# Class 8 NCERT Mathematics Guide: Rational Numbers - properties and important points

### Class 8, Mathematics - NCERT Guide

#### RATIONAL NUMBERS

Properties of Closure
Whole Numbers
>> Whole Numbers are closed under addition. In general, a + b is a Whole Numbers for any two Whole Numbers a and b.
>> Whole Numbers are not closed under subtraction. 5 - 7 = -2, this is not a Whole Number.
>> Whole Numbers are closed under multiplication. In general, if a and b are any two Whole Numbers, their product ab is Whole Number.
>> Whole Numbers are not closed under division..

Integers
>> Integers are closed under addition. In general, a + b is an integer for any two integers a and b.
>> Integers are closed under subtraction. For any two integers a and b, a - b is an integer.
>> Integers are closed under multiplication. For any two integers a and b, a x b is an integer.
>> Integers e not closed under division.

Rational Numbers
>> Sum of two rational numbers is again a rational number. Rational Numbers are closed under addition.
>> The difference of two rational numbers is a rational number. Rational numbers are closed under subtraction
>> Rational numbers are closed under multiplication.
>> Rational numbers are not closed under division.

Properties of Commutativity
Whole Numbers
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is commutative.

Integers
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is commutative.

Rational Numbers
>> Subtraction is not commutative.
>> Multiplication is commutative.
>> Division is not commutative.

Properties of Associativity
Whole Numbers
>> Subtraction is not associative.
>> Multiplication is associative.
>> Division is not associative.

Integers
>> Subtraction is not associative.
>> Multiplication is associative.
>> Division is not associative.

Rational Numbers
>> Subtraction is not associative.
>> Multiplication is associative.
>> Division is not associative.

Points to Remember
>> Zero is called the identity for addition of rational numbers. It is additive identity for integers and whole numbers.
>> 1 is multiplicative identity for rational numbers.
>> The additive inverse of the rational number a / b is (- a / b) and vice-versa.
>> The multiplicative or reciprocal inverse of the rational number a / b  is c / d  if, a / b x c / d = 1
>> Rational numbers can be represented on a number line.
>> Between any two rational numbers there are countless rational numbers.

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