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\frac{1}{6}-\frac{4}{6}
Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{2}{3} to fractions with denominator 6.
\frac{1-4}{6}
Since \frac{1}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{-3}{6}
Subtract 4 from 1 to get -3.
-\frac{1}{2}
Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.