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\frac{8}{18}-\frac{27}{18}
Least common multiple of 9 and 2 is 18. Convert \frac{4}{9} and \frac{3}{2} to fractions with denominator 18.
\frac{8-27}{18}
Since \frac{8}{18} and \frac{27}{18} have the same denominator, subtract them by subtracting their numerators.
-\frac{19}{18}
Subtract 27 from 8 to get -19.