Addition is written using the [[Plus and minus signs|plus sign]] "+" between the terms;<ref name=":0" /><ref>{{Cite web|title=Addition|url=https://www.mathsisfun.com/numbers/addition.html|access-date=2020-08-25|website=www.mathsisfun.com}}</ref> that is, in [[infix notation]]. The result is expressed with an [[equals sign]]. For example, :<math>1 + 1 = 2</math> ("one plus one equals two") :<math>2 + 2 = 4</math> ("two plus two equals four") :<math>1 + 2 = 3</math> ("one plus two equals three") :<math>5 + 4 + 2 = 11</math> (see "associativity" [[#Associativity|below]]) :<math>3 + 3 + 3 + 3 = 12</math> (see "multiplication" [[#Related operations|below]])

There are also situations where addition is "understood", even though no symbol appears:

• A whole number followed immediately by a [[fraction (mathematics)|fraction]] indicates the sum of the two, called a ''mixed number''.<ref>Devine et al. p. 263</ref> For example,<math display="block">3\frac{1}{2}=3+\frac{1}{2}=3.5.</math>This notation can cause confusion, since in most other contexts, [[Juxtaposition#Mathematics|juxtaposition]] denotes [[multiplication]] instead.<ref>Mazur, Joseph. ''Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers''. Princeton University Press, 2014. p. 161</ref>

The sum of a [[series (mathematics)|series]] of related numbers can be expressed through [[capital sigma notation]], which compactly denotes [[iteration]]. For example, :<math>\sum_{k=1}^5 k^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55.</math>

{{anchor|summand|addend}} The numbers or the objects to be added in general addition are collectively referred to as the '''terms''',<ref>Department of the Army (1961) Army Technical Manual TM 11-684: Principles and Applications of Mathematics for Communications-Electronics. Section 5.1</ref> the '''addends'''<ref name="Shmerko">{{cite book |last1=Shmerko |first1=V.P. |last2=Yanushkevich [Ânuškevič] |first2=Svetlana N. [Svitlana N.] |last3=Lyshevski |first3=S.E. |date=2009 |title=Computer arithmetics for nanoelectronics |publisher=[[CRC Press]] |page=80}}</ref><ref name="Schmid_1974"/><ref name=":1">{{Cite web|last=Weisstein|first=Eric W.|title=Addition|url=https://mathworld.wolfram.com/Addition.html|access-date=2020-08-25|website=mathworld.wolfram.com|language=en}}</ref> or the '''summands''';<ref>Hosch, W.L. (Ed.). (2010). The Britannica Guide to Numbers and Measurement. The Rosen Publishing Group. p. 38</ref> this terminology carries over to the summation of multiple terms. This is to be distinguished from ''factors'', which are [[multiplication|multiplied]]. Some authors call the first addend the ''augend''.<ref name="Shmerko"/><ref name="Schmid_1974">{{cite book |title=Decimal Computation |first=Hermann |last=Schmid |author-link=Hermann Schmid (computer scientist) |date=1974 |edition=1st |publisher=[[John Wiley & Sons]] |location=Binghamton, NY |isbn=0-471-76180-X |url=https://archive.org/details/decimalcomputati0000schm }} and {{cite book |title=Decimal Computation |first=Hermann |last=Schmid|author-link=Hermann Schmid (computer scientist) |orig-year=1974 |date=1983 |edition=reprint of 1st|publisher=Robert E. Krieger Publishing Company |location=Malabar, FL|isbn=978-0-89874-318-0}}</ref><ref name=":1" /> In fact, during the [[Renaissance]], many authors did not consider the first addend an "addend" at all. Today, due to the [[commutative property]] of addition, "augend" is rarely used, and both terms are generally called addends.<ref name="Schwartzman p. 19">Schwartzman p. 19</ref>

Wow!