fraction

a number usually expressed as 1/2, 1/4, etc.; a part as distinct from the whole of anything; portion or section: He received only a fraction of what he was owed.
Not to be confused with:friction – surface resistance to relative motion; the rubbing of one surface against another; discord, dissidence, antagonism, clash, contention: The disagreement caused a lot of friction between the friends.

frac·tion

F0290200 (frăk′shən)n.1. Mathematics An expression that indicates the quotient of two quantities, such as ¹/₃ .2. A disconnected piece; a fragment.3. A small part; a bit: moved a fraction of a step.4. 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.]

fraction

(ˈfrækʃən) n1. (Mathematics) maths a. a ratio of two expressions or numbers other than zerob. any rational number that is not an integer2. any part or subdivision: a substantial fraction of the nation. 3. a small piece; fragment4. (Chemistry) chem a component of a mixture separated by a fractional process, such as fractional distillation5. (Ecclesiastical Terms) Christianity the formal breaking of the bread in Communion6. the act of breakingvb (tr) to divide[C14: from Late Latin fractiō a breaking into pieces, from Latin fractus broken, from frangere to break]

frac•tion

(ˈfræk ʃən)

n. 1. a. a number usu. expressed in the form a/b. b. a ratio of algebraic quantities similarly expressed. 2. a component in a volatile mixture whose range of boiling point temperatures allows it to be separated from other components by fractionation. 3. a part of a whole: Only a fraction of the members were present. 4. a small part or segment: only a fraction of the cost. 5. a piece broken off; fragment. v.t., v.i. 6. to break into fractions. [1350–1400; Middle English fraccioun < Late Latin frāctiō act of breaking]

frac·tion

(frăk′shən) 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.

fraction

Past participle: fractioned
Gerund: fractioning

Imperative
fraction
fraction

Present
I fraction
you fraction
he/she/it fractions
we fraction
you fraction
they fraction

Preterite
I fractioned
you fractioned
he/she/it fractioned
we fractioned
you fractioned
they fractioned

Present Continuous
I am fractioning
you are fractioning
he/she/it is fractioning
we are fractioning
you are fractioning
they are fractioning

Present Perfect
I have fractioned
you have fractioned
he/she/it has fractioned
we have fractioned
you have fractioned
they have fractioned

Past Continuous
I was fractioning
you were fractioning
he/she/it was fractioning
we were fractioning
you were fractioning
they were fractioning

Past Perfect
I had fractioned
you had fractioned
he/she/it had fractioned
we had fractioned
you had fractioned
they had fractioned

Future
I will fraction
you will fraction
he/she/it will fraction
we will fraction
you will fraction
they will fraction

Future Perfect
I will have fractioned
you will have fractioned
he/she/it will have fractioned
we will have fractioned
you will have fractioned
they will have fractioned

Future Continuous
I will be fractioning
you will be fractioning
he/she/it will be fractioning
we will be fractioning
you will be fractioning
they will be fractioning

Present Perfect Continuous
I have been fractioning
you have been fractioning
he/she/it has been fractioning
we have been fractioning
you have been fractioning
they have been fractioning

Future Perfect Continuous
I will have been fractioning
you will have been fractioning
he/she/it will have been fractioning
we will have been fractioning
you will have been fractioning
they will have been fractioning

Past Perfect Continuous
I had been fractioning
you had been fractioning
he/she/it had been fractioning
we had been fractioning
you had been fractioning
they had been fractioning

Conditional
I would fraction
you would fraction
he/she/it would fraction
we would fraction
you would fraction
they would fraction

Past Conditional
I would have fractioned
you would have fractioned
he/she/it would have fractioned
we would have fractioned
you would have fractioned
they would have fractioned

Thesaurus

Noun	1.	$fraction - a component of a mixture that has been separated by a fractional process$ fraction - a component of a mixture that has been separated by a fractional processchemical, chemical substance - material produced by or used in a reaction involving changes in atoms or molecules
	2.	fraction - a small part or item forming a piece of a wholepart, portion - something less than the whole of a human artifact; "the rear part of the house"; "glue the two parts together"
	3.	fraction - the quotient of two rational numbersfixed-point part, mantissa - the positive fractional part of the representation of a logarithm; in the expression log 643 = 2.808 the mantissa is .808rational, rational number - an integer or a fractioncommon fraction, simple fraction - the quotient of two integersimproper fraction - a fraction whose numerator is larger than the denominatorproper fraction - a fraction with a numerator smaller than the denominatorcomplex fraction, compound fraction - a fraction with fractions in the numerator or denominatorcontinued 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
Verb	1.	fraction - perform a division; "Can you divide 49 by seven?"dividearithmetic - the branch of pure mathematics dealing with the theory of numerical calculationscompute, calculate, cipher, cypher, figure, reckon, work out - make a mathematical calculation or computationhalve - divide by two; divide into halves; "Halve the cake"quarter - divide by four; divide into quarters

fraction

noun1. bit, little bit, mite, jot, tiny amount, iota, scintilla I opened my eyes a fraction.2. percentage, share, cut, division, section, proportion, slice, ratio, portion, quota, subdivision, moiety only a small fraction of the cost3. fragment, part, piece, section, sector, selection, segment You will find only a fraction of the collection on display.

Translations

分数小部分

fraction

(ˈfrӕkʃən) noun1. a part; not a whole number eg 1/4, 3/8, 7/6 etc. 分数2. a small part. She has only a fraction of her brother's intelligence.小部分ˈfractional adjective very small. a fractional amount.极小的

fraction

[Lat.,=breaking], in arithmetic, an expression representing a part, or several equal parts, of a unit.

Notation for Fractions

In writing a fraction, e.g., 2-5 or 2/5, the number after or below the bar represents the total number of parts into which the unit has been divided. This number is called the denominator. The number before or above the bar, the numerator, denotes how many of the equal parts of the unit have been taken. The expression 2-5, then, represents the fact that two of the five parts of the unit or quantity have been taken. The present notation for fractions is of Hindu origin, but some types of fractions were used by the Egyptians before 1600 B.C. Another way of representing fractions is by decimal notation (see decimal systemdecimal system
[Lat.,=of tenths], numeration system based on powers of 10. A number is written as a row of digits, with each position in the row corresponding to a certain power of 10.
..... Click the link for more information. ).

Characteristics of Fractions

When the numerator is less than the denominator, the fraction is proper, i.e., less than unity. When the reverse is true, e.g., 5-2, the fraction is improper, i.e., greater than unity. When a fraction is written with a whole number, e.g., 3 1-2, the expression is called a mixed number. This may also be written as an improper fraction, as 7-2, since three is equal to six halves, and by adding the one half, the total becomes seven halves, or 7-2. A fraction has been reduced to its lowest terms when the numerator and denominator are not divisible by any common divisor except 1, e.g., when 4-6 is reduced to 2-3.

Arithmetic Operations Involving Fractions

When fractions having the same denominator, as 3-10 and 4-10, are added, only the numerators are added, and their sum is then written over the common denominator: 3-10+ 4-10= 7-10. Fractions having unlike denominators, e.g., 1-4 and 1-6, must first be converted into fractions having a common denominator, a denominator into which each denominator may be divided, before addition may be performed. In the case of 1-4 and 1-6, for example, the lowest number into which both 4 and 6 are divisible is 12. When both fractions are converted into fractions having this number as a denominator, then 1-4 becomes 3-12, and 1-6 becomes 2-12. The change is accomplished in the same way in both cases—the denominator is divided into the 12 and the numerator is multiplied by the result of this division. The addition then is performed as in the case of fractions having the same denominator: 1-4+ 1-6= 3-12+ 2-12= 5-12. In subtraction, the numerator and the denominator are subjected to the same preliminary procedure, but then the numerators of the converted fractions are subtracted: 1-4− 1-6= 3-12− 2-12= 1-12.

In multiplication the numerators of the fractions are multiplied together as are the denominators without needing change: 2-3× 3-5= 6-15. It should be noted that the result, here 6-15, may be reduced to 2-5 by dividing both numerator and denominator by 3. The division of one fraction by another, e.g., 3-5÷ 1-2, is performed by inverting the divisor and multiplying: 3-5÷ 1-2= 3-5× 2-1= 6-5. The same rules apply to the addition, subtraction, multiplication, and division of fractions in which the numerators and denominators are algebraic expressions.

Fraction

in arithmetic, a quantity consisting of an integral number of parts of a unit. A fraction is represented by the symbol m/n, where n, the denominator of the fraction, indicates the number of parts into which the unit is to be divided and m, the numerator of the fraction, indicates the number of such parts taken. A fraction may be viewed as the quotient obtained by dividing one integer (m) by another (n). If m is divisible by n without a remainder, then the quotient m\ denotes an integer (for example, 6/3 = 2, 33/11 = 3). The numerator and denominator of a fraction may be simultaneously multiplied or divided by the same number without changing the value of the fraction. Any fraction can be represented in reduced form, that is, as a fraction whose numerator and denominator do not have common factors; for example, 16/72 is not in reduced form [16/72 = 2x8/9x 8 = 2/9], but 27/64 is. To add fractions with the same denominator, we add their numerators and take the same denominator: (a/b) + (c/b) + (d/b) = (a + c + d)/b. To add several fractions with different denominators, it is necessary to bring them to a common denominator. Subtraction of fractions is done in the same way. To multiply several fractions, we divide the product of their numerators by the product of their denominators: (a/b) x (c/d) = ac/bd. Defining division as an inverse operation of multiplication implies the following rule for division: (a/b) ÷ (c/d) = ad/bc. If the numerator of a fraction is less than the denominator, the fraction is called a proper fraction; if the opposite is true, it is called an improper fraction. An improper fraction may be shown to be the sum of an integer and a proper fraction (a mixed number). For this it is necessary to divide the numerator (with remainder) by the denominator; for example,

This proposition of elementary arithmetic can be extended to all real numbers: a real number x can be represented uniquely as x = n + d, where n is an integer and 0 ≤ d < 1. The integer n is called the integral part of x and is denoted by [x]. The number d = x - [x] is called the fractional part of x.

Decimal fractions are fractions whose denominator is a power of 10. Such fractions are written without denominators; for example, 5,481,475/10,000 = 548.1475 and 23/1,000 = 0.023.

Operations with fractions are encountered in the ancient Egyptian Ahmes papyrus (c. 2000 B.C.) where the only admissible fractions are fractions of the type l/n (aliquot fractions). Hence the distinctive “Egyptian” problem of representing any fraction as the sum of unequal fractions of the type l/n (in addition to aliquot fractions, the Egyptians had a special symbol for the fraction 2/3); for example, 7/29 = (1/5) + (1/29) + (1/145).

In ancient Babylonian manuscripts we encounter so-called sexagesimal fractions, that is, fractions having a denominator that is a power of 60. The number 60 played a significant role in classical arithmetic; the division of a unit into 60 and 3,600 = 60² parts has been preserved to the present day in the division of an hour or a degree into 60 minutes (1/60) and of a minute into 60 seconds. The ancient Hindus, apparently, were the first to conceive the modern symbol for a fraction.

REFERENCES

Entsiklopediia elementarnoi matematiki, book 1: Arifmetika. Moscow-Leningrad, 1951.
Depman, I. la. Istoriia arifmetiki, 2nd ed. Moscow, 1965.

Fraction

a portion of a granular or lumpy solid (such as crushed rock, sand, or powder) or of a liquid mixture (such as petroleum) isolated according to a specific criterion. In sieve analysis, fractions are isolated by particle or grain size; in gravity concentration, by density; and in petroleum distillation, by boiling point.

fraction

[′frak·shən] (chemistry) One of the portions of a volatile liquid within certain boiling point ranges, such as petroleum naphtha fractions or gas-oil fractions. (mathematics) An expression which is the product of a real number or complex number with the multiplicative inverse of a real or complex number. (metallurgy) In powder metallurgy, that portion of sample that lies between two stated particle sizes. Also known as cut. (science and technology) A portion of a mixture which represents a discrete unit and can be isolated from the whole system.

fraction

1. Mathsa. a ratio of two expressions or numbers other than zero b. any rational number that is not an integer 2. Chem a component of a mixture separated by a fractional process, such as fractional distillation 3. Christianity the formal breaking of the bread in Communion

fraction

fraction

frac·tion

fraction

frac•tion

frac·tion

fraction

fraction

fraction

fraction

split in (number or fraction)

split into (number or fraction)

fraction

fraction

Notation for Fractions

Characteristics of Fractions

Arithmetic Operations Involving Fractions

Fraction

REFERENCES

Fraction

fraction

fraction

fraction

frac·tion

fraction

fraction

frac·tion

frac·tion

fraction

Synonyms for fraction

noun bit

Synonyms

noun percentage

Synonyms

noun fragment

Synonyms

Synonyms for fraction

noun a component of a mixture that has been separated by a fractional process

Related Words

noun a small part or item forming a piece of a whole

Related Words

noun the quotient of two rational numbers

Related Words

verb perform a division

Synonyms

Related Words