Question

Find three rational numbers between –1 and –2

Answer 1

Let y = –1 and x = –2

Here, x > y and we have to find three rational numbers, so n = 3

∵ `d = (y - x)/(n + 1)`

= `(-1 + 2)/(3 + 1)`

= `1/4`

Since, the three rational numbers between x and y are x + d, x + 2d and x + 3d.

Now, `x + d = -2 + 1/4`

= `(-8 + 1)/4`

= `(-7)/4`

`x + 2d = -2 + 2/4`

= `(-8 + 2)/4`

= `(-6)/4`

= `(-3)/2`

And `x + 3d = - 2 + 3/4`

= `(-8 + 3)/4`

= `(-5)/4`

Hence, three rational numbers between –1 and –2 are `(-7)/4, (-3)/2` and `(-5)/4`

Answer 2

Let x = –1 and y = –2

We know, a rational number between x and y = `(x + y)/2`

A rational number between –1 and –2

= `(-1 - 2)/2`

= `-3/2`

And a rational number between –1 and `-3/2`

= `(-1 - 3/2)/2`

= `(-2 - 3)/4`

= `-5/4`

Similarly, `-7/4` is a rational number between –1 and –2.

Hence, required solution = `-3/2, -5/4, -7/4`