The given numbers are
[tex]-8\frac{1}{3},-5\frac{1}{2}[/tex]To find the distance between, we must subtract them. However, first, we need to transform each number into a normal fraction
[tex]-8\frac{1}{3}=\frac{8\cdot3+1}{3}=-\frac{24+1}{3}=-\frac{25}{3}[/tex]Using the same process, we have
[tex]-5\frac{1}{2}=-\frac{5\cdot2+1}{2}=-\frac{10+1}{2}=-\frac{11}{2}[/tex]Now, we subtract those fractions
[tex]-\frac{11}{2}-(-\frac{25}{3})=-\frac{11}{2}+\frac{25}{3}=\frac{-33+50}{6}=\frac{17}{6}[/tex]However, we need the result as a mixed number
[tex]\frac{17}{6}=2\frac{5}{6}[/tex]