 Rational number

A rational number is a quotient $a/b$ of integers with $b\ne 0$. The numerator $a$ can be negative or zero; the denominator $b$ can be chosen positive by transferring its sign to $a$. For example, $-6/8=-3/4$ and $0/7=0$.

Different fractions describe the same rational number exactly when cross multiplication gives $ad=bc$. Dividing the entries by their greatest common divisor produces the unique reduced fraction with positive denominator, including $0/1$ for zero.

The rational numbers form a field: addition, subtraction, multiplication and division by a nonzero rational number remain rational. They are dense in the real line, by density of the rational numbers, although they do not fill it: the square root of two is an irrational number.

A rational number is any number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \) is not equal to zero. In other words, rational numbers include integers, finite decimals, and repeating decimals. For example: - The number \( \frac{1}{2} \) is a rational number.