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Topic: Unit fraction

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Proper fraction

Partial fraction

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	Unit fraction - Wikipedia, the free encyclopedia
		A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.
		A unit fraction is therefore the reciprocal of a positive integer, 1/n.
		Using fractions 2/3 or 3/4 is adequate in terms of pure mathematics but breaks down in human terms as for example in distributing rations of grain and beer where the number of people is not really a variable.
	en.wikipedia.org /wiki/Unit_fraction (277 words)

	Fraction article - Fraction unit mathematics vulgar fraction rational number integer divided - What-Means.com (Site not responding. Last check: 2007-11-06)
		A vulgar fraction is a rational number written as one integer (the numerator) divided by a non-zero integer (the denominator).
		Irreducible fraction: a vulgar fraction "in lowest terms", where the numerator is an integer, the denominator is a positive integer, and the highest common factor of the numerator and the denominator is 1.
		Unit fraction: A vulgar fraction with a numerator of 1.
	www.what-means.com /encyclopedia/Fractions (334 words)

	PlanetMath: unit fraction
		Such fractions are known from Egyptian mathematics where we can find a lot of special representations of the numbers as a sum of an unit fractions, which are now called Egyptian fractions.
		Many unit fractions are in the pairs of the adjacent fractions.
		This is version 7 of unit fraction, born on 2002-06-21, modified 2002-06-24.
	planetmath.org /encyclopedia/UnitFraction.html (180 words)

	Internal Revenue Bulletin - August 30, 2004 - Rev. Rul. 2004-82
		Section 42(c)(1)(D) defines the floor space fraction as the fraction the numerator of which is the total floor space of the low-income units in the building and the denominator of which is the total floor space of the residential rental units, whether or not occupied, in the building.
		The unit occupied by a full-time security officer is similar to the units described in the examples contained in § 1.103-8(b)(4)(iii), and is reasonably required by the project because of the level of crime in the area.
		The unit is treated as a low-income unit eligible for inclusion in the numerator and denominator of the monthly applicable fraction calculated under § 42(f)(2)(A)(i) if the tenant, who meets the income limitation under § 42(g)(1), resides in the rent-restricted unit on the last day of the month.
	www.irs.gov /irb/2004-35_IRB/ar09.html (5620 words)

	Fraction Type as a Factor Contributing to Prospective Teachers' Abilities to Solve Part-Whole Division Problems
		The factors investigated were fraction type, that is, how prospective teachers' success was related to the type of fraction (unit fraction or common fraction) presented in part-whole division problems and whether or not a visual image of the data presented in the problem contributes to successful solution strategies.
		Subjects who used the fraction presented in the problem in an equation or divided the whole number part by the fraction were classified as using an operator strategy.
		Subjects were classified as using a concept of unit strategy when the number that corresponds to the unit fractional amount was used to find the whole.
	www.west.asu.edu /cmw/pme/resrepweb/PME-rr-stone.htm (1690 words)

	[No title]
		Elaborate on the equivalent fraction activities already discussed and the idea that equivalent fractions stem from multiplying or dividing the numerator and denominator of a fraction by the same value is established.
		Subtracting fractions using Cuisenaire rods As with the egg cartons, the assumption is that the students are appropriately familiar with using the Cuisenaire rods.
		Subtracting fractions using the number line As with other operations involving fractions, the number line could be used, although it may not be as easy to comprehend for some students.
	pegasus.cc.ucf.edu /~mathed/text4.txt (9913 words)

	Teaching Models: Grade 4
		Fractions are numbers that are needed to solve certain kinds of division problems.
		A unit fraction is a fraction with a numerator of 1 (for example,
		A fraction is in simplest form if the numerators and denominators are as small as possible.
	www.eduplace.com /math/mw/models/overview/4_19_4.html (512 words)

	Minimizing the Denominators of Unit Fraction Expansions
		For any proper fraction n/d let f(n,d) denote the least integer k such that n/d can be expressed as a sum of distinct unit fractions with denominators less than or equal to kd.
		Of course, this assumes the remainder u/v can be expanded into a sum of unit fractions with max denominator less than p*xj, which is ordinarily the case, because v can only be a product of divisors of the x's, each of which is smaller than roughly log(p).
		From the standpoint of determining the upper bound on max denominators this is not a serious limitation because the greatest values of (max denom in expansion)/(denom) are known to occur for prime denominators.
	www.mathpages.com /home/kmath348.htm (976 words)

	Teaching Models: Grade 2
		A fraction can be used to represent a part of a whole or part of a group or collection of things.
		One of these smaller pieces is the amount represented by the unit fraction.
		At this grade level, the comparing and ordering of fractions is limited to unit fractions, and pictures are provided to aid a child in deciding which of two fractions is the greater or lesser.
	www.eduplace.com /math/mw/models/overview/2_9_4.html (244 words)

	page1
		For each of these fractions, there is a representation by sums of unit fractions (fractions with 1 in the numerator, of the form 1/n).
		Since they only used unit fractions, and their methods for division and multiplication required them to double their numbers and fractions (as we will see in the next section) they needed to know the doubles of unit fractions.
		From their table in the papyrus, we know exactly which unit fraction composition they ended up chosing, but we don't know for sure how they chose it, that is the mystery.
	www.math.sfu.ca /histmath/Egypt/Ahmes/intro2.html (478 words)

	Problem C: Unit Fraction Partition (Site not responding. Last check: 2007-11-06)
		A fraction whose numerator is 1 and whose denominator is a positive integer is called a unit fraction.
		A representation of a positive rational number p/q as the sum of finitely many unit fractions is called a partition of p/q into unit fractions.
		The output integer corresponding to a data set p, q, a, n should be the number of all partitions of p/q into at most n many unit fractions such that the product of the denominators of the unit fractions is less than or equal to a.
	www.ehime-u.ac.jp /ICPC/problems/domestic/d2004/C.en/C.html (337 words)

	[No title]
		It was then a simple matter of uniting the four unit fraction pieces to establish the share as 4/45 of the whole.
		Arthur writes: Took a unit bar, divided it by 3, took a third of that, divided it by 4, took a fourth of that divided it by 3, took a third of that divided it by 4, took a fourth divided by 3.
		Coupled with the notion of a fraction as a measurement unit these were strong indications that their fraction schemes were undergoing modifications that would result in a scheme for the rational numbers of arithmetic.
	jwilson.coe.uga.edu /olive/ICME8TG19/ICME8TG19.html (7640 words)

	TASKS TO ASSESS CHILDREN'S PERCEPTION OF THE SIZE OF A FRACTION
		These fractions were to be understood as representing concentrations of mixtures consisting of fl ink and water in a way previously explained to the subject (e.g., 2/4 means "2 of 4 parts is fl ink" which results in a mixture that is "two-fourths dark").
		The task was to order the fraction cards from lightest to darkest and put each at a corresponding gray level in the scale; permitted was placement between two gray levels to allow for finer discrimination.
		Explanations for responses in this category indicate that the given fractional part was first decomposed into unit fractions (of the form 1/n), and then other fractions, and the unit-whole, were composed by an iteration of the unit fraction.
	education.umn.edu /rationalnumberproject/84_1.html (2554 words)

	[No title]
		The fact that the sum of the fractions is the original input number is a straightforward but tedious exercise in algebraic manipulation.
		The number of terms in the Egyptian fraction representation of x/y is the sum of the odd terms after the first in the continued fraction list, which is at most x.
		Within a progression, we determine which groups of terms can be combined to form a unit fraction, and represent each group as an edge in a graph, labelled with the corresponding unit fraction.
	www.ics.uci.edu /~eppstein/numth/egypt/cfrac.html (2028 words)

	Egyptian Fractions
		minimizing denominators in unit fraction expansions, minimizing the max denominator in a t-term expansion of 1, odd greedy stubbornness, irrationality of quadratic sums, and wagon trains and sticky wickets
		Terrance Nevin uses greedy Egyptian fraction methods as a basis for investigating the dimensions of the Egyptian pyramids.
		Unit Fractions from Eric Weisstein's treasure trove of Mathematics.
	www.ics.uci.edu /~eppstein/numth/egypt (1135 words)

	Math Forum - Ask Dr. Math
		Date: 07/16/2001 at 13:39:59 From: Doctor Greenie Subject: Re: Unit Fractions Hi, Pamela - Your teacher does not need a vacation; there is an infinite number of answers, but the arithmetic required to find most of them is unmanageable except for a computer.
		If we can write the second "1/32" as the sum of two unit fractions, then we will be done with the problem.
		Whenever we have a unit fraction 1/x where the denominator is an even number, the fraction 1/x can be written as the sum of two different unit fractions, one of which is twice the other.
	mathforum.org /library/drmath/view/56821.html (582 words)

	Egyptian Fractions
		A fraction written as a sum of distinct unit fractions is called an Egyptian Fraction.
		An Egyptian Fraction for t/b is a sum of unit fractions, all different, whose sum is t/b.
		However, the egyptian fraction produced by the greedy method may not be the shortest such fraction.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fractions/egyptian.html (3406 words)

	Unit Fraction Partitions
		Letting G(k,j) denote the number of 3-part unit fraction partitions of 1/k whose denominators have a gcd of j, we have G(kn,jn) = G(k,j) It follows that, for example, the sum of G(24,2j) for j=1,2,...
		It follows that 8/11 cannot be expressed as a sum of three unit fractions.
		Another approach is based on the fact that for any positive integer k there exists a least integer D(k) such that the partitions of 1/k into three unit fractions correspond to the partitions of D(k)/k into three divisors of D(k).
	www.mathpages.com /home/kmath332.htm (981 words)

	egfrac.html
		One thing that would be nice to do is take an egyptian fraction and print out an equation whose left hand side is the usual form of the fraction and whose right hand side is the fraction written as a sum of unit fractions.
		Continue this until the remainder is a unit fraction.
		as a sum of distinct unit fractions which are all distinct from the consecutive ones already used.
	www.ms.uky.edu /~carl/ma330/html/egfrac1.html (1091 words)

	Unit fractions -- A complete course in arithmetic
		Each unit fraction is a part of 1.
		The denominator of a fraction names the unit -- the part.
		We see that every fraction is a multiple of some unit fraction:
	www.themathpage.com /ARITH/unit-fractions.htm (240 words)

	PYR 2nd
		When I made the first "set" of four unit fractions an important assumption was that the four base lengths are proportional to the four unit fractions.
		The best set of unit fractions from graph 1 can thus be thought of as actual base lengths on a pyramid model.
		This means that each of the denominators of the fourth term in the unit fractions of the "best set" can be substituted in turn for X in equation 4 to find the normal fractions that equals it.
	www.aloha.net /~hawmtn/pyr-2nd.htm (1087 words)

	Unit fraction -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		Unit fraction -- Facts, Info, and Encyclopedia article
		A unit fraction is therefore the (Something (a term or expression or concept) that has a reciprocal relation to something else) reciprocal of a positive integer, 1/n.
		The result is an (additional info and facts about Egyptian fraction) Egyptian fraction, but the expression is not unique.
	www.absoluteastronomy.com /encyclopedia/u/un/unit_fraction.htm (132 words)

	History of Mathematics: Recto table (Site not responding. Last check: 2007-11-06)
		The Egyptian concept of fraction requires that any fraction be represented as a sum of unit fractions without any repetitions, except 2/3 which was allowed.
		The problem is to divide 2 by 5; the answer would be any sum of unit fractions without repetition.
		In one column appears the denominator of the unit fraction to be doubled, and in the next column appear the denominators of the unit fractions for that double.
	aleph0.clarku.edu /~djoyce/ma105/2byn.html (268 words)

	Lesson Exchange: Fractions unit introduction (Elementary, Mathematics)
		Strategy: pass out the plasticene and tell the students to flatten it out into a pancake 1/2 a cm thick and big enough to cut 2-3 shapes using the cookie cutter they have.
		Question them about the importance of equal parts within the whole: If the parts are not equal is the whole divided up into proper fractions, why or why not.
		Tasks: Have the students demonstrate fraction sentences by writing the sentence on a piece of paper and have the plasticene shapes that demonstrate each fraction below on the paper.
	www.teachers.net /lessons/posts/412.html (273 words)

	Unit fractions. The evolution of the real numbers
		A UNIT FRACTION is a fraction whose numerator is 1.
		We see: Each fraction is a multiple of a unit fraction.
		For more on the arithemtic of unit fractions, click here.
	www.themathpage.com /aReal/unit-fraction.htm (113 words)

	Carolyn's Unit Planning
		The students will be learning that fractions can be found in all kinds of things such as in cooking, shapes, etc. They will also learn that they can find or create fractions in the world around them.
		Fractional concepts is a topic that you will generally be teaching throughout the year.
		This unit is basically an introduction to fractionthat you can build on as you progress to deeper levels of math concepts such as problem solving and pre-algebraic skills.
	paws.wcu.edu /cc22459/unitplan.html (2751 words)

	responses
		7/8 cannot be written as the sum of 2 distinct unit fractions because if you subtract the greatest unit fraction (1/2), you end up with 3/8.
		You end up with 1/8 but this is a sum of three unit fractions not two.
		Every fraction can be written as a sum of unit fractions.
	www.ms.uky.edu /~carl/ma330/responses.html (932 words)

	Unit fraction - Encyclopedia, History, Geography and Biography
		Unit fraction - Encyclopedia, History, Geography and Biography
		This page was last modified 02:58, 27 Apr 2005.
		This encyclopedia, history, geography and biography article about Unit fraction contains research on
	www.arikah.net /encyclopedia/Unit_fraction (148 words)

	Swett, Research, Erdos-Strauss Conj
		A unit fraction (sometimes called an Egyptian fraction) is a fraction of the form 1/k for k a positive integer.
		Then n/d is the sum of two unit fractions if and only if there are positive integer divisors A and B of d such that A+B is divisible by n.
		Since Mathematica's Divisors[] function provides the set of positive integer divisors of a given positive integer, it is a relatively straightforward matter to design a Mathematica function which determines whether a given rational is the sum of two unit fractions.
	math.uindy.edu /swett/esc.htm (916 words)

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