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What is the name of the number that is being added to another number?

I am writting a paper, and I want to know how to call the number that you add to another number (for example: 2+4, how can I call the four without saying the word "4"). Thanks.

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    $\begingroup$ Addend. ${}{}{}{}$ $\endgroup$ – ÍgjøgnumMeg May 20 '18 at 23:13
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Either addend or summand is correct. If you are adding more than two numbers, it might be more appropriate to use the term addend or summand to refer to any term being added, e.g. $$\text{summand} + \text{summand} + \dotsb + \text{summand} = \text{sum (or total)} $$ or $$\text{addend} + \text{addend} + \dotsb + \text{addend} = \text{sum (or total)}. $$ If you need to refer to a specific term, the phrase "the $n$-th summand (or addend)" gets the job done.

In a case when you are adding exactly two numbers, you can use augend and addend, to refer to the first and second terms in a summation, i.e. you can write $$\text{augend} + \text{addend} = \text{sum}.$$ That being said, this use of the term "addend" is not unambiguous: for example, Mathworld defines "summand" as a synonym of addend, with augend referring to the first summand (or addend) in any sum. Hence it might be inadvisable to use "addend" to refer to only the second term in a sum, as the term "addend" is not unambiguously understood in this way; it could refer to any term in a sum. Moreover, the term "augend" is somewhat esoteric, and its use will likely draw requests for clarification.

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    $\begingroup$ augend seems esoteric to me $\endgroup$ – Ooker May 21 '18 at 7:15
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    $\begingroup$ @Ooker Personally, I find anything other than "summand" to be kind of esoteric, I would rather write "the second summand" than "the addend," as there is no chance of ambiguity with the former. That being said, if each summand is going to be given a distinct word, "augend" and "addend" are the correct terms. $\endgroup$ – Xander Henderson May 21 '18 at 15:32
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    $\begingroup$ Hmm... Probably it is different in different countries. I did elementary schooling in India, and "addend" is the word we were taught there. This is the first time that I have seen "summand". $\endgroup$ – Ajoy Bhatia May 21 '18 at 18:36
  • $\begingroup$ I don't recall using any of these terms during my education up to and including BSc Maths. Conversely my 2nd grader already has already needed to use addend in her homework. YMMV. $\endgroup$ – Digital Trauma May 21 '18 at 19:32
  • $\begingroup$ @DigitalTrauma In my Google bubble, a search for "summand" returns about 1 million results, while a search for "addend" returns about 2.4 million results (indicating that while "addend" is somewhat more common, "summand" should not be seen as terribly out there). "augend" returns about a tenth as many results, indicating that it is significantly less common (i.e. esoteric). As for my own experience, while the term "addend" is not unfamiliar to me, "summand" is a term that I have seen much more often in my own life. $\endgroup$ – Xander Henderson May 22 '18 at 3:08
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The word you're looking for is addend.

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The word summand would denote $2$ as well as $4$ in your example, and is not what you want.

Then, augend would denote the $2$ alone, and addend the $4$ alone.

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Addend is not a very familiar term, whereas summand makes no distinction between the number being added to and the number being added. Perhaps the term you are looking for is simply increment. This is certainly in common use in calculus when you speak of $\Delta x$ as being the $x$-increment and evaluate $f$ at $x+\Delta x$.

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