

Now we add fractions:

\begin{align} 19 \,\dfrac{2}{3} = \dfrac{57}{3} + \dfrac{2}{3} = \dfrac{59}{3} \end{align}