Editing Multiplication (section)

==Notation==
{{main|Multiplication sign}}
{{See also|Multiplier (linguistics)}}

In [[arithmetic]], multiplication is often written using the [[multiplication sign]] (either {{char|&times;}} or {{char|<math>\times</math>}}) between the factors (that is, in [[infix notation]]).<ref name="mpb">{{cite book
 | last1 = Musser | first1 = Gary L.
 | last2 = Peterson | first2 = Blake E.
 | last3 = Burger | first3 = William F.
 | year = 2013
 | title = Mathematics for Elementary Teachers: A Contemporary Approach
 | publisher = [[John Wiley & Sons]]
 | isbn = 978-1-118-48700-6
 | url = https://books.google.com/books?id=8jh7DwAAQBAJ&pg=PA101
 | page = 101
}}</ref> For example,
:<math>2\times 3 = 6,</math> ("two times three [[equals sign|equals]] six")
:<math>3\times 4 = 12  ,</math>
:<math>2\times 3\times 5 = 6\times  5 = 30,</math>
:<math>2\times 2\times 2\times 2 \times 2 = 32.</math>

There are other [[mathematical notation]]s for multiplication:
* To reduce confusion between the multiplication sign × and the common variable {{mvar|x}}, multiplication is also denoted by dot signs, usually a middle-position dot (rarely [[full stop|period]]): <math>5 \cdot 2</math>.{{r|mpb}} The middle dot notation or '''dot operator''' is now standard in the United States{{r|mpb}}<ref>{{cite book
 | last = Klose | first = Orval
 | year = 1966
 | title = The Number Systems and Operations of Arithmetic
 | publisher = Pergamon Press
 | url = http://books.google.com/books?id=rG7iBQAAQBAJ&pg=PA39
 | page = 39
}}</ref> and other countries.<ref name="humez">{{cite book
 | last1 = Humez | first1 = Alexander
 | last2 = Humez | first2 = Nicholas
 | title = On the Dot: The Speck That Changed the World
 | url = http://books.google.com/books?id=RaWdkz9NCYYC&pg=PT115
 | page = 103
 | publisher = [[Oxford University Press]]
}}</ref>{{clarification needed|date=May 2025|reason=Unclear for no specific countries use the dot operator as the multiplication symbol.}} When the dot operator character is not accessible, the [[interpunct]]&nbsp;({{char|·}}) is used.{{r|humez}} In most European and other countries that use a [[Comma (punctuation)|comma]] as a [[decimal point]] (and a period as a [[thousands separator]]), the multiplication sign or a middle dot is used to indicate multiplication. Historically, in the United Kingdom and Ireland, the middle dot was sometimes used for the decimal point to prevent it from disappearing in the ruled line, and the full stop (period) was used for multiplication. However, since the [[Ministry of Technology]] ruled in 1968 that the period be used as the decimal point,<ref>{{Cite journal |doi=10.1038/218111c0 |title=Victory on Points |journal=Nature |volume=218 |issue = 5137 |page=111 |date=1968 |bibcode=1968Natur.218S.111. |doi-access=free}}</ref> and the [[International System of Units]] (SI) standard has since been widely adopted, this usage is now found only in the more traditional journals such as ''[[The Lancet]]''.<ref>{{cite web |title=The Lancet – Formatting guidelines for electronic submission of manuscripts |url=http://download.thelancet.com/pb/assets/raw/Lancet/authors/artwork-guidelines.pdf |access-date=2017-04-25}}</ref>
* {{anchor|Implicit|Explicit}}In [[algebra]], multiplication involving [[Variable (mathematics)|variables]] is often written as a [[Juxtaposition#Mathematics|juxtaposition]] (e.g., <math>xy</math> for <math>x</math> times <math>y</math> or <math>5x</math> for five times <math>x</math>), also called '''implied multiplication'''. The notation can also be used for quantities that are surrounded by [[parentheses]] (e.g., <math>5(2)</math>, <math>(5)2</math> or <math>(5)(2)</math> for five times two). <ref>{{cite journal
 | last = Tall | first = David
 | title = Introducing Algebra on the Computer: Today and Tomorrow
 | journal = Mathematics in School
 | volume = 12 | issue = 5 | year = 1983 | pages = 37&ndash;40
 | jstor = 30213874
}}</ref>This implicit usage of multiplication can cause ambiguity when the concatenated variables happen to match the name of another variable, when a variable name in front of a parenthesis can be confused with a function name, or in the correct determination of the [[order of operations]].<ref name="Peterson_2019"/><ref name="Peterson_2023"/>
* In [[vector multiplication]], there is a distinction between the cross and the dot symbols. The cross symbol generally denotes the taking a [[cross product]] of two [[vector (mathematics)|vectors]], yielding a vector as its result, while the dot denotes taking the [[dot product]] of two vectors, resulting in a [[scalar (mathematics)|scalar]].

In [[computer programming]], the [[asterisk]] (as in <code>5*2</code>) is still the most common notation. This is because most computers historically were limited to small [[character set]]s (such as [[ASCII]] and [[EBCDIC]]) that lacked a multiplication sign (such as <code>⋅</code> or <code>×</code>),{{citation needed|date=May 2025}} while the asterisk appeared on every keyboard.<ref>{{cite book
 | last = Gookin | first = Dan
 | year = 2004
 | title = C For Dummies
 | edition = 2nd
 | publisher = Wiley
 | url = http://books.google.com/books?id=ruPPRwBYdjIC&pg=PA88
 | page = 88
}} </ref> This usage originated in the [[Fortran|FORTRAN]] programming language.<ref name="fortran">{{cite book
|last = Fuller |first = William R.
|title = FORTRAN Programming: A Supplement for Calculus Courses
|series = Universitext
|date = 1977
|url = https://books.google.com/books?id=mnLjBwAAQBAJ&pg=PA10
|page = 10
|publisher = Springer
|doi = 10.1007/978-1-4612-9938-7
|isbn = 978-0-387-90283-8
}}</ref>

{{anchor|Terminology|multiplier}}
The numbers to be multiplied are generally called the "factors" (as in [[factorization]]). The number to be multiplied is the "multiplicand", and the number by which it is multiplied is the "multiplier". Usually, the multiplier is placed first, and the multiplicand is placed second;<ref name="multiplicand on Britannica">{{cite web |title=Multiplicand {{!}} mathematics {{!}} Britannica |url=https://www.britannica.com/science/multiplicand |website=www.britannica.com |publisher=Encyclopædia Britannica, Inc. |access-date=15 November 2024 |language=en}}</ref><ref name="multiplicand via Wolfram Mathworld">{{cite web |last1=Weisstein |first1=Eric W. |title=Multiplicand |url=https://mathworld.wolfram.com/Multiplicand.html |website=mathworld.wolfram.com |publisher=Wolfram Research, Inc. |access-date=15 November 2024 |language=en}}</ref> however, sometimes the first factor is considered the multiplicand and the second the multiplier.
Also, as the result of multiplication does not depend on the order of the factors, the distinction between "multiplicand" and "multiplier" is useful only at a very elementary level and in some [[multiplication algorithm]]s, such as the [[long multiplication]]. Therefore, in some sources, the term "multiplicand" is regarded as a synonym for "factor".<ref>{{cite book |last=Litvin |first=Chester |url=https://books.google.com/books?id=-ULmPYAA8voC&q=Can+the+multiplicand+be+the+first+number&pg=PA6 |title=Advance Brain Stimulation by Psychoconduction |date=2012 |publisher=Trafford |isbn=978-1-4669-0152-0 |pages=2–3, 5–6 |via=[[Google Book Search]]}}</ref>
In algebra, a number that is the multiplier of a variable or expression (e.g., the 3 in <math>3xy^2</math>) is called a [[coefficient]].

The result of a multiplication is called a [[product (mathematics)|product]]. When one factor is an integer, the product is a [[multiple (mathematics)|''multiple'']] of the other or of the product of the others. Thus, <math>2\times \pi</math> is a multiple of <math>\pi</math>, as is <math>5133 \times 486 \times \pi</math>. A product of integers is a multiple of each factor; for example, 15 is the product of 3 and 5 and is both a multiple of 3 and a multiple of 5.