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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 ...
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.
Because of the relative difficulty of remembering 60 × 60 different products, Babylonian mathematicians employed multiplication tables. These tables consisted of a list of the first twenty multiples of a certain principal number n: n, 2n, ..., 20n; followed by the multiples of 10n: 30n 40n, and 50n.
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Using regular numbers simplifies multiplication and division in base 60 because dividing a by b can be done by multiplying a by b 's reciprocal when b is a regular number. [11] [12] For instance, division by 54 can be achieved in the Assyro-Babylonian system by multiplying by 4000 because 60 3 ÷ 54 = 60 3 × (1/54) = 4000. In base 60, 4000 can ...
Multiplication table problem. For each positive integer , let () be the number of distinct integers in an multiplication table. In 1960, [5] Erdős ...
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If the tables are held on single-sided rods, 40 rods are needed in order to multiply 4-digit numbers – since numbers may have repeated digits, four copies of the multiplication table for each of the digits 0 to 9 are needed. If square rods are used, the 40 multiplication tables can be inscribed on 10 rods.