Same Denominator

$\frac{2}{9}+\frac{4}{9}$: both fractions count ninths. 2 ninths and 4 ninths make 6 ninths, so the sum is $\frac{6}{9}$. Add the tops and keep the bottom.

Why keep the bottom? The denominator names the size of the pieces, and adding does not change their size, just as 2 apples and 4 apples make 6 apples. Adding the bottoms as well would give $\frac{6}{18}$, which is $\frac{1}{3}$: smaller than $\frac{4}{9}$ on its own, so it cannot be the sum.

Finish by simplifying, as in the last chapter: 6 and 9 share a 3, so $\frac{6}{9}$ is $\frac{2}{3}$. The board will not call a sum finished until it is in lowest terms.