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Topic: Proper fraction

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Unit fraction

Partial fraction

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	fraction (mathematics)
		A proper fraction is one in which the numerator is less than the denominator.
		Fractions are also known as rational numbers;; that is, numbers formed by a ratio.
		To add or subtract with fractions a common denominator (a number divisible by both the bottom numbers) needs to be identified.
	www.tiscali.co.uk /reference/encyclopaedia/hutchinson/m0006681.html (432 words)

	Fraction
		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.brainyencyclopedia.com /encyclopedia/f/fr/fraction.html (305 words)

	Marlene's How To Work With Fractions - Basics Page
		Fractions are used to express portions smaller than a whole and to divide multiple objects into groups.
		A Proper Fraction is a fraction where the denominator is greater than the numerator.
		An Improper Fraction is a fraction where the numerator is greater than or equal to the denominator.
	www.marlenesite.com /aspmar/convertfraction/basics.htm (426 words)

	Fractions - Definitions - In Depth (Site not responding. Last check: 2007-10-21)
		One way to think of a fraction is as a division that hasn't been done yet.
		Fractions were invented long before decimal numbers, as a way of showing portions less than 1, and they're still hanging around.
		An improper fraction occurs when the numerator is greater than or equal to the denominator.
	www.mr.math.com /school/subject1/lessons/S1U4L1DP.html (422 words)

	What is a Fraction
		Normally the numerator (top of fraction) is smaller than the denominator (bottom of fraction) in which case the fraction is called a 'Proper Fraction'.
		A proper fraction is always less than the whole number 1 and we can relate proper fractions to a part of a whole object.
		Two fractions are equivalent if you can find a whole number which when divided into both the numerator (top) and denominator (bottom) of one fraction gives the other fraction OR if there is a third fraction that can be found that is equivalent to both.
	www.bacsoftware.co.uk /fcalc1/wi (597 words)

	Teaching Models: Grade 3
		Improper fractions can also be written as the sum of a whole number and a proper fraction.
		Proper fractions can be modeled in terms of a "part of a whole." Here the "whole" may be a group consisting of n objects where "part" of the group consists of k objects and k < n.
		A unit fraction is defined as a fraction with a numerator of 1 (for example,
	www.eduplace.com /math/mw/models/overview/3_18_1.html (368 words)

	BMCC Math Tutorials -- Fractions -- Improper Fractions & Mixed Numbers (Site not responding. Last check: 2007-10-21)
		A fraction is a representation of some number of those portions compared to the original amount of the whole.
		A proper fraction is one in which the numerator is smaller than the denominator, so a proper fraction has a value less than 1.
		An improper fraction is one in which the numerator is greater than or equal to the denominator.
	www.bmcc.edu /nish/MathTutorials/Fractions/fr-imp.htm (1114 words)

	PROPER - Definition
		Pertaining to one of a species, but not common to the whole; not appellative; -- opposed to {common}; as, a proper name; Dublin is the proper name of a city.
		{Proper flower} or {corolla} (Bot.), one of the single florets, or corollets, in an aggregate or compound flower.
		{Proper fraction} (Arith.) a fraction in which the numerator is less than the denominator.
	www.hyperdictionary.com /dictionary/proper (320 words)

	PlanetMath: fraction
		A fraction is a rational number expressed in the form
		To get a fraction in lowest terms, simply divide the numerator and the denominator by their greatest common divisor:
		This is version 8 of fraction, born on 2002-04-06, modified 2004-12-12.
	planetmath.org /encyclopedia/Fraction.html (95 words)

	Business Math FAQ Ch 2 (Site not responding. Last check: 2007-10-21)
		To convert an improper fraction to a mixed number, divide the numerator of the improper fraction by the denominator.
		To convert a decimal to a fraction remove the decimal point, the remaining number is the numerator of the fraction, the denominator of the fraction is 1 followed by as many zeros as there were digits to the right of the decimal point in the original number.
		To convert a fraction to a decimal divides the numerator by the denominator.
	go.dbcc.edu /learningcenter/busmath2.html (604 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Proper Fractions and Improper Fractions A HYPERLINK "javascript:CharacterWindow('http://www.sparknotes.com/math/prealgebra/fractions/terms/term_B.9.html',%20'2f22a76d0e',%20500);" proper fraction is a fraction whose numerator is smaller than its denominator.
		This is the numerator of the improper fraction; the denominator of the new fraction is the same as the original denominator.
		To multiply two (proper or improper) fractions, multiply their numerators together and then multiply their denominators together--these two numbers will be the numerator and the denominator of the new fraction.
	www.ma.utexas.edu /~lefcourt/temp/Fractions.doc (3075 words)

	Fraction biography .ms (Site not responding. Last check: 2007-10-21)
		In common usage a fraction is any part of a unit.
		A Mixed fraction: A mixed fraction is an integer plus a proper fraction.
		Partial fractions can be used to decompose a rational function.
	fraction.biography.ms (254 words)

	Partial Fraction Decomposition
		A rational expression is a fraction whose numerator and denominator are both polynomials.
		An improper rational expression is the sum of a polynomial and a proper rational expression.
		Partial fraction decomposition is the process of rewriting a rational expression as the sum of a quotient polynomial plus partial fractions.
	jwbales.home.mindspring.com /precal/part7/part7.6.html (458 words)

	Math Lair - Egyptian Fractions (Site not responding. Last check: 2007-10-21)
		With the exception of ⅔ (two-thirds), for which the Egyptians had a special symbol (literally "one over one and a half"), they had symbols only for unit fractions (fractions that are the reciprocals of natural numbers.
		It is obvious that any proper fraction can be expressed as the sum of unit fractions if a repetition of terms is allowed.
		A famous algorithm for writing any proper fraction as the sum of a finite number of distinct Egyptian fractions was first published in 1202 by Fibonacci in his book
	www.stormloader.com /ajy/egyptfract.html (513 words)

	Fractions Calculator (Site not responding. Last check: 2007-10-21)
		When the word 'fraction' is used on its own then usually it is the common fraction that is meant.
		In a proper fraction the numerator is smaller than the denominator.
		A reduced fraction is a common fraction in its simplest possible form.
	www.projects.ex.ac.uk /trol/scol/calfract.htm (390 words)

	Introduction to fractions -- A complete course in arithmetic (Site not responding. Last check: 2007-10-21)
		A fraction is a number, and, as any number, we know it relative to 1.
		Fractions are also called rational numbers, because a fraction has the same ratio to 1 as a natural number has to a natural number; namely, the ratio of the numerator to the denominator.
		To summarize: Fractions that are less than 1 are called proper fractions, while fractions greater than or equal to 1 are improper.
	www.themathpage.com /ARITH/proper-fractions-mixed-numbers-improper-fractions.htm (1125 words)

	BMCC Math Tutorials -- Fractions -- Division of Fractions (Site not responding. Last check: 2007-10-21)
		That is, if you start with a fraction in which the denominator is larger than the numerator, after inversion the numerator will be larger than the denominator.
		The upshot of this is that if a proper fraction (value less than 1) is inverted, the resulting fraction will be an improper fraction (value greater than 1).
		Dividing one fraction by another is equivalent to multiplying the original dividend by the reciprocal of the original divisor.
	www.bmcc.org /nish/MathTutorials/Fractions/fr-div.htm (720 words)

	Mixed Numbers
		An improper fraction is a fraction that has a numerator larger than or equal to its denominator.
		A proper fraction is a fraction with the numerator smaller than the denominator.
		A mixed number consists of an integer followed by a proper fraction.
	www.aaamath.com /B/fra57cx3.htm (83 words)

	Homework 1 (Site not responding. Last check: 2007-10-21)
		Proper Fractions: when the numerator is smaller than the denominator, it is called a proper fraction.
		Improper Fractions: when the numerator is larger than the denominator, it is called an improper fraction.
		Mixed Fractions: The value of an improper fraction can also be written as a combination of an integer and a fraction.
	www.utdallas.edu /~rnuma/cs3345/hw1-programming.html (442 words)

	Online Dictionary for French English, Spanish English, Italian English, and more.
		A fraction with fractions in the numerator or denominator; SYN: compound fraction.
		A fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose numerator is an integer and whose denominator is an integer plus a fraction and so on.
		A proper fraction whose denominator is a power of 10; SYN: decimal.
	www.ultralingua.net /?service=ee&text=fraction (253 words)

	THE DEVELOPMENT OF THE PART-WHOLE AND MEASURE SUBCONSTRUCTS
		She could not give a second fraction to describe the region that was 6/8 shaded, but after a period of trial and error could shade 2/3 of a rectangle with 6 equivalent parts.
		Jim could not model an improper fraction with an area model yet he successfully modeled an improper fraction on the number line.
		Measuring to the nearest eighth-inch with a ruler was not addressed in instruction as the teacher ran out of time and decided that she needed to begin a unit on a new mathematical topic.
	www.west.asu.edu /cmw/pme/resrepweb/PME-rr-larson.htm (2311 words)

	[No title]
		fractions, denominator, have a, on top, on the bottom, must have, so they, improper, of the two, is a, has a, multiple, numerator, proper, reciprocal, bigger than, in life, mixed number, every day, for example, regrouping, rewrite, at work, at home 3.
		All fractions have a numerator and a denominator.
		All fractions have a __________ and a denominator.
	www.palmbeach.k12.fl.us /multicultural/ESOLCurriculumDocs/Secondary/MSMathU11.DOC (2451 words)

	Grade 7: Converting proper fractions to decimals
		The indicated division meaning of fraction is critical later on in algebra.
		Ask students to convert the fractions to decimal form, using a calculator, and to tell whether the decimal is repeating or terminating.
		They confirm that the marked fraction is in between the two other fractions by using a calculator to convert the fractions to decimals.
	io.uwinnipeg.ca /~jameis/PAGES/MYR54.html (1551 words)

	FRACTIONS FAST FACTS: (Site not responding. Last check: 2007-10-21)
		To build the fraction to a higher denominator, both numerator and denominator must be multiplied by the same factor.
		To change a mixed number into an improper fraction, multiply the whole number times the denominator and add the numerator of the fraction, place the new number over the original denominator.
		A fraction with zero in the denominator is undefined or meaningless.
	www.mccc.edu /~kelld/fraff.htm (494 words)

	Reducing Fractions The Easy Way
		Reducing fractions is another way of saying, "finding the lowest equivalent fraction." That's because you are normally trying to reduce a proper fraction to its simplest term.
		In this example all of the 2s are eliminated because there are an equal number of 2s in both the numerator and denominator.
		That's what we mean by a fraction mix that has the value of "1".
	www.helpwithfractions.com /reducing-fractions.html (190 words)

	Count On (Site not responding. Last check: 2007-10-21)
		So 6/12 is a fraction less than 1 but not a proper one since it can be simplified to 1/2, which is a proper fraction.
		(a recurring fraction which goes on for ever), mathematicians use one of two common notations to indicate which (if any) of the digits are in the repeating part (also called the period or cycle).
		Pick one and the fraction with an initial segment of this series as its periodic decimal expansion will be filled in for you in the calculator's boxes.
	www.mathsyear2000.org /explorer/fractions (1889 words)

	Fraction (Lang 2.1 API)
		This method uses the continued fraction algorithm, computing a maximum of 25 convergents and bounding the denominator by 10,000.
		This calculates the fraction as the numerator divided by denominator.
		a new fraction instance with the numerator and denominator inverted.
	jakarta.apache.org /commons/lang/api/org/apache/commons/lang/math/Fraction.html (938 words)

	5.4 - Partial Fractions
		Partial Fraction Decomposition only works for proper rational expressions, that is, the degree of the numerator must be less than the degree of the denominator.
		The implications of this for partial fraction decomposition are that when you have a repeated factor (a factor with a multiplicity other than one), you need to include a factor in the expansion for each power possible.
		A proper fraction is a fraction where the numerator is less than the denominator.
	www.richland.edu /james/lecture/m116/systems/partial.html (1322 words)

	Fractions - Definitions - First Glance (Site not responding. Last check: 2007-10-21)
		In a fraction, the denominator tells us how many parts the whole is divided into, and the numerator tells us how many of those parts we're dealing with.
		Proper fraction: numerator is less than the denominator.
		Improper fraction: numerator is greater than or equal to denominator.
	www.math.com /school/subject1/lessons/S1U4L1GL.html (80 words)

	Fractions. Evolution of the real numbers.
		In other words, the fractions are named (in English) according to the ratio of the numerator to the denominator.
		The fraction called "two-thirds" is two thirds of 1.
		In general, every fraction has the same ratio to 1 as the numerator has to the denominator.
	www.themathpage.com /aReal/fractions.htm (359 words)

	Lesson 1
		a fraction on the board and have he student copy it into their notebooks.
		Discuss the properties of a fraction and try to evoke the terms numerator and denominator from the students.
		that a proper fraction has a lower numerator than denominator, and that an improper fraction is "top-heavy" or has a larger numerator than denominator.
	www.oswego.org /staff/adamato/unit03/lesson1.cfm (196 words)

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