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A fraction (from (ラテン語:fractus), "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 17/3) consists of an integer numerator, displayed above a line (or before a slash), and a non-zero integer denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not ''common'', including compound fractions, complex fractions, and mixed numerals. The numerator represents a number of equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole. The picture to the right illustrates or 3/4 of a cake. Fractional numbers can also be written without using explicit numerators or denominators, by using decimals, percent signs, or negative exponents (as in 0.01, 1%, and 10−2 respectively, all of which are equivalent to 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 to represent division.〔H. Wu, ''The Mis-Education of Mathematics Teachers'', Notices of the American Mathematical Society, Volume 58, Issue 03 (March 2011), (page 374 ) 〕 Thus the fraction 3/4 is also used to represent the ratio 3:4 (the ratio of the part to the whole) and the division 3 ÷ 4 (three divided by four). In mathematics the set of all numbers which 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 that it can be written in that form (i.e., as a common fraction). However, the word ''fraction'' is also used to describe mathematical expressions that are not rational numbers, for example algebraic fractions (quotients of algebraic expressions), and expressions that contain irrational numbers, such as √2/2 (see square root of 2) and π/4 (see proof that π is irrational). ==Vocabulary== When reading fractions it is customary in English to pronounce the denominator using the corresponding ordinal number, in plural if the numerator is not one, as in "fifths" for fractions with a 5 in the denominator. Thus, 3/5 is rendered as ''three fifths'' and 5/32 as ''five thirty-seconds''. This generally applies to whole number denominators greater than 2, though large denominators that are not powers of ten are often rendered using the cardinal number. Thus, 5/123 might be rendered as "five one-hundred-twenty-thirds", but is often "five ''over'' one hundred twenty-three". In contrast, because one million is a power of ten, 6/1,000,000 is usually expressed as "six millionths" or "six one-millionths", rather than as "six ''over'' one million". The denominators 1, 2, and 4 are special cases. The fraction 3/1 may be spoken of as ''three wholes''. The denominator 2 is expressed as ''half'' (plural ''halves''); "−" is ''minus three-halves'' or ''negative three-halves''. The fraction 3/4 may be either "three fourths" or "three quarters". Furthermore, since most fractions in prose function as adjectives, the fractional modifier is hyphenated. This is evident in standard prose in which one might write about "every two-tenths of a mile", "the quarter-mile run", or the Three-Fifths Compromise. When the fraction's numerator is 1, then the word ''one'' may be omitted, such as "every tenth of a second" or "during the final quarter of the year". In the examples 2/5 and 7/3, the slanting line is called a solidus or forward slash. In the examples and , the horizontal line is called a "fraction bar". When the solidus is encountered in a fraction, a speaker will sometimes parse it by pronouncing it ''over'' as in the examples above. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fraction (mathematics)」の詳細全文を読む スポンサード リンク
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