My Eclipse builds had been fine. Then I updated my android-sdk to the latest version.
And thinks went to heck.
And I finally found what appears to be a solution for the errors mentioning 'android.support.v4.app.fragment' and the mysterious 'java build path'.
Right click on your project and bring up the Properties.
Click on 'Java Build Path' and then its 'Libraries' tab.
Click on 'Add External JARs...'.
(The following assumes that all your android stuff is in C:\Android and the android sdk is in C:\Android\android-sdk. Adjust as necessary for your installation.)
Navigate to C:\Android\android-sdk\extras\android\support\v4.
Select 'android-support-v4.jar' and click on the 'Open' button.
Refresh your project and the android.support.v4.app.fragment errors should be gone.
Cheers,
Ancient Lady
AGK Community Tester and AppGameKit Master