remainder
American Heritage Dictionary:
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re·main·der
(rĭ-mān'dər) 
n.
To sell or dispose of as a remainder.
n.
- Something left over after other parts have been taken away.
- Mathematics.
- The number left over when one integer is divided by another: The remainder plus the product of the quotient times the divisor equals the dividend.
- The number obtained when one number is subtracted from another; the difference.
- Law. An estate in land that is conveyed only after the termination of a preceding estate created at the same time.
- A book that remains with a publisher after sales have fallen off, usually sold at a reduced price.
To sell or dispose of as a remainder.
[Middle English, second party's right of ownership, from Anglo-Norman, from remeindre, to remain, variant of Old French remaindre, remainer. See remain.]
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remainder
Barron's Marketing Dictionary:
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remainder
Merchandise that remains unsold at its original price due to lack of demand; also called overstock. The remainder is usually then sold at a lower price. Calendars sold months after the year has begun would be considered remainder merchandise and thus sold at a substantial discount.
Barron's Business Dictionary:
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remainder
Part of an estate in land that is left upon the termination of the immediately preceding estate (often a life estate or estate for a term of years) and that does not amount to a reversion to the original grantor or his heirs.
| Relocation Service, Relocation Clause, Relocate | |
| Remainderperson, Remediation, Remedy |
Barron's Real Estate Dictionary:
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remainder
1. an estate that takes effect after the termination of a prior estate such as a life estate.
Example: At the death of her husband, Polly Rowen inherits a life estate in their home. The remainder is devised to their son, Paul Rowen. When Polly dies, Paul will gain title to their house.
Paul is the remainderman.
2. that portion of a parcel of property that the owner retains after the government exercises its powers of eminent domain to acquire a partial taking from the larger parcel.
Example: The taking was from the larger parcel or parent tract and left the owner with a remnant parcel as a remainder. Because of the remainder’s odd shape, it had little value.
| Relocation Service, Relocation Network | |
| Remainderman, Remaining Economic Life |
Roget's Thesaurus:
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remainder
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An interest in property that confers a right to possession in someone other than the grantor or his heirs upon the termination of a prior interest, such as following the death of a life tenant.
West's Encyclopedia of American Law:
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Remainder
This entry contains information applicable to United States law only.
A future interest held by one person in the real property of another that will take effect upon the expiration of the other property interests created at the same time as the future interest.
The law of real property permits a person who owns real estate to convey all or part of her rights in the property to another person or persons. Legal conveyances of property become more complicated when the person who owns the property, the grantor, gives a present interest (the right to the possession and use of the property) in the property to one person for either life or a set period of time, and also gives a future interest (also called a nonpossessory interest) in the property to another person. The future interest is called a remainder, and the holder of this interest is called the remainderman.
Remainders are subdivided into two principal categories: contingent remainders and vested remainders. A contingent remainder can be created in two different ways. First, it can be a remainder to a person not ascertained at the time the interest is created. For example, Tom owns Blackacre in fee simple, which means he owns it with no ownership limitations. While Bob and Jane are alive, Tom conveys Blackacre to Bob for life, with a remainder to the heirs of Jane. The heirs of Jane are not yet known, so they have a contingent remainder.
A remainder also will be classified as contingent, whether or not the remainderman is ascertained, where the possibility of becoming a present interest is subject not only to the expiration of the preceding property interest but also to some specific event occurring before the expiration of the preceding interest. This event is called a special condition precedent. For example, if Tom owns Blackacre in fee and conveys Blackacre to Bob for life and then to Jane if she marries Bill, then Jane has a contingent remainder in fee, conditioned on the death of Bob and the marriage to Bill.
A vested remainder is a future interest to an ascertained person, with the certainty or possibility of becoming a present interest subject only to the expiration of the preceding property interests. If Tom owns Blackacre in fee simple and conveys Blackacre to Bob for life and to Jane in fee simple, Jane has a vested remainder in fee that becomes a present interest upon the death of Bob. As a remainderman, she simply has to wait for Bob's death before assuming a present interest in Blackacre.
For a remainder to be effective, it must be contained in the same instrument of conveyance (document, such as a deed) that grants the present interest to another person.
See: estate.
Word Tutor:
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remainder
IN BRIEF: The part, group, or number left over.
Most people can't think, most of the remainder won't think, the small fraction who do think mostly can't do it very well.
— Robert Heinlein (1907-1988)
LearnThatWord.com is a free vocabulary and spelling program where you only pay for results!
Random House Word Menu:
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categories related to 'remainder'
- Quantities, Relationships, and Operations - remainder: number left after subtraction; portion of the dividend, not evenly divisible, left after division
- Publishing - remainder: (vb) sell book at lowered price, usu. from overstock; (n) book that has been remaindered
Wikipedia on Answers.com:
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Remainder
For other uses, see Remainder (disambiguation).
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This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Please improve this article by introducing more precise citations. (April 2010) |
In arithmetic, the remainder (or residue) is the amount "left over" after the division of two integers which cannot be expressed with an integer quotient.
The general form of a linear equation can be expressed as a = q × d + r. In this equation, q can be referred to as the quotient and d as the divisor, while r as the remainder. The equation can be transformed to find the remainder as: r = a - q × d. However, a and d must be natural numbers, with d being non-zero. The quotient is the integer result (rounded down) of the division of a by d. The remainder must also be an integer.
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The remainder for natural numbers
If a and d are natural numbers, with d non-zero, it can be proven 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. The division algorithm provides a proof of this result and also an algorithm describing how to calculate the remainder.
The case of general integers
If a and d are integers, with d non-zero, then a remainder is an integer r such that a = qd + r for some integer q, and with |r| < |d|.
When defined this way, there are two possible remainders. For example, the division of −42 by −5 can be expressed as either
- −42 = 9×(−5) + 3
as is usual for mathematicians,[citation needed] or
- −42 = 8×(−5) + (−2).
So the remainder is then either 3 or −2.
This ambiguity in the value of the remainder can be quite serious computationally; for mission critical computing systems, the wrong choice can lead to dangerous consequences. In the case above, the negative remainder is obtained from the positive one just by subtracting 5, which is d. This holds in general. When dividing by d, if the positive remainder is r1, and the negative one is r2, then
- r1 = r2 + d.
The remainder for real numbers
When a and d are real numbers, with d non-zero, a can be divided by d without remainder, with the quotient being another real number. If the quotient is constrained to being an integer however, the concept of remainder is still necessary. It can be proved that there exists a unique integer quotient q and a unique real remainder r such that a=qd+r with 0≤r < |d|. As in the case of division of integers, the remainder could be required to be negative, that is, -|d| < r ≤ 0.
Extending the definition of remainder for real numbers as described above is not of theoretical importance in mathematics; however, many programming languages implement this definition—see modulo operation.
The inequality satisfied by the remainder
The way remainder was defined, in addition to the equality a=qd+r an inequality was also imposed, which was either 0≤ r < |d| or -|d| < r ≤ 0. Such an inequality is necessary in order for the remainder to be unique—that is, for it to be well-defined. The choice of such an inequality is somewhat arbitrary. Any condition of the form x < r ≤ x+|d| (or x ≤ r < x+|d|), where x is a constant, is enough to guarantee the uniqueness of the remainder.
Quotient and remainder in programming languages
Main article: Modulo operation
With two choices for the inequality, there are two choices for the remainder, one negative and the other positive. This means that there are also two possible choices for the quotient. In number theory the positive remainder is chosen by convention. But programming languages need not, and different languages have adopted different conventions: C99 and Pascal choose the remainder with the same sign as the dividend a. (Before C99, the C language allowed either choice.) Perl, Python (only modern versions), and Common Lisp choose the remainder with the same sign as the divisor d. Haskell and Scheme offer two functions, remainder and modulo – Fortran has mod and modulo; the former agrees in sign with the dividend, and the latter with the divisor.
See also
- Chinese remainder theorem
- Division algorithm
- Euclidean algorithm
- Modular arithmetic
- Modulo operation
- Divisibility rule
References
- Davenport, Harold (1999). The higher arithmetic: an introduction to the theory of numbers. Cambridge, UK: Cambridge University Press. p. 25. ISBN 0-521-63446-6.
- Zuckerman, Martin M. Arithmetic: A Straightforward Approach. Lanham, Md: Rowman & Littlefield Publishers, Inc. ISBN 0-912675-07-1.
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
Translations:
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Remainder
Dansk (Danish)
n. - rest, tilbageværende del
v. tr. - sælge til nedsat pris
Nederlands (Dutch)
overschot, rest, gesubstitueerd erfdeel, restantpartij boeken (verkopen)
Français (French)
n. - reste, restant, autres (personnes), (Math) reste, (Jur) retour en pleine propriété, (Comm) invendus
v. tr. - solder
Deutsch (German)
n. - Rest, Restbestand
v. - Restbestand billig verkaufen
Ελληνική (Greek)
n. - υπόλοιπο, κατάλοιπο, (πληθ.) υπολείμματα, λείψανα, λείψανο
v. - ξεπουλάω βιβλία χωρίς κίνηση
Italiano (Italian)
resto, rimanenza
Português (Portuguese)
n. - restante (m), saldo (m), resíduo (m)
v. - saldar
Español (Spanish)
n. - resto, remanente
v. tr. - vender como remanente
Svenska (Swedish)
n. - återstod, (jur) hemfallsrätt, (mat) rest
v. - sälja ut
中文（简体）(Chinese (Simplified))
剩余物, 差数, 其余的人, 余数, 余项, 削价出售
中文（繁體）(Chinese (Traditional))
n. - 剩餘物, 差數, 其餘的人, 餘數, 余項
v. tr. - 削價出售
한국어 (Korean)
n. - 잔여물, 나머지, 잉여, 유물
v. tr. - 싸게 처분하다
العربيه (Arabic)
(الاسم) الباقي, بقيه (فعل) يبيع بسعر منخفض
עברית (Hebrew)
n. - יתרה, שארית
v. tr. - מכר (שאריות) בזול
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The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.
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Dictionary of Marketing Terms. Copyright © 2000 by Barron's Educational Series, Inc. All rights reserved.
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Dictionary of Business Terms. Copyright © 2007 by Barron's Educational Series, Inc. All rights reserved.
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Dictionary of Real Estate Terms. Copyright © 2008 by Barron's Educational Series, Inc. All rights reserved.
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