Should I be able to download apps purchased via iOS onto my new iMac? When I do, only the sound files download. What am I doing wrong?
No. Apps that run on an iOS device cannot run on Mac OS X and vice versa.
Two different operating systems.
IOS apps don't run on OS X, they don't download from one to other either. There may be an OS X version available if you check, you will have to buy it if it is not free.
iOS applications downloaded to a device running iOS 9 or newer are thinned for it and can't be transferred to a computer's iTunes library. If desired, you can download them from the iTunes Store on your computer, but you can't run them on it.
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Downloading apps from iOS to iMac
