# fraction

## Definitions

• WordNet 3.6
• v fraction perform a division "Can you divide 49 by seven?"
• n fraction a small part or item forming a piece of a whole
• n fraction the quotient of two rational numbers
• n fraction a component of a mixture that has been separated by a fractional process
• ***
Webster's Revised Unabridged Dictionary
• Interesting fact: The number 2,520 can be divided by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 without having a fractional leftover.
• Fraction A portion; a fragment. "Some niggard fractions of an hour."
• Fraction (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.
• fraction see Commutation Draught Incidence Reflection Refraction, etc.
• Fraction The act of breaking, or state of being broken, especially by violence. "Neither can the natural body of Christ be subject to any fraction or breaking up."
• v. t Fraction (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.
• ***
Century Dictionary and Cyclopedia
• Interesting fact: The slanted line that divides dates, fractions, choices, etc. (6/1/04) is called a virgule.
• n fraction The act of breaking, or the state of being broken, especially by violence; a breaking or fracture.
• n fraction Specifically (ecclesiastical), the liturgical act of breaking or dividing the eucharistic bread, or host. Four such fractions are found in different liturgies at different points in the office, but all do not occur in any one liturgy, namely: A preparatory cutting or separation of portions at the beginning of the office or in the office of prothesis; a breaking at the word “brake” (fregit) in the institution; the solemn fraction after consecration and before communion; a division for distribution among the communicants.
• n fraction A fragment; a separated portion; a disconnected part.
• n fraction In mathematics: In arithmetic, a part, or a number of aliquot parts, of unity. Unity is regarded as divided into equal parts, and one or more of these parts as taken to constitute the fraction. The number of parts into which the unit is divided is termed the denominator, and the number of these parts taken the numerator. The denominator is commonly written below, and the numerator above, a horizontal or diagonal line: thus, 2/5, ⅞,½. Fractions written in this form are called common or vulgar fractions. (See decimal.) A proper fraction is one whose numerator is less than its denominator; an improper fraction, one whose numerator is greater than its denominator: as, 2/5, 17/8. A simple fraction expresses the ratio between two whole numbers: as,; a compound or complex fraction expresses the ratio between fractions (or mixed numbers), or between a fraction (or mixed number)and a whole number: as, Compound or complex fractions can always be reduced to simple fractions. A compound fraction is also defined as a fraction of a fraction. A fraction is said to be reduced to its lowest terms when the numerator and denominator contain no common factor.
• n fraction In algebra, a ration of algebraic quantities analogous to the arithmetical vulgar fraction, and similarly expressed.
• n fraction In mathematics: In geometry, any multiple of any submultiple of a magnitude.
• n fraction In chem., one of the parts into which a substance is separated in the process of fractional distillation. See fractionation.
• fraction Same as fractionate.
• ***
Chambers's Twentieth Century Dictionary
• n Fraction frak′shun a fragment or very small piece:
• v.t Fraction to break through
• n Fraction frak′shun (arith.) any part of a unit: a technical term to indicate the breaking of the bread in the sacrifice of the Eucharist
• ***

## Quotations

• Woodrow T. Wilson
“Most men are individuals no longer so far as their business, its activities, or its moralities are concerned. They are not units but fractions.”
• Paul Gauguin
“Life is hardly more than a fraction of a second. Such a little time to prepare oneself for eternity!”
• Rosalyn Sussman
“We still live in a world in which a significant fraction of people, including women, believe that a woman belongs and wants to belong exclusively in the home.”
• Count Leo Tolstoy
“A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator the smaller the fraction.”

## Etymology

Webster's Revised Unabridged Dictionary
F. fraction, L. fractio, a breaking, fr. frangere, fractum, to break. See Break
Chambers's Twentieth Century Dictionary
O. Fr. fraccion—L. fraction-emfrangĕre, fractum, to break.

## Usage

### In literature:

Aristide paused for the fraction of a second.
"The Joyous Adventures of Aristide Pujol" by William J. Locke
That youngster weighs seventeen pounds and a fraction already.
"The Indifference of Juliet" by Grace S. Richmond
There had been the fraction of a pause.
"Antony Gray,--Gardener" by Leslie Moore
He hoped Otto wasn't cross-eyed, and he quite longed to ask if fractions and spelling came hard to him.
"Sonny Boy" by Sophie Swett
The placing of all fractions in their order in line, in column, or for battle.
"Manual of Military Training" by James A. Moss
The problem of hours, minutes, seconds, and fractions of them was something they scarcely dreamed of.
"Christopher and the Clockmakers" by Sara Ware Bassett
Official figures show that the average March has but twenty-nine and a fraction hours of sunshine.
"East of Suez" by Frederic Courtland Penfield
Of course, fractions are not allowed, nor any tricks whatever.
"The Canterbury Puzzles" by Henry Ernest Dudeney
There was no sign of Lieutenant Ferrers, and in the Army lack of punctuality, even to the fraction of a minute, is a grave offense.
"Uncle Sam's Boys as Sergeants" by H. Irving Hancock
It remained in his a fraction of a second longer than he had expected, and gripped him with a virility that was surprising.
"Masterpieces of Mystery, Vol. 1 (of 4)" by Various
You can move it a fraction of an inch as easily as a hundred miles.
"Empire" by Clifford Donald Simak
It was done in the fraction of a second.
"Astounding Stories of Super-Science February 1930" by Various
The other seemed to wink, just the mere fraction of a wink, and then, like a flash, it came to Joe.
"Joe Strong on the Trapeze" by Vance Barnum
The other is the restriction of this knowledge to a tiny fraction of the population.
"The Next Step" by Scott Nearing
It was all done in the fraction of a second.
"The Twins of Suffering Creek" by Ridgwell Cullum
And in a moment, in the fraction of a second, and solely by reason of Aunt Annie's question, the situation became serious.
"A Great Man" by Arnold Bennett
A pointer on this last staff also carries the hand that indicates fractions of a second.
"The Auburndale Watch Company" by Edwin A. Battison
All these rivers appear to be but mere fractions of their former selves.
"A Year in the Fields" by John Burroughs
I don't know a thing about blood fractions or epidemics.
"The Planet Savers" by Marion Zimmer Bradley
But as that's the smallest boy in the lot I'll take him for my fraction.
"Si Klegg, Book 6 (of 6) Si And Shorty, With Their Boy Recruits, Enter On The Atlanta Campaign" by John McElroy
***

### In poetry:

Love and boredom and pity I'd take,
Even the nightingale in the wood -
Every tiny fraction of life
We live on earth, I'd take - if I could.
""If God in his almighty Power..."" by Konstantin Simonov
G was a giddy Gazelle,
Who never could learn how to spell;
But she managed to pass
To the head of her class,
Because she did fractions so well.
"An Alphabet Zoo" by Carolyn Wells
"And the great fight raged furious all the night
Till every integer was made a fraction;
Reader, wouldst know what history has to show
As net result of the above transaction?
"How To Not Settle It" by Oliver Wendell Holmes
She dropped on her knees and silently prayed,
With anguished hands and tears delayed
To a painful slowness. The minutes drew
To fractions. Then the west wind blew
The sound of a bell,
On a gusty swell.
"The Book Of Hours Of Sister Clotilde" by Amy Lowell
Only this veil which Thou hast broke,
And must be broken yet in me,
This veil, I say, is all the cloak
And cloud which shadows Thee from me.
This veil Thy full-eyed love denies,
And only gleams and fractions spies.
"Cock-Crowing" by Henry Vaughan
Perchance a loftier fate
Removed thy radiance from our feeble sight.
Did HE, whose Spirit wills but to create,
Far upward urge thy flight
From this low fraction of expiring time,
To realms where ages roll, as hours, in peace sublime?
"The Lost Pleiad" by Mary Gardiner Horsford

### In news:

The music earned Tom Waits an Oscar nomination, but the film was a monumental flop, making back only a small fraction of its production costs at the box office and sending Coppola into bankruptcy.
City plans to reallocate its fraction of bed tax to help bring in visitors.
A British handbag brand, has just released a new metallic collection -- for a fraction of the cost of designer brands such as Prada and Michael Kors.
Comparatively Speaking—Water vs Oil vs Fluoro vs Silicone Extraction of Broccoli Fractions.
Tab for a Cause, a Chrome and Firefox browser extension, lets you donate a fraction of a penny for each new tab you open.
A local woman is proving you can do the same thing for a fraction of the cost.
For a fraction of that, you can use a headlight lens cleaning kit.
Kid's Closet Connection is a local, semi-annual sale, which connects people who want to get rid of gently-used children's items to those who want to purchase quality kid's items at a fraction of retail prices.
Still, the official counts represent just a fraction of the actual number of people who contract the virus.
Get your creative cap on, we've got the simple steps to help you make your own gold lace cuff for a fraction of the retail price.
MathFileFolderGames.com's New '4 Dice ' Math App Introduces a Fun Way for Children to Learn Fractions on an iPhone or iPad.
What do you say when your town is offered the most iconic piece of property at a fraction of its value.
Funding for the state's anti-bullying initiative covers just a fraction of the real cost to public schools, said school officials in Hudson County, shocked by how little they were awarded.
Every professional desires to become more distinctive, yet only a fraction really are.
It only takes a small fraction of your time and minimal effort to help carry out various projects to improve the community.
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### In science:

The remnant fraction of liquid represent normal fraction of He II.
Hierarchic Models of Turbulence, Superfluidity and Superconductivity
Since in the hot CNO cycle the seed nuclei are mostly 14O or 15O waiting to β decay, we take the gas to be a mixture of hydrogen (mass fraction X given by eq.), 14O and 15O (mass fraction ZCNO ) and helium (mass fraction Y = 1 - X - ZCNO ).
Rotational Evolution During Type I X-Ray Bursts
The GPDs describe the emission of a quark with momentum fraction ( ¯x + ξ )/(1 + ξ ) from the proton and the reabsorption of a quark with momentum fraction ( ¯x − ξ )/(1 − ξ ).
Generalized parton distributions at large momentum transfer
Ring D is a skew ﬁeld that can be constructed both as the ring of left fractions a−1 b and as the ring of right fractions cd−1 , where a, b, c, d ∈ A.
Algorithmic proofs of two theorems of Stafford
There may be several (?) non-fractionalized insulating states with broken translational invariance; here, we focus on the fractionalized state only.
Exotic order in simple models of bosonic systems
The transformation z → z + 1/i switches these fractions around except for the extra 1 for the fraction with λ(g ) < 1 i .
McKay correspondence for elliptic genera
Ia is the fraction of SN Ia’s, fII,Ib = 1 − fIa is the fraction of SNe of other type, and fﬁeld OBs is the fraction of massive stars that form outside of the Galactic spiral arms.
The Spiral Structure of the Milky Way, Cosmic Rays, and Ice Age Epochs on Earth
As we discuss in Section 4, ob jects with virial temperatures above the feedback temperature, kTSN , retain a fraction of reheated gas which slightly increases their hot gas fraction.
The impact of galaxy formation on X-ray groups
If the ﬁducial model does behave in this way, we expect the feedback only to reduce the fraction of galactic material, leaving the hot gas fraction (and hence X-ray properties) intact.
The impact of galaxy formation on X-ray groups
In general, in higher dimensions, only a fraction of the original supersymmetries can be reinterpreted as yielding BRST charges and it is only this fraction that we can hope to preserve on the lattice.
Lattice Supersymmetry and Topological Field Theory
We truncate the stellar SIS at 0.16 rvir in order for the total stellar mass fraction to equal the universal baryon fraction, Ωb /ΩM .
The formation of galaxy stellar cores by the hierarchical merging of supermassive black holes
This dark region occupies approximately 60% of the volume when smoothed with a tophat sphere of R = 1h−1 Mpc, and contains a fraction ∼ 8% of the total mass (these fractions are larger for voids that are operationally deﬁned in observations: these numbers will be derived in Section 2.4).
The Probability Distribution Function of Light in the Universe: Results from Hydrodynamic Simulations
Fig. 4.— Mass fraction (panel (a)) and light fraction (panel (b)) that is contained in regions of < log y .
The Probability Distribution Function of Light in the Universe: Results from Hydrodynamic Simulations
That is, a constant fraction of the clauses must remain unsatisﬁed, but this fraction — ε3 /3 at most — is surprisingly small.
Random MAX SAT, Random MAX CUT, and Their Phase Transitions
That is, a linear fraction of clauses must be rejected, but this fraction, at most Θ(ε3 ) , is surprisingly small.
Random MAX SAT, Random MAX CUT, and Their Phase Transitions
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