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In IEEE arithmetic, division of 0/0 or ∞/∞ results in NaN, but otherwise division always produces a well-defined result. Dividing any non-zero number by positive zero (+0) results in an infinity of the same sign as the dividend. Dividing any non-zero number by negative zero (−0
A company’s dividend rate is the amount of its payout. For example, if Apple pays $0.63 per share in dividends every quarter, its annual dividend rate is $2.52, or four times $0.63. But when it ...
In these enlarged number systems, division is the inverse operation to multiplication, that is a = c / b means a × b = c, as long as b is not zero. If b = 0, then this is a division by zero, which is not defined. [a] [4]: 246 In the 21-apples example, everyone would receive 5 apple and a quarter of an apple, thus avoiding any leftover.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Polynomial long division is an algorithm that implements the Euclidean division of polynomials, which starting from two polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that A = BQ + R, and either R = 0 or the degree of R is lower than the degree of B.
Given an integer a and a non-zero integer d, it can be shown that there exist unique integers q and r, such that a = qd + r and 0 ≤ r < | d |. The number q is called the quotient, while r is called the remainder. (For a proof of this result, see Euclidean division. For algorithms describing how to calculate the remainder, see Division algorithm.)
Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [ 1 ] For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0 ...
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