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\frac{1}{2}+\left(\frac{9}{12}-\frac{1}{12}\right)\times \frac{4}{5}
Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{1}{12} to fractions with denominator 12.
\frac{1}{2}+\frac{9-1}{12}\times \frac{4}{5}
Since \frac{9}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.
\frac{1}{2}+\frac{8}{12}\times \frac{4}{5}
Subtract 1 from 9 to get 8.
\frac{1}{2}+\frac{2}{3}\times \frac{4}{5}
Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.
\frac{1}{2}+\frac{2\times 4}{3\times 5}
Multiply \frac{2}{3} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{2}+\frac{8}{15}
Do the multiplications in the fraction \frac{2\times 4}{3\times 5}.
\frac{15}{30}+\frac{16}{30}
Least common multiple of 2 and 15 is 30. Convert \frac{1}{2} and \frac{8}{15} to fractions with denominator 30.
\frac{15+16}{30}
Since \frac{15}{30} and \frac{16}{30} have the same denominator, add them by adding their numerators.
\frac{31}{30}
Add 15 and 16 to get 31.