Editing Arithmetic (section)

=== Multiplication and division ===
{{main|Multiplication|Division (mathematics)}}

{{multiple image
|perrow            = 1 / 1
|total_width       = 300
|image1            = Multiplication1.png
|alt1              = Diagram showing multiplication
|image2            = Division1.png
|alt2              = Diagram showing division
|footer            = Multiplication and division
}}

Multiplication  is an arithmetic operation in which two numbers, called the multiplier and the multiplicand, are combined into a single number called the [[Product (mathematics)|product]].<ref>{{multiref | {{harvnb|Romanowski|2008|p=303}} | {{harvnb|Musser|Peterson|Burger|2013|pp=[https://books.google.com/books?id=8jh7DwAAQBAJ&pg=PA101 101–102]}} }}</ref>{{efn|Some authors use a different terminology and refer to the first number as multiplicand and the second number as the multiplier.<ref>{{harvnb|Cavanagh|2017|p=275}}</ref> }} The symbols of multiplication are <math>\times</math>, <math>\cdot</math>, and *. Examples are <math>2 \times 3 = 6</math> and <math>0.3 \cdot 5 = 1.5</math>. If the multiplicand is a natural number then multiplication is the same as repeated addition, as in <math>2 \times 3 = 2 + 2 + 2</math>.<ref>{{multiref | {{harvnb|Romanowski|2008|p=304}} | {{harvnb|Wright|Ellemor-Collins|Tabor|2011|p=[https://books.google.com/books?id=3yqdEAAAQBAJ&pg=PA136 136]}} | {{harvnb|Musser|Peterson|Burger|2013|pp=[https://books.google.com/books?id=8jh7DwAAQBAJ&pg=PA101 101–102]}} }}</ref>

Division is the inverse of multiplication. In it, one number, known as the dividend, is split into several equal parts by another number, known as the divisor. The result of this operation is called the [[quotient]]. The symbols of division are <math>\div</math> and <math>/</math>. Examples are <math>48 \div 8 = 6</math> and <math>29.4 / 1.4 = 21</math>.<ref>{{multiref | {{harvnb|Romanowski|2008|p=303}} | {{harvnb|Wheater|2015|p=[https://books.google.com/books?id=Q7R3EAAAQBAJ&pg=PP19 19]}} | {{harvnb|Wright|Ellemor-Collins|Tabor|2011|p=[https://books.google.com/books?id=3yqdEAAAQBAJ&pg=PA136 136]}} }}</ref> Division is often treated as a special case of multiplication: instead of dividing by a number, it is also possible to multiply by its [[Multiplicative inverse|reciprocal]]. The reciprocal of a number is 1 divided by that number. For instance, <math>48 \div 8 = 48 \times \tfrac{1}{8}</math>.<ref>{{multiref | {{harvnb|Kay|2021|p=[https://books.google.com/books?id=aw81EAAAQBAJ&pg=PA117 117]}} | {{harvnb|Wheater|2015|p=[https://books.google.com/books?id=Q7R3EAAAQBAJ&pg=PP19 19]}} | {{harvnb|Wright|Ellemor-Collins|Tabor|2011|pp=[https://books.google.com/books?id=3yqdEAAAQBAJ&pg=PA136 136–137]}} }}</ref>

The [[multiplicative identity]] element is 1 and the multiplicative inverse of a number is the reciprocal of that number. For example, <math>13 \times 1 = 13</math> and <math>13 \times \tfrac{1}{13} = 1</math>. Multiplication is both commutative and associative.<ref>{{multiref | {{harvnb|Mazzola|Milmeister|Weissmann|2004|p=[https://books.google.com/books?id=CkFCCA-2sRgC&pg=PA66 66]}} | {{harvnb|Romanowski|2008|pp=303–304}} | {{harvnb|Nagel|2002|pp=179–180}} }}</ref>