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In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps.
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.
In the division of 43 by 5, we have: 43 = 8 × 5 + 3, so 3 is the least positive remainder. We also have that: 43 = 9 × 5 − 2, and −2 is the least absolute remainder. These definitions are also valid if d is negative, for example, in the division of 43 by −5, 43 = (−8) × (−5) + 3, and 3 is the least positive remainder, while,
Modern calculators and computers compute division either by methods similar to long division, or by faster methods; see Division algorithm. In modular arithmetic (modulo a prime number) and for real numbers, nonzero numbers have a multiplicative inverse. In these cases, a division by x may be computed as the product by the multiplicative ...
Setting up for Division Division in the Trachtenberg System is done much the same as in multiplication but with subtraction instead of addition. Splitting the dividend into smaller Partial Dividends, then dividing this Partial Dividend by only the left-most digit of the divisor will provide the answer one digit at a time.
In elementary arithmetic, a standard algorithm or method is a specific method of computation which is conventionally taught for solving particular mathematical problems. . These methods vary somewhat by nation and time, but generally include exchanging, regrouping, long division, and long multiplication using a standard notation, and standard formulas for average, area, and vol
Polynomial long division can be used to find the equation of the line that is tangent to the graph of the function defined by the polynomial P(x) at a particular point x = r. [3] If R ( x ) is the remainder of the division of P ( x ) by ( x – r ) 2 , then the equation of the tangent line at x = r to the graph of the function y = P ( x ) is y ...
Presently, most division algorithms, including long division, are based on this notation or its variants, such as binary numerals. A notable exception is Newton–Raphson division, which is independent from any numeral system. The term "Euclidean division" was introduced during the 20th century as a shorthand for "division of Euclidean rings".