Multiplication algorithm: Difference between revisions

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A '''multiplication algorithm''' is an [[algorithm]] (or method) to [[multiplication|multiply]] two numbers. Depending on the size of the numbers, different algorithms are in use. Efficient multiplication algorithms have existed since the advent of the decimal system.

== BoxGrid method ==

{{main|Grid method multiplication}}

The [[grid method multiplication|grid method]] (or box method) is an introductory method for multiple-digit multiplication that is often taught to pupils at [[primary school]] or [[elementary school]] level. It has been a standard part of the primary-school mathematics curriculum in England and Wales since the late 1990s.<ref>Gary Eason, [http://news.bbc.co.uk/1/hi/education/639937.stm Back to school for parents], ''[[BBC News]]'', 13 Febraury 2000<br>Rob Eastaway, [http://www.bbc.co.uk/news/magazine-11258175 Why parents can't do maths today], ''[[BBC News]]'', 10 September 2010</ref>

Both factors are broken up ("partitioned") into their hundreds, tens and units parts, and the products of these parts are then calculated explicitly in a relatively simple multiplication-only stage, before these contributions are then totalled to give the final answer in a separate addition stage.

Thus for example the calculation 34 &times; 13 might be represented

:{|class="wikitable" border=1 cellspacing=0 cellpadding=15 style="text-align: center;"

! scope="col" width="40pt" | &nbsp;

! scope="col" width="40pt" | 30

! scope="col" width="40pt" | 4

|-

! scope="row" | 10

|300

|40

|-

! scope="row" | 3

|90

|12

|}

followed by the addition (300 + 40) + (90 + 12) = 340 + 102 = 442.

This calculation approach (though not necessarily with the explicit grid arrangement) is also known as the [[partial products algorithm]]. Its essence is the calculation of the simple multiplications separately, with all addition being left to the final gathering-up stage.

The grid method can in principle be applied to factors of any size, although the number of sub-products becomes cumbersome as the number of digits increases. Nevertheless it is seen as a usefully explicit method to introduce the idea of multiple-digit multiplications; and, in an age when most multiplication calculations are done using a calculator or a spreadsheet, it may in practice be the only multiplication algorithm that some students will ever need.

== Long multiplication ==

Line 113 ⟶ 141:

= 139,676,498,390

|}

== Box method ==

{{Main|Box method}}

The box method is a simplified version of the lattice method that is taught in some British schools. <ref>[http://www.bbc.co.uk/schools/gcsebitesize/maths/number/multiplicationdivisionrev1.shtml Long multiplication and division]</ref>

== Peasant or binary multiplication ==

{{Main|Peasant multiplication}}