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-\frac{10}{9}+\frac{1}{6}
The opposite of -\frac{1}{6} is \frac{1}{6}.
-\frac{20}{18}+\frac{3}{18}
Least common multiple of 9 and 6 is 18. Convert -\frac{10}{9} and \frac{1}{6} to fractions with denominator 18.
\frac{-20+3}{18}
Since -\frac{20}{18} and \frac{3}{18} have the same denominator, add them by adding their numerators.
-\frac{17}{18}
Add -20 and 3 to get -17.