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# Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. [1]

126 relations: Absolute value, Abu Bakr al-Hassar, Abu'l-Hasan al-Uqlidisi, Accuracy and precision, Addition, Akhmim wooden tablets, Algebraic expression, Algebraic fraction, American English, American Mathematical Monthly, Ancient Egypt, Ancient Greece, Ancient Greek philosophy, Aryabhata, Associative property, £sd, Baghdad, Bhāskara I, Bhāskara II, Binary relation, Binomial (polynomial), Brahmagupta, British English, Cardinal number, Chinese mathematics, Coefficient, Common Core State Standards Initiative, Commutative property, Complex number, Conjugate element (field theory), Continued fraction, Coprime integers, Cuisenaire rods, Dash, Decimal, Decimal separator, Dirk Jan Struik, Distributive property, Division (mathematics), Division by zero, Divisor, Dyadic rational, Egyptian fraction, Em (typography), En (typography), Equivalence relation, Euclidean algorithm, Fez, Morocco, Fibonacci, Field (mathematics), ... Expand index (76 more) »

## Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

## Abu Bakr al-Hassar

Al-Hassar or Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar was a Muslim mathematician from Morocco, living in the 12th century.

## Abu'l-Hasan al-Uqlidisi

Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi was an Arab mathematician, who was active in Damascus and Baghdad.

## Accuracy and precision

Precision is a description of random errors, a measure of statistical variability.

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

## Akhmim wooden tablets

The Akhmim wooden tablets or Cairo wooden tablets (Cairo Cat. 25367 and 25368) are two wooden writing tablets dating from ancient Egypt.

## Algebraic expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

## Algebraic fraction

In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions.

## American English

American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States.

## American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

## Ancient Egypt

Ancient Egypt was a civilization of ancient Northeastern Africa, concentrated along the lower reaches of the Nile River - geographically Lower Egypt and Upper Egypt, in the place that is now occupied by the countries of Egypt and Sudan.

## Ancient Greece

Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 13th–9th centuries BC to the end of antiquity (AD 600).

## Ancient Greek philosophy

Ancient Greek philosophy arose in the 6th century BC and continued throughout the Hellenistic period and the period in which Ancient Greece was part of the Roman Empire.

## Aryabhata

Aryabhata (IAST) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.

## Associative property

In mathematics, the associative property is a property of some binary operations.

## £sd

£sd (pronounced /ɛlɛsˈdiː/ ell-ess-dee and occasionally written Lsd) is the popular name for the pre-decimal currencies once common throughout Europe, especially in the British Isles and hence in several countries of the British Empire and subsequently the Commonwealth.

Baghdad (بغداد) is the capital of Iraq.

## Bhāskara I

Bhāskara (c. 600 – c. 680) (commonly called Bhaskara I to avoid confusion with the 12th century mathematician Bhāskara II) was a 7th-century mathematician, who was the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.

## Bhāskara II

Bhāskara (also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhaskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer.

## Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

## Binomial (polynomial)

In algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial.

## Brahmagupta

Brahmagupta (born, died) was an Indian mathematician and astronomer.

## British English

British English is the standard dialect of English language as spoken and written in the United Kingdom.

## Cardinal number

In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets.

## Chinese mathematics

Mathematics in China emerged independently by the 11th century BC.

## Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

## Common Core State Standards Initiative

The Common Core State Standards Initiative is an educational initiative from 2010 that details what K–12 students throughout the United States should know in English language arts and mathematics at the conclusion of each school grade.

## Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

## Conjugate element (field theory)

In mathematics, in particular field theory, the conjugate elements of an algebraic element α, over a field extension L/K, are the roots of the minimal polynomial pK,α(x) of α over K. Conjugate elements are also called Galois conjugates or simply conjugates.

## Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

## Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

## Cuisenaire rods

Cuisenaire rods are mathematics learning aids for students that provide an enactive, hands-on way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors.

## Dash

The dash is a punctuation mark that is similar in appearance to and, but differs from these symbols in both length and height.

## Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

## Decimal separator

A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form.

## Dirk Jan Struik

Dirk Jan Struik (September 30, 1894 &ndash; October 21, 2000) was a Dutch mathematician, historian of mathematics and Marxian theoretician who spent most of his life in the United States.

## Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

## Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

## Division by zero

In mathematics, division by zero is division where the divisor (denominator) is zero.

## Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

In mathematics, a dyadic fraction or dyadic rational is a rational number whose denominator, when the ratio is in minimal (coprime) terms, is a power of two, i.e., a number of the form \frac where a is an integer and b is a natural number; for example, 1/2 or 3/8, but not 1/3.

## Egyptian fraction

An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other.

## Em (typography)

An em is a unit in the field of typography, equal to the currently specified point size.

## En (typography)

An en is a typographic unit, half of the width of an em.

## Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

## Euclidean algorithm

. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.

## Fez, Morocco

Fez (فاس, Berber: Fas, ⴼⴰⵙ, Fès) is a city in northern inland Morocco and the capital of the Fas-Meknas administrative region.

## Fibonacci

Fibonacci (c. 1175 – c. 1250) was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".

## Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

## Field of fractions

In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded.

## Flemish Region

The Flemish Region (Vlaams Gewest,; Région flamande) is one of the three official regions of the Kingdom of Belgium—alongside the Walloon Region and the Brussels-Capital Region.

## Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

## Fraction Bars

Fraction Bars are a type of mathematical manipulative, developed in the sixties by Albert B. Bennett, Jr.

## Fractional part

The fractional part or decimal part of a non‐negative real number x is the excess beyond that number's integer part.

## Geoboard

A geoboard is a mathematical manipulative used to explore basic concepts in plane geometry such as perimeter, area and the characteristics of triangles and other polygons.

## Greatest common divisor

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

## Half crown (British coin)

The half crown was a denomination of British money, equivalent to two shillings and sixpence, or one-eighth of a pound.

## Hippasus

Hippasus of Metapontum (Ἵππασος ὁ Μεταποντῖνος, Híppasos; fl. 5th century BC), was a Pythagorean philosopher.

## History of Egypt

The history of Egypt has been long and rich, due to the flow of the Nile River with its fertile banks and delta, as well as the accomplishments of Egypt's native inhabitants and outside influence.

## History of India

The history of India includes the prehistoric settlements and societies in the Indian subcontinent; the advancement of civilisation from the Indus Valley Civilisation to the eventual blending of the Indo-Aryan culture to form the Vedic Civilisation; the rise of Hinduism, Jainism and Buddhism;Sanderson, Alexis (2009), "The Śaiva Age: The Rise and Dominance of Śaivism during the Early Medieval Period." In: Genesis and Development of Tantrism, edited by Shingo Einoo, Tokyo: Institute of Oriental Culture, University of Tokyo, 2009.

## Infix notation

Infix notation is the notation commonly used in arithmetical and logical formulae and statements.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Integral domain

In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.

## Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

## Irreducible fraction

An irreducible fraction (or fraction in lowest terms or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and -1, when negative numbers are considered).

## Islamic inheritance jurisprudence

Islamic Inheritance jurisprudence is a field of Islamic jurisprudence (فقه) that deals with inheritance, a topic that is prominently dealt with in the Qur'an.

## Jainism

Jainism, traditionally known as Jain Dharma, is an ancient Indian religion.

## Jamshīd al-Kāshī

Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī) (غیاث الدین جمشید کاشانی Ghiyās-ud-dīn Jamshīd Kāshānī) (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer and mathematician.

## Latin

Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation.

## Least common multiple

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.

## Leiden

Leiden (in English and archaic Dutch also Leyden) is a city and municipality in the province of South Holland, Netherlands.

## Mathematics in medieval Islam

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).

## Mental calculation

Mental calculation comprises arithmetical calculations using only the human brain, with no help from any supplies (such as pencil and paper) or devices such as a calculator.

## Metapontum

Metapontum or Metapontium (Metapontion) was an important city of Magna Graecia, situated on the gulf of Tarentum, between the river Bradanus and the Casuentus (modern Basento).

## Monomial

In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.

## Morocco

Morocco (officially known as the Kingdom of Morocco, is a unitary sovereign state located in the Maghreb region of North Africa. It is one of the native homelands of the indigenous Berber people. Geographically, Morocco is characterised by a rugged mountainous interior, large tracts of desert and a lengthy coastline along the Atlantic Ocean and Mediterranean Sea. Morocco has a population of over 33.8 million and an area of. Its capital is Rabat, and the largest city is Casablanca. Other major cities include Marrakesh, Tangier, Salé, Fes, Meknes and Oujda. A historically prominent regional power, Morocco has a history of independence not shared by its neighbours. Since the foundation of the first Moroccan state by Idris I in 788 AD, the country has been ruled by a series of independent dynasties, reaching its zenith under the Almoravid dynasty and Almohad dynasty, spanning parts of Iberia and northwestern Africa. The Marinid and Saadi dynasties continued the struggle against foreign domination, and Morocco remained the only North African country to avoid Ottoman occupation. The Alaouite dynasty, the current ruling dynasty, seized power in 1631. In 1912, Morocco was divided into French and Spanish protectorates, with an international zone in Tangier, and regained its independence in 1956. Moroccan culture is a blend of Berber, Arab, West African and European influences. Morocco claims the non-self-governing territory of Western Sahara, formerly Spanish Sahara, as its Southern Provinces. After Spain agreed to decolonise the territory to Morocco and Mauritania in 1975, a guerrilla war arose with local forces. Mauritania relinquished its claim in 1979, and the war lasted until a cease-fire in 1991. Morocco currently occupies two thirds of the territory, and peace processes have thus far failed to break the political deadlock. Morocco is a constitutional monarchy with an elected parliament. The King of Morocco holds vast executive and legislative powers, especially over the military, foreign policy and religious affairs. Executive power is exercised by the government, while legislative power is vested in both the government and the two chambers of parliament, the Assembly of Representatives and the Assembly of Councillors. The king can issue decrees called dahirs, which have the force of law. He can also dissolve the parliament after consulting the Prime Minister and the president of the constitutional court. Morocco's predominant religion is Islam, and the official languages are Arabic and Berber, with Berber being the native language of Morocco before the Arab conquest in the 600s AD. The Moroccan dialect of Arabic, referred to as Darija, and French are also widely spoken. Morocco is a member of the Arab League, the Union for the Mediterranean and the African Union. It has the fifth largest economy of Africa.

## Multiple (mathematics)

In science, a multiple is the product of any quantity and an integer.

## Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

## Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x&minus;1, is a number which when multiplied by x yields the multiplicative identity, 1.

## Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

## Netherlands

The Netherlands (Nederland), often referred to as Holland, is a country located mostly in Western Europe with a population of seventeen million.

## Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

## Number Forms

Number Forms is a Unicode block containing characters that have specific meaning as numbers, but are constructed from other characters.

## Numerical digit

A numerical digit is a single symbol (such as "2" or "5") used alone, or in combinations (such as "25"), to represent numbers (such as the number 25) according to some positional numeral systems.

## One half

One half is the irreducible fraction resulting from dividing one by two or the fraction resulting from dividing any number by its double.

## Partial fraction decomposition

In algebra, the partial fraction decomposition or partial fraction expansion of a rational function (that is, a fraction such that the numerator and the denominator are both polynomials) is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

## Parts-per notation

In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction.

## Pattern Blocks

Pattern Blocks are one of the mathematical manipulatives developed in the 1960s by Education Development Center as part of their Elementary Science Study project.

## Per mille

A per milleCambridge Dictionary Online.

## Percentage

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

## Persian people

The Persians--> are an Iranian ethnic group that make up over half the population of Iran.

## Point Roberts, Washington

Point Roberts is a pene exclave of the United States on the southernmost tip of the Tsawwassen Peninsula, south of Vancouver in British Columbia.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

## Primary school

A primary school (or elementary school in American English and often in Canadian English) is a school in which children receive primary or elementary education from the age of about seven to twelve, coming after preschool, infant school and before secondary school.

## Probability

Probability is the measure of the likelihood that an event will occur.

## Proof that π is irrational

In the 18th century, Johann Heinrich Lambert proved that the number pi (pi) is irrational: that is, it cannot be expressed as a fraction a/b, where a is an integer and b is a non-zero integer.

## Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.

## Pythagoreanism

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

## Quotient

In arithmetic, a quotient (from quotiens "how many times", pronounced) is the quantity produced by the division of two numbers.

## Ratio

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

## Rational function

In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.

## Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

## Rationalisation (mathematics)

In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Repeating decimal

A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely-repeated portion is not zero.

## Rhind Mathematical Papyrus

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of Egyptian mathematics.

## Robert Bringhurst

Robert Bringhurst Appointments to the Order of Canada (2013).

## Samarkand

Samarkand (Uzbek language Uzbek alphabet: Samarqand; سمرقند; Самарканд; Σαμαρκάνδη), alternatively Samarqand, is a city in modern-day Uzbekistan and is one of the oldest continuously inhabited cities in Central Asia.

## Scientific notation

Scientific notation (also referred to as scientific form or standard index form, or standard form in the UK) is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.

## Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

## Sexagesimal

Sexagesimal (base 60) is a numeral system with sixty as its base.

## Simon Stevin

Simon Stevin (1548–1620), sometimes called Stevinus, was a Flemish mathematician, physicist and military engineer.

## Slash (punctuation)

The slash is an oblique slanting line punctuation mark.

## Square root of 2

The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.

## Sthananga Sutra

Sthananga Sutra (Sanskrit: Sthānāṅgasūtra Prakrit: Ṭhāṇaṃgasutta) (c. 3rd-4th century CE) forms part of the first eleven Angas of the Jaina Canon which have survived despite the bad effects of this Hundavasarpini kala as per the Śvetāmbara belief.

## Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

## Trailing zero

In mathematics, trailing zeros are a sequence of 0 in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow.

## Typography

Typography is the art and technique of arranging type to make written language legible, readable, and appealing when displayed.

## Unicode

Unicode is a computing industry standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems.

## Unit fraction

A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

## Vedic and Sanskrit literature

Vedic and Sanskrit literature comprises the spoken or sung literature of the Vedas from the early-to-mid 2nd to mid 1st millennium BCE, and continues with the oral tradition of the Sanskrit epics of Iron Age India; the golden age of Classical Sanskrit literature dates to Late Antiquity (roughly the 3rd to 8th centuries CE).

## Well-defined

In mathematics, an expression is called well-defined or unambiguous if its definition assigns it a unique interpretation or value.

## 0.999...

In mathematics, 0.999... (also written 0., among other ways), denotes the repeating decimal consisting of infinitely many 9s after the decimal point (and one 0 before it).

## References

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