Rational Numbers (Advanced)
The rational numbers are those numbers which can be expressed as a ratio between two integers. For example, the fractions and are both rational numbers. All the integers are included in the rational numbers, since any integer can be written as the ratio .
Numbers which cannot be written as a ratio of integers are called irrational .
The set of rational numbers is closed under all four basic operations: that is, given any two rational numbers, their sum, difference, product, and quotient is also a rational number (as long as we don't divide by .)
The Venn diagram below shows the relationships of the various sets of numbers.