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In these examples, the (negative) least absolute remainder is obtained from the least positive remainder by subtracting 5, which is d. This holds in general. When dividing by d, either both remainders are positive and therefore equal, or they have opposite signs. If the positive remainder is r 1, and the negative one is r 2, then r 1 = r 2 + d.
The word "remainder" means "leftover", "residue". As such, the remainder of division of 5 by 3 is not 5, is not 8, it is 2, and only 2. As such, your addition of the section "Other definitions" in the remainder article is not mathematically correct. The concept of remainder is well-defined in Mathematics.
The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of ...
Remainder is the amount "left over" when dividing two integers. Remainder may also refer to: Remaindered book, a publisher liquidating the remaining unsold copies of a book; Remainder (law), in property law, a future interest created in a transferee
The remainder is multiplied by 3 to get feet and carried up to the feet column. Long division of the feet gives 1 remainder 29 which is then multiplied by twelve to get 348 inches. Long division continues with the final remainder of 15 inches being shown on the result line.
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.
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The synonyms remainderer, remainderperson, and remainor may be found in legal dictionaries, but are rarely used in practice. A female person in the position of a remainderman is also termed a remainderman. For instance, in a will chattels are left to one person, who can then offer it to a second person, who can then offer it to a third person ...