$ sudo apt-get install python-software-properties
$ sudo apt-get install apt-file
$ apt-file update
$ apt-file search add-apt-repository
As you can see add-apt-repository is in software-properties-common:
software-properties-common: /usr/bin/add-apt-repository software-properties-common: /usr/share/man/man1/add-apt-repository.1.gz
After installing software-properties-common I was able to use add-apt-repository without any further issue:
$ sudo apt-get install software-properties-common
ref. https://pricklytech.wordpress.com/2014/05/16/ubuntu-server-14-4-trusty-add-apt-repository-command-not-found/
