Solve the following addition problems with mixed numbers: a) 2 rac12 + 3 rac34 b) 1 rac38 + 9 rac13

$$2 + 3 = 5$$ $$\frac{1}{2} + \frac{3}{4}$$

The least common multiple of 2 and 4 is 4.

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

$$5 + 1\frac{1}{4} = 6\frac{1}{4}$$

The final answer is $\boxed{6\frac{1}{4}}$.

$$1 + 9 = 10$$ $$\frac{3}{8} + \frac{1}{3}$$

The least common multiple of 8 and 3 is 24.

$$\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}$$ $$\frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24}$$

$$10 + \frac{17}{24} = 10\frac{17}{24}$$

The final answer is $\boxed{10\frac{17}{24}}$.