Reduction — Do they work for unrelated problems? I think I understand that a P class problem is reducible to an NP class problem (P≤NP).

I´d like to understand if I need to figure out a potential algorithm which could solve the NP class problem to know if it can be used as a subroutine for a P class problem. 

So for example, if I ask you if the problem from class P —sum of integers— is reducible to a problem of class NP —Clique graph problem—, how would you reply to it? 

Is this a valid reduction as the more complicated Clique problem is NP and the easier problem sum of integers is a P problem even though they deal with different math branches (one being algebra and the other one being graph theory)?
If you have a problem $X$ that is in P, then you can construct a polynomial time reduction to any problem $Y$ in NP (or in 'any' other class of problems*). This is possible, as our 'reduction' is allowed to spend polynomial time on the input of $X$, so it can simply determine whether a given input $I$ for $X$ is a 'yes'-input in polynomial time and map to a trivial input for $Y$ with the same truth-value.



*: To be precise, any decision problem such that we can find at least one 'yes'-instance and one 'no'-instance, which holds for pretty much any interesting decision problem.