If "multiples" is to "product", "_____" is to "sum" I know this might be a really simple question for those fluent in English, but I can't find the term that describes numbers that make up a sum. 
The numbers of a certain product are called "multiples" of that "product". 
Then what are the numbers of a certain sum called?
 A: To approach the question from another direction: A "multiple" of 7 is a number that is the result of multiplying 7 with something else.
If your try to generalize that to sums, you get something like: A "__" of 7 is a number that is the result of adding 7 to something. But that's everything -- at least as long as we allow negative numbers, and if we don't allow negative numbers, then it just means something that is larger than 7. Neither of these concepts feel useful enough in themselves that it is worth it deciding on a particular noun for it.
A: According to Wikipedia, "summands", "addends", or "terms" are all acceptable.
Also, I've never heard "multiples" used as the corresponding word for multiplication. Wikipedia lists the words "factors" and "multiplicands" both of which I'm familiar with.
A: "Summands" 
$\phantom{\text{(hmm, first time MSE says my answer is too short; P.S., added by mixedmath: either this or adding empty sets is a good way to add to the length ;p)}}$
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A: the answer is addend.  a number that is added to another. "as its name suggests, the Accumulator ‘accumulates’ by keeping its addend in memory and incrementing by the addend it receives from another transmitting unit"
