Which sign makes the statement true? \( \begin{array}{l} 6 \frac{5}{6} ? 7 \frac{1}{2}-\frac{4}{6} \\ > \\ \end{array} \)

To determine the appropriate sign for the statement \( 6 \frac{5}{6} ? 7 \frac{1}{2}-\frac{4}{6} \), let's first convert everything to improper fractions or equivalent decimals for clarity. The mixed number \( 6 \frac{5}{6} \) converts to \( \frac{41}{6} \) and \( 7 \frac{1}{2} \) to \( \frac{15}{2} \) or \( 7.5 \). The fraction \( -\frac{4}{6} \) simplifies to \( -\frac{2}{3} \), and when we calculate \( 7 \frac{1}{2} - \frac{4}{6} \), it is \( 7.5 - 0.6667 = 6.8333 \). Now, comparing \( 6 \frac{5}{6} \) (which is approximately 6.8333) to \( 7.5 - \frac{2}{3} \) shows that both sides equal \( 6.8333 \). Therefore, the appropriate sign to make the statement true would be \( = \) (or we could also conclude that \( 6 \frac{5}{6} \) is less than \( 7 \frac{1}{2} - \frac{4}{6} \)). Thus, we would use \( < \) for the statement \( 6 \frac{5}{6} < 7 \frac{1}{2} - \frac{4}{6} \).