Is there any rational numbers between 5/7 and 6/7 and why? ... ?

There are * infinitely * many rational numbers between those two. But perhaps they want them evenly spaced?

5/6 is equal to 35/42

6/7 is equal to 36/42

Halfway between would be the average:

(35/42 + 36/42) / 2

= (71/42) / 2

= 71/84

Then find the two numbers halfway between those.

First convert 5/6 to x/84:

5/6 = 35/42 = 70/84

Halfway between 5/6 and 71/84:

(70/84 + 71/84) / 2

= 141/168

Reduce that:

= 47/56

Next convert 6/7 to x/84:

6/7 = 36/42 = 72/84

Halfway between 71/84 and 6/7:

(71/84 + 72/84) / 2

= 143/168

Answer:

47/56, 71/84, 143/168