Question

Find three rational numbers between `5/7` and `6/7`

Answer 1

Let `x = 5/7` and `y = 6/7`

Here, x < y

Here, we have to find three rational numbers.

Consider, n = 3

∵ `d = (y - x)/(n + 1)`

∴ `d = (6/7 - 5/7)/4 = (1/7)/4 = 1/28`

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

Now, `x + d = 5/7 + 1/28`

= `(20 + 1)/28`

= `21/28`

`x + 2d = 5/7 + 2/28`

= `(20 + 2)/28`

= `22/28`

And `x + 3d = 5/7 + 3/28`

= `(20 + 3)/28`

= `23/28`

Hence, three rational numbers between `5/7` and `6/7` are `21/28, 22/28, 23/28`

Also, without using above formula the three rational numbers between `5/7` and `6/7` are `51/70, 52/70, 53/70`