\( \left. \begin{array} { l } { \frac { 3 } { 7 } + \frac { 5 } { 14 } + \frac { 8 } { 21 } } \\ { \frac { 16 } { 42 } } \\ { \frac { 49 } { 42 } } \\ \hline \end{array} \right. \)

To solve \( \frac{3}{7} + \frac{5}{14} + \frac{8}{21} \), we need to find a common denominator. The least common multiple (LCM) of 7, 14, and 21 is 42. Now, convert each fraction: - Convert \( \frac{3}{7} \) to \( \frac{18}{42} \) (multiply top and bottom by 6), - Convert \( \frac{5}{14} \) to \( \frac{15}{42} \) (multiply top and bottom by 3), - Convert \( \frac{8}{21} \) to \( \frac{16}{42} \) (multiply top and bottom by 2). Now, add them up: \[ \frac{18}{42} + \frac{15}{42} + \frac{16}{42} = \frac{49}{42}. \] So the final answer is \( \frac{49}{42} \) which can also be expressed as \( 1 \frac{7}{42} \) or simplified further to \( 1 \frac{1}{6} \).