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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 ...
If a number is divisible by 9, its digital root is 9. Otherwise, its digital root is the remainder it leaves after being divided by 9. A sanity test in which the above-mentioned procedures are used to check for errors in arithmetical calculations. The test is carried out by applying the same sequence of arithmetical operations to the digital ...
In Indian mathematics, a Vedic square is a variation on a typical 9 × 9 multiplication table where the entry in each cell is the digital root of the product of the column and row headings i.e. the remainder when the product of the row and column headings is divided by 9 (with remainder 0 represented by 9).
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 is also known as nine-nine song (or poem), [2] as the table consists of eighty-one lines with four or five Chinese characters per lines; this thus created a constant metre and render the multiplication table as a poem. For example, 9 × 9 = 81 would be rendered as "九九八十一", or "nine nine eighty one", with the world for "begets" "得 ...
In this same way the tables for subtracting digits from 10 or 9 are to be memorized. And whenever the rule calls for adding half of the neighbor, always add 5 if the current digit is odd. This makes up for dropping 0.5 in the next digit's calculation.
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The group {1, −1} above and the cyclic group of order 3 under ordinary multiplication are both examples of abelian groups, and inspection of the symmetry of their Cayley tables verifies this. In contrast, the smallest non-abelian group, the dihedral group of order 6, does not have a symmetric Cayley table.
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