Editing Multiplication (section)

===Modern methods===
[[Image:Gelosia multiplication 45 256.png|right|upright 1.0|thumb|Product of 45 and 256. Note the order of the numerals in 45 is reversed down the left column. The carry step of the multiplication can be performed at the final stage of the calculation (in bold), returning the final product of {{nowrap|1=45 × 256 = 11520}}. This is a variant of [[Lattice multiplication]].]]
The modern method of multiplication based on the [[Hindu–Arabic numeral system]] was first described by [[Brahmagupta]]. Brahmagupta gave rules for addition, subtraction, multiplication, and division. [[Henry Burchard Fine]], then a professor of mathematics at [[Princeton University]], wrote the following:
:''The Indians are the inventors not only of the positional decimal system itself, but of most of the processes involved in elementary reckoning with the system. Addition and subtraction they performed quite as they are performed nowadays; multiplication they effected in many ways, ours among them, but division they did cumbrously.''<ref>{{cite book |last=Fine |first=Henry B. |author-link=Henry Burchard Fine |title=The Number System of Algebra – Treated Theoretically and Historically |edition=2nd |date=1907 |page=90 |url=https://archive.org/download/numbersystemofal00fineuoft/numbersystemofal00fineuoft.pdf}}</ref>
These place value decimal arithmetic algorithms were introduced to Arab countries by [[Al Khwarizmi]] in the early 9th&nbsp;century and popularized in the Western world by [[Fibonacci]] in the 13th century.<ref>{{Cite web |last=Bernhard |first=Adrienne |title=How modern mathematics emerged from a lost Islamic library |url=https://www.bbc.com/future/article/20201204-lost-islamic-library-maths |access-date=2022-04-22 |website=bbc.com |language=en}}</ref>

====Grid method====
[[Grid method multiplication]], or the box method, is used in primary schools in England and Wales and in some areas{{Which|date=December 2021}} of the United States to help teach an understanding of how multiple digit multiplication works. An example of multiplying 34 by 13 would be to lay the numbers out in a grid as follows:

:{| class="wikitable" style="text-align: center;"
! scope="col" | ×
! scope="col" | 30
! scope="col" | 4
|-
! scope="row" | 10
|300
|40
|-
! scope="row" | 3
|90
|12
|}

and then add the entries.