Long division

Long division

:"For the album by Rustic Overtones, see "Long Division.

In arithmetic, long division is the standard procedure suitable for dividing simple or complex multidigit numbers. 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. [MathWorld | urlname=LongDivision | title= Long Division]

Education

Today, inexpensive calculators and computers have become the most common way to solve division problems. (Internally, those devices use one of a variety of division algorithms). 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. Some curricula such as Everyday Mathematics teach non-standard methods unfamiliar to most adults, or in the case of TERC argue that long division notation is itself no longer in mathematics. However many in the mathematics community have argued that standard arithmetic methods such as long division should be continued to be taught [" [http://www.csun.edu/~vcmth00m/longdivision.pdf The Role of Long Division in the K-12 Curriculum] " by David Klein, R. James Milgram.] .

An abbreviated form of long division is called short division.

Notation

Long division does not use the slash (/) or obelus (÷) signs, instead displaying the dividend, divisor, and (once it is found) quotient in a tableau. An example is shown below, representing the division of 500 by 4 (with a result of 125). 125 (Explanations) 4)500 4 (4 × 1 = 4) 10 (5 - 4 = 1) 8 (4 × 2 = 8) 20 (10 - 8 = 2) 20 (4 × 5 = 20) 0 (20 - 20 = 0)

another example where there is a remainder: 31.75 4)127 12 (12-12=0 which is written on the following line) 07 (the seven is brought down from the dividend 127) 4 3.0 (3 is the remainder which is divided by 4 to give 0.75)

#First of all look at the first digit of the dividend (127) to see if any 4's (the divisor) can be subtracted from it (in our case there aren't any because we have 1 as the first digit and we aren't allowed to use negative numbers so we can't write -3)
#If the number in the first digit isn't big enough we take the second one along with it (so in our case we will deal with 12 as our first number)
#See the maximum number of 4s that can subtracted from it (in our case that will be 3 fours which is 12)
#Write in the quotient part (above the second digit since that is the last one you used) that 3 you concluded and write under the dividend the 12
#Subtract the 12 you wrote from the one above it (the result will be of course zero)
#Repeat the first step again
#Since the zero won't work bring down the next digit in the dividend (which is 7) next to the zero and you get 07
#Repeat step 3,4 and 5
#You will have in the quotient 31 and 3 as a remainder and no more digits in the dividend
#You can bring down a zero beside the 3 after you put the point and continue the division
#The result will be 31.75

Generalisations

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.

Polynomials

A generalised version of this method called polynomial long division is also used for dividing polynomials (sometimes using a shorthand version called synthetic division).

ee also

*Short division
*Elementary arithmetic
*Arbitrary-precision arithmetic
*Polynomial long division

References

External links

*Alternative Division Algorithms: [http://www.doubledivision.org Double Division] , [http://www.math.nyu.edu/~braams/links/em-arith.html Partial Quotients & Column Division] , [http://mb.msdpt.k12.in.us/Math/PartialQuotients.wmv Partial Quotients Movie]

*Step By Step Polynomial Long Division: [http://www.webgraphing.com/polydivision.jsp WebGraphing.com]


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Look at other dictionaries:

  • Long division — Long Long, a. [Compar. {Longer}; superl. {Longest}.] [AS. long, lang; akin to OS, OFries., D., & G. lang, Icel. langr, Sw. l[*a]ng, Dan. lang, Goth. laggs, L. longus. [root]125. Cf. {Length}, {Ling} a fish, {Linger}, {Lunge}, {Purloin}.] 1. Drawn …   The Collaborative International Dictionary of English

  • Long division — Division Di*vi sion, n. [F. division, L. divisio, from dividere. See {Divide}.] 1. The act or process of diving anything into parts, or the state of being so divided; separation. [1913 Webster] I was overlooked in the division of the spoil.… …   The Collaborative International Dictionary of English

  • long division — ► NOUN ▪ division of numbers with details of intermediate calculations written down …   English terms dictionary

  • long division — n. the process of dividing a number by another number containing, ordinarily, two or more figures, and of putting the steps down in full …   English World dictionary

  • Long Division — Infobox Album | Name = Long Division Type = Album Artist = Rustic Overtones Released = 1995 Recorded = Big Sound Studios, Westbrook, Maine Genre = Rock and Roll Length = 67:11 Label = Ripcord Records rr 101 Producer = Colin Decker Reviews = Last… …   Wikipedia

  • long division — noun the operation of division in which the sequence of steps are indicated in detail • Hypernyms: ↑division * * * noun [noncount] mathematics : a way of dividing one number by another number that involves several steps which are written out… …   Useful english dictionary

  • long division — n. to do long division * * * [ˌlɒŋdɪ vɪʒ(ə)n] to do long division …   Combinatory dictionary

  • long division — long′ divi′sion n. math. division, usu. by a number of two or more digits, in which each step of the process is written down • Etymology: 1820–30 …   From formal English to slang

  • long division — long di vision n [U] a method of dividing one large number by another …   Dictionary of contemporary English

  • long division — long di vision noun uncount in mathematics, a calculation in which you divide one large number by another …   Usage of the words and phrases in modern English

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