add together vs add up

add together and add up both are verbs.

Word	Noun	Adjective	Verb	Adverb
add together	No	No	Yes	No
add up	No	No	Yes	No

As verbs, add together and add up are synonyms defined as:

Other synonyms of add together include add, sum, sum up, summate, tally, tot, tot up, total, tote up.

add together (verb)	add up (verb)
make an addition by combining numbers	determine the sum of
determine the sum of	be reasonable or logical or comprehensible
	to measure up to in kind or quality
	add up in number or quantity