Solve the following addition problems with fractions: 2/3 + 1/6, 2 1/3 + 1 2/3, and 3 1/2 + 2 1/4.

$$
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
$$

$$
\frac{4}{6} + \frac{1}{6} = \frac{4+1}{6} = \frac{5}{6}
$$
The sum is $\boxed{\frac{5}{6}}$.

$$
2 + 1 = 3
$$

$$
\frac{1}{3} + \frac{2}{3} = \frac{1+2}{3} = \frac{3}{3} = 1
$$

$$
3 + 1 = 4
$$
The sum is $\boxed{4}$.

$$
3 + 2 = 5
$$

$$
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
$$

$$
\frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \frac{3}{4}
$$

$$
5 + \frac{3}{4} = 5\frac{3}{4}
$$
The sum is $\boxed{5\frac{3}{4}}$.

$$
6\frac{2}{5} = \frac{(6 \times 5) + 2}{5} = \frac{30 + 2}{5} = \frac{32}{5}
$$
$$
1\frac{3}{5} = \frac{(1 \times 5) + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5}
$$

$$
\frac{32}{5} \text{ and } \frac{8}{5}
$$
Since $32 \neq 8$, then $\frac{32}{5} \neq \frac{8}{5}$.

The statement $6\frac{2}{5} = 1\frac{3}{5}$ is $\boxed{\text{False}}$.