In order to find the required fraction, you can write the following inequality:
[tex]\frac{2}{15}+x>\frac{1}{2}[/tex]Solve the previous inequality for x by subtracting 2/15 both sides and simplifying:
[tex]\begin{gathered} x>\frac{1}{2}-\frac{2}{15} \\ x>\frac{15-4}{30} \\ x>\frac{11}{30} \end{gathered}[/tex]Then, you hava that x must be greater than 11/30.
You can notice that from the given choices, 8/15 is the only number that is greater than 11/30 (you can check it by subtracting 11/30 to 8/15, you'll get a positive number).
Hence, 8/15 is the value you can add to 2/15 to get a greater number than 1/2
