Now do the following:

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

The fractions are $\frac{5}{3}$, $\frac{1}{2}$, $\frac{2}{3}$, and $\frac{1}{2}$.

$$\frac{5}{3} + \frac{1}{2} + \frac{2}{3} + \frac{1}{2} = \left(\frac{5}{3} + \frac{2}{3}\right) + \left(\frac{1}{2} + \frac{1}{2}\right)$$ $$= \frac{7}{3} + \frac{2}{2}$$ $$= \frac{7}{3} + 1$$ $$= \frac{7}{3} + \frac{3}{3}$$ $$= \frac{10}{3}$$

$$\frac{10}{3} = 3\frac{1}{3}$$

The value for (1) is $\boxed{3\frac{1}{3}}$.

2)

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

The fractions are $\frac{6}{5}$, $\frac{1}{2}$, $\frac{2}{3}$, and $\frac{2}{5}$.

$$\frac{6}{5} = \frac{6 \times 6}{5 \times 6} = \frac{36}{30}$$ $$\frac{1}{2} = \frac{1 \times 15}{2 \times 15} = \frac{15}{30}$$ $$\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}$$ $$\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}$$

$$\frac{83}{30} = 2\frac{23}{30}$$

The value for (2) is $\boxed{2\frac{23}{30}}$.

3)

$$1\frac{1}{7} = \frac{1 \times 7 + 1}{7} = \frac{8}{7}$$ $$\frac{2}{14} = \frac{1}{7}$$

The fractions are $\frac{8}{7}$, $\frac{3}{4}$, $\frac{1}{7}$, and $\frac{2}{9}$.

$$\frac{8}{7} = \frac{8 \times 36}{7 \times 36} = \frac{288}{252}$$ $$\frac{3}{4} = \frac{3 \times 63}{4 \times 63} = \frac{189}{252}$$ $$\frac{1}{7} = \frac{1 \times 36}{7 \times 36} = \frac{36}{252}$$ $$\frac{2}{9} = \frac{2 \times 28}{9 \times 28} = \frac{56}{252}$$

$$\frac{569}{252} = 2\frac{65}{252}$$

The value for (3) is $\boxed{2\frac{65}{252}}$.

4)

$$2\frac{1}{8} = \frac{2 \times 8 + 1}{8} = \frac{17}{8}$$ $$3\frac{5}{12} = \frac{3 \times 12 + 5}{12} = \frac{41}{12}$$

The fractions are $\frac{17}{8}$, $\frac{41}{12}$, $\frac{1}{9}$, and $\frac{1}{2}$.

$$\frac{17}{8} = \frac{17 \times 9}{8 \times 9} = \frac{153}{72}$$ $$\frac{41}{12} = \frac{41 \times 6}{12 \times 6} = \frac{246}{72}$$ $$\frac{1}{9} = \frac{1 \times 8}{9 \times 8} = \frac{8}{72}$$ $$\frac{1}{2} = \frac{1 \times 36}{2 \times 36} = \frac{36}{72}$$

$$\frac{443}{72} = 6\frac{11}{72}$$

The value for (4) is $\boxed{6\frac{11}{72}}$.

5)

$$1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4}$$ $$\frac{2}{10} = \frac{1}{5}$$

The fractions are $\frac{7}{4}$, $\frac{4}{5}$, $\frac{1}{5}$, and $\frac{2}{7}$.

$$\frac{7}{4} + \frac{4}{5} + \frac{1}{5} + \frac{2}{7} = \frac{7}{4} + \left(\frac{4}{5} + \frac{1}{5}\right) + \frac{2}{7}$$ $$= \frac{7}{4} + \frac{5}{5} + \frac{2}{7}$$ $$= \frac{7}{4} + 1 + \frac{2}{7}$$ $$= \frac{11}{4} + \frac{2}{7}$$

$$\frac{11}{4} = \frac{11 \times 7}{4 \times 7} = \frac{77}{28}$$ $$\frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28}$$

$$\frac{85}{28} = 3\frac{1}{28}$$

The value for (5) is $\boxed{3\frac{1}{28}}$.

6)

$$4\frac{3}{10} = \frac{4 \times 10 + 3}{10} = \frac{43}{10}$$ $$\frac{2}{6} = \frac{1}{3}$$ $$\frac{2}{1} = 2$$

The fractions are $\frac{43}{10}$, $\frac{7}{10}$, $\frac{1}{3}$, and 2.

$$\frac{43}{10} + \frac{7}{10} + \frac{1}{3} + 2 = \left(\frac{43}{10} + \frac{7}{10}\right) + \frac{1}{3} + 2$$ $$= \frac{50}{10} + \frac{1}{3} + 2$$ $$= 5 + \frac{1}{3} + 2$$ $$= 7 + \frac{1}{3}$$

$$7 + \frac{1}{3} = 7\frac{1}{3}$$

The value for (6) is $\boxed{7\frac{1}{3}}$.