The last time I encountered the add-apt-repository: command not found error I was using Ubuntu Server 12.4 Lucid. The solution then was to install python-software-properties as follows:
sudo apt-get install python-software-properties
This did not resolve the issue on my minimal virtual machine installation on Trusty so I installed apt-file – which is an apt package searching utility:
sudo apt-get install apt-file
Update apt-file:
apt-file update
Finally use apt-file to search for the add-apt-repository package:
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