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\frac{9}{36}-\frac{8}{36}
Least common multiple of 4 and 9 is 36. Convert \frac{1}{4} and \frac{2}{9} to fractions with denominator 36.
\frac{9-8}{36}
Since \frac{9}{36} and \frac{8}{36} have the same denominator, subtract them by subtracting their numerators.
\frac{1}{36}
Subtract 8 from 9 to get 1.