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Multiple (mathematics)
In mathematics, a multiple is the Product (mathematics), product of any quantity and an integer. In other words, for the quantities ''a'' and ''b'', it can be said that ''b'' is a multiple of ''a'' if ''b'' = ''na'' for some integer ''n'', which is called the Multiplication, multiplier. If ''a'' is not zero, this is equivalent to saying that b/a is an integer. When ''a'' and ''b'' are both integers, and ''b'' is a multiple of ''a'', then ''a'' is called a ''divisor'' of ''b''. One says also that ''a'' divides ''b''. If ''a'' and ''b'' are not integers, mathematicians prefer generally to use integer multiple instead of ''multiple'', for clarification. In fact, ''multiple'' is used for other kinds of product; for example, a polynomial ''p'' is a multiple of another polynomial ''q'' if there exists third polynomial ''r'' such that ''p'' = ''qr''. Examples 14, 49, −21 and 0 are multiples of 7, whereas 3 and −6 are not. This is because there are integers that 7 may be multiplied by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prefix
A prefix is an affix which is placed before the stem of a word. Particularly in the study of languages, a prefix is also called a preformative, because it alters the form of the word to which it is affixed. Prefixes, like other affixes, can be either inflectional, creating a new form of a word with the same basic meaning and same lexical category, or derivational, creating a new word with a new semantic meaning and sometimes also a different lexical category. Prefixes, like all affixes, are usually bound morphemes. English has no inflectional prefixes, using only suffixes for that purpose. Adding a prefix to the beginning of an English word changes it to a different word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy''. The word ''prefix'' is itself made up of the stem ''fix'' (meaning "attach", in this case), and the prefix ''pre-'' (meaning "before"), both of which are derived from Latin roots. English language ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplier (linguistics)
In linguistics, more precisely in traditional grammar, a multiplier is a word that counts how many times its object should be multiplied, such as ''single'' or ''double''. They are contrasted with distributive numbers. In English, this part of speech is relatively marginal, and less recognized than cardinal numbers and ordinal numbers. English In English native multipliers exist, formed by the suffix ''-fold'', as in ''onefold'', ''twofold'', ''threefold''. However, these have largely been replaced by ''single'', ''double'', and ''triple'', which are of Latin origin, via French. They have a corresponding distributive number formed by suffixing ''-y'' (reduction of Middle English ''-lely'' > ''-ly''), as in ''singly''. However, the series is primarily used for the first few numbers; ''quadruple'' and ''quintuple'' are less common, and ''hextuple'' and above are quite rare. For larger multiples a cardinal number and a counter are used instead, such as "five portions" or "a porti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SI Prefix
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The SI system is coordinated by the International Bureau of Weights and Measures, which is abbreviated BIPM from . The SI comprises a coherent system of units of measurement starting with seven base units, which are the second (symbol s, the unit of time), metre (m, length), kilogram (kg, mass), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (mol, amount of substance), and candela (cd, luminous intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always be represented as products of powers of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A decimal numeral (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (ring Theory)
In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group. Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. However, in other rings, the ideals may not correspond directly to the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Fraction
A unit fraction is a positive fraction with one as its numerator, 1/. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc. When an object is divided into equal parts, each part is a unit fraction of the whole. Multiplying two unit fractions produces another unit fraction, but other arithmetic operations do not preserve unit fractions. In modular arithmetic, unit fractions can be converted into equivalent whole numbers, allowing modular division to be transformed into multiplication. Every rational number can be represented as a sum of distinct unit fractions; these representations are called Egyptian fractions based on their use in ancient Egyptian mathematics. Many infinite sums of unit fractions are meaningful mathematically. In geometry, unit fractions can be used to characterize the curvature of triangle groups and the tangencies of Ford circles. Unit fractions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yard (unit)
The yard (symbol: yd) is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches. Since 1959 it has been by international agreement standardized as exactly 0.9144 meter. A distance of 1,760 yards is equal to 1 mile. The theoretical US survey yard is very slightly longer. Name The term, ''yard'' derives from the Old English , etc., which was used for branches, staves and measuring rods. It is first attested in the late 7th century laws of Ine of Wessex, wherein the "yard of land" mentioned is the yardland, an old English unit of tax assessment equal to hide. Around the same time the Lindisfarne Gospels account of the messengers from John the Baptist in the Gospel of Matthew used it for a branch swayed by the wind. In addition to the yardland, Old and Middle English both used their forms of "yard" to denote the surveying lengths of or , used in computing acres, a dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foot (unit)
The foot (standard symbol: ft) is a Units of measurement, unit of length in the imperial units, British imperial and United States customary units, United States customary systems of metrology, measurement. The prime (symbol), prime symbol, , is commonly used to represent the foot. In both customary and imperial units, one foot comprises 12 inches, and one yard comprises three feet. Since international yard and pound, an international agreement in 1959, the foot is defined as equal to exactly 0.3048 meters. Historically, the "foot" was a part of many local systems of units, including the Ancient Greek units of measurement, Greek, Ancient Roman units of measurement, Roman, Chinese units of measurement, Chinese, Units of measurement in France before the French Revolution, French, and English units, English systems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between 250 mm and 335 mm and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inch
The inch (symbol: in or prime (symbol), ) is a Units of measurement, unit of length in the imperial units, British Imperial and the United States customary units, United States customary System of measurement, systems of measurement. It is equal to yard or of a foot (unit), foot. Derived from the Uncia (unit), Roman uncia ("twelfth"), the word ''inch'' is also sometimes used to translate similar units in other measurement systems, anthropic units, usually understood as deriving from the width of the human thumb. Standards for the exact length of an inch have varied in the past, but since the adoption of the international yard during the 1950s and 1960s the inch has been based on the metric system and defined as exactly 25.4Millimetre, mm. Name The English word "inch" () was an early borrowing from Latin ' ("one-twelfth; Roman inch; Roman ounce"). The vowel change from Latin to Old English (which became Modern English ) is known as Germanic umlaut, umlaut. The consonant c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metre
The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of a second, where the second is defined by a hyperfine transition frequency of caesium. The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately . In 1799, the metre was redefined in terms of a prototype metre bar. The bar used was changed in 1889, and in 1960 the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length. From 1983 until 2019, the metre was formally defined as the length of the pat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Millimetre
330px, Different lengths as in respect of the electromagnetic spectrum, measured by the metre and its derived scales. The microwave is between 1 metre to 1 millimetre. The millimetre (American and British English spelling differences#-re, -er, international spelling; International System of Units, SI unit symbol mm) or millimeter (American and British English spelling differences#-re, -er, American spelling) is a Units of measurement, unit of length in the International System of Units (SI), equal to one thousandth of a metre, which is the SI base unit of length. Therefore, there are one thousand millimetres in a metre, and there are ten millimetres in a centimetre. One millimetre is equal to micrometres or nanometres. Since an inch is officially defined as exactly 25.4 millimetres, a millimetre is equal to exactly (≈ 0.03937) of an inch. Definition Since 1983, the metre has been defined as "the length of the path travelled by light in vacuum during a time interval of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
