Question

which is the biggest fraction 2 3/4, 2 3/5, 2 1/2, 2 5/8, or 2 7/10

Answer 1

Those are all mixed numbers with a whole part of 2, so that can be ignored.
There are several ways to compare fractions. One is to give them all common denominators. An equivalent way is to turn them all into decimal fractions.

Another way to compare fractions is to cross-multiply and compare the products.

Answer 2

2 3/4