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