Add the following mixed numbers: a) 5 rac13 + 1 rac24 b) 4 rac35 + 3 rac46

$$5 + 1 = 6$$

The denominators are 3 and 4. The least common multiple of 3 and 4 is 12.
Convert the fractions:

$$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$ $$\frac{2}{4} = \frac{2 \times 3}{4 \times 3} = \frac{6}{12}$$

$$6 + \frac{10}{12} = 6\frac{10}{12}$$

Divide the numerator and denominator of the fraction by their greatest common divisor, which is 2.

$$\frac{10 \div 2}{12 \div 2} = \frac{5}{6}$$

So, the mixed number is $6\frac{5}{6}$.

$$\boxed{\mathbf{6\frac{5}{6}}}$$

$$4 + 3 = 7$$

The denominators are 5 and 6. The least common multiple of 5 and 6 is 30.
Convert the fractions:

$$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$$ $$\frac{4}{6} = \frac{4 \times 5}{6 \times 5} = \frac{20}{30}$$

Divide the numerator and denominator by their greatest common divisor, which is 2.

$$\frac{8 \div 2}{30 \div 2} = \frac{4}{15}$$

So, the final answer is $8\frac{4}{15}$.

$$\boxed{\mathbf{8\frac{4}{15}}}$$

$$1 + 12 = 13$$

The denominators are 12 and 4. The least common multiple of 12 and 4 is 12.
Convert the fractions:

$$\frac{9}{12}$$ $$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$

$$13 + 1 = 14$$ $$\boxed{\mathbf{14}}$$