The set of numbers obtained from the quotient of

*a*and*b*where*a*and*b*are integers and*b*is not equal to 0.### Symbol

The set of rational numbers is denoted by the symbol \(\mathbb{Q}\).

- The set of positive rational numbers : \(\mathbb{Q}\)\(_{+}\) = {
*x*∈ \(\mathbb{Q}\) |*x*≥ 0} - The set of negative rational numbers : \(\mathbb{Q}\)\(_{–}\) = {
*x*∈ \(\mathbb{Q}\) |*x*≤ 0} - The set of strictly positive rational numbers : \(\mathbb{Q}\)\(_{+}^{*}\) = {
*x*∈ \(\mathbb{Q}\) |*x*> 0} - The set of strictly negative rational numbers : \(\mathbb{Q}\)\(_{–}^{*}\) = {
*x*∈ \(\mathbb{Q}\) |*x*< 0}

All natural numbers, integers and decimals are rational numbers.

### Examples

The following numbers are rational numbers :

- \(\frac{3}{4}\)
- –\(\frac{1}{3}\)
- 5
- –7