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\frac{44}{36}-\frac{63}{36}
Least common multiple of 9 and 4 is 36. Convert \frac{11}{9} and \frac{7}{4} to fractions with denominator 36.
\frac{44-63}{36}
Since \frac{44}{36} and \frac{63}{36} have the same denominator, subtract them by subtracting their numerators.
-\frac{19}{36}
Subtract 63 from 44 to get -19.