Reinstalling Numbers on Mac OS X
For Apple's "free" apps, such as Numbers, I've had success doing the following:


Leave Numbers.app in the /Applications folder
Start App Store, and check for updates.  This should show an update for Numbers, but do not try to update it yet.
Move Numbers.app/Contents/_MASReceipt/receipt to your Desktop
Go back to the App Store, and update Numbers


This will download the new version, and create a new receipt file, with your new ownership credentials.

NOTE: This may not work if your second set of credentials is not already authorized to download Numbers via a different Mac, etc.