Mathematics
Mathematically, the ability to break up a multiplication in this way is known as the distributive law, which can be expressed in algebra as the property that a(b+c) = ab + ac. The grid method uses the distibutive property twice to expand the product, once for the horizontal factor, and once for the vertical factor.
Historically the grid calculation (tweaked slightly) was the basis of a method called lattice multiplication, which was the standard method of multiple-digit multiplication developed in medieval Arabic and Hindu mathematics. Lattice multiplication was introduced into Europe by Fibonacci at the start of the thirteenth century along with the so-called Arabic numerals themselves; although, like the numerals also, the ways he suggested to calculate with them were initially slow to catch on. Napier's bones were a calculating help introduced by the Scot John Napier in 1617 to assist lattice method calculations.
Read more about this topic: Grid Method Multiplication
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