Arithmetic tables for children, Lausanne, 1835 **Arithmetic** or **arithmetics** (from the Greek word *αριθμός* = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. In common usage, the word refers to a branch of (or the forerunner of) mathematics which records elementary properties of certain *operations* on numbers. Professional mathematicians sometimes use the term *higher arithmetic*^{[1]} when referring to number theory, but this should not be confused with elementary arithmetic. Image File history File linksMetadata Size of this preview: 399 Ã— 599 pixelsFull resolution (2691 Ã— 4038 pixel, file size: 1,015 KB, MIME type: image/jpeg) Work by Rama File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Arithmetic Metadata...
Image File history File linksMetadata Size of this preview: 399 Ã— 599 pixelsFull resolution (2691 Ã— 4038 pixel, file size: 1,015 KB, MIME type: image/jpeg) Work by Rama File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Arithmetic Metadata...
Part of a scientific laboratory at the University of Cologne. ...
In economics, a business is a legally-recognized organizational entity existing within an economically free country designed to sell goods and/or services to consumers, usually in an effort to generate profit. ...
Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...
For other uses, see Number (disambiguation). ...
Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ...
Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...
Elementary arithmetic is the most basic kind of mathematics: it concerns the operations of addition, subtraction, multiplication, and division. ...
## History
The prehistory of arithmetic is limited to a very small number of small artifacts indicating a clear conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 18,000 and 20,000 BC. The Ishango bone is a tally stick, made of bone, which contains sequences of prime numbers, and some series of multiples. ...
It is clear that the Babylonians had solid knowledge of almost all aspects of elementary arithmetic by 1800 BC, although historians can only guess at the methods utilized to generate the arithmetical results - as shown, for instance, in the clay tablet Plimpton 322, which appears to be a list of Pythagorean triples, but with no workings to show how the list was originally produced. Likewise, the Egyptian Rhind Mathematical Papyrus (dating from c. 1650 BC, though evidently a copy of an older text from c. 1850 BC) shows evidence of addition, subtraction, multiplication, and division being used within a unit fraction system. Babylonia was an ancient state in Iraq), combining the territories of Sumer and Akkad. ...
Of the approximately half million clay tablets excavated at the beginning of the 19th century, about 400 are of a mathematical nature. ...
The Pythagorean theorem: a2 + b2 = c2 A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ...
The Rhind Mathematical Papyrus ( papyrus British Museum 10057 and pBM 10058), is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. ...
An Egyptian fraction is the sum of distinct unit fractions, such as . ...
Nicomachus (c. AD60 - c. AD120) summarised the philosophical Pythagorean approach to numbers, and their relationships to each other, in his *Introduction to Arithmetic*. At this time, basic arithmetical operations were highly complicated affairs; it was the method known as the "Method of the Indians" (Latin "Modus Indorum") that became the arithmetic that we know today. Indian arithmetic was much simpler than Greek arithmetic due to the simplicity of the Indian number system, which had a zero and place-value notation. The 7th century Syriac bishop Severus Sebhokt mentioned this method with admiration, stating however that the Method of the Indians was beyond description. The Arabs learned this new method and called it "Hesab" or "Hindu Science". Fibonacci (also known as Leonardo of Pisa) introduced the "Method of the Indians" to Europe in 1202. In his book "Liber Abaci", Fibonacci says that, compared to this new method, all other methods had been mistakes. In the Middle Ages, arithmetic was one of the seven liberal arts taught in universities. Nicomachus (Gr. ...
Events Boudicca sacks London (approximate date). ...
For other uses, see number 120. ...
Bust of Pythagoras Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a main inspirational source for Plato and platonism. ...
Introduction to Arithmetic was written by Nicomachus almost two thousand years ago, and contains both philosophical prose and very basic mathematical ideas. ...
For other senses of this word, see zero or 0. ...
A positional notation or place-value notation system is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base or radix of that numeral system. ...
The 7th century is the period from 601 - 700 in accordance with the Julian calendar in the Christian Era. ...
Topics in Christianity Movements Â· Denominations Ecumenism Â· Preaching Â· Prayer Music Â· Liturgy Â· Calendar Symbols Â· Art Â· Criticism Important figures Apostle Paul Â· Church Fathers Constantine Â· Athanasius Â· Augustine Anselm Â· Aquinas Â· Palamas Â· Luther Calvin Â· Wesley Arius Â· Marcion of Sinope Pope Â· Archbishop of Canterbury Patriarch of Constantinople Christianity Portal This box: Syriac Christianity is a culturally and...
For the number sequence, see Fibonacci number. ...
// Events August 1 - Arthur of Brittany captured in Mirebeau, north of Poitiers Beginning of the Fourth Crusade. ...
Liber Abaci (1202) is an historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. ...
The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ...
In the history of education, the seven liberal arts comprise two groups of studies, the trivium and the quadrivium. ...
Modern algorithms for arithmetic (both for hand and electronic computation) were made possible by the introduction of Hindu-Arabic numerals and decimal place notation for numbers. Hindu-Arabic numeral based arithmetic was developed by the great Indian mathematicians Aryabhatta, Brahmagupta and Bhaskara. Aryabhatta tried different place value notations and Brahmagupta added zero to the Indian number system. Brahmagupta developed modern multiplication, division, addition and subtraction based on Hindu-Arabic numerals. Although it is now considered elementary, its simplicity is the culmination of thousands of years of mathematical development. By contrast, the ancient mathematician Archimedes devoted an entire work, The Sand Reckoner, to devising a notation for a certain large integer. The flourishing of algebra in the medieval Islamic world and in Renaissance Europe was an outgrowth of the enormous simplification of computation through decimal notation. Flowcharts are often used to represent algorithms. ...
Numerals sans-serif Arabic numerals, known formally as Hindu-Arabic numerals, and also as Indian numerals, Hindu numerals, Western Arabic numerals, European numerals, or Western numerals, are the most common symbolic representation of numbers around the world. ...
For other uses, see Decimal (disambiguation). ...
Aryabhata (आर्यभट) (Āryabhaṭa) is the first of the great astronomers of the classical age of India. ...
Brahmagupta (à¤¬à¥à¤°à¤¹à¥à¤®à¤—à¥à¤ªà¥à¤¤) ( ) (589â€“668) was an Indian mathematician and astronomer. ...
Bhaskara (1114-1185), also known as Bhaskara II and Bhaskara AchÄrya (Bhaskara the teacher), was an Indian mathematician-astronomer. ...
Wikiquote has a collection of quotations related to: Simplicity Simplicity is the property, condition, or quality of being simple or un-combined. ...
Archimedes of Syracuse (Greek: c. ...
The Sand Reckoner (Greek: Î¨Î±Î¼Î¼Î¯Ï„Î·Ï‚, Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. ...
This article is about the branch of mathematics. ...
The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times. ...
Islam (Arabic: ; ( â–¶ (helpÂ· info)), the submission to God) is a monotheistic faith, one of the Abrahamic religions and the worlds second-largest religion. ...
The Renaissance (French for rebirth, or Rinascimento in Italian), was a cultural movement in Italy (and in Europe in general) that began in the late Middle Ages, and spanned roughly the 14th through the 17th century. ...
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The term notation can be used in several contexts. ...
## Decimal arithmetic Decimal notation constructs all real numbers from the basic digits, the first ten non-negative integers 0,1,2,...,9. A decimal numeral consists of a sequence of these basic digits, with the "denomination" of each digit depending on its *position* with respect to the decimal point: for example, 507.36 denotes 5 hundreds (10²), plus 0 tens (10^{1}), plus 7 units (10^{0}), plus 3 tenths (10^{-1}) plus 6 hundredths (10^{-2}). An essential part of this notation (and a major stumbling block in achieving it) was conceiving of zero as a number comparable to the other basic digits. Decimal, or denary, notation is the most common way of writing the base 10 numeral system, which uses various symbols for ten distinct quantities (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits) together with the decimal point and the sign symbols + (plus) and − (minus...
For other senses of this word, see zero or 0. ...
Algorism comprises all of the rules of performing arithmetic computations using a decimal system for representing numbers in which numbers written using ten symbols having the values 0 through 9 are combined using a place-value system (positional notation), where each symbol has ten times the weight of the one to its right. This notation allows the addition of arbitrary numbers by adding the digits in each place, which is accomplished with a 10 x 10 addition table. (A sum of digits which exceeds 9 must have its 10-digit carried to the next place leftward.) One can make a similar algorithm for multiplying arbitrary numbers because the set of denominations {...,10²,10,1,10^{-1},...} is closed under multiplication. Subtraction and division are achieved by similar, though more complicated algorithms. Algorism comprises all of the rules of performing arithmetic computations using a decimal system for representing numbers in which numbers written using ten symbols having the values 0 through 9 are combined using a place-value system (positional notation), where each symbol has ten times the weight of the one...
## Arithmetic operations The traditional arithmetic operations are addition, subtraction, multiplication and division, although more advanced operations (such as manipulations of percentages, square root, exponentiation, and logarithmic functions) are also sometimes included in this subject. Arithmetic is performed according to an order of operations. Any set of objects upon which all four operations of arithmetic can be performed (except division by zero), and wherein these four operations obey the usual laws, is called a field. 3 + 2 = 5 with apples, a popular choice in textbooks[1] This article is about addition in mathematics. ...
5 - 2 = 3 (verbally, five minus two equals three) An example problem Subtraction is one of the four basic arithmetic operations; it is essentially the opposite of addition. ...
In mathematics, multiplication is an elementary arithmetic operation. ...
In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ...
The percent sign. ...
In mathematics, a square root of a number x is a number r such that , or in words, a number r whose square (the result of multiplying the number by itself) is x. ...
Exponentiation is a mathematical operation, written an, involving two numbers, the base a and the exponent n. ...
Logarithms to various bases: is to base e, is to base 10, and is to base 1. ...
In arithmetic and algebra, when a number or expression is both preceded and followed by a binary operation, a rule is required for which operation should be applied first. ...
In mathematics, a division is called a division by zero if the divisor is zero. ...
In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers. ...
### Addition (+) -
Addition is the basic operation of arithmetic. In its simplest form, addition combines two numbers, the *addends* or *terms*, into a single number, the *sum*. 3 + 2 = 5 with apples, a popular choice in textbooks[1] This article is about addition in mathematics. ...
In mathematics, an operator is a function that performs some sort of operation on a number, variable, or function. ...
For other uses, see Number (disambiguation). ...
In elementary mathematics, a term is either a single number or variable, or the product of several numbers and/or variables. ...
Adding more than two numbers can be viewed as repeated addition; this procedure is known as summation and includes ways to add infinitely many numbers in an infinite series; repeated addition of the number one is the most basic form of counting. For evaluation of sums in closed form see evaluating sums. ...
In mathematics, a series is often represented as the sum of a sequence of terms. ...
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Counting is the mathematical action of repeatedly adding (or subtracting) one, usually to find out how many objects there are or to set aside a desired number of objects (starting with one for the first object and proceeding with an injective function from the remaining objects to the natural numbers...
Addition is commutative and associative so the order in which the terms are added does not matter. The identity element of addition (the additive identity) is 0, that is, adding zero to any number will yield that same number. Also, the inverse element of addition (the additive inverse) is the opposite of any number, that is, adding the opposite of any number to the number itself will yield the additive identity, 0. For example, the opposite of 7 is (-7), so 7 + (-7) = 0. In mathematics, especially abstract algebra, a binary operation * on a set S is commutative if x * y = y * x for all x and y in S. Otherwise * is noncommutative. ...
In mathematics, associativity is a property that a binary operation can have. ...
In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set. ...
The additive identity of a number n is the number which, when added to n will yield n. ...
In mathematics, the inverse of an element x, with respect to an operation *, is an element x such that their compose gives a neutral element. ...
The additive inverse, or opposite, of a number n is the number which, when added to n, yields zero. ...
### Subtraction (−) -
Subtraction is essentially the opposite of addition. Subtraction finds the *difference* between two numbers, the *minuend* minus the *subtrahend*. If the minuend is larger than the subtrahend, the difference will be positive; if the minuend is smaller than the subtrahend, the difference will be negative; and if they are equal, the difference will be zero. 5 - 2 = 3 (verbally, five minus two equals three) An example problem Subtraction is one of the four basic arithmetic operations; it is essentially the opposite of addition. ...
For other senses of this word, see zero or 0. ...
Subtraction is neither commutative nor associative. For that reason, it is often helpful to look at subtraction as addition of the minuend and the opposite of the subtrahend, that is *a* − *b* = *a* + (−*b*). When written as a sum, all the properties of addition hold.
### Multiplication (× or ·) -
Multiplication is in essence repeated addition, or the sum of a list of identical numbers. Multiplication finds the *product* of two numbers, the *multiplier* and the *multiplicand*, sometimes both simply called *factors*. In mathematics, multiplication is an elementary arithmetic operation. ...
Multiplication, as it is really repeated addition, is commutative and associative; further it is distributive over addition and subtraction. The multiplicative identity is 1, that is, multiplying any number by 1 will yield that same number. Also, the multiplicative inverse is the reciprocal of any number, that is, multiplying the reciprocal of any number by the number itself will yield the multiplicative identity, 1. In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. ...
One redirects here. ...
The reciprocal function: y = 1/x. ...
The reciprocal function: y = 1/x. ...
### Division (÷ or /) -
Division is essentially the opposite of multiplication. Division finds the *quotient* of two numbers, the *dividend* divided by the *divisor*. Any dividend divided by zero is undefined. For positive numbers, if the dividend is larger than the divisor, the quotient will be greater than one, otherwise it will be less than one (a similar rule applies for negative numbers). The quotient multiplied by the divisor always yields the dividend. In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ...
In mathematics, a division is called a division by zero if the divisor is zero. ...
Division is neither commutative nor associative. As it is helpful to look at subtraction as addition, it is helpful to look at division as multiplication of the dividend times the reciprocal of the divisor, that is *a* ÷ *b* = *a* × ^{1}⁄_{b}. When written as a product, it will obey all the properties of multiplication. The reciprocal function: y = 1/x. ...
### Examples #### Multiplication table × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | 38 | 40 | 42 | 44 | 46 | 48 | 50 | 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 | 48 | 51 | 54 | 57 | 60 | 63 | 66 | 69 | 72 | 75 | 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60 | 64 | 68 | 72 | 76 | 80 | 84 | 88 | 92 | 96 | 100 | 5 | 5 | 10 | 15 | 20 | **25** | 30 | 35 | 40 | 45 | **50** | 55 | 60 | 65 | 70 | **75** | 80 | 85 | 90 | 95 | **100** | 105 | 110 | 115 | 120 | 125 | 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 | 78 | 84 | 90 | 96 | 102 | 108 | 114 | 120 | 126 | 132 | 138 | 144 | 150 | 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 | 91 | 98 | 105 | 112 | 119 | 126 | 133 | 140 | 147 | 154 | 161 | 168 | 175 | 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 | 112 | 120 | 128 | 136 | 144 | 152 | 160 | 168 | 176 | 184 | 192 | 200 | 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 | 117 | 126 | 135 | 144 | 153 | 162 | 171 | 180 | 189 | 198 | 207 | 216 | 225 | 10 | 10 | 20 | 30 | 40 | **50** | 60 | 70 | 80 | 90 | **100** | 110 | 120 | 130 | 140 | **150** | 160 | 170 | 180 | 190 | **200** | 210 | 220 | 230 | 240 | 250 | 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 | 143 | 154 | 165 | 176 | 187 | 198 | 209 | 220 | 231 | 242 | 253 | 264 | 275 | 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 | 156 | 168 | 180 | 192 | 204 | 216 | 228 | 240 | 252 | 264 | 276 | 288 | 300 | 13 | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | 130 | 143 | 156 | 169 | 182 | 195 | 208 | 221 | 234 | 247 | 260 | 273 | 286 | 299 | 312 | 325 | 14 | 14 | 28 | 42 | 56 | 70 | 84 | 98 | 112 | 126 | 140 | 154 | 168 | 182 | 196 | 210 | 224 | 238 | 252 | 266 | 280 | 294 | 308 | 322 | 336 | 350 | 15 | 15 | 30 | 45 | 60 | **75** | 90 | 105 | 120 | 135 | **150** | 165 | 180 | 195 | 210 | **225** | 240 | 255 | 270 | 285 | **300** | 315 | 330 | 345 | 360 | 375 | 16 | 16 | 32 | 48 | 64 | 80 | 96 | 112 | 128 | 144 | 160 | 176 | 192 | 208 | 224 | 240 | 256 | 272 | 288 | 304 | 320 | 336 | 352 | 368 | 384 | 400 | 17 | 17 | 34 | 51 | 68 | 85 | 102 | 119 | 136 | 153 | 170 | 187 | 204 | 221 | 238 | 255 | 272 | 289 | 306 | 323 | 340 | 357 | 374 | 391 | 408 | 425 | 18 | 18 | 36 | 54 | 72 | 90 | 108 | 126 | 144 | 162 | 180 | 198 | 216 | 234 | 252 | 270 | 288 | 306 | 324 | 342 | 360 | 378 | 396 | 414 | 432 | 450 | 19 | 19 | 38 | 57 | 76 | 95 | 114 | 133 | 152 | 171 | 190 | 209 | 228 | 247 | 266 | 285 | 304 | 323 | 342 | 361 | 380 | 399 | 418 | 437 | 456 | 475 | 20 | 20 | 40 | 60 | 80 | **100** | 120 | 140 | 160 | 180 | **200** | 220 | 240 | 260 | 280 | **300** | 320 | 340 | 360 | 380 | **400** | 420 | 440 | 460 | 480 | 500 | 21 | 21 | 42 | 63 | 84 | 105 | 126 | 147 | 168 | 189 | 210 | 231 | 252 | 273 | 294 | 315 | 336 | 357 | 378 | 399 | 420 | 441 | 462 | 483 | 504 | 525 | 22 | 22 | 44 | 66 | 88 | 110 | 132 | 154 | 176 | 198 | 220 | 242 | 264 | 286 | 308 | 330 | 352 | 374 | 396 | 418 | 440 | 462 | 484 | 506 | 528 | 550 | 23 | 23 | 46 | 69 | 92 | 115 | 138 | 161 | 184 | 207 | 230 | 253 | 276 | 299 | 322 | 345 | 368 | 391 | 414 | 437 | 460 | 483 | 506 | 529 | 552 | 575 | 24 | 24 | 48 | 72 | 96 | 120 | 144 | 168 | 192 | 216 | 240 | 264 | 288 | 312 | 336 | 360 | 384 | 408 | 432 | 456 | 480 | 504 | 528 | 552 | 576 | 600 | 25 | 25 | 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 | 300 | 325 | 350 | 375 | 400 | 425 | 450 | 475 | 500 | 525 | 550 | 575 | 600 | 625 | | ## Number theory The term *arithmetic* is also used to refer to number theory. This includes the properties of integers related to primality, divisibility, and the solution of equations by integers, as well as modern research which is an outgrowth of this study. It is in this context that one runs across the fundamental theorem of arithmetic and arithmetic functions. *A Course in Arithmetic* by Serre reflects this usage, as do such phrases as *first order arithmetic* or *arithmetical algebraic geometry*. Number theory is also referred to as 'the higher arithmetic', as in the title of H. Davenport's book on the subject. Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...
In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. ...
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ...
In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. ...
In number theory, the fundamental theorem of arithmetic (or unique factorization theorem) states that every natural number either is itself a prime number, or can be written as a unique product of prime numbers. ...
In number theory and computability theory, subfields of mathematics, a number-theoretic function is any function whose domain is the set of natural numbers. ...
Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ...
Harold Davenport (30 October 1907 - 9 June 1969) was an English mathematician, known for his extensive work in number theory. ...
## Arithmetic in education Primary education in mathematics often places a strong focus on algorithms for the arithmetic of natural numbers, integers, rational numbers (vulgar fractions), and real numbers (using the decimal place-value system). This study is sometimes known as algorism. A primary school in ÄŒeskÃ½ TÄ›Å¡Ãn, Poland Primary education is the first stage of compulsory education. ...
In mathematics, a natural number can mean either an element of the set {1, 2, 3, ...} (i. ...
The integers are commonly denoted by the above symbol. ...
In mathematics, a rational number is a number which can be expressed as a ratio of two integers. ...
In arithmetic, a vulgar fraction (or common fraction) consists of one integer divided by a non-zero integer. ...
In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ...
For other uses, see Decimal (disambiguation). ...
Algorism comprises all of the rules of performing arithmetic computations using a decimal system for representing numbers in which numbers written using ten symbols having the values 0 through 9 are combined using a place-value system (positional notation), where each symbol has ten times the weight of the one...
The difficulty and unmotivated appearance of these algorithms has long led educators to question this curriculum, advocating the early teaching of more central and intuitive mathematical ideas. One notable movement in this direction was the New Math of the 1960s and '70s, which attempted to teach arithmetic in the spirit of axiomatic development from set theory, an echo of the prevailing trend in higher mathematics.^{[2]} New math is a term referring to a brief dramatic change in the way mathematics was taught in American grade schools during the 1960s. ...
Since the introduction of the electronic calculator, which can perform the algorithms far more efficiently than humans, an influential school of educators has argued that mechanical mastery of the standard arithmetic algorithms is no longer necessary. In their view, the first years of school mathematics could be more profitably spent on understanding higher-level ideas about what numbers are used for and relationships among number, quantity, measurement, and so on. However, most research mathematicians still consider mastery of the manual algorithms to be a necessary foundation for the study of algebra and computer science. This controversy was central to the "Math Wars" over California's primary school curriculum in the 1990s, and continues today.^{[3]} For other uses, see Calculator (disambiguation). ...
Many mathematics texts for K-12 instruction were developed, funded by grants from the United States National Science Foundation based on standards created by the NCTM and given high ratings by United States Department of Education, though condemned by many mathematicians. Some widely adopted texts such as TERC were based on the spirit of research papers which found that instruction of basic arithmetic was harmful to mathematical understanding. Rather than teaching any traditional method of arithemtic, teachers are instructed to instead guide students to invent their own (some critics claim inefficient) methods, instead using such techniques as skip counting, and the heavy use of manipulatives, scissors and paste, and even singing rather than multiplication tables or long division. Although such texts were designed to be a complete curricula, in the face of intense protest and criticism, many districts have chosen to circumvent the intent of such radical approaches by supplementing with traditional texts. Other districts have since adopted traditional mathematics texts and discarded such reform-based approaches as misguided failures. The logo of the National Science Foundation The National Science Foundation (NSF) is an independent United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. ...
The National Council of Teachers of Mathematics (NCTM) was founded in 1920. ...
Investigations in Number, Data, and Space is a complete K-5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts. ...
Skip counting is a mathematics technique taught in place of formal multiplication in standards-based mathematics textbooks such as TERC. Another similar method is coloring in squares in a 100s chart to show multiplication patterns. ...
Traditional mathematics is the term used for the style of mathematics instruction used for a period in the 20th century before the appearance of reform mathematics based on NCTM standards, so it is best defined by contrast with the alternatives. ...
## See also ### Lists Arithmetic is the oldest and simplest branch of mathematics, used by almost everyone. ...
These list of mathematical topics pages collect pointers to all articles related to mathematics. ...
### Related topics Addition of natural numbers is the most basic arithmetic operation. ...
The additive inverse, or opposite, of a number n is the number which, when added to n, yields zero. ...
In mathematics, associativity is a property that a binary operation can have. ...
A map or binary operation from a set to a set is said to be commutative if, (A common example in school-math is the + function: , thus the + function is commutative) Otherwise, the operation is noncommutative. ...
In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. ...
Elementary arithmetic is the most basic kind of mathematics: it concerns the operations of addition, subtraction, multiplication, and division. ...
Arithmetic in a finite field is different from standard integer arithmetic. ...
A number line, invented by John Wallis, is a one-dimensional picture in which the integers are shown as specially-marked points evenly spaced on a line. ...
This is a list of important publications in mathematics, organized by field. ...
The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...
In mathematics and statistics, the arithmetic mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. ...
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. ...
## Footnotes ## References - Cunnington, Susan. The story of arithmetic, a short history of its origin and development. Swan Sonnenschein, London, 1904.
- Dickson, Leonard Eugene. History of the theory of numbers. Three volumes. Reprints: Carnegie Institute of Washington, Washington, 1932. Chelsea, New York, 1952, 1966.
- Leonhard Euler,
*Elements of Algebra* Tarquin Press, 2007 - Fine, Henry Burchard (1858-1928). The number system of algebra treated theoretically and historically. Leach, Shewell & Sanborn, Boston, 1891.
- Karpinski, Louis Charles (1878-1956). The history of arithmetic. Rand McNally, Chicago, 1925. Reprint: Russell & Russell, New York, 1965.
- Ore, Øystein. Number theory and its history. McGraw-Hill, New York, 1948.
- Weil, Andre. Number theory: an approach through history. Birkhauser, Boston, 1984. Reviewed: Math. Rev. 85c:01004.
Louis Charles Karpinski (1878â€“1956) was an American mathematician born in Rochester, N. Y. and educated at Cornell and in Europe at Strassburg. ...
## External links |