Arithmetic is an elementary branch of mathematics that deals with numerical operations such as addition, subtraction, multiplication and division. In a wider sense it also covers exponentiation, the extraction of roots and the taking of logarithms. Its practice reaches back to antiquity: the Egyptians and the Sumerians had already invented numeral systems to solve practical arithmetic problems by about 3000 BCE. Arithmetic is often distinguished from the related field of number theory, which narrows its focus to the integers and their properties, such as divisibility, factorization and primality.
Facts
Central QuestionArithmetic asks how quantities can be represented as numbers and combined by the basic operations of addition, subtraction, multiplication and division, and, more broadly, what structural and axiomatic properties those operations have. 1 Key DebateScholars disagree on how broadly to define arithmetic's own scope: a narrow characterization restricts it to computation with natural numbers, while the more common view extends it to integers, rational numbers, real numbers and sometimes complex numbers, and some definitions restrict it further to numerical calculation alone. 1 Classification
Pure or Applied Connections
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1. Arithmetic (Wikipedia)
Wikimedia FoundationLead section
Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, and division.
Definition, etymology, and related fields section
There are disagreements about its precise definition. According to a narrow characterization, arithmetic deals only with natural numbers. However, the more common view is to include operations on integers, rational numbers, real numbers, and sometimes also complex numbers in its scope.
Lead section, ancient numeral systems sentence
Ancient civilizations like the Egyptians and the Sumerians invented numeral systems to solve practical arithmetic problems in about 3000 BCE.
In Group: Elementary and General Number Theory, lead paragraph
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division.
View the Source Brahmagupta (MacTutor)
Includes: Brahmagupta, Biography, number systemsQuote, Includes: Brahmagupta, Biography, number systems
Brahmagupta's understanding of the number systems went far beyond that of others of the period.
View the Source Baha al-Din al-Amili (Wikipedia)
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A prolific author in both Arabic and Persian, Sheikh Bahaʾī composed over one hundred treatises spanning jurisprudence, logic, astronomy, mathematics, and theology-primarily in his mother tongue, Arabic.
View the Source Cheng Dawei (Wikipedia)
Includes: Cheng Dawei, Lead, field of workQuote, Includes: Cheng Dawei, Lead, field of work
Cheng Dawei (程大位, 1533-1606), also known as Da Wei Cheng or Ch'eng Ta-wei, was a Chinese mathematician and writer who was known mainly as the author of Suanfa Tongzong (算法統宗) (General Source of Computational Methods).
View the Source Christian Wurstisen (Wikipedia)
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Christian Wurstisen (Latin: Christianus Urstisius; 23 December 1544-29 March 1588) was a mathematician, theologian, historian from Basel.
View the Source Albert Girard (MacTutor)
Includes: Albert Girard, Biography, fields of workQuote, Includes: Albert Girard, Biography, fields of work
Girard worked on algebra, trigonometry and arithmetic.
View the Source Robert Recorde (MacTutor)
Includes: Robert Recorde, Biography, Grounde of ArtesQuote, Includes: Robert Recorde, Biography, Grounde of Artes
Recorde published The Grounde of Artes in 1543 which was a very successful commercial arithmetic book
View the Source Joan Francés Fulcònis (Wikipedia)
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Joan Francés Fulcònis (in classical Occitan; Johan Frances Fulconis, as written in his original edition) was a mathematician born in Lieusola (today and in French Isola) ca 1520 and who lived in Nice.
View the Source Pedro Chacón (Wikipedia)
Includes: Pedro Chacón, Lead, field of workQuote, Includes: Pedro Chacón, Lead, field of work
Pedro Chacón (b. c.1526 in Toledo, 1581 in Rome) was a Spanish mathematician and theologian. == Life == He worked as professor of Greek at the University of Salamanca, whose history, consulting ancient documents in the library, he published in 1569.
View the Source Thomas Harriot (Wikipedia)
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Thomas Harriot (; c. 1560-2 July 1621), also spelled Harriott, Hariot or Heriot, was an English astronomer, mathematician, ethnographer and translator to whom the theory of refraction is attributed.
View the Source Jerónimo Cortés (Wikipedia)
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Jerónimo Cortés (c. 1560 - c. 1611) was a Spanish mathematician, astronomer, naturalist and Valencian compiler. == Works == Many of Cortés works involved compilations of knowledge and writings of other authors.
View the Source Sigismundus Suevus (Wikipedia)
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Sigismund Schwabe, known by his Latin name Sigismundus Suevus (Freistadt, 1526-1596), was a German mathematician and Evangelical theologian.
View the Source Johann Lantz (Wikipedia)
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Johann Lantz or Lanz (1564-20 September 1638) was a German mathematician and Jesuit. == Biography == Born in Tettnang on Lake Constance in 1564, he was admitted as novice in Landsberg in 1589.
View the Source Yoshida Mitsuyoshi (Wikipedia)
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Yoshida Mitsuyoshi (吉田 光由; 1598, January 8, 1672), also known as Yoshida Kōyū, was a Japanese mathematician in the Edo period.
View the Source Christoffer Dybvad (Wikipedia)
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på dansk udgav sit første matematiske skrift
View the Source Abraham Fletcher (Wikipedia)
Includes: Abraham Fletcher, Article textQuote, Includes: Abraham Fletcher, Article text
applying himself particularly to the study of arithmetic
View the Source François Barrême (Wikipedia)
Includes: François Barrême, Lead, field of workQuote, Includes: François Barrême, Lead, field of work
Les Comptes faits : ou Le Tarif général de toutes les monnoyes (1669) Le Livre facile pour apprendre l’arithmétique de soy-même & sans maître (1672) La géométrie servant au mesurage et à l'arpentage : ,ouvrage si facile & si commode, que par la seule
View the Source Juan Caramuel y Lobkowitz (Wikipedia)
Includes: Juan Caramuel y Lobkowitz, MathematicsQuote, Includes: Juan Caramuel y Lobkowitz, Mathematics
thus making a significant contribution to the development of the binary numeral system
View the Source Jonas Moore (Wikipedia)
Includes: Jonas Moore, Mathematician and surveyor, arithmeticQuote, Includes: Jonas Moore, Mathematician and surveyor, arithmetic
published his first book, Moores Arithmetick
View the Source Giuseppe Maria Figatelli (Wikipedia)
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Ristretto aritmetico (in Italian).
View the Source John Collins (mathematician) (Wikipedia)
Includes: John Collins, Life, merchants accountsQuote, Includes: John Collins, Life, merchants accounts
In 1652 he published An Introduction to Merchants' Accounts
View the Source Jean-Joseph Rallier des Ourmes (Wikipedia)
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His numerous writings are scattered in various collections, in particular in the Encyclopédie, where he provided 14 articles on arithmetics, and in the Mémoires des savants étrangers of the Académie des sciences.
View the Source Pietro De Martino (Wikipedia)
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He authored various works; his Nuove istituzioni di aritmetica pratica, published originally in 1739 in Naples, had many reprints (the better known of the 1758; one also in Turin in 1762).
View the Source María Andrea Casamayor (Wikipedia)
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She stood out for her mathematical thinking and work with numbers and made significant contributions to arithmetic, which at the time was considered the exclusive domain of men.
View the Source Mihalj Šilobod Bolšić (Wikipedia)
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Mihalj Šilobod Bolšić (1 November 1724-4 April 1787) was a Croatian Roman Catholic priest, mathematician, writer, and musical theorist primarily known for writing the first Croatian arithmetics textbook Arithmetika Horvatzka (published in Zagreb, 1758).
View the Source John Colson (Wikipedia)
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In 1726 he published his "Negativo-Affirmativo Arithmetik", which advocated a modified decimal system of numeration.
View the Source Gilles-François de Gottignies (Wikipedia)
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Arithmetica introductio ad logisticam universae mathesi servientem continens vulgo usitatam arithmeticam practicam.
View the Source Charles Étienne Louis Camus (Wikipedia)
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Part 1: Élémens d'arithmétique (1749).
View the Source Leonty Magnitsky (Wikipedia)
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From 1701 and until his death, he taught arithmetic, geometry and trigonometry at the Moscow School of Mathematics and Navigation, becoming its director in 1716.
View the Source André Tacquet (Wikipedia)
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1651: Cylindricorum et annularium libri IV (Antwerp) full text 1654: Elementa geometriae (Antwerp) 1656: Arithmeticae theoria et praxis (Louvain) 1659: Cylindricorum et annularium liber V (Antwerp) full text 1669: Opera mathematica (in Latin).
View the Source Nicholas Pike (mathematician) (Wikipedia)
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The book was called A New and Complete System of Arithmetic Composed for Use of Citizens of the United States (1788).
View the Source Thomas Exley (Wikipedia)
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work on the extraction of cube roots did attract favourable attention
View the Source Kambei Mori (Wikipedia)
Includes: Kambei Mori, Life and workQuote, Includes: Kambei Mori, Life and work
which dealt with arithmetic and the use of the abacus
View the Source Onofrio Puglisi (Wikipedia)
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Aritmetica [Arithmetic]
View the Source Oberto Cantone (Wikipedia)
Includes: Oberto Cantone, WorksQuote, Includes: Oberto Cantone, Works
L'vso prattico dell'aritmetica
View the Source Francesco Barberino Benici (Wikipedia)
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Aritmetica prattica
View the Source Giovanni Giacomo Pierantoni (Wikipedia)
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Diverse operationi d'aritmetica
View the Source Stefano da San Gregorio (Wikipedia)
Includes: Stefano da San Gregorio, WorksQuote, Includes: Stefano da San Gregorio, Works
Aritmetica pratica
View the Source Mathieu de la Porte (Wikipedia)
Includes: Mathieu de la Porte, LifeQuote, Includes: Mathieu de la Porte, Life
taught accounting and arithmetic
View the Source Domenico Griminelli (Wikipedia)
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a tutorial book on arithmetic for shopkeepers and merchants
View the Source Ferdinando Piretti (Wikipedia)
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Lumi aritmetici
View the Source Petrus Apianus (Wikipedia)
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A handbook of commercial arithmetic
View the Source Warren Colburn (Wikipedia)
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His reputation rests largely on his First Lessons in Intellectual Arithmetic
View the Source Al-Kindi (Wikipedia)
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al-Kindi played an important role in introducing Hindu-Arabic numerals to the Islamic world
View the Source Adam Ries (Wikipedia)
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He is known as the "father of modern calculating"
View the Source Johannes Widmann (Wikipedia)
Includes: Johannes Widmann, LeadQuote, Includes: Johannes Widmann, Lead
Mercantile Arithmetic or Behende und hüpsche Rechenung auff allen Kauffmanschafft
View the Source Abraham ben Meir ibn Ezra (MacTutor)
Includes: Abraham ibn Ezra, Biography, work on numbersQuote, Includes: Abraham ibn Ezra, Biography, work on numbers
three treatises on numbers which helped to bring the Indian symbols and ideas of decimal fractions to the attention of some of the learned people in Europe
View the Source Euclidean Division (Wikipedia)
Includes: Euclidean Division, Lead sectionQuote, Includes: Euclidean Division, Lead section
In arithmetic, Euclidean division - or division with remainder - is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor.
View the Source Addition (Wikipedia)
Includes: Addition, Lead sentenceQuote, Includes: Addition, Lead sentence
us sign +, is one of the four basic operations of arithmetic, the other three being subtraction, multiplication, and division.
View the Source Wikipedia: Henry Briggs
Includes: Henry Briggs, LeadQuote, Includes: Henry Briggs, Lead
The specific algorithm for long division in modern use was introduced by Briggs c. 1600 AD.
View the Source Commutative Property (Wikipedia)
Includes: Commutative property, Lead paragraphQuote, Includes: Commutative property, Lead paragraph
Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings.
View the Source Division by Zero (Wikipedia)
Includes: Division by Zero, Lead paragraphQuote, Includes: Division by Zero, Lead paragraph
The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplied by the divisor.
View the Source Number (Wikipedia)
Includes: Number, Lead paragraphQuote, Includes: Number, Lead paragraph
Their study or usage is called arithmetic, a term which may also refer to number theory, the study of the properties of numbers.
View the Source Wolfram MathWorld: Midy's Theorem
Wolfram MathWorldIncludes: Midy's Theorem, Subject classificationsQuote, Includes: Midy's Theorem, Subject classifications
Number Theory Arithmetic
View the Source Wolfram MathWorld: Radix
Wolfram MathWorldIncludes: Radix, Subject classificationsQuote, Includes: Radix, Subject classifications
Number Theory Arithmetic
View the Source Wolfram MathWorld: Minus Sign
Wolfram MathWorldIncludes: Minus Sign, Subject classificationsQuote, Includes: Minus Sign, Subject classifications
Number Theory Arithmetic
View the Source Farey Sequence, from Wolfram MathWorld
Includes: Farey Sequence, Subject classificationsQuote, Includes: Farey Sequence, Subject classifications
Number Theory Arithmetic
View the Source 0.999..., Wikipedia
Includes: 0.999..., Lead sectionQuote, Includes: 0.999..., Lead section
0.999... is a repeating decimal that represents the number 1. The three dots
View the Source Successor Function (Wikipedia)
Includes: Successor Function, Lead sectionQuote, Includes: Successor Function, Lead section
natural number to the next one
View the Source Lowest Common Denominator (Wikipedia)
Includes: Lowest Common Denominator, Lead sectionQuote, Includes: Lowest Common Denominator, Lead section
or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It
View the Source Bhāskara II, Biography (MacTutor History of Mathematics)
Includes: Bhāskara II, SummaryQuote, Includes: Bhāskara II, Summary
Bhaskara II or Bhaskaracharya was an Indian mathematician and astronomer who extended Brahmagupta's work on number systems.
View the Source Luca Pacioli, Biography (MacTutor History of Mathematics)
Includes: Luca Pacioli, BiographyQuote, Includes: Luca Pacioli, Biography
In 1477 Pacioli began a life of travelling, spending time at various universities teaching mathematics, particularly arithmetic.
View the Source Simon Stevin, Biography (MacTutor History of Mathematics)
Includes: Simon Stevin, SummaryQuote, Includes: Simon Stevin, Summary
Simon Stevin was a Flemish mathematician who presented the first elementary and thorough account of decimal fractions and introduced their use in mathematics.
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