NCERT Solution for Class 8 Maths-Rational Numbers Class 8 Maths - Rational Numbers In mathematics, we usually come across different terms like natural number, whole numbers, integers and rational number. We will discuss rational number in this article from 8th Class Maths. Let’s us revisit the properties of Rational numbers in class 8.
Rational Numbers A rational number is a number that can be written in the form of P/Q where P and Q are integers and Q is not equal to 0. Example:-5/7, (-2/3)
Properties of Rational numbers We will first discuss the properties of rational numbers.
Closure Property We call a set of numbers closed under operation if performance of that operation on members of the set of numbers always creates a member of the same set only; in this case we also say that the set is closed under the operation. Under addition
Rational numbers are closed under addition.For any two rational numbers a and b,a+b is also a rational number. Under subtraction Rational numbers are closed under addition.For any two rational numbersaand b, a-b is also a rational number. Under Multiplication Rational statistics are closed under multiplication.For any two rational numbers a and b, a*b is also a rational number. Under Division Rational numbers are not closed under multiplication.For any rational number a, a/0 is not defined.
Commutative Property As per commutative property, the interchanging order of numbers will not change the result. Under addition Two rational numbers can be added in any order.Addition is commutative for rational numbers.For any two rational numbers a and b, a+b=b+a Under subtraction Subtraction is not commutative for rational numbers. Under Multiplication Multiplication is commutative for rational numbers. For any two rational numbers a and b, a*b=b*a Under Division Division is not commutative for rational numbers
Associative Property Under addition Addition is associative for rational numbers.For any 3 rational numbers a,b, and c. a + (b+c) = (a+b) +c Under subtraction
Subtraction is not associative for rational numbers Under Multiplication Multiplication is associative for rational numbers.For any 3 rational numbers a,b, and c. a *(b * c) = (a * b) *c Under Division Division is not associative for rational numbers. For illustrations and solved NCERT solutions, click on Class 8 NCERT Maths solutions
The Role of Zero Zero is called the identity for the addition of rational numbers.It is the additive identity for integers and whole numbers as well. a+0=0+a=a b+0=0+b=b
The role of 1 1 is the multiplicative identity of rational numbers. a*1=1*a=a
Negative of a number For any rational number a/b, we have a/b+(-a/b)=(-a/b)+a/b=0.We say that (-a/b) is the additive inverse of a/b and a/b is the additive inverse of (-a/b).
Reciprocal A rational number c/d is called the reciprocal or multiplicative inverse of another rational number a/b, if a/b*c/d=1.
Distributive property of multiplication over addition and subtraction For all rational numbers a,b, and c a (b+c)=ab+ ac a(b-c)=ab-ac
Rational Numbers between two rational numbers
Let’s consider the below example for 8th class maths Q - Find rational number -1/10 and 3/10? Sol- Rational numbers -1/10 and 3/10 are 0/10,1/10/2/10 For Class 8 Maths NCERT solutions, CBSE Guide, sample papers for exam preparation, online classes for school courses, register with Takshila Learning.
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