add together vs work out

add together and work out both are verbs.

Word	Noun	Adjective	Verb	Adverb
add together	No	No	Yes	No
work out	No	No	Yes	No

As verbs, work out is a hypernym of add together; that is, work out is a word with a broader meaning than add together:

Other hypernyms of add together include calculate, cipher, compute, cypher, figure, reckon.

add together (verb)	work out (verb)
make an addition by combining numbers	do physical exercise
determine the sum of	give a workout to
	come up with
	work out in detail
	find the solution to (a problem or question) or understand the meaning of
	make a mathematical calculation or computation
	be calculated
	happen in a certain way, leading to, producing, or resulting in a certain outcome, often well