I have a fraction for my ti-84 plus silver edition 3 1/6-7/8 ad it comes out 2.291666667 then converts to 55/24 but how do i simplify it into 2 7/24?

Unfortunately, there is not a simple solution to this, however there is a solution. It is easy to get it displayed as a fraction using the >Frac from the MATH button. It is also easy to find that 24 goes into 55 two times. Now, there is a function that is on the calculator Remainder. This can be found either in the catalog or by going to MATH arrow to NUM and Remainder should be listed. So, you could type Remainder(55,24) and it will return 7. Seven is the numerator and 24 will still be the denominator. So, it is not an extremely fast way to find the mixed number, but it works.
An alternative to using the remainder function would be to just type 55-24(2), which would also return 7. Either method works, just a matter of preference.
Best Wishes!