(redirected from Fractions)
Also found in: Dictionary, Thesaurus, Medical, Idioms.


[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.

The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



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\n 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.


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



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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.


One of the portions of a volatile liquid within certain boiling point ranges, such as petroleum naphtha fractions or gas-oil fractions.
An expression which is the product of a real number or complex number with the multiplicative inverse of a real or complex number.
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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


1. Maths
a. 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
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
While fraction 6 (isolated from the acetone originated fraction) was near to fraction 1 in its mortal effect with LC50 values of 403 and 292 ug/ml after 24 and 48 hours exposure, respectively without significant differences between each other, fraction 2 (isolated from the solvent system I) significantly exceeded the previously mentioned two fractions (1 and 6) exhibiting mortality percents increasingly with increasing the tested concentration to complete lethality of the treated population at 2000 ug/ml achieving 321 and 166.8 ug/ml LC50 values after 24 and 48 hours, respectively.
This sticky residue was suspended in distilled water and divided into fractions by using different solvents such as n-hexane (35 g), ethyl acetate (70 g) and n-butanol (80 g) on the basis of their polarity.
The combination of the importance of, and difficulty with, manipulating fractions as students begin to learn about adding fractions, highlights the value of research into developing activities that enable students to visualise and manipulate unit fraction addition (Kerenxhi and Gjoci, 2017; Tsai and Li, 2017).
The microdilution method was used to determine the MIC and MBC value from extract and the most active fraction. The first well of microplate was negative control (only filled 100 [mu]L Mueller-Hinton Broth (MHB), and the second well was an extract or fraction control (50 [mu]L extract or fraction and 50 [mu]L MHB).
In particular, the player in control learns to make decisions to pursue fractions either greater than or less than onehalf based on the particular cards available.
Water- and oil-holding capacities did not change significantly when blending both pea starch fraction and pea flour.
Predicted relative bubble radius as a function of dimensionless treatment time at various bubble volume fractions of 0.33%, 0.67%, and 1.33% at an ultrasonic amplitude of 10 [micro]m and hydrostatic pressures of 1 MPa.
Learning and mastering fractions is still a major issue for students in both primary and middle schools [15].
[10.sup.6] cells/mL Bel-7404 cells were seeded into a 6-well plate for 24 h followed by treatments with or without 40 [micro]g/mL fractions C4 and C5 for 72 h.
The flavonoid contents of Zm and Op extracts and their fractions were determined, based on a colorimetric assay [10] in which 0.5 ml of different concentrations of quercetin (12.5-300 [micro]g/ml) was used as a standard.
The developer has created an educational venue for children to analyze and apply knowledge of fractions in an engaging and fun way.
INTRODUCTION: Ejection fraction (EF) is the fraction of outbound blood pumped from the heart with each heartbeat.