Using the instant rule from the text (which is actually a bit unwieldy here): $$\frac{1}{10}+\frac{1}{5}=\frac{1\times 5+10\times 1}{10\times 5}=\frac{5+10}{50}=\frac{15}{50}$$ Notice that this can actually be made simpler: it is the same thing as $\frac{3}{10}$, because when we take $\frac{3}{10}$ and split each $\frac{1}{10}$-block into five equal pieces, we obtain $15$ copies of the $\frac{1}{50}$-block.

Alternatively, one could spot that $\frac{1}{10}$-blocks actually can already be used to make $\frac{1}{5}$-blocks: $\frac{1}{5}=\frac{2}{10}$. Therefore we're actually trying to find $\frac{1}{10}+\frac{2}{10}$, which is easy: it's $\frac{3}{10}$.