Answer:
[tex]-3\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]2\frac{1}{6}-5\frac{2}{3}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\\\quad 2\frac{1}{6}=\frac{13}{6}\\\\\frac{13}{6}-5\frac{2}{3}\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\\\quad 5\frac{2}{3}=\frac{17}{3}\\\\\frac{13}{6}-\frac{17}{3}\\\\\mathrm{Least\:Common\:Multiplier\:of\:}6,\:3:\quad 6\\\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\=\frac{13}{6}-\frac{34}{6}\\\\=\frac{13-34}{6}\\\\=\frac{-21}{6}\\\\=-\frac{21}{6}\\\\=-\frac{7}{2}\\[/tex]
[tex]\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\quad \frac{7}{2}=3\frac{1}{2}\\\\=-3\frac{1}{2}[/tex]
