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\frac{12}{9}-\frac{1}{9}-\frac{1}{3}-\frac{2}{3}-1+\frac{17}{18}
Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{1}{9} to fractions with denominator 9.
\frac{12-1}{9}-\frac{1}{3}-\frac{2}{3}-1+\frac{17}{18}
Since \frac{12}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.
\frac{11}{9}-\frac{1}{3}-\frac{2}{3}-1+\frac{17}{18}
Subtract 1 from 12 to get 11.
\frac{11}{9}-\frac{3}{9}-\frac{2}{3}-1+\frac{17}{18}
Least common multiple of 9 and 3 is 9. Convert \frac{11}{9} and \frac{1}{3} to fractions with denominator 9.
\frac{11-3}{9}-\frac{2}{3}-1+\frac{17}{18}
Since \frac{11}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.
\frac{8}{9}-\frac{2}{3}-1+\frac{17}{18}
Subtract 3 from 11 to get 8.
\frac{8}{9}-\frac{6}{9}-1+\frac{17}{18}
Least common multiple of 9 and 3 is 9. Convert \frac{8}{9} and \frac{2}{3} to fractions with denominator 9.
\frac{8-6}{9}-1+\frac{17}{18}
Since \frac{8}{9} and \frac{6}{9} have the same denominator, subtract them by subtracting their numerators.
\frac{2}{9}-1+\frac{17}{18}
Subtract 6 from 8 to get 2.
\frac{2}{9}-\frac{9}{9}+\frac{17}{18}
Convert 1 to fraction \frac{9}{9}.
\frac{2-9}{9}+\frac{17}{18}
Since \frac{2}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.
-\frac{7}{9}+\frac{17}{18}
Subtract 9 from 2 to get -7.
-\frac{14}{18}+\frac{17}{18}
Least common multiple of 9 and 18 is 18. Convert -\frac{7}{9} and \frac{17}{18} to fractions with denominator 18.
\frac{-14+17}{18}
Since -\frac{14}{18} and \frac{17}{18} have the same denominator, add them by adding their numerators.
\frac{3}{18}
Add -14 and 17 to get 3.
\frac{1}{6}
Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.