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\frac{9}{18}-\frac{8}{18}
Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{4}{9} to fractions with denominator 18.
\frac{9-8}{18}
Since \frac{9}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.
\frac{1}{18}
Subtract 8 from 9 to get 1.