Question

Find three rational numbers between `1/4` and `1/5`

Answer 1

Let `x = 1/5` and `y = 1/4`

Here, x < y

Here, we have to find three rational numbers.

Consider, n = 3

∵ `d = (y - x)/(n + 1)`

= `(1/4 - 1/5)/(3 + 1)`

= `((5 - 4)/20)/4`

= `1/80`

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

Now, `x + d = 1/5 + 1/80`

= `(16 + 1)/80`

= `17/80`

`x + 2d = 1/5 + 2/80`

= `(16 + 2)/80`

= `18/80`

= `9/40`

And `x + 3d = 1/5 + 3/80`

= `(16 + 3)/80`

= `19/80`

Hence, three rational numbers between `1/4` and `1/5` are `17/80, 9/40, 19/80`

Answer 2

Let `x = 1/4` and `y = 1/5`

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

∴ A rational number between `1/4` and `1/5`

= `(1/4 + 1/5)/2`

= `((5 + 4)/20)/2`

= `9/(2 xx 20)`

= `9/40`

Again, a rational number between `1/4` and `9/40`

= `(1/4 + 9/40)/2`

= `((10 + 9)/40)/2`

= `19/(2 xx 40)`

= `19/80`

Again, a rational number between `1/5` and `9/40`

= `(1/5 + 9/40)/2`

= `((8 + 9)/40)/2`

= `(17/40)/2`

= `17/(40 xx 2)`

= `17/80`

Hence, three rational numbers between `1/4` and `1/5` are `9/40, 19/80, 17/80`