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The common denominator of the two fractions is: 45

$ \frac{2}{5 }= \frac{(2*9)}{(5*9)} =\frac{ 18}{45} $

$ \frac{1}{9 }= \frac{(1*5)}{(5*9)} =\frac{ 5}{45} $

Fractions adjusted to a common denominator

$ \frac{2}{5 }+\frac{ 1}{9 }=\frac{ 18}{45 }+\frac{ 5}{45} $

$ \frac{18}{45 }+\frac{ 5}{45 }= \frac{(5+18)}{45} $

$ \frac{(5+18)}{45 }=\frac{ 23}{45} $

$ $

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