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2+\frac{5}{6}r=\frac{9}{2}
Reduce the fraction \frac{27}{6} to lowest terms by extracting and canceling out 3.
\frac{5}{6}r=\frac{9}{2}-2
Subtract 2 from both sides.
\frac{5}{6}r=\frac{9}{2}-\frac{4}{2}
Convert 2 to fraction \frac{4}{2}.
\frac{5}{6}r=\frac{9-4}{2}
Since \frac{9}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{5}{6}r=\frac{5}{2}
Subtract 4 from 9 to get 5.
r=\frac{5}{2}\times \frac{6}{5}
Multiply both sides by \frac{6}{5}, the reciprocal of \frac{5}{6}.
r=\frac{5\times 6}{2\times 5}
Multiply \frac{5}{2} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.
r=\frac{6}{2}
Cancel out 5 in both numerator and denominator.
r=3
Divide 6 by 2 to get 3.