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In arithmetic, long division is a procedure for calculating the division of one integer, called the dividend, by another integer called the divisor, to produce a result called the quotient. It requires only the means to write the numbers down, and is simple to perform, even for large dividends. The procedure converts the problem of dividing a divisor into a large dividend into a series of divisions of the divisor into smaller numbers. Since the late 20th century, many widely adopted K-12 standards-based mathematics curricula no longer provide instruction in long division, stating that it is harmful to understanding, and poor use of time in the age of calculators. Arithmetic or arithmetics (from the Greek word αÏιθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. ...
In mathematics, computing, linguistics, and related disciplines, an algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminate in a defined end-state. ...
In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ...
The integers are commonly denoted by the above symbol. ...
In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ...
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ...
In mathematics, a quotient is the end result of a division problem. ...
Principles and Standards for School Mathematics is a document produced in 1989 by the National Council of Teachers of Mathematics [5] (NCTM) to set forth a national vision for precollege mathematics education in the US and Canada. ...
Notation
In long division notation, 500 divided by 4 equals 125 is denoted as follows: 
Example The procedure involves several steps. As an example, consider the problem of 950 divided by 4:
1. Write the dividend and divisor in this form:
 The procedure involves dividing the divisor (4) into a number for each digit of the dividend (950).
2.The first number to be divided by the divisor (4) is the leftmost digit (9) of the dividend. Ignoring any remainder, write the result (2), above the line over the leftmost digit of the dividend. Multiply the divisor by that number (4 times 2) and write the result (8) under the leftmost digit of the dividend.
 3. Subtract the bottom number (8) from the number immediately above it (9). Write the result (1), under the bottom number (8), then copy the next digit of the dividend (5) to the right of the result of the subtraction.  4. Repeat steps 2 and 3, using the newly created bottom number (15) as the number to be divided by the divisor (4), and write the results above and under the next digit of the dividend.  5. Repeat step 4 until there are no digits remaining in the dividend. The number written above the bar (237) is the quotient, and the result of the last subtraction is the remainder for the entire problem (2).  The answer to the above example is expressed as 237 with remainder 2. Alternatively, one can continue the above procedure to produce a decimal answer. We continue the process by adding a decimal and zeroes as necessary to the right of the dividend, treating each zero as another digit of the dividend. Thus the next step in such a calculation would give the following: 
Division algorithm The above procedure relies on the division algorithm, which states that given any two integers a and d, with d ≠ 0, there exist unique integers q and r such that a = qd + r and 0 ≤ r < |d |, where |d | denotes the absolute value of d. The division algorithm is a theorem in mathematics which precisely expresses the outcome of the usual process of division of integers. ...
In mathematics, the absolute value (or modulus1) of a real number is its numerical value without regard to its sign. ...
Generalizations
Rational numbers Long division of integers can easily be extended to include non-integer dividends, as long as they are rational. This is because every rational number has a recurring decimal expansion. The procedure can also be extended to include divisors which have a finite or terminating decimal expansion (i.e. decimal fractions). In this case the procedure involves multiplying the divisor and dividend by the appropriate power of ten so that the new divisor is an integer — taking advantage of the fact that a/b = (ca)/(cb) — and then proceeding as above. In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero. ...
A recurring decimal is an expression representing a real number in the decimal numeral system, in which after some point the same sequence of digits repeats infinitely many times. ...
The decimal (base ten or occasionally denary) numeral system has ten as its base. ...
Decimal, or denary, notation is the most common way of writing the base 10 numeral system, which uses various symbols for ten distinct quantities (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits) together with the decimal point and the sign symbols + (plus) and − (minus...
Polynomials A generalized version of this method called polynomial long division is also used for dividing polynomials (sometimes using a shorthand version called synthetic division). In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of lower degree, a generalized version of the familiar arithmetic technique called long division. ...
In mathematics, a polynomial is an expression in which constants and variables are combined using only addition, subtraction, multiplication, and positive whole number exponents (raising to a power). ...
In mathematics, Ruffinis rule allows the rapid division of any polynomial by a binomial of the form x − r. ...
Standards based mathematics reform Many mathematics text series were created in response to the recommendations of the NCTM. Some of these, such as TERC omit any instruction in long division. In fact the fifth grade teachers manual states that mathematicans no longer use the notation of long division, students should be discouraged from using the method if they were taught outside the classroom. It also states that the letter "R" should not be used to signify a remainder. Parents who are unfamiliar with such methods of teaching division have protested the adoption of such text on websites such as Mathematically Correct. The National Council of Teachers of Mathematics (NCTM) was founded in 1920. ...
Investigations in Number, Data, and Space is a complete K-5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts. ...
Mathematically Correct is a website created by educators, parents, citizens and mathematicians / scientists who are concerned about the direction of standards-based mathematics and education reform. ...
See also Elementary arithmetic is the most basic kind of mathematics: it concerns the operations of addition, subtraction, multiplication, and division. ...
On a computer, arbitrary-precision arithmetic, also called bignum arithmetic, is a technique that allows computer programs to perform calculations on integers or rational numbers (including floating-point numbers) with an arbitrary number of digits of precision, typically limited only by the available memory of the host system. ...
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of lower degree, a generalized version of the familiar arithmetic technique called long division. ...
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