Transitive and separable. Intransitive:
1. To sum together all the constituent parts of something. To come to the total of.
For example: Could you add these figures up, please?
2. If something does not add up this means that a situation, or series of events do not make sense, we can not understand why they have occurred.
For example: I have repaired all the leaks in this bicycle tyre, but the air is still escaping, it just does not make sense.