Do you really get 30,000 CP for each fragment

Fragment skills are tied to specific milestones throughout the game: completing the main storyline, completing certain episodes, collecting a set of fragments that relate to each other, and so on.

These are the ones I've been able to find:

• Two you get right off the bat in Serendipity: Mog's Manifestation and Haggler
• Two you get for completing episode 5: Anti-grav Jump and Bargain Hunter
• One you get for completing the main storyline: Paradox scope
• One you get for getting all the fragments in the game: Clock Master

A guide by Krystal109 on GameFAQs lists the locations of all the rest, but if you happen to collect all 160 fragments, you'll wind up getting the vast majority of the skills.

i believe it would be in 110af yaschas massif, from the ruins follow the path to the west(DO NOT GO SOUTH) till you see a canyon at you're right.
It should be in there(it's quite far away, i couldn't see it till had rown in mog).
If that doesn't work then you might want to try getting more fragments in the yaschas massif area. (since my second suspicion would be to much open quests open in the area).

Good luck.