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In this case, s is called the least absolute remainder. [3] As with the quotient and remainder, k and s are uniquely determined, except in the case where d = 2n and s = ± n. For this exception, we have: a = k⋅d + n = (k + 1)d − n. A unique remainder can be obtained in this case by some convention—such as always taking the positive value ...
v. t. e. The quota methods are a family of apportionment rules, i.e. algorithms for distributing the seats in a legislative body among a number of administrative divisions. The quota methods are based on calculating a fixed electoral quota, i.e. a given number of votes needed to win a seat. This is used to calculate each party's seat entitlement.
The stepped reckoner or Leibniz calculator was a mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz (started in 1673, when he presented a wooden model to the Royal Society of London [2] and completed in 1694). [1] The name comes from the translation of the German term for its operating mechanism, Staffelwalze ...
Casting out nines. Casting out nines is any of three arithmetical procedures: [1] Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits which sum to 9 or a multiple of 9. The result of this procedure is a number which is smaller than the original whenever the original has more than one digit, leaves ...
e. In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced / ˈkwoʊʃənt /) is a quantity produced by the division of two numbers. [1] The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division) [2] or a fraction or ratio (in the ...
e. The highest averages, divisor, or divide-and-round methods[1] are a family of apportionment algorithms that aim to fairly divide a legislature between several groups, such as political parties or states. [1][2] More generally, divisor methods can be used to round shares of a total, e.g. percentage points (which must add up to 100). [2]
Long division. In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another ...
The process is shown in the diagram. The cycle is repeated until the result of subtraction is less than the divisor. The number left is the remainder. So in this example, what remains is a quotient of 485 with a remainder of 16364. The process usually stops here and the answer uses the fractional form 485 + 16364 / 96431 .