Fraction (mathematics)
A fraction (from Latin: 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: \tfrac{1}{2} 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 \tfrac{3}{4} 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.
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).
See also
External links
- [ ] @ Wikipedia
