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\frac{10}{18}+\frac{9}{18}
Least common multiple of 9 and 2 is 18. Convert \frac{5}{9} and \frac{1}{2} to fractions with denominator 18.
\frac{10+9}{18}
Since \frac{10}{18} and \frac{9}{18} have the same denominator, add them by adding their numerators.
\frac{19}{18}
Add 10 and 9 to get 19.