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\frac{\frac{11}{16}}{\frac{5}{6}+\frac{4}{6}}-\frac{1}{3}
Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{2}{3} to fractions with denominator 6.
\frac{\frac{11}{16}}{\frac{5+4}{6}}-\frac{1}{3}
Since \frac{5}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.
\frac{\frac{11}{16}}{\frac{9}{6}}-\frac{1}{3}
Add 5 and 4 to get 9.
\frac{\frac{11}{16}}{\frac{3}{2}}-\frac{1}{3}
Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.
\frac{11}{16}\times \frac{2}{3}-\frac{1}{3}
Divide \frac{11}{16} by \frac{3}{2} by multiplying \frac{11}{16} by the reciprocal of \frac{3}{2}.
\frac{11\times 2}{16\times 3}-\frac{1}{3}
Multiply \frac{11}{16} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{22}{48}-\frac{1}{3}
Do the multiplications in the fraction \frac{11\times 2}{16\times 3}.
\frac{11}{24}-\frac{1}{3}
Reduce the fraction \frac{22}{48} to lowest terms by extracting and canceling out 2.
\frac{11}{24}-\frac{8}{24}
Least common multiple of 24 and 3 is 24. Convert \frac{11}{24} and \frac{1}{3} to fractions with denominator 24.
\frac{11-8}{24}
Since \frac{11}{24} and \frac{8}{24} have the same denominator, subtract them by subtracting their numerators.
\frac{3}{24}
Subtract 8 from 11 to get 3.
\frac{1}{8}
Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.