Fraction (mathematics)

In mathematics, a fraction is a concept used to convey a proportional relation between a part and the whole. It consists of a numerator (an integer - the part) and a denominator (a natural number - the whole). For instance, the fraction $\scriptstyle {\frac {3}{5}}$ can represent three equal parts of a whole object, if the object is divided into five equal parts. A fraction with equal numerator and denominator is equal to one (e.g., $\scriptstyle {\frac {5}{5}}=1$). We can represent all rational numbers with fractions.

Fractions are a special case of ratios. For instance, $\scriptstyle {\frac {e}{\pi }}$ is a valid ratio, but it is not a fraction since we cannot compute an equivalent fraction with integer numerator and integer denominator.

Since we can compute the quotient from a fraction, we can represent any fraction with a decimal number (e.g., $\scriptstyle {\frac {3}{5}}=0.6$). However, because the division by zero is undefined, zero should never be the denominator of a fraction.

Due to tradition and conventions, there are at least two ways to write a fraction. The numerator and the denominator may be separated by a slash (a slanted line : 3/4), or by a vinculum (an horizontal line : $\scriptstyle {\frac {3}{4}}$).