What is software-properties-common
Solution 1:
As described in apt-show software-properties-common
This software provides an abstraction of the used apt repositories. It allows you to easily manage your distribution and independent software vendor software sources.
In practice that means it provides some useful scripts for adding and removing PPAs:
$ dpkg -L software-properties-common | grep 'bin/'
/usr/bin/add-apt-repository
/usr/bin/apt-add-repository
plus the DBUS backends to do the same via the Software and Updates GUI.
Without it, you would need to add and remove repositories (such as PPAs) manually by editing /etc/apt/sources.list
and/or any subsidiary files in /etc/apt/sources.list.d