CBSE Class 8 Maths Notes on Rational Numbers PDF

Revision Notes Class - 8 Maths Chapter 1 - Rational Numbers p Rational Numbers are numbers in the form of such that q  0. It is...

Revision Notes Class - 8 Maths Chapter 1 - Rational Numbers p Rational Numbers are numbers in the form of such that q  0. It is q denoted by “Q”. If the numerator and denominator are coprime and q  0 then the Rational Number is of the standard form. Types of Rational Numbers: i. Positive Rational Numbers: The sign of both the numerator and denominator are the same, i.e., either both are positive or both are 2 −7 negative. Ex: , ,... 3 −8 ii. Negative Rational Numbers: The sign of both the numerator and denominator are the same, i.e., if the numerator is negative, the denominator will be positive. Similarly, if the numerator is positive, 2 −7 the denominator is negative. Ex: , ,... −3 8 0 0 iii. Zero Rational Numbers: The numerator is always zero. Ex: , ,... 3 8 Properties of Rational Numbers: i. Closure Property: The addition, subtraction and multiplication operations result in closure Property, i.e., for any two rational numbers in these operations, the answer is always a rational number. ii. Commutative Property: The various order of rational numbers in the operations like addition and multiplication results in the same answer. 2 4 4 2 Ex: + = + ,... 3 8 8 3 Class VIII Maths www.vedantu.com 1  iii. Associative Property: The grouping order does not matter in the operations like addition or multiplication, i.e., the place where we add the parenthesis does not change the answer. 8 4 6 8 4 6 Ex: +  +  =  +  + 9 5 7 9 5 7 iv. Distributive Property: The rational numbers are distributed in the following way: ▪ a ( b + c ) = ab + ac ▪ a ( b − c ) = ab − ac v. General Properties: ▪ A rational number can be a fraction or not, but vice versa is true. ▪ Rational numbers can be denoted on a number line. ▪ There is 'n' number of rational numbers between any two rational numbers. Role of Zero: Also known as the Additive Identity Whenever '0' is added to any rational number, the answer is the Rational number itself. Ex: If 'a ' is any rational number, then a + 0 = 0 + a = a Role of One: Also known as the Multiplicative Identity. Whenever '1' is multiplied by any rational number, the answer is the Rational number itself. Ex: If 'a ' is any rational number, then a 1 = 1 a = a Additive Inverse: The Additive Inverse of any rational number is the same rational number a a with the opposite sign. The additive inverse of is −. Similarly, the b b a a a additive inverse of − is , where is the rational number. b b b Multiplicative Inverse: Also known as the Reciprocal. Class VIII Maths www.vedantu.com 2  The Multiplicative Inverse of any rational number is the inverse of the same a b rational number. The multiplicative inverse of is. Similarly, the b a b a a b multiplicative inverse of is , where and is any rational number. a b b a Class VIII Maths www.vedantu.com 3