Fraction (mathematics)

A fraction represents a part of a whole or, more 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 consists of an integer numerator displayed above a line, a non-zero integer denominator, displayed below that line. Numerators and denominators are used in fractions that are not common, including compound fractions, complex fractions, mixed numerals. We begin with positive common fractions, where the denominator are natural numbers; the numerator represents a number of equal parts, the denominator indicates how many of those parts make up a unit or a whole. The denominator can not be zero. For example, in the fraction 3/4, the numerator, 3, tells us that the fraction represents 3 equal parts, the denominator, 4, tells us that 4 parts make up a whole; the picture to the right illustrates 3⁄4 of a cake. A common fraction is a numeral; that same number can be represented as a decimal, a percent, or with a negative exponent.

For example, 0.01, 1%, 10−2 all equal the fraction 1/100. An integer such as the number 7 can be thought of as having an implicit denominator of one: 7 equals 7/1. Other uses for fractions are to represent ratios and division, thus the fraction 3/4 is used to represent the ratio 3:4 and the division 3 ÷ 4. The non-zero denominator in the case using a fraction to represent division is an example of the rule that division by zero is undefined. We can write negative fractions, which represent the opposite of a positive fraction. For example, if 1/2 represents a half dollar profit −1/2 represents a half dollar loss; because of the rules of division of signed numbers, which require that, for example, negative divided by positive is negative, −1/2, -1/2 and 1/-2, all represent the same fraction, negative one-half. Because a negative divided by a negative produces a positive, -1/-2 represents positive one-half. In mathematics the set of all numbers that can be expressed in the form a/b, where a and b are integers and b is not zero, is called the set of rational numbers and is represented by the symbol Q, which stands for quotient.

The test for a number being a rational number is. However, the word fraction is used to describe mathematical expressions that are not rational numbers, for example algebraic fractions, expressions that contain irrational numbers, such as √2/2 and π/4. In a fraction, the number of equal parts being described is the numerator, the type or variety of the parts is the denominator; as an example, the fraction ​8⁄5 amounts to eight parts, each of, of the type named "fifth". In terms of division, the numerator corresponds to the dividend, the denominator corresponds to the divisor. Informally, the numerator and denominator may be distinguished by placement alone but in formal contexts they are separated by a fraction bar; the fraction bar may be oblique, or diagonal. These marks are known as the horizontal bar. In typography, fractions stacked vertically are known as "en" or "nut fractions", diagonal ones as "em" or "mutton fractions", based on whether a fraction with a single-digit numerator and denominator occupies the proportion of a narrow en square, or a wider em square.

In traditional typefounding, a piece of type bearing a complete fraction was known as a "case fraction," while those representing only part of fraction were called "piece fractions." The denominators of English fractions are expressed as ordinal numbers, in the plural if the numerator is not one. Exceptions include the denominator 2, always read "half" or "halves", the denominator 4, which may be alternatively expressed as "quarter"/"quarters" or as "fourth"/"fourths", the denominator 100, which may be alternatively expressed as "hundredth"/"hundredths" or "percent"; when the denominator is 1, it may be expressed in terms of "wholes" but is more ignored, with the numerator read out as a whole number. When the numerator is one, it may be omitted; the entire fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. Fractions should always be hyphenated. Alternatively, a fraction may be described by reading it out as the numerator "over" the denominator, with the denominator expressed as a cardinal number.

The term "over" is used in the case of solidus fractions, where the numbers are placed left and right of a slash mark. (For example, 1/

Borodino, Krasnoyarsk Krai

Borodino is a town in Krasnoyarsk Krai, located 186 kilometers northeast of Krasnoyarsk, the administrative center of the krai. Population: 17,416 , it was founded in 1949 as a coal miners' settlement. Town status was granted to it in 1981. Within the framework of administrative divisions, it is incorporated as the krai town of Borodino—an administrative unit with the status equal to that of the districts; as a municipal division, the krai town of Borodino is incorporated as Borodino Urban Okrug. Законодательное собрание Красноярского края. Закон №10-4765 от 10 июня 2010 г. «О перечне административно-территориальных единиц и территориальных единиц Красноярского края», в ред. Закона №7-3007 от 16 декабря 2014 г. «Об изменении административно-территориального устройства Большеулуйского района и о внесении изменений в Закон края "О перечне административно-территориальных единиц и территориальных единиц Красноярского края"». Вступил в силу 1 июля 2010 г. Опубликован: "Ведомости высших органов государственной власти Красноярского края", №33, 5 июля 2010 г..

Законодательное собрание Красноярского края. Закон №12-2507 от 12 ноября 2004 г. «Об установлении границ муниципального образования город Бородино и о наделении его статусом городского округа», в ред. Закона №7-2267 от 30 октября 2008 г «О внесении изменений в Закон края "Об установлении границ муниципального образования город Бородино и о наделении его статусом городского округа"». Вступил в силу через десять дней после официального опубликования. Опубликован: "Ведомости высших органов государственной власти Красноярского края", №32, 29 ноября 2004 г

Howard County, Iowa

Howard County is a county located in the US state of Iowa. As of the 2010 census, the population was 9,566; the county seat is Cresco. The county was founded in 1851. According to the U. S. Census Bureau, the county has a total area of 474 square miles, of which 473 square miles is land and 0.4 square miles is water. U. S. Highway 63 Iowa Highway 9 Iowa Highway 139 Mower County, Minnesota Fillmore County, Minnesota Winnesheik County Chickasaw County Mitchell County Floyd County The 2010 census recorded a population of 9,566 in the county, with a population density of 20.207/sq mi. There were 4,367 housing units. At the 2000 census, there were 9,932 people, 3,974 households and 2,650 families residing in the county; the population density was 21 per square mile. There were 4,327 housing units at an average density of 9 per square mile; the racial makeup of the county was 99.06% White, 0.11% Black or African American, 0.15% Native American, 0.17% Asian, 0.08% from other races, 0.42% from two or more races.

0.55% of the population were Hispanic or Latino of any race. There were 3,974 households of which 31.1% had children under the age of 18 living with them, 56.8% were married couples living together, 6.6% had a female householder with no husband present, 33.3% were non-families. 29.5% of all households were made up of individuals and 15.6% had someone living alone, 65 years of age or older. The average household size was 2.43 and the average family size was 3.03. 26.30% of the population were under the age of 18, 6.8% from 18 to 24, 25.4% from 25 to 44, 21.3% from 45 to 64, 20.1% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 97.0 males. For every 100 females age 18 and over, there were 96.3 males. The median household income was $34,641 and the median family income was $43,284. Males had a median income of $28,856 compared $21,367 for females; the per capita income for the county was $17,842. About 5.6% of families and 9.3% of the population were below the poverty line, including 8.7% of those under age 18 and 8.8% of those age 65 or over.

The Mighty Howard County Fair is held annually in the last full week of June. This celebration originated in 1858, three fairs were celebrated before being interrupted by the American Civil War, they resumed from 1866 through 1899, were resumed in 1923 under aegis of the present directorship. The population ranking of the following table is based on the 2010 census of Howard County.† county seat Norman Borlaug - Nobel Peace Prize winner, raised and went to school in the county. National Register of Historic Places listings in Howard County, Iowa Howard County Development Commission's website Howard County Government Website