Fraction

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: ${\displaystyle {\tfrac {1}{2}}}$ and ${\displaystyle {\tfrac {17}{3}}}$) consists of an integer numerator, displayed above a line (or before a slash like 1⁄2), and a non-zero integer denominator, displayed below (or after) that line. If these integers are positive, then the numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates 3/4 of a cake.

Other uses for fractions are to represent ratios and division.^[1] Thus the fraction 3/4 can also be used to represent the ratio 3:4 (the ratio of the part to the whole), and the division 3 ÷ 4 (three divided by four).

We can also write negative fractions, which represent the opposite of a positive fraction. For example, if 1/2 represents a half-dollar profit, then −1/2 represents a half-dollar loss. Because of the rules of division of signed numbers (which states in part that negative divided by positive is negative), −1/2, −1/2 and 1/−2 all represent the same fraction – negative one-half. And because a negative divided by a negative produces a positive, −1/−2 represents positive one-half.

In mathematics a rational number is a number that can be represented by a fraction of the form a/b, where a and b are integers and b is not zero; the set of all rational numbers is commonly represented by the symbol Q or ${\displaystyle \mathbb {Q} }$, which stands for quotient. The term fraction and the notation a/b can also be used for mathematical expressions that do not represent a rational number (for example ${\displaystyle \textstyle {\frac {\sqrt {2}}{2}}}$), and even do not represent any number (for example the rational fraction ${\displaystyle \textstyle {\frac {1}{x}}}$).