(i) −1 and 0

$\frac{-1}{10}, \frac{-1}{20}, \frac{-1}{30}, \frac{-1}{40}, \frac{-1}{50}$

(ii) −2 and −1

$-2=\frac{-12}{6} \mathrm{and} -1 = \frac{-6}{6}$

Five rational numbers are

$\frac{-11}{6}, \frac{-10}{6}, \frac{-9}{6}, \frac{-8}{6}, \frac{-7}{6}$

(iii) $\frac{-4}{5} \mathrm{and} \frac{-2}{3}$

$\frac{-4}{5}=\frac{-4\times 9}{5\times 9}=\frac{-36}{45}and \frac{-2}{3}=\frac{-2\times 15}{3\times 15}=\frac{-30}{45}$

Five rational numbers are

$\frac{-35}{45}, \frac{-34}{45}, \frac{-33}{45}, \frac{-32}{45}, \frac{-31}{45}$

(iv) $\frac{1}{2} \mathrm{and} \frac{2}{3}$

$\frac{1}{2}=\frac{1\times 18}{2\times 18}=\frac{18}{36} \mathrm{and} \frac{2}{3}=\frac{2\times 12}{3\times 12}=\frac{24}{36}$

Five rational numbers are

$\frac{19}{36},\frac{20}{36}, \frac{21}{36}, \frac{22}{36}, \frac{23}{36}$

(i) $\frac{-3}{5},\frac{-6}{10},\frac{-9}{15},\frac{-12}{20},.....$

$\frac{-3}{5},\frac{-3\times 2}{5\times 2},\frac{-3\times 3}{5\times 3},\frac{-3\times 4}{5\times 4}.....$

It can be observed that the numerator is a multiple of 3 while the denominator is a multiple of 5 and as we increase them further, these multiples are increasing. Therefore, the next four rational numbers in this pattern are

$$\begin{gathered} \frac{-3\times 5}{5\times 5},\frac{-3\times 6}{5\times 6},\frac{-3\times 7}{5\times 7},\frac{-3\times 8}{5\times 8}... \\ \frac{-15}{25},\frac{-18}{30},\frac{-21}{35},\frac{-24}{40}... \end{gathered}$$

(ii)

$$\begin{gathered} \frac{-1}{4},\frac{-2}{8},\frac{-3}{12}... \\ \frac{-1}{4},\frac{-1\times 2}{4\times 2},\frac{-1\times 3}{4\times 3}... \end{gathered}$$

The next four rational numbers in this pattern are

$$\begin{gathered} \frac{-1\times 4}{4\times 4},\frac{-1\times 5}{4\times 5},\frac{-1\times 6}{4\times 6},\frac{-1\times 7}{4\times 7}.... \\ \frac{-4}{16}, \frac{-5}{20}, \frac{-6}{24}, \frac{-7}{28}... \end{gathered}$$

(iii)

$$\begin{gathered} \frac{-1}{6}, \frac{2}{-12}, \frac{3}{-18}, \frac{4}{-24}... \\ \frac{-1}{6},\frac{1\times 2}{-6\times 2},\frac{1\times 3}{-6\times 3},\frac{1\times 4}{-6\times 4}... \end{gathered}$$

The next four rational numbers in this pattern are

$$\begin{gathered} \frac{1\times 5}{-6\times 5}, \frac{1\times 6}{-6\times 6}, \frac{1\times 7}{-6\times 7}, \frac{1\times 8}{-6\times 8}.... \\ \frac{5}{-30}, \frac{6}{-36}, \frac{7}{-42}, \frac{8}{-48}... \end{gathered}$$

(iv) $\frac{-2}{3}, \frac{2}{-3}, \frac{4}{-6}, \frac{6}{-9}...$

$\frac{-2}{3}, \frac{2}{-3}, \frac{2\times 2}{-3\times 2}, \frac{2\times 3}{-3\times 3}....$

The next four rational numbers in this pattern are

$$\begin{gathered} \frac{2\times 4}{-3\times 4}, \frac{2\times 5}{-3\times 5}, \frac{2\times 6}{-3\times 6}, \frac{2\times 7}{-3\times 7}.... \\ \frac{8}{-12}, \frac{10}{-15}, \frac{12}{-18}, \frac{14}{-21}... \end{gathered}$$

(i) $\frac{-2}{7}$

Four rational numbers are

$$\begin{gathered} \frac{-2\times 2}{7\times 2}, \frac{-2\times 3}{7\times 3}, \frac{-2\times 4}{7\times 4}, \frac{-2\times 5}{7\times 5} \\ \frac{-4}{14},\frac{-6}{21}, \frac{-8}{28}, \frac{-10}{35} \end{gathered}$$

(ii) $\frac{5}{-3}$

Four rational numbers are

$$\begin{gathered} \frac{5\times 2}{-3\times 2}, \frac{5\times 3}{-3\times 3}, \frac{5\times 4}{-3\times 4}, \frac{5\times 5}{-3\times 5} \\ \frac{10}{-6}, \frac{15}{-9}, \frac{20}{-12}, \frac{25}{-15} \end{gathered}$$

(iii) $\frac{4}{9}$

Four rational numbers are

$$\begin{gathered} \frac{4\times 2}{9\times 2}, \frac{4\times 3}{9\times 3}, \frac{4\times 4}{9\times 4}, \frac{4\times 5}{9\times 5} \\ \frac{8}{18}, \frac{12}{27}, \frac{16}{36}, \frac{20}{45} \end{gathered}$$

(i) $\frac{3}{4}$

This fraction represents 3 parts out of 4 equal parts. Therefore, each space between two integers on number line must be divided into 4 equal parts.

$\frac{3}{4}$ can be represented as

(ii) $\frac{-5}{8}$

This fraction represents 5 parts out of 8 equal parts. Negative sign represents that it is on the negative side of number line. Therefore, each space between two integers on number line must be divided into 8 equal parts.

$\frac{-5}{8}$ can be represented as

(iii) $\frac{-7}{4}=-1\frac{3}{4}$

This fraction represents 1 full part and 3 parts out of 4 equal parts. Negative sign represents that it is on the negative side of number line. Therefore, each space between two integers on number line must be divided into 4 equal parts.

$\frac{-7}{4}$ can be represented as

(iv) $\frac{7}{8}$

This fraction represents 7 parts out of 8 equal parts. Therefore, each space between two integers on number line must be divided into 8 equal parts.

$\frac{7}{8}$ can be represented as