Number System and Operations
Category : 8th Class
Number System and Operations
In Mathematics we frequently come across different types of numbers. The different types of numbers are natural numbers, whole numbers/ rational numbers, integers/ irrational numbers, and real numbers« The natural number starts form 1 and goes to infinity. Thus we can say that all the positive real numbers starting from 1 are called natural numbers. The whole numbers are all counting numbers together with 0. The set of all natural numbers, 0 and negative of all natural numbers including 0 are called integers. The rational numbers are the numbers which can be written in the P form of \[\frac{p}{q}\], where p and q are integers and\[q\ne 0.\].
Properties of Rational Number
Rational numbers satisfy various properties which are given below:
Closure Property
When we add two rational numbers the result is also a rational number i.e. rational numbers are closed under addition.
For example,\[\frac{5}{6}+\frac{8}{9}=\frac{31}{18}\] which is also by a rational number.
Commutative Property
The two rational numbers can be added in any order, the result in both cases will be same. Hence we can say that addition of two rational numbers is commutative.
For example,\[\frac{2}{3}+\frac{5}{6}=\frac{5}{6}+\frac{2}{3}=\frac{9}{6}.\]
This is called the commutative property of addition.
Associative Property
Distributive Property
For all rational numbers x, y and z, we have:
Rules of Divisibility
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