Answer :
The given expression is
[tex]6\frac{1}{4}+(-7\frac{6}{7})[/tex]First, we transform each mixed number into a fraction.
[tex]\begin{gathered} 6\frac{1}{4}=\frac{6\cdot4+1}{4}=\frac{24+1}{4}=\frac{25}{4} \\ 7\frac{6}{7}=\frac{7\cdot7+6}{7}=\frac{49+6}{7}=\frac{55}{7} \end{gathered}[/tex]Then, subtract the fractions.
[tex]\frac{25}{4}-\frac{55}{7}=\frac{25\cdot7-55\cdot4}{4\cdot7}=\frac{175-220}{28}=\frac{-45}{28}[/tex]