NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Exercise 1.1 introduces the concept of rational numbers and their properties. The exercise includes problems on identifying, comparing, and ordering rational numbers, as well as performing basic operations like addition, subtraction, multiplication, and division. It helps students understand and work with rational numbers.

Access NCERT Solutions for Class 8 Maths Chapter 1 – Rational Numbers

Exercise 1.1

1. Name the property under multiplication used in each of the following:

I. $\dfrac{-4}{5}\times 1=1\times\dfrac{-4}{5}=\dfrac{-4}{5}$

Ans: Since, after multiplying by 1 , we are getting the same number.

Therefore, 1 is the multiplicative identity.

Ii.$-\dfrac{13}{17}\times \dfrac{-2}{7}=\dfrac{-2}{7}\times\dfrac{-13}{17}$

Ans: Since, $a\times b = b\times a$.

Therefore, its Commutative property.

iii. $\dfrac{-19}{29}\times \dfrac{29}{-19}=1$

Ans: Since, $-a\times \dfrac{1}{-a}=1$

Therefore, the property is Multiplicative inverse.

2. Tell what property allows you to compute 

$\dfrac{1}{3}\times(6 \times \dfrac{4}{3})$ as $(\dfrac{1}{3}\times 6)\times \dfrac{4}{3} $

Ans: Since, $a\times(b\times c)= (a \times b)\times c$.

Therefore, its associative property.

3. The product of two rational numbers is always a __________.

Ans: The product of two rational numbers is always a Rational number.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers - PDF Download

Points to Remember to Solve Chapter 1 of Class 8 NCERT

Rational Number: Any number that can be expressed in the form of p/q, where p and q are integers and q ≠ 0, is known as a rational number. The collection or group of rational numbers is denoted by Q.

Properties of a Rational Number

• Example: Let p and q be any two rational numbers. Then their sum, difference and product will also be a rational number. This is known as the Closure property.

• Commutativity: Rational numbers will be commutative under addition and multiplication. 

Let p and q be any two rational numbers, then

Commutative law under addition is p + q = q + p.

Commutative law under multiplication is p x q = q x p.

(Note: Rational numbers, integers and whole numbers are commutative under addition and multiplication. Also, they are non-commutative under subtraction and division.)

• Associativity: Rational numbers will be associative under addition and multiplication. 

Let p, q and r be the rational numbers, then

Associative property under addition is: p + (q + r) = (p + q) + r

Associative property under multiplication is: p(qr) = (pq)r

• Role of Zero and One: 0 will be the additive identity for rational numbers. 1 will be the multiplicative identity for the rational numbers.

• Multiplicative Inverse: When the product of two rational numbers is 1, then they are called as the multiplicative inverse of each other.

Overview of Deleted Syllabus for CBSE Class 8 Maths Chapter 1 Ratinal Numbers

Class 8 Maths Chapter 1: Exercises Breakdown

Conclusion

It is emphasized by Vedantu's "NCERT Class 8 Maths Chapter 1 Solutions: Rational Numbers" how important it is to understand rational numbers, their characteristics, and addition, subtraction, multiplication, and division operations. Students should concentrate on improving their problem-solving abilities by practicing the different kinds of questions that are given in ch 1 class 8. Approximately 10-15 questions from this chapter have appeared in prior years' exams, demonstrating how important it is to prepare thoroughly. Putting these problems into practice can help you develop a solid mathematical foundation.

Other Study Material for CBSE Class 8 Maths Chapter 1

Chapter-Specific NCERT Solutions for Class 8 Maths

Given below are the chapter-wise NCERT Solutions for Class 8 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

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