Q: My ipod touch 4th gen is too old to install applications

No. If desired, download the current versions of those applications to a computer or compatible iOS device, click here, and try following the instructions.

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If you have an iPod touch 4th Gen, 6.1.6 is the highest it can go. Many apps keep a compatible version on the server for those with old iOS, but you have to try to download it for your purchase history.  If it's a new app you have never downloaded, the trick is to use iTunes on the computer to get the app, then use your iOS device's purchase history to try and download a compatible version after that. I hope this helps.

Install the latest compatible version of an app on an earlier version of iOS or OS X - Apple Support