A) 1(4)/(7) + 3(1)/(21)

$$1\frac{4}{7} = \frac{(1 \times 7) + 4}{7} = \frac{11}{7}$$ $$3\frac{1}{21} = \frac{(3 \times 21) + 1}{21} = \frac{64}{21}$$

The least common denominator (LCD) for 7 and 21 is 21. Convert $\frac{11}{7}$ to an equivalent fraction with a denominator of 21.

$$\frac{11}{7} = \frac{11 \times 3}{7 \times 3} = \frac{33}{21}$$

$$\frac{97}{21} = 4\frac{13}{21}$$

The fraction $\frac{13}{21}$ is already in simplest form.
The answer is $\boxed{4\frac{13}{21}}$

The LCD for 7 and 2 is 14. Convert both fractions to equivalent fractions with a denominator of 14.

$$\frac{22}{7} = \frac{22 \times 2}{7 \times 2} = \frac{44}{14}$$ $$\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}$$

$$\frac{37}{14} = 2\frac{9}{14}$$

The fraction $\frac{9}{14}$ is already in simplest form.
The answer is $\boxed{2\frac{9}{14}}$

$$2\frac{5}{9} = \frac{(2 \times 9) + 5}{9} = \frac{23}{9}$$ $$1\frac{3}{8} = \frac{(1 \times 8) + 3}{8} = \frac{11}{8}$$

The LCD for 9 and 8 is 72. Convert both fractions to equivalent fractions with a denominator of 72.

$$\frac{23}{9} = \frac{23 \times 8}{9 \times 8} = \frac{184}{72}$$ $$\frac{11}{8} = \frac{11 \times 9}{8 \times 9} = \frac{99}{72}$$

$$\frac{283}{72} = 3\frac{67}{72}$$

The fraction $\frac{67}{72}$ is already in simplest form.
The answer is $\boxed{3\frac{67}{72}}$

$$5\frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{16}{3}$$ $$2\frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{11}{4}$$

The LCD for 3 and 4 is 12. Convert both fractions to equivalent fractions with a denominator of 12.

$$\frac{16}{3} = \frac{16 \times 4}{3 \times 4} = \frac{64}{12}$$ $$\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}$$

$$\frac{31}{12} = 2\frac{7}{12}$$

The fraction $\frac{7}{12}$ is already in simplest form.
The answer is $\boxed{2\frac{7}{12}}$