Rational number

In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠

          p
          q
        
      
    
  

{\displaystyle {\tfrac {p}{q}}}

⁠ of two integers, a numerator p and a non-zero denominator q. For example, ⁠

          3
          7
        
      
    
  

{\displaystyle {\tfrac {3}{7}}}

⁠ is a rational number, as is every integer (for example,

    −
    5
    =
    
      
        
          
            −
            5
          
          1
        
      
    
  

{\displaystyle -5={\tfrac {-5}{1}}}

). The set of all rational numbers is often referred to as "the rationals", and is closed under addition, subtraction, multiplication, and division by a nonzero rational number.

Extends: [Elementary mathematics](https://wikipedia.org.ai/Elementary mathematics), Field (mathematics), Fractions (mathematics), [Rational numbers](https://wikipedia.org.ai/Rational numbers), [Sets of real numbers](https://wikipedia.org.ai/Sets of real numbers)