a ratio of algebraic quantities similarly expressed.
2.
Chemistry. (in a volatile mixture) a component whose range of boiling point temperatures allows it to be separated from other components by fractionation.
3.
a part as distinct from the whole of anything; portion or section: The meeting started with a fraction of us present.
4.
a very small part or segment of anything; minute portion: Only a fraction of the work was completed on time.
5.
a very small amount; a little bit: It was only a fraction away from completion.
6.
a piece broken off; fragment or bit.
7.
the act of breaking.
8.
Ecclesiastical. (in a Eucharistic service) the breaking of the Host.
–verb (used with object), verb (used without object)
9.
to divide or break into fractions, sections, factions, etc.: Dissension threatens to fraction the powerful union.
[Origin: 1350–1400; ME fraccioun < LL frāctiōn- (s. of frāctiō) a breaking (in pieces), equiv. to L frāct(us) (ptp. of frangere to break) + -iōn--ion]
Mathematics An expression that indicates the quotient of two quantities, such as 1/3 .
A disconnected piece; a fragment.
A small part; a bit: moved a fraction of a step.
A chemical component separated by fractionation.
[Middle English fraccioun, a breaking, from Anglo-Norman, from Late Latin frāctiō, frāctiōn-, from Latin frāctus, past participle of frangere, to break; see bhreg- in Indo-European roots.]
Word History: Our word fraction did not originally have a mathematical sense. It goes back ultimately to the Latin verb frangere, "to break." From the stem of the past participle frāctus is derived Late Latin frāctiō (stem frāctiōn-), "a breaking" or "a breaking in pieces," as in the breaking of the Eucharistic Host. In Medieval Latin the word frāctiō developed its mathematical sense, which was taken into Middle English along with the word. The earliest recorded sense of our word is "an aliquot part of a unit, a fraction or subdivision," found in a work by Chaucer written about 1400. One of the next recorded instances of the word recalls its origins, referring to the "brekying or fraccioun" of a bone.
1391, from L.L. fractionem (nom. fractio) "a breaking," especially into pieces, from root of L. frangere (pt. fregi) "to break," from PIE base *bhr(e)g- (cf. Skt. (giri)-bhraj "breaking-forth (out of the mountains);" Goth. brikan, O.E. brecan "to break;" Lith. brasketi "crash, crack;" O.Ir. braigim "break" wind). Mathematical sense was the original one in Eng. Sense of "broken off piece, fragment," is from 1606.
A number that compares part of an object or a set with the whole, especially the quotient of two whole numbers written in the form a/b. The fraction 1/2 , which means 1 divided by 2, can represent such things as 10 pencils out of a box of 20, or 50 cents out of a dollar. See also decimal fraction, improper fraction, proper fraction.
A mathematical expression representing the division of one whole number by another. Usually written as two numbers separated by a horizontal or diagonal line, fractions are also used to indicate a part of a whole number or a ratio between two numbers. Fractions may have a value of less than one, as with 1/2, or equal to one, as with 2/2, or more than one, as with 3/2. The top number of a fraction is the numerator and the bottom number is the denominator.
Main Entry: frac·tion Pronunciation: 'frak-sh&n Function: noun : one of several portions (as of a distillate) separable by fractionation <gamma
globulin is a fraction of blood plasma>
An"gle\ ([a^][ng]"g'l), n. [F. angle, L. angulus angle, corner; akin to uncus hook, Gr. 'agky`los bent, crooked, angular, 'a`gkos a bend or hollow, AS. angel hook, fish-hook, G. angel, and F. anchor.]1. The inclosed space near the point where two lines meet; a corner; a nook. Into the utmost angle of the world. --Spenser. To search the tenderest angles of the heart. --Milton. 2. (Geom.) (a) The figure made by. two lines which meet. (b) The difference of direction of two lines. In the lines meet, the point of meeting is the vertex of the angle. 3. A projecting or sharp corner; an angular fragment. Though but an angle reached him of the stone. --Dryden. 4. (Astrol.) A name given to four of the twelve astrological "houses." [Obs.] --Chaucer. 5. [AS. angel.] A fishhook; tackle for catching fish, consisting of a line, hook, and bait, with or without a rod. Give me mine angle: we 'll to the river there. --Shak. A fisher next his trembling angle bears. --Pope. Acute angle, one less than a right angle, or less than 90[deg]. Adjacent or Contiguous angles, such as have one leg common to both angles. Alternate angles. See Alternate. Angle bar. (a) (Carp.) An upright bar at the angle where two faces of a polygonal or bay window meet. --Knight. (b) (Mach.) Same as Angle iron. Angle bead (Arch.), a bead worked on or fixed to the angle of any architectural work, esp. for protecting an angle of a wall. Angle brace, Angle tie (Carp.), a brace across an interior angle of a wooden frame, forming the hypothenuse and securing the two side pieces together. --Knight. Angle iron (Mach.), a rolled bar or plate of iron having one or more angles, used for forming the corners, or connecting or sustaining the sides of an iron structure to which it is riveted. Angle leaf (Arch.), a detail in the form of a leaf, more or less conventionalized, used to decorate and sometimes to strengthen an angle. Angle meter, an instrument for measuring angles, esp. for ascertaining the dip of strata. Angle shaft (Arch.), an enriched angle bead, often having a capital or base, or both. Curvilineal angle, one formed by two curved lines. External angles, angles formed by the sides of any right-lined figure, when the sides are produced or lengthened. Facial angle. See under Facial. Internal angles, those which are within any right-lined figure. Mixtilineal angle, one formed by a right line with a curved line. Oblique angle, one acute or obtuse, in opposition to a right angle. Obtuse angle, one greater than a right angle, or more than 90[deg]. Optic angle. See under Optic. Rectilineal or Right-lined angle, one formed by two right lines. Right angle, one formed by a right line falling on another perpendicularly, or an angle of 90[deg] (measured by a quarter circle). Solid angle, the figure formed by the meeting of three or more plane angles at one point. Spherical angle, one made by the meeting of two arcs of great circles, which mutually cut one another on the surface of a globe or sphere. Visual angle, the angle formed by two rays of light, or two straight lines drawn from the extreme points of an object to the center of the eye. For Angles of commutation, draught, incidence, reflection, refraction, position, repose, fraction, see Commutation, Draught, Incidence, Reflection, Refraction, etc.
Com"plex\, a. [L. complexus, p. p. of complecti to entwine around, comprise; com- + plectere to twist, akin to plicare to fold. See Plait, n.]1. Composed of two or more parts; composite; not simple; as, a complex being; a complex idea. Ideas thus made up of several simple ones put together, I call complex; such as beauty, gratitude, a man, an army, the universe. --Locke. 2. Involving many parts; complicated; intricate. When the actual motions of the heavens are calculated in the best possible way, the process is difficult and complex. --Whewell. Complex fraction. See Fraction. Complex number (Math.), in the theory of numbers, an expression of the form a + b[root]-1, when a and b are ordinary integers. Syn: See Intricate.
Com"pound\, a. [OE. compouned, p. p. of compounen. See Compound, v. t.] Composed of two or more elements, ingredients, parts; produced by the union of several ingredients, parts, or things; composite; as, a compound word. Compound substances are made up of two or more simple substances. --I. Watts. Compound addition, subtraction, multiplication, division (Arith.), the addition, subtraction, etc., of compound numbers. Compound crystal (Crystallog.), a twin crystal, or one seeming to be made up of two or more crystals combined according to regular laws of composition. Compound engine (Mech.), a form of steam engine in which the steam that has been used in a high-pressure cylinder is made to do further service in a larger low-pressure cylinder, sometimes in several larger cylinders, successively. Compound ether. (Chem.) See under Ether. Compound flower (Bot.), a flower head resembling a single flower, but really composed of several florets inclosed in a common calyxlike involucre, as the sunflower or dandelion. Compound fraction. (Math.) See Fraction. Compound fracture. See Fracture. Compound householder, a householder who compounds or arranges with his landlord that his rates shall be included in his rents. [Eng.] Compound interest. See Interest. Compound larceny. (Law) See Larceny. Compound leaf (Bot.), a leaf having two or more separate blades or leaflets on a common leafstalk. Compound microscope. See Microscope. Compound motion. See Motion. Compound number (Math.), one constructed according to a varying scale of denomination; as, 3 cwt., 1 qr., 5 lb.; -- called also denominate number. Compound pier (Arch.), a clustered column. Compound quantity (Alg.), a quantity composed of two or more simple quantities or terms, connected by the sign + (plus) or - (minus). Thus, a + b - c, and bb - b, are compound quantities. Compound radical. (Chem.) See Radical. Compound ratio (Math.), the product of two or more ratios; thus ab:cd is a ratio compounded of the simple ratios a:c and b:d. Compound rest (Mech.), the tool carriage of an engine lathe. Compound screw (Mech.), a screw having on the same axis two or more screws with different pitch (a differential screw), or running in different directions (a right and left screw). Compound time (Mus.), that in which two or more simple measures are combined in one; as, 6-8 time is the joining of two measures of 3-8 time. Compound word, a word composed of two or more words; specifically, two or more words joined together by a hyphen.
Frac"tion\, n. [F. fraction, L. fractio a breaking, fr. frangere, fractum, to break. See Break.]1. The act of breaking, or state of being broken, especially by violence. [Obs.] Neither can the natural body of Christ be subject to any fraction or breaking up. --Foxe. 2. A portion; a fragment. Some niggard fractions of an hour. --Tennyson. 3. (Arith. or Alg.) One or more aliquot parts of a unit or whole number; an expression for a definite portion of a unit or magnitude. Common, or Vulgar, fraction, a fraction in which the number of equal parts into which the integer is supposed to be divided is indicated by figures or letters, called the denominator, written below a line, over which is the numerator, indicating the number of these parts included in the fraction; as 1/2, one half, 2/5, two fifths. Complex fraction, a fraction having a fraction or mixed number in the numerator or denominator, or in both. --Davies & Peck. Compound fraction, a fraction of a fraction; two or more fractions connected by of. Continued fraction, Decimal fraction, Partial fraction, etc. See under Continued, Decimal, Partial, etc. Improper fraction, a fraction in which the numerator is greater than the denominator. Proper fraction, a fraction in which the numerator is less than the denominator.
Frac"tion\, n. [F. fraction, L. fractio a breaking, fr. frangere, fractum, to break. See Break.]1. The act of breaking, or state of being broken, especially by violence. [Obs.] Neither can the natural body of Christ be subject to any fraction or breaking up. --Foxe. 2. A portion; a fragment. Some niggard fractions of an hour. --Tennyson. 3. (Arith. or Alg.) One or more aliquot parts of a unit or whole number; an expression for a definite portion of a unit or magnitude. Common, or Vulgar, fraction, a fraction in which the number of equal parts into which the integer is supposed to be divided is indicated by figures or letters, called the denominator, written below a line, over which is the numerator, indicating the number of these parts included in the fraction; as 1/2, one half, 2/5, two fifths. Complex fraction, a fraction having a fraction or mixed number in the numerator or denominator, or in both. --Davies & Peck. Compound fraction, a fraction of a fraction; two or more fractions connected by of. Continued fraction, Decimal fraction, Partial fraction, etc. See under Continued, Decimal, Partial, etc. Improper fraction, a fraction in which the numerator is greater than the denominator. Proper fraction, a fraction in which the numerator is less than the denominator.
Frac"tion\, v. t. (Chem.) To separate by means of, or to subject to, fractional distillation or crystallization; to fractionate; -- frequently used with out; as, to fraction out a certain grade of oil from pretroleum.
Frac"ture\ (?; 135), n. [L. fractura, fr. frangere, fractum, to break: cf. F. fracture. See Fraction.]1. The act of breaking or snapping asunder; rupture; breach. 2. (Surg.) The breaking of a bone. 3. (Min.) The texture of a freshly broken surface; as, a compact fracture; an even, hackly, or conchoidal fracture. Comminuted fracture (Surg.), a fracture in which the bone is broken into several parts. Complicated fracture (Surg.), a fracture of the bone combined with the lesion of some artery, nervous trunk, or joint. Compound fracture (Surg.), a fracture in which there is an open wound from the surface down to the fracture. Simple fracture (Surg.), a fracture in which the bone only is ruptured. It does not communicate with the surface by an open wound. Syn: Fracture, Rupture. Usage: These words denote different kinds of breaking, according to the objects to which they are applied. Fracture is applied to hard substances; as, the fracture of a bone. Rupture is oftener applied to soft substances; as, the rupture of a blood vessel. It is also used figuratively. "To be an enemy and once to have been a friend, does it not embitter the rupture?" --South.
Im*prop"er\, a. [F. impropre, L. improprius; pref. im- not + proprius proper. See Proper.]1. Not proper; not suitable; not fitted to the circumstances, design, or end; unfit; not becoming; incongruous; inappropriate; indecent; as, an improper medicine; improper thought, behavior, language, dress. Follow'd his enemy king, and did him service, Improper for a slave. --Shak. And to their proper operation still, Ascribe all Good; to their improper, Ill. --Pope. 2. Not peculiar or appropriate to individuals; general; common. [Obs.] Not to be adorned with any art but such improper ones as nature is said to bestow, as singing and poetry. --J. Fletcher. 3. Not according to facts; inaccurate; erroneous. Improper diphthong. See under Diphthong. Improper feud, an original feud, not earned by military service. --Mozley & W. Improper fraction. See under Fraction.
In*fringe"\, v. t. [imp. & p. p. Infringed; p. pr. & vb. n. Infringing.] [L. infringere; pref. in- in + frangere to break. See Fraction, and cf. Infract .]1. To break; to violate; to transgress; to neglect to fulfill or obey; as, to infringe a law or contract. If the first that did the edict infringe, Had answered for his deed. --Shak. The peace . . . was infringed by Appius Claudius. --Golding. 2. To hinder; to destroy; as, to infringe efficacy; to infringe delight or power. [Obs.] --Hooker.
Nu"mer*a"tor\, n. [L. numerator: cf. F. num['e]rateur.]1. One who numbers. 2. (Math.) The term in a fraction which indicates the number of fractional units that are taken. Note: In a vulgar fraction the numerator is written above a line; thus, in the fraction 5/9 (five ninths) 5 is the numerator; in a decimal fraction it is the number which follows the decimal point. See Fraction.
Vul"gar\, a. [L. vulgaris, from vulgus the multitude, the common people; of uncertain origin: cf. F. vulgaire. Cf. Divulge.]1. Of or pertaining to the mass, or multitude, of people; common; general; ordinary; public; hence, in general use; vernacular. "As common as any the most vulgar thing to sense. " -- Shak. Things vulgar, and well-weighed, scarce worth the praise. --Milton. It might be more useful to the English reader . . . to write in our vulgar language. --Bp. Fell. The mechanical process of multiplying books had brought the New Testament in the vulgar tongue within the reach of every class. --Bancroft. 2. Belonging or relating to the common people, as distinguished from the cultivated or educated; pertaining to common life; plebeian; not select or distinguished; hence, sometimes, of little or no value. "Like the vulgar sort of market men." --Shak. Men who have passed all their time in low and vulgar life. --Addison. In reading an account of a battle, we follow the hero with our whole attention, but seldom reflect on the vulgar heaps of slaughter. --Rambler. 3. Hence, lacking cultivation or refinement; rustic; boorish; also, offensive to good taste or refined feelings; low; coarse; mean; base; as, vulgar men, minds, language, or manners. Be thou familiar, but by no means vulgar. --Shak. Vulgar fraction. (Arith.) See under Fraction.
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