# Rational Numbers

We all know that real number is something which exists in nature as real. Rational number is a part of it. Rational number is all about expressing the numbers in Fractions or Decimals. Let us study more about it in this section.

## What is a Rational Number?

Rational Numbers are those numbers which can be represented in the form of form. We generally use q to represent rational numbers in mathematical world.

Characteristics of Rational Numbers:

1. All the rational numbers are subset of Real Numbers or we can say all rational numbers lie in real line.
2. Countless rational numbers lie between two rational numbers.
3. There can be infinite numbers of rational numbers between two integers.
4. Any Integer can be represented as rational number.
5. Rational numbers are countable numbers as we can easily count them.

Rational numbers are very densely populated as mentioned above that there can be infinite rational number between two integers. We can also find many rational numbers between two numbers. We can also perform various Operations on Rational Numbers like addition, subtraction, division and multiplication can also be done.

## Rational Number Properties:

Let us consider rational number p,q and r . The law holds good if it is true for addition and multiplication.

Associative law for rational numbers :
Additive law : (p + q) + r = p + (q + r)

Multiplicative law : (p * q) * r = p * (q * r).

Commutative law for rational numbers :
Additive law : p + q = q + p

Multiplicative law : p * q = q * p

Identity for rational numbers:
0 is the additive identity for rational numbers

i.e., p + 0 = p and

1 is the multiplication identity for rational numbers

i.e., p * 1 = p.

## What is a Rational Number

The Rational Numbers are those numbers which can either be whole numbers or Fractions or Decimals. Rational numbers are the Subsets of Real Numbers and can be written as a Ratio of two integers in the form $\frac{p}{q}$ where 'p' and 'q' are integers and 'q' is non zero.
A Set of rational numbers is denoted by capital Q. The rational numbers are contrasted ...Read More

## Rational Inequalities

Inequalities are something where Functions are compared involving sign of inequality. These points can be represented in the number line. The inequality is represented as <,>,$\leq$ and $\geq$.
Consider a rarional function f(x) = $\frac{p}{q}$, where p and q are integers and q $\neq$ 0 is said to be function of rational inequality iff

f(x) < 0
or
f(x) > 0

## Introduction to Rational numbers

Initially we only had the family of Natural Numbers. After the invention of the family changed into the family of Whole numbers. Then, after the invention of negative numbers the family became the family of Integers. So now the number line is as,

-$\infty$.……..-3,-2,-1,0,1,2,3,…….+$\infty$

## Positive Rational Numbers

Positive Rational Numbers can be expressed as the ratio $\frac{p}{q}$ where, 'p' and 'q' are both Positive integers. Any positive rational number can be expressed as a sum of distinct Reciprocals of positive integers.

e.g $\frac{13}{18}$ = $\frac{1}{3}$ + $\frac{2}{6}$ + $\frac{1}{18}$

A rational number is simply a number that can b...Read More

## Negative Rational Numbers

Negative Rational Numbers can be expressed as the ratio $\frac{p}{q}$, where either 'p' or 'q' should be a Negative integer. Any negative rational number can be expressed as a sum of distinct Reciprocals of negative integers or the sum of distinct Reciprocals of both positive and negative integer provided the negative integer should be of least value compared wi...Read More

## Properties of Rational Numbers

Rational numbers are terminating or recurring decimal numbers written in the form of fraction $\frac{p}{q}$ in which 'p' and 'q' are integers and the denominator 'q' not equal to zero.

## Operations on Rational Numbers

Rational numbers are terminating or recurring decimal numbers written in the form of fraction    $\frac{a}{b}$ in which 'a' and 'b' are integers and the denominator 'b' not equal to zero. The operations per...Read More

## Rational Numbers on a Number Line

Rational numbers are terminating or recurring decimal numbers written in the form of fraction $\frac{a}{b}$ in which 'a' and 'b' are integers and the denominator 'b' not equal to zero. The numbers from -...Read More