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Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations ...
In mathematics, Light's associativity test is a procedure invented by F. W. Light for testing whether a binary operation defined in a finite set by a Cayley multiplication table is associative. The naive procedure for verification of the associativity of a binary operation specified by a Cayley table, which compares the two products that can be ...
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.
36 represented in chisanbop, where four fingers and a thumb are touching the table and the rest of the digits are raised. The three fingers on the left hand represent 10+10+10 = 30; the thumb and one finger on the right hand represent 5+1=6. Counting from 1 to 20 in Chisanbop. Each finger has a value of one, while the thumb has a value of five.
Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]
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