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\frac{18}{2\left(1\times 18+7\right)}
Divide \frac{1}{2} by \frac{1\times 18+7}{18} by multiplying \frac{1}{2} by the reciprocal of \frac{1\times 18+7}{18}.
\frac{18}{2\left(18+7\right)}
Multiply 1 and 18 to get 18.
\frac{18}{2\times 25}
Add 18 and 7 to get 25.
\frac{18}{50}
Multiply 2 and 25 to get 50.
\frac{9}{25}
Reduce the fraction \frac{18}{50} to lowest terms by extracting and canceling out 2.