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 

 

47/56, 71/84, 143/168