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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.
Division is often shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a fraction bar, between them. For example, "a divided by b" can be written as: which can also be read out loud as "divide a by b" or "a over b".
Divided differences is a recursive division process. Given a sequence of data points (,), …, (,), the method calculates the coefficients of the interpolation polynomial of these points in the Newton form.
The combination of these two symbols is sometimes known as a long division symbol or division bracket. [8] It developed in the 18th century from an earlier single-line notation separating the dividend from the quotient by a left parenthesis. [9] [10] The process is begun by dividing the left-most digit of the dividend by the divisor.
Blomqvist's method [1] is an abbreviated version of the long division above. This pen-and-paper method uses the same algorithm as polynomial long division, but mental calculation is used to determine remainders. This requires less writing, and can therefore be a faster method once mastered.
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...
In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is mostly taught for division by linear monic polynomials (known as Ruffini's rule ), but the method can be generalized to division by any polynomial .
In arithmetic, the galley method, also known as the batello or the scratch method, was the most widely used method of division in use prior to 1600. The names galea and batello refer to a boat which the outline of the work was thought to resemble. An earlier version of this method was used as early as 825 by Al-Khwarizmi.