Why is 6/8 greater than 5/8 but less than 7/8?

6/8=0.75

5/8=0.625

7/8=0.875

Since 7/8 is closer to 8/8 (1) therefore it is the largest among the three. And since 5/8 is the furthest from 8/8 (1) therefore it is behind 6/8. Therefore 5/8<6/8<7/8

Think about it like this - 6 is greater than 5 but less than 7. This trick works because all the fractions have the same denominational number.