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\left(\frac{1}{9}\times 3-\frac{1}{6}\right)\times 6
Anything divided by one gives itself.
\left(\frac{3}{9}-\frac{1}{6}\right)\times 6
Multiply \frac{1}{9} and 3 to get \frac{3}{9}.
\left(\frac{1}{3}-\frac{1}{6}\right)\times 6
Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.
\left(\frac{2}{6}-\frac{1}{6}\right)\times 6
Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{1}{6} to fractions with denominator 6.
\frac{2-1}{6}\times 6
Since \frac{2}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{1}{6}\times 6
Subtract 1 from 2 to get 1.
1
Cancel out 6 and 6.