Editing Addition (section)

=== Extending a length ===
{{multiple image
 | image1 = AdditionLineAlgebraic.svg
 | caption1 = A number-line visualization of the algebraic addition <math> 2 + 4 = 6 </math>. A "jump" that has a distance of <math> 2 </math> followed by another that is as long as <math> 4 </math>, is the same as a translation by <math> 6 </math>.
 | image2 = AdditionLineUnary.svg
 | caption2 = A number-line visualization of the unary addition <math> 2 + 4 = 6 </math>. A translation by <math> 4 </math> is equivalent to four translations by <math> 1 </math>.
 | direction = vertical
 | total_width = 400
}}
A second interpretation of addition comes from extending an initial length by a given length:{{sfnp|Mosley|2001|p=[http://books.google.com/books?id=I-__WcWjemUC&pg=PA8 8]}}
{{blockquote|When an original length is extended by a given amount, the final length is the sum of the original length and the length of the extension.}}
The sum <math> a + b </math> can be interpreted as a [[binary operation]] that combines <math> a </math> and <math> b </math> algebraically, or it can be interpreted as the addition of <math> b </math> more units to <math> a </math>. Under the latter interpretation, the parts of a sum <math> a + b </math> play asymmetric roles, and the operation <math> a + b </math> is viewed as applying the [[unary operation]] <math> +b </math> to <math> a </math>.{{sfnp|Li|Lappan|2014|p=204}} Instead of calling both <math> a </math> and <math> b </math> addends, it is more appropriate to call <math> a </math> the "augend" in this case, since <math> a </math> plays a passive role. The unary view is also useful when discussing [[subtraction]], because each unary addition operation has an inverse unary subtraction operation, and vice versa.
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