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\frac{15}{36}-\frac{16}{36}
Least common multiple of 12 and 9 is 36. Convert \frac{5}{12} and \frac{4}{9} to fractions with denominator 36.
\frac{15-16}{36}
Since \frac{15}{36} and \frac{16}{36} have the same denominator, subtract them by subtracting their numerators.
-\frac{1}{36}
Subtract 16 from 15 to get -1.