Represent rational numbers $-\dfrac{7}{3}$ and $\dfrac{7}{4}$ on the same number line.

The rational numbers are $-\dfrac{7}{3}$ and $\dfrac{7}{4}$.

LCM of 3 and 4 is 2 x 2 x 3 = 12

Hence, the rational number will be-

$-\dfrac{7 \times 4}{3 \times 4} , \dfrac{7 \times 3}{4 \times 3}\\[1em] = -\dfrac{28}{12} , \dfrac{21}{12}\\[1em] = -2\dfrac{4}{12} , 1\dfrac{9}{12}$

Draw a number line as shown below:

In this number line OA = AB = ……….. = OA' = A'B' = 1 unit

Since, the denominator of each given rational numbers is 12, divide each of OA, AB,…,OA', A'B', etc. into twelve equal parts.

To represent $\dfrac{1}{12}$, moves one step towards the right side of O to reach point P as shown.

Hence, OA = 1 unit , therefore OP = $\dfrac{1}{12}$ unit and so P represents $\dfrac{1}{12}$.

In the same way, to represent $-2\dfrac{4}{12}$ , move 4 steps toward the left side of B' to reach point Q. Clearly, Q represents $-\dfrac{7}{3}$.

Similarly, to represent $1\dfrac{9}{12}$ , move 9 steps toward the right side of A to reach point R. Clearly, R represents $\dfrac{7}{4}$.