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It requires memorization of the multiplication table for single digits. This is the usual algorithm for multiplying larger numbers by hand in base 10. A person doing long multiplication on paper will write down all the products and then add them together; an abacus-user will sum the products as soon as each one is computed.
3.1 Numbers and digits (base 10) ... Download as PDF; ... Trachtenberg defined this algorithm with a kind of pairwise multiplication where two digits are multiplied ...
[1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n-digit numbers to three multiplications of n/2-digit numbers and, by repeating this reduction, to at most single-digit multiplications.
Indeed, multiplication by 3, followed by division by 3, yields the original number. The division of a number other than 0 by itself equals 1. Several mathematical concepts expand upon the fundamental idea of multiplication. The product of a sequence, vector multiplication, complex numbers, and matrices are all examples where this can be seen.
[3] The lunar addition and multiplication operations satisfy the commutative and associative laws. The lunar multiplication distributes over the lunar addition. The digit 0 is the identity under lunar addition. No non-zero number has an inverse under lunar addition. The digit 9 is the identity under lunar multiplication.
Any number multiplied by 1 is itself: =. Zero. Any number multiplied by 0 is 0: =. In the multiplication algorithm, the "tens" digit of the product of a pair of digits is referred to as the "carry digit".
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