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Topic: Long division

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	Why Long Division? Speech by Professor of Mathematics 1999
		At this point the skills that have come from long division through handling polynomials become essential to things like partial fraction decomposition which is important in calculus but finds its main applications in the study of systems of linear differential equations, particularly in using Laplace transforms, which is the critical construction in control theory.
		Long division is the only process in the K - 12 mathematics curriculum in which approximation is really essential.
		But notice that long division is also a continuous process of approximation, the answer keeps getting more and more accurate and when the students learn how to do long division with decimals they learn to carry the process to many decimal places.
	www.shearonforschools.com /why_long_division.htm (4057 words)

	[No title]
		This relates to division with a remainder within the limits of the multiplication table, that is, where the result is smaller than 10, and long division is not really necessary, as yet.
		Long division consists of stages: each stage includes a division operation within the limits of the multiplication table (that is — resulting in a number smaller than 10) and the calculation of the remainder — what has not yet been divided.
		Therefore, when teaching long division, it is important to dwell on dividing by 2 for a prolonged period of time.
	www.math.technion.ac.il /~ra/englongdivision.doc (3665 words)

	math lessons - Polynomial long 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.
		This method is entirely reminiscent of the long division learned in elementary arithmetic classes -- in fact, that technique is simply a special case of polynomial long division, where x=10.
		Therefore, the remainder of the division is 20.
	www.mathdaily.com /lessons/Polynomial_long_division (3685 words)

	Long Division Algorithm
		As I write this, in 2003 A.D., students in the third or fourth grades in school are still being taught long division, although in the higher grades most students obtain quotients using calculators.
		In the long division procedure, the dividend must equal the sum of the remainder and all the numbers that have been subtracted.
		That is, the q we have found in the long division is indeed the one and only value possible, namely the quotient of a when divided by d.
	www.mathpath.org /Algor/algor.long.div.htm (481 words)

	Long Division -- from Wolfram MathWorld
		Long division is an algorithm for dividing two numbers, obtaining the quotient one digit at a time.
		The term "long division" is also used to refer to the method of dividing one polynomial by another, as illustrated above.
		Long Division (1995) is also the name of the second album by the band Low.
	mathworld.wolfram.com /LongDivision.html (181 words)

	Long division - Wikipedia, the free encyclopedia
		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.
		Long division of integers can easily be extended to include non-integer dividends, as long as they are rational.
		A generalized version of this method called polynomial long division is also used for dividing polynomials (sometimes using a shorthand version called synthetic division).
	en.wikipedia.org /wiki/Long_division (558 words)

	Great River National Wildlife Refuge: Long Island Division
		Long Island Division was established in 1958 as one of the original Mark Twain NWR units.
		This 6,300 acre division is comprised of a complex of islands and floodplain.
		The Long Island Division is open to the public year round with many hunting and fishing opportunities.
	www.fws.gov /midwest/GreatRiver/long_island.html (301 words)

	Teaching Long Division and Double Division
		Double Division eliminates long division trial and error guessing - which is frustrating for many students.
		It could be argued that if students seldom use long division after leaving school then it might be better for them to have a simpler and more intuitive method at their disposal - one that is easier to remember and understand.
		In long division you write the answer on the top and have to get each digit of the answer exactly right - because there is only room there to write one number.
	www.doubledivision.org (771 words)

	Division
		Division 'undoes' multiplication and involves a number called the dividend being 'divided' by another number called the divisor.
		Now, we will consider division in which the dividend is greater than 100 and the divisor is still less than or equal to 10.
		As division is the inverse of multiplication, start by dividing 4 into the column furthest to the left.
	www.mathsteacher.com.au /year7/ch01_whole/05_div/div.htm (221 words)

	SparkNotes: Polynomial Functions: Long Division of Polynomials
		Long division of polynomials is a lot like long division of real numbers.
		To divide polynomials using long division, first divide the first term of the dividend by the first term of the divisor.
		It is both a way to calculate the value of a function at c (Remainder Theorem) as well as to check whether or not c is a root of the polynomial (Factor Theorem).
	www.sparknotes.com /math/precalc/polynomialfunctions/section4.rhtml (556 words)

	Long Division of Polynomials
		One method is long division, a process similar to long division of two whole numbers.
		Setup the long division as you would do with whole numbers, with the first polynomial (called the dividend) under the long division line, and the polynomial we are dividing by (called the divisor) on the left:
		Now, we repeat the process of long division, taking the highest degree of our new polynomial (which is 2x) and dividing it by the highest degree term of the divisor (again, x); the result is 2.
	www.math.unt.edu /mathlab/longdiv.html (486 words)

	MathSteps: Grade 4: Division: What Is It?
		Since division and multiplication are inverse operations, students can use models similar to the models used in multiplication, to divide.
		It would be prudent to begin with 2-digit dividends by 1-digit divisor to introduce the long division algorithm.
		When beginning the long division algorithm, realize that you are asking questions such as "what number times 6 is less than or equal to 300?" Remember that the 3 is in the hundreds place.
	www.eduplace.com /math/mathsteps/4/d/index.html (485 words)

	Long division (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-10)
		In arithmetic, long division is an algorithm for division of two real numbers.
		It requires only the means to write the numbers down, and is simple to perform even for large dividends because the algorithm separates a complex division problem into smaller problems.
		A more generalized version of this method is used for dividing polynomials (sometimes using a shorthand version called synthetic division).
	long-division.iqnaut.net.cob-web.org:8888 (344 words)

	Long Division With Remainders
		When we are given a long division to do it will not always work out to a whole number.
		If you feel happy with the process on the long division page you can skip the first bit.
		With a long division with remainders the answer is expressed as 17 remainder 10 as shown in the diagram
	www.mathsisfun.com /long_division2.html (232 words)

	Long division and why it works - Free lesson plan from HomeschoolMath.net
		Also, in the conventional long division, you only place one digit into the quotient in each step, not with all the zeros.
		But since the ones digit (9) won't be important in the next step (which deals with the tens digit), in the traditional way, you only subtract 7-6 and then you 'drop' down the tens digit 8 from the dividend.
		These examples show how long division is done, with all of the dropping down of digits and such.
	www.homeschoolmath.net /teaching/md/long_division_why.php (881 words)

	Long Division
		Try the example, then enter your own examples to study the long division pattern.
		Be sure that your divisor, or the number "outside" of the division bar, is an integer (that is, a number with no decimal point).
		The rest of the rules are the same as long division using whole numbers:
	argyll.epsb.ca /jreed/extras/longdiv (240 words)

	Polynomial Long Division
		The method is called "long division", and works just like the long division you did back in elementary school, except that now you're dividing with variables.
		Think back to when you were doing long division with plain old numbers.
		When you do regular division with numbers and the division comes out even, it means that the number you divided by is a factor of the number you're dividing (for instance, if you divide
	www.purplemath.com /modules/polydiv2.htm (243 words)

	PlanetMath: long division
		In this entry we treat two cases of long division.
		as in the theorem is called the remainder of the division of
		This is version 4 of long division, born on 2005-03-22, modified 2006-02-21.
	planetmath.org /encyclopedia/Dividend.html (124 words)

	Member Info - Long Island Division (Site not responding. Last check: 2007-10-10)
		You may join the USFA at one of the Long Island Division qualifiers (fencers under18 must have a parent or guardian signature to join).
		The Division organizes and schedules the qualifiers for the Junior Olympics and the Summer Nationals.
		A major point of a petition is that the fencer should be able to demonstrate by documenting an established record in the event for which he / or she is petitioning for entry.
	www.liusfa.org /meminfo.shtml (1269 words)

	1.3 Long Division Algorithm (Site not responding. Last check: 2007-10-10)
		The first point to note is that the school method for long division involves a ``guess''.
		There are two procedures for long division, each with its own level of complexity.
		This completes the long division which takes about 3rq steps upto terms linear in p and q (such as additions and subtractions).
	www.imsc.res.in /~kapil/crypto/notes/node4.html (493 words)

	Math 4 - Act. 04: Long Division (Site not responding. Last check: 2007-10-10)
		The goal of this lesson is to further develop the sharing concept of division by using objects.
		One type of division strategy is known as sharing or partitioning.
		The first player rolls a number cube, divides the current number of counters by that number, and states the division problem (e.g., if I take 20 counters and divide them equally into 3 rows, there will be 6 in each row with 2 left over).
	www.uen.org /Lessonplan/preview.cgi?LPid=6096 (714 words)

	Division
		Place the divisor before the division bracket and place the dividend (4138) under it.
		Divide 73 by 17 and place that answer above the division bracket and to the right of the two.
		Divide 58 by 17 and place that answer (3) above the division bracket and to the right of the four.
	www.aaamath.com /B/div55_x2.htm (278 words)

	PlanetMath: polynomial long division
		polynomial (long) division is a method for calculating
		The method looks very similar to integer division since a polynomial
		This is version 2 of polynomial long division, born on 2004-04-25, modified 2006-01-08.
	planetmath.org /encyclopedia/PolynomialLongDivision.html (121 words)

	City of Long Beach, CA - Records Division
		Jonathan Stafford is the Administrator of the Records Division.
		Stafford began his career with the Long Beach Police Department as a Communications Dispatcher I. He was a Dispatcher, Trainer and Assistant Supervisor in the Communications Division for a total of seven years before transferring to the Port of Long Beach as an Assistant Administrative Analyst in February 2003.
		Administrator Stafford serves on the Board of Directors of the Long Beach Police Athletic League and he is the Chief’s liaison to the Long Beach Police Department Chaplain’s Advisory Group.
	www.ci.long-beach.ca.us /police/about/administration_bureau_manager/records_division.asp (290 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-10)
		First of all, division is the opposite of multiplication.
		The process of long division goes sort of like this: 1.
		It's pretty hard to explain long division over e-mail though, so write us back with questions if you have them.
	mathforum.org /library/drmath/view/58816.html (460 words)

	Division as repeated subtraction and introduction to long division - Homeschool Math
		Division as repeated subtraction and introduction to long division - Homeschool Math
		Division as repeated subtraction - introduction to long division
		Note: some of these divisions are even, some have remainder.
	www.homeschoolmath.net /teaching/md/long_division.php (573 words)

	Math Forum - Ask Dr. Math Archives: Elementary Division
		We were trying to find a division fraction question and everything we came up with turned into a multiplication fraction problem.
		For example, "if the sum of the digits of a number is divisible by three, the number is divisible by three." I remember the rules for all the numbers except "7".
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /dr.math/tocs/division.elem.html (588 words)

	Long Beach State Athletics
		LONG BEACH, CA – 22nd year Head Coach Brian Gimmillaro needs just two more victories to secure 600 for his career at Long Beach State.
		LONG BEACH, CA – Led by another quality performance from Alexis Crimes, and a solid contribution from Mischa Hasalikova, the Long Beach State women’s volleyball team toppled CS Fullerton, 3-0, in the Walter Pyramid on Saturday night.
		LONG BEACH, CA -- Long Beach State cruised to a 3-0 match sweep of UC Riverside at the Walter Pyramid on Friday night.
	www.longbeachstate.com /vol/wvol (208 words)

	Long division - The Boston Globe
		A misunderstanding over lemons turns into a tiff, which escalates into a fight, and suddenly long-nursed grievances are being aired.
		She does all the planning and never gets any thanks for it; he can't unwind after a long day without being nagged about picking up.
		He doesn't want to go to the ballet; she doesn't want a pool table in the living room.
	www.boston.com /news/globe/living/articles/2006/06/02/long_division (775 words)

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