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Quotition And Partition
In arithmetic, quotition and partition are two ways of viewing fractions and division. In quotitive division one asks "how many parts are there?" while in partitive division one asks "what is the size of each part?" In general, a quotient Q = N / D, where , , and are integers or rational numbers, can be conceived of in either of 2 ways: # Quotition: "How many parts of size must be added to get a sum of ?" N = Q \times D = \underbrace_. # Partition: "What is the size of each of equal parts whose sum is ?" N = D \times Q = \underbrace_. For example, the quotient 6 / 2 = 3 can be conceived of as representing either of the decompositions: 6 = \underbrace_ = \underbrace_. In the rational number system used in elementary mathematics, the numerical answer is always the same no matter which way you put it, as a consequence of the commutativity of multiplication. Quotition Thought of quotitively, a division problem can be solved by repeatedly subtracting groups of the size ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measurement
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International Vocabulary of Metrology (VIM) published by the International Bureau of Weights and Measures (BIPM). However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales. Measurement is a cornerstone of trade, science, technology and quantitative research in many disciplines. Historically, many measurement syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (for example, The set of all rational numbers is often referred to as "the rationals", and is closed under addition, subtraction, multiplication, and division by a nonzero rational number. It is a field under these operations and therefore also called the field of rationals or the field of rational numbers. It is usually denoted by boldface , or blackboard bold A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: ), or eventually begins to repeat the same finite sequence of digits over and over (example: ). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see ). A real n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integers
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ratio
In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be Positive integer, positive. A ratio may be specified either by giving both constituting numbers, written as "''a'' to ''b''" or "''a'':''b''", or by giving just the value of their quotient Equal quotients correspond to equal ratios. A statement expressing the equality of two ratios is called a ''proportion''. Consequently, a ratio may be considered as an ordered pair of numbers, a Fraction (mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Partition Topics
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are * partition of a set or an ordered partition of a set, * partition of a graph, * partition of an integer, * partition of an interval, * partition of unity, * partition of a matrix; see block matrix, and * partition of the sum of squares in statistics problems, especially in the analysis of variance, * quotition and partition, two ways of viewing the operation of division of integers. Integer partitions * Composition (combinatorics) * Ewens's sampling formula * Ferrers graph * Glaisher's theorem * Landau's function * Partition function (number theory) * Pentagonal number theorem * Plane partition * Quotition and partition * Rank of a partition ** Crank of a partition * Solid partition * Young tableau * Young's lattice Set partitions {{main, Partition of a set * Bell number * Bell polynomials ** Dobinski's formula * Cumu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Card Player
Card players are those participating in a card game. Various names are given to card players based on their role or position. Position Games of Anglo-American origin In games of Anglo-American origin played in English-speaking countries, age refers to the order of priority in which players make the first lead, bid or bet, based on their position at the table.''The Language of Cards'' at www.parlettgames.uk. Retrieved 4 August 2018 This changes constantly as the dealer rotates either clockwise or anticlockwise around the table. They are traditionally referred to as follows: ; Eldest hand (or elder hand): the player who enjoys greatest priority and e.g. is the first to receive cards in the deal. Elder is the non-dealer in two-hand games. ; Youngest hand (or younger hand): the player who has the lowest p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Of Measurement
A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity. The metre (symbol m) is a unit of length that represents a definite predetermined length. For instance, when referencing "10 metres" (or 10 m), what is actually meant is 10 times the definite predetermined length called "metre". The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to the present. A multitude of System of measurement, systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system. In trade, weights and measures are often a su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rounding
Rounding or rounding off is the process of adjusting a number to an approximate, more convenient value, often with a shorter or simpler representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression √2 with . Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid false precision, misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as but is known to be accuracy and precision, accurate only to within a few hundred units is usually better stated as "about ". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fraction
A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A ''common'', ''vulgar'', or ''simple'' fraction (examples: and ) consists of an integer numerator, displayed above a line (or before a slash like ), and a division by zero, non-zero integer denominator, displayed below (or after) that line. If these integers are positive, then the numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction , the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates of a cake. Fractions can be used to represent ratios and division (mathematics), division. Thus the fraction can be used to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Remainder
In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient ( integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The ''modulo operation'' is the operation that produces such a remainder when given a dividend and divisor. Alternatively, a remainder is also what is left after subtracting one number from another, although this is more precisely called the '' difference''. This usage can be found in some elementary textbooks; colloquially it is replaced by the expression "the rest" as in "Give me two dollars back and keep the rest." However, the term "remainder" is still used in this sense when a function is approximated by a series expansion, where the error expression ("the rest") is referred to as the remainder term. Integer division Gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathematics), product''. Multiplication is often denoted by the cross symbol, , by the mid-line dot operator, , by juxtaposition, or, in programming languages, by an asterisk, . The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''; both numbers can be referred to as ''factors''. This is to be distinguished from term (arithmetic), ''terms'', which are added. :a\times b = \underbrace_ . Whether the first factor is the multiplier or the multiplicand may be ambiguous or depend upon context. For example, the expression 3 \times 4 , can be phrased as "3 ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
