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\frac{1}{3}-\frac{13}{9}
Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.
\frac{3}{9}-\frac{13}{9}
Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{13}{9} to fractions with denominator 9.
\frac{3-13}{9}
Since \frac{3}{9} and \frac{13}{9} have the same denominator, subtract them by subtracting their numerators.
-\frac{10}{9}
Subtract 13 from 3 to get -10.