number vs add together

number is a noun but add together is not a noun.

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

As verbs, add together is a hyponym of number; that is, add together is a word with a more specific, narrower meaning than number:

Other hyponyms of number include recount, miscount, census, add, add up, sum, sum up, summate, tally, tot, tot up, total, tote up.

number (noun)	add together (noun)
an item of clothing
the property possessed by a sum or total or indefinite quantity of units or individuals
a clothing measurement
one of a series published periodically
a symbol used to represent a number
a numeral or string of numerals that is used for identification and may be attached to accounts, memberships, etc.
the number is used in calling a particular telephone
a short performance that is part of a longer program
the grammatical category for the forms of nouns and pronouns and verbs that are used depending on the number of entities involved (singular or dual or plural)
a numbered item in a series
a select company of people
a concept of quantity involving zero and units

number (verb)	add together (verb)
place a limit on the number of	make an addition by combining numbers
determine the number or amount of	determine the sum of
enumerate
give numbers to
add up in number or quantity
put into a group