A number that appears as a ratio of any two integers is called a rational number.

The integers are often appeared in antecedent and consequent positions of the ratio in some cases. The ratio of them is also a number and it is called as a rational number.

$\dfrac{1}{4}$, $\dfrac{-7}{2}$, $\dfrac{0}{8}$, $\dfrac{11}{8}$, $\dfrac{15}{5}$, $\dfrac{14}{-7}$, $\cdots$

The rational numbers are mainly used to represent the fractions in mathematical form.

There are two rules for forming the rational numbers by the integers.

- The antecedent can be any integer.
- The consequent should be a non-zero integer.

$10$ and $2$ are two integers and find the ratio of $10$ to $2$ by the division.

$Ratio \,=\, \dfrac{10}{2}$

It is a rational number basically and now, find their quotient.

$\implies$ $\dfrac{10}{2}$ $\,=\,$ $5$

It proves that a rational number can be an integer but an integer may not always be a rational number.

The heights of a boy and his sister are $150 \, cm$ and $100 \, cm$ respectively.

Calculate the ratio of boy’s height to his sister’s height.

$Ratio \,=\, \dfrac{150}{100}$

$\implies$ $\require{cancel} Ratio \,=\, \dfrac{\cancel{150}}{\cancel{100}}$

$\implies$ $\require{cancel} Ratio \,=\, \dfrac{3}{2}$

Similarly, calculate the ratio of girl’s height to her brother’s height.

$Ratio \,=\, \dfrac{100}{150}$

$\implies$ $\require{cancel} Ratio \,=\, \dfrac{\cancel{100}}{\cancel{150}}$

$\implies$ $\require{cancel} Ratio \,=\, \dfrac{2}{3}$

$\dfrac{2}{3}$ and $\dfrac{3}{2}$ are two ratios but $2$ and $3$ are integers. So, if any two integers are expressed in ratio form, then they are called the rational numbers. Therefore, $\dfrac{2}{3}$ and $\dfrac{3}{2}$ are called as the rational numbers.

The collection of all rational numbers can be represented as a set and denoted by $Q$, which is a first letter of the “Quotient”. The rational numbers are infinite. So, the set of rational numbers is called as an infinite set.

$Q$ $\,=\,$ $\Big\{\cdots, -2, \dfrac{-9}{7}, -1, \dfrac{-1}{2}, 0, \dfrac{3}{4}, 1, \dfrac{7}{6}, 2, \cdots\Big\}$

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved