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\frac{13}{18}-\frac{16}{18}+\frac{1}{6}
Least common multiple of 18 and 9 is 18. Convert \frac{13}{18} and \frac{8}{9} to fractions with denominator 18.
\frac{13-16}{18}+\frac{1}{6}
Since \frac{13}{18} and \frac{16}{18} have the same denominator, subtract them by subtracting their numerators.
\frac{-3}{18}+\frac{1}{6}
Subtract 16 from 13 to get -3.
-\frac{1}{6}+\frac{1}{6}
Reduce the fraction \frac{-3}{18} to lowest terms by extracting and canceling out 3.
0
Add -\frac{1}{6} and \frac{1}{6} to get 0.