Long division

In arithmetic, long division is a standard division algorithm suitable for dividing multidigit numbers that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. It enables computations involving arbitrarily large numbers to be performed by following a series of simple steps. The abbreviated form of long division is called short division, which is almost always used instead of long division when the divisor has only one digit. Chunking (also known as the partial quotients method or the hangman method) is a less-efficient form of long division which may be easier to understand.

While related algorithms have existed since the 12th century AD, the specific algorithm in modern use was introduced by Henry Briggs c. 1600 AD.

Inexpensive calculators and computers have become the most common way to solve division problems, eliminating a traditional mathematical exercise, and decreasing the educational opportunity to show how to do so by paper and pencil techniques. (Internally, those devices use one of a variety of division algorithms). In the United States, long division has been especially targeted for de-emphasis, or even elimination from the school curriculum, by reform mathematics, though traditionally introduced in the 4th or 5th grades.

In English-speaking countries, long division does not use the division slash ⟨∕⟩ or obelus ⟨÷⟩ signs but instead constructs a tableau or table. The divisor is separated from the dividend by a right parenthesis ⟨)⟩ or vertical bar ⟨|⟩; the dividend is separated from the quotient by a vinculum (i.e., overbar). The combination of these two symbols is sometimes known as a long division symbol or division bracket. It developed in the 18th century from an earlier single-line notation separating the dividend from the quotient by a left parenthesis.

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