Editing Multiplication (section)

===Historical algorithms===
Methods of multiplication were documented in the writings of [[ancient Egypt]]ian, {{Citation needed span|text=Greek, Indian,|date=December 2021|reason=This claim is not sourced in the subsections below.}} and [[History of China#Ancient China|Chinese]] civilizations.

The [[Ishango bone]], dated to about 18,000 to 20,000&nbsp;BC, may hint at a knowledge of multiplication in the [[Upper Paleolithic]] era in [[Central Africa]], but this is speculative.<ref>{{cite arXiv|last=Pletser|first=Vladimir|date=2012-04-04|title=Does the Ishango Bone Indicate Knowledge of the Base 12? An Interpretation of a Prehistoric Discovery, the First Mathematical Tool of Humankind|class=math.HO|eprint=1204.1019}}</ref>{{Verification needed|date=December 2021}}

====Egyptians====
{{Main|Ancient Egyptian multiplication}}
The Egyptian method of multiplication of integers and fractions, which is documented in the [[Rhind Mathematical Papyrus]], was by successive additions and doubling. For instance, to find the product of 13 and 21 one had to double 21 three times, obtaining {{nowrap|1=2 × 21 = 42}}, {{nowrap|1=4 × 21 = 2 × 42 = 84}}, {{nowrap|1=8 × 21 =  2 × 84 = 168}}. The full product could then be found by adding the appropriate terms found in the doubling sequence:<ref>{{Cite web |title=Peasant Multiplication |url=http://www.cut-the-knot.org/Curriculum/Algebra/PeasantMultiplication.shtml |access-date=2021-12-29 |website=cut-the-knot.org}}</ref>
:13 × 21 = (1 + 4 + 8) × 21 = (1 × 21) + (4 × 21) + (8 × 21) = 21 + 84 + 168 = 273.

====Babylonians====
The [[Babylonians]] used a [[sexagesimal]] [[positional number system]], analogous to the modern-day [[decimal expansion|decimal system]]. Thus, Babylonian multiplication was very similar to modern decimal multiplication. Because of the relative difficulty of remembering {{nowrap|60 × 60}} different products, Babylonian mathematicians employed [[multiplication table]]s. These tables consisted of a list of the first twenty multiples of a certain ''principal number'' ''n'': ''n'', 2''n'', ..., 20''n''; followed by the multiples of 10''n'': 30''n'' 40''n'', and 50''n''. Then to compute any sexagesimal product, say 53''n'', one only needed to add 50''n'' and 3''n'' computed from the table.{{Citation needed|date=December 2021}}

====Chinese====
{{see also|Chinese multiplication table}}
[[File:Multiplication algorithm.GIF|thumb|right|upright 1.0|{{nowrap|1=38 × 76 = 2888}}]]
In the mathematical text ''[[Zhoubi Suanjing]]'', dated prior to 300&nbsp;BC, and the ''[[Nine Chapters on the Mathematical Art]]'', multiplication calculations were written out in words, although the early Chinese mathematicians employed [[Rod calculus]] involving place value addition, subtraction, multiplication, and division. The Chinese were already using a [[Chinese multiplication table|decimal multiplication table]] by the end of the [[Warring States]] period.<ref name="Nature">{{cite journal | url =http://www.nature.com/news/ancient-times-table-hidden-in-chinese-bamboo-strips-1.14482 | title =Ancient times table hidden in Chinese bamboo strips | journal =Nature | first =Jane |last=Qiu |author-link=Jane Qiu| date =7 January 2014 | access-date =22 January 2014 | doi =10.1038/nature.2014.14482 | s2cid =130132289 | archive-url =https://web.archive.org/web/20140122064930/http://www.nature.com/news/ancient-times-table-hidden-in-chinese-bamboo-strips-1.14482 | archive-date =22 January 2014 | url-status =live | doi-access =free }}</ref>