Insert five rational numbers between:

(i) (-2)/3 and -1

(ii) -1/2 and (-3)/2

(i) We have -2/3 and -1

LCM of 3 and 1 = 3

∴ (-2 × 1)/(3 × 1) = -2/3 and (-1 × 3)/(1 × 3) = -3/3

We know that there is no integer between -2 and -3.

∴ Multiplying and dividing by 6 to each of the rational numbers, we have

(-2 × 6)/(3 × 6) = -12/18 and (-3 × 6)/(3 × 6) = -18/18

Here, integers between -12 and -18 are -13, -14, -15, -16, and -17.

∴ The required rational numbers are -13/18, -14/18, -15/18, -16/18, and -17/18.

i.e., -13/18, -7/9, -5/6, -8/9, -17/18.

(ii) We have -1/2 and -3/2

Since the denominators are the same and there is only one integer between -1 and -3,

∴ Multiplying and dividing by 6 to each of the rational numbers, we have

(-1 × 6)/(2 × 6) = -6/12 and (-3 × 6)/(2 × 6) = -18/12

Here, the integers between -6 and -18 are -7, -8, -9, -10, -11.

∴ The required rational numbers are -7/12, -8/12, -9/12, -10/12, -11/12

i.e., -7/12, -2/3, -3/4, -5/6, -11/12.