section_path: Forms of fractions/Reciprocals and the "invisible denominator"
section_name: Reciprocals and the "invisible denominator"
paragraph_text: Reciprocals and the "invisible denominator"
  
  The reciprocal of a fraction is another fraction with the numerator and denominator exchanged. The reciprocal of 3 / 7, for instance, is 7 / 3. The product of a fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1 (that is, numerator and denominator are not equal) is a proper fraction.
  
  When the numerator and denominator of a fraction are equal (for example, 7 / 7), its value is 1, and the fraction therefore is improper. Its reciprocal is identical and hence also equal to 1 and improper.
  
  Any integer can be written as a fraction with the number one as denominator. For example, 17 can be written as 17 / 1, where 1 is sometimes referred to as the invisible denominator. Therefore, every fraction or integer, except for zero, has a reciprocal. For example, the reciprocal of 17 is 1 / 17.