Editing Arithmetic (section)

=== Addition and subtraction ===
{{main|Addition|Subtraction}}

{{multiple image
|perrow            = 1 / 1
|total_width       = 300
|image1            = Addition1.png
|alt1              = Diagram showing addition
|image2            = Subtraction.png
|alt2              = Diagram showing subtraction
|footer            = Addition and subtraction
}}

Addition is an arithmetic operation in which two numbers, called the addends, are combined into a single number, called the sum. The symbol of addition is <math>+</math>. Examples are <math>2 + 2 = 4</math> and <math>6.3 + 1.26 = 7.56</math>.<ref>{{multiref | {{harvnb|Musser|Peterson|Burger|2013|p=[https://books.google.com/books?id=8jh7DwAAQBAJ&pg=PA87 87]}} | {{harvnb|Romanowski|2008|p=303}} }}</ref> The term [[summation]] is used if several additions are performed in a row.<ref>{{harvnb|Burgin|2022|p=[https://books.google.com/books?id=rWF2EAAAQBAJ&pg=PA25 25]}}</ref> Counting is a type of repeated addition in which the number 1 is continuously added.<ref>{{harvnb|Confrey|1994|p=[https://books.google.com/books?id=4MwZlzgvaGYC&pg=PA308 308]}}</ref>

Subtraction is the inverse of addition. In it, one number, known as the subtrahend, is taken away from another, known as the minuend. The result of this operation is called the difference. The symbol of subtraction is <math>-</math>.<ref>{{multiref | {{harvnb|Romanowski|2008|p=303}} | {{harvnb|Musser|Peterson|Burger|2013|pp=[https://books.google.com/books?id=8jh7DwAAQBAJ&pg=PA93 93–94]}} | {{harvnb|Kay|2021|pp=[https://books.google.com/books?id=aw81EAAAQBAJ&pg=PA44 44–45]}} | {{harvnb|Wright|Ellemor-Collins|Tabor|2011|p=[https://books.google.com/books?id=3yqdEAAAQBAJ&pg=PA136 136]}} }}</ref> Examples are <math>14 - 8 = 6</math> and <math>45 - 1.7 = 43.3</math>. Subtraction is often treated as a special case of addition: instead of subtracting a positive number, it is also possible to add a negative number. For instance <math>14 - 8 = 14 + (-8)</math>. This helps to simplify mathematical computations by reducing the number of basic arithmetic operations needed to perform calculations.<ref>{{multiref | {{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]}} | {{harvnb|Achatz|Anderson|2005|p=[https://books.google.com/books?id=YOdtemSmzQQC&pg=PA18 18]}} }}</ref>

The additive identity element is 0 and the additive inverse of a number is the negative of that number. For instance, <math>13 + 0 = 13</math> and <math>13 + (-13) = 0</math>. Addition 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|p=303}} | {{harvnb|Nagel|2002|pp=179–180}} }}</ref>