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The common denominator of the two fractions is: 385

$ \frac{3}{55 }= \frac{(3*7)}{(7*55)} =\frac{ 21}{385} $

$ \frac{9}{77 }= \frac{(5*9)}{(5*77)} =\frac{ 45}{385} $

Fractions adjusted to a common denominator

$ \frac{3}{55 }+\frac{ 9}{77 }=\frac{ 21}{385 }+\frac{ 45}{385} $

$ \frac{21}{385 }+\frac{ 45}{385 }= \frac{(21+45)}{385} $

$ \frac{(21+45)}{385 }=\frac{ 66}{385} $

$ \frac{66}{385 }=\frac{ 6}{35} $

$ $

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