In this case, the least common multiple of 10 and 15 is 30. So, we can rewrite $\frac{3}{10}$ as $\frac{9}{30}$ and $\frac{4}{15}$ as $\frac{8}{30}$. Then, we can add them:
$$\frac{3}{10}+\frac{4}{15}=\frac{9}{30}+\frac{8}{30}=\frac{17}{30}$$
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