In mathematics, a fraction (from the Latin fractus, broken) is a way of expressing a number of equal parts. A fraction consists of two numbers, a numerator which gives the number of equal parts and a denominator which gives the number of those parts that make up a whole. For example, the fraction 3⁄4 could be used to represent three equal parts of a cake, where the whole cake is divided into four equal parts.
A fraction is a quotient of numbers, the quantity obtained when the numerator is divided by the denominator. Thus 3⁄4 represents three divided by four, in decimals 0.75, in percents 75%. The three equal parts of the cake are 75% of the whole cake.
Historically, any number that did not represent a whole was called a "fraction". The numbers that we now call "decimals" were originally called "decimal fractions"; the numbers we now call "fractions" were called "vulgar fractions", the word "vulgar" meaning "commonplace".
The numerator and denominator of a fraction may be separated by a slanting line called a solidus or slash, for example 3⁄4, or may be written above and below a horizontal line called a vinculum, thus:
The solidus may be omitted from the slanting style (e.g. 34) where space is short and the meaning is obvious from context, for example in road signs in some countries.
Fractions are used most often when the denominator is small. For example, it is much easier to multiply 15 by 1⁄3 than it is to multiply 15 by a decimal approximation of one third. To change a fraction to a decimal, divide the numerator by the denominator, and round off to the desired accuracy.
The word is also used in related expressions, such as continued fraction and algebraic fraction — see Special cases below.