Remainder

In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algebra, the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo operation is the operation that produces such a remainder when given a dividend and divisor.

Formally it is also true that a remainder is what is left after subtracting one number from another, although this is more properly called the difference. This usage can be found in some elementary textbooks; colloquially it is replaced by the expression "the rest" as in "Give me two dollars back and keep the rest." However, the term "remainder" is still used in this sense when a function is approximated by a series expansion and the error expression ("the rest") is referred to as the remainder term.

Integer division

If a and d are integers, 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.

Remainder (film)

Remainder is a 2015 British drama film directed by Omer Fast. It was shown in the Panorama section at the 66th Berlin International Film Festival.

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Remainder (law)

A remainder in property law of the United Kingdom and the United States is a future interest given to a person (who is referred to as the transferee or remainderman) that is capable of becoming possessory upon the natural end of a prior estate created by the same instrument. Thus, the prior estate must be one that is capable of ending naturally, for example upon the expiration of a term of years or the death of a life tenant. A future interest following a fee simple absolute cannot be a remainder because of the preceding infinite duration.

For example, a person, D, gives ("conveys") a piece of real property called Blackacre “to A for life, and then to B and her heirs.” A receives a life estate in Blackacre and B holds a remainder, which can become possessory when the prior estate naturally terminates (A’s death). However, B cannot claim the property until A's death.

There are two types of remainders in property law, vested and contingent. A vested remainder is held by a specific person without any conditions precedent; a contingent remainder is one for which the holder has not been identified, or for which a condition precedent must be satisfied.