to add- to increase. to add up - to draw a (total) sum of something. -When you add 2 +2 you get 4.- -2+4+1+7 = 4 does not add up correctly.- -His story doesn't add up about how the suitcase was lost at the hotel.-

If you use "add up" it can imply you're adding up to a specific number. Using add doesn't create any confusion on what you're doing so I would say use add in most situations unless you're describing something(a number) you're adding up to.