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\frac{18}{45}+\frac{20}{45}
Least common multiple of 5 and 9 is 45. Convert \frac{2}{5} and \frac{4}{9} to fractions with denominator 45.
\frac{18+20}{45}
Since \frac{18}{45} and \frac{20}{45} have the same denominator, add them by adding their numerators.
\frac{38}{45}
Add 18 and 20 to get 38.