NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Edited By Komal Miglani | Updated on Jul 10, 2025 10:18 AM IST

Before we start investigating real numbers, it is important to first understand one of their close relatives - rational numbers. In a world full of numbers and uncertainty, rational numbers provide insight that everything can actually be divided logically and fairly. With rational numbers, it even begins to help to make sense of fractions, providing clarity where there was confusion. This is possible because rational numbers are numbers that can be written as $\frac{p}{q}$ , where p and q are integers, and q is not zero. Class 8 Maths NCERT Chapter 1, Rational Numbers, introduces students to rational numbers and their properties, including closure, associativity, commutativity, and distributivity. The main goal of these NCERT Solutions for class 8 of Rational Numbers is to provide students with solutions for the exercises in the textbook step-by-step so that they can always refer to the study material with the exercises when they are dealing with difficulties.

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This Story also Contains

Rational Numbers Class 8 Questions And Answers PDF Free Download
Rational Numbers Class 8 NCERT Solutions (Exercise)
Rational Numbers Class 8 Maths Chapter 1: Topics
Rational Numbers Class 8 Solutions - Important Formulae
NCERT Solutions for Class 8 Maths: Chapter Wise

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Rational numbers provide us with the understanding of sharing, measuring and balancing in the world of numbers. Rational numbers are everywhere and impact our lives daily, when sharing a bill, baking a cake, sharing a pizza, or solving an equation. In previous classes, students have already studied real numbers, whole numbers, natural numbers, and integers. So, these NCERT solutions for class 8 Maths on Rational Numbers Class 8 will complete the learning of the number system like a cherry on the cake. For quick access to your syllabus, notes, and PDFs, head over to the following link: NCERT.

Rational Numbers Class 8 Questions And Answers PDF Free Download

Students who wish to access the NCERT solutions for class 8, chapter 1, Rational Numbers, can click on the link below to download the entire solution in PDF.

Rational Numbers Class 8 NCERT Solutions (Exercise)

Try These Questions: Closure Property
Page Number: 4

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	Yes	...	No
Integers	...	Yes	...	No
Whole Numbers	...	...	Yes	...
Natural Numbers	...	No	...	...

Answer:
It can be seen that rational numbers, integers, whole numbers, and natural numbers are not closed under division because Zero is included in these numbers. Any number divided by zero is not defined.

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	Yes	Yes	No
Integers	Yes	Yes	Yes	No
Whole Numbers	Yes	No	Yes	No
Natural Numbers	Yes	No	Yes	Yes

Try These Questions: Commutative Property
Page Number: 6

Complete the following table:

Commutative for

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	..	...	...
Integers	...	No	...	...
Whole Numbers	...	...	Yes	...
Natural Numbers	...	...	...	No

Answer:
In rational numbers, a ÷ b ≠ b ÷ a

also a-b ≠ b-a

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	No	Yes	No
Integers	Yes	No	Yes	No
Whole Numbers	Yes	No	Yes	No
Natural Numbers	Yes	No	Yes	No

Try These Questions: Associative Property
Page Number: 9

Complete the following table:

Associative for

	Addition	Subtraction	Multiplication	Division
Rational Numbers	...	...	...	No
Integers	...	...	Yes	...
Whole Numbers	Yes	...	...	...
Natural Numbers	...	No	...	...

Answer:
For associative in multiplication:- a × (b × c) = (a × b) × c

	Addition	Subtraction	Multiplication	Division
Rational Numbers	Yes	No	Yes	No
Integers	Yes	No	Yes	No
Whole Numbers	Yes	No	Yes	No
Natural Numbers	Yes	No	Yes	No

Try These Questions: Distributivity
Page Number: 12

Find using distributivity:

Find using distributivity.
(i) ${\frac{7}{5} \times (\frac{- 3}{12})} + {\frac{7}{5} \times \frac{5}{12}}$
(ii) ${\frac{9}{16} \times \frac{4}{12}} + {\frac{9}{16} \times \frac{- 3}{9}}$

Answer:
(i)
${\frac{7}{5} \times (\frac{- 3}{12})} + {\frac{7}{5} \times \frac{5}{12}}$
$= \frac{7}{5} \times (\frac{- 3}{12} + \frac{5}{12})$
$= \frac{7}{5} \times (\frac{- 3 + 5}{12})$
$= \frac{7}{5} \times \frac{1}{6}$
$= \frac{7 \times 1}{5 \times 6}$
$= \frac{7}{30}$

(ii)
${\frac{9}{16} \times \frac{4}{12}} + {\frac{9}{16} \times \frac{- 3}{9}}$
$= \frac{9}{16} \times (\frac{4}{12} + \frac{- 3}{9})$
$= \frac{9}{16} \times (\frac{1}{3} - \frac{1}{3})$
$= \frac{9}{16} \times 0$
$= 0$

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers: Exercise: 1.1
Total Questions: 3
Page Number: 12

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

(i) $\frac{- 4}{5} \times 1 = 1 \times \frac{- 4}{5} = - \frac{4}{5}$
(ii) $- \frac{13}{17} \times \frac{- 2}{7} = \frac{- 2}{7} \times \frac{- 13}{17}$
(iii) $\frac{- 19}{29} \times \frac{29}{- 19} = 1$

Answer:
(i) Multiplying any number by 1, we get the same number back.

i.e., a × 1 = 1 × a = a

Hence, 1 is the multiplicative identity for rational numbers.

(ii) Commutativity property states that a × b = b × a

(iii) Here Multiplicative Inverse Property is used.
Each number has an inverse (reciprocal), and the product of a number and its inverse is 1.
In this case, $\frac{- 19}{29}$ and $\frac{29}{- 19}$ are multiplicative inverses.

Question 2: Tell what property allows you to compute $\frac{1}{3} \times (6 \times \frac{4}{3})$ as $(\frac{1}{3} \times 6) \times \frac{4}{3}$

Answer:
By the Associativity property for multiplication, we know that a × (b × c) = (a × b) × c.
Thus property used here is associativity.

Question 3: The product of two rational numbers is always a _______.

Answer:

Rational number. We know that if p and q are 2 rational numbers, then pq is also a rational number.

Rational Numbers Class 8 Maths Chapter 1: Topics

The topics discussed in the NCERT Solutions for class 8, chapter 1, Rational numbers, are:

Properties Of Rational Numbers
Representation Of Rational Numbers On The Number Line
Rational Numbers Between Rational Numbers

Rational Numbers Class 8 Solutions - Important Formulae

Here are some important formulas that will help students to solve problems related to rational numbers.

Property	Formula
Additive Identity	$\frac{a}{b} + 0 = \frac{a}{b}$
Multiplicative Identity	$\frac{a}{b} \times 1 = \frac{a}{b}$
Additive Inverse	$\frac{a}{b} + (- \frac{a}{b}) = 0$
Multiplicative Inverse	$\frac{a}{b} \times \frac{b}{a} = 1$
Closure (Addition)	$\frac{a}{b} + \frac{c}{d}$ is a rational number
Closure (Subtraction)	$\frac{a}{b} - \frac{c}{d}$ is a rational number
Closure (Multiplication)	$\frac{a}{b} \times \frac{c}{d}$ is a rational number
Closure (Division)	Not closed under division
Commutative (Addition)	$\frac{a}{b} + \frac{c}{d} = \frac{c}{d} + \frac{a}{b}$
Commutative (Multiplication)	$\frac{a}{b} \times \frac{c}{d} = \frac{c}{d} \times \frac{a}{b}$
Associative (Addition)	$(\frac{a}{b} + \frac{c}{d}) + \frac{e}{f} = \frac{a}{b} + (\frac{c}{d} + \frac{e}{f})$
Associative (Multiplication)	$(\frac{a}{b} \times \frac{c}{d}) \times \frac{e}{f} = \frac{a}{b} \times (\frac{c}{d} \times \frac{e}{f})$
Distributive Property	$\frac{a}{b} \times (\frac{c}{d} + \frac{e}{f}) = (\frac{a}{b} \times \frac{c}{d}) + (\frac{a}{b} \times \frac{e}{f})$

NCERT Solutions for Class 8 Maths: Chapter Wise

For students' preparation, Careers360 has gathered all Class 8 Maths NCERT solutions here for quick and convenient access.

NCERT Solutions for class 8 Mathematics chapter 1: Rational Numbers

NCERT Solutions for class 8 Mathematics chapter 2: Linear Equations in One Variable

NCERT Solutions for class 8 Mathematics chapter 3: Understanding Quadrilaterals

NCERT Solutions for class 8 Mathematics chapter 4: Data Handling

NCERT Solutions for class 8 Mathematics chapter 5: Squares and Square Roots

NCERT Solutions for class 8 Mathematics chapter 6: Cubes and Cube Roots

NCERT Solutions for class 8 Mathematics chapter 7: Comparing Quantities

NCERT Solutions for class 8 Mathematics chapter 8: Algebraic Expressions and Identities

NCERT Solutions for class 8 Mathematics chapter 9: Mensuration

NCERT Solutions for class 8 Mathematics chapter 10: Exponents and Powers

NCERT Solutions for class 8 Mathematics chapter 11: Direct and Inverse Proportions

NCERT Solutions for class 8 Mathematics chapter 12: Factorisation

NCERT Solutions for class 8 Mathematics chapter 13: Introduction to Graphs

NCERT Solutions for Class 8: Subject-Wise

Careers360 also provides well-structured and well-explained solutions for other subjects. The following links can be used for those purposes.

NCERT Books and NCERT Syllabus

Students can use the following links to download the latest version of the CBSE syllabus and some other reference books for class 8.

Also Read

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable

NCERT Solutions for Class 8 Science Chapter 13 Light

NCERT Solutions for Class 8 Science Chapter 8 Force and Pressure

NCERT Solutions for Class 8 Science Chapter 11 Chemical Effects Of Electric Current

NCERT Solutions for Class 8 Science Chapter 12 Some Natural Phenomena

NCERT Books for Class 8 Maths 2025-26: Download PDF Here

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NCERT Books for Class 8 Social Science 2025-26 - Download PDF

NCERT Books for Class 8 English 2025-26: Download PDF

NCERT Syllabus for Class 8 2025-26, Download All Subjects Latest Syllabus PDF

NCERT Syllabus for Class 8 Hindi 2025-26: Download All Chapters PDF Here

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