Fractions, theory: rational numbers

Fractions and rational numbers Q

The connection between fractions and rational numbers Q

  • All these fractions: 3/4, 6/8, 9/12, ... 27/36, ... that are set by reducing (or by expanding), are equivalent fractions, ie they represent the same quantity, the unique rational number:
  • 3/4 = 3 ÷ 4 = 0.75.
  • 3/4 has a double meaning: it represents a fraction and a rational number, that is, it represents all fractions calculated out of 3/4 by expanding it, but at the same time it is equal to the rational number 0.75.
  • The fractions with 1 as a denominator and those calculated by expanding them are also contained in the set of the rational numbers; for example:
  • 31 = 6/2 = 9/3 = ... = 27/9 = ... They can be substituted for each other, being equivalent.
  • The integer 0 can be substituted for by an infinite number of fractions having 0 as a numerator:
  • 0/1 = 0/2 = 0/3 = ... 0/125 = ...
  • The denominator 0 is excluded. There cannot be a fraction such us:
  • 0/0 or 9/0 or 200/0...

A rational number has no predecessor and no unique successor.

  • Between two rational numbers r1 and r2 there is an infinite number of rational numbers r:
  • r1 < r < r2 or r1 > r > r2;

More on ordinary (common) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers