Question

1. List five rational numbers between:
(1) -1 and 0
(ii) -2 and -1​

Answer 1

Answer:

Let x = -1 ; y = 1

y > x ; n = 5

d = y - x / n + 1

= 1 - (-1) / 5 + 1

= 1 + 1/6

= 2/6

= 1/3

1st rational number = x + d

= -1 + 1/3

= -3 + 1/3

= -2/3

2nd rational number = x + 2d

= -1 + 2 × 1/3

= -1 + 2/3

= -3 + 2/3

= -1/3

3rd rational number = x + 3d

= -1 + 3 × 1/3

= -1 + 1

= 0

4th rational number = x + 4d

= -1 + 4 × 1/3

= -1 + 4/3

= -3 + 4/3

= 1/3

5th rational number = x + 5d

= -1 + 5 × 1/3

= -1 + 5/3

= -3 + 5/3

= 2/3