i purchased garageband on my iPad
The GarageBand version for the iPad cannot run on a Mac. It has been written for a different kind of processor and operating system. You need to install GarageBand 10 from the Mac AppStore, if you want to run GarageBand on a Mac.
Is there GarageBand 10 installed on your Mac in the Applications folder? New Macs come with GarageBand preinstalled. What happens when you try to launch the preinstalled GarageBand? Any error message?