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