足す

(1) to add (numbers) / (2) to add (something) /to top up (with something) / (3) to take care of

加える

(1) to add/to add up/to sum up/to append/to annex/ (2) to increase/to gather /to pick up/ (3) to include/to count in/to let join/ (4) to inflict (damage) /to deal/to give