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Assignments For Class 8 Mathematics Rational Numbers

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• Rational Numbers Class 8 Notes CBSE Maths Chapter 1 (Free PDF Download)
• Revision Notes

Comprehensive Revision Notes for CBSE Class 8 Maths Chapter 1: Rational Numbers

Students of Class 8 study hard throughout the year to score high marks in annual examinations. However, unfortunately, they fail to revise the whole concept during exam time because of the bulky syllabus. As a result, they skip some concepts which are important and though they have studied them earlier they have not revised them. Many students even don't know the concept of making notes, they simply keep on reading the whole syllabus. 

Realizing all these problems, Vedantu subject experts are at your door. Vedantu Mathematics experts have designed CBSE Class 8 Maths Chapter 1 Revision Notes in such a way that all the definitions, formulas, and properties of Rational numbers are covered here. 

Vedantu is a platform that provides free NCERT Solutions and other study materials for students. Students just have to download CBSE Class 8 Maths Rational Numbers Notes free PDF by clicking once on the link given below and can use it even without the internet, from anywhere. You can also download NCERT Solutions for Class 8 Maths and NCERT Solution for Class 8 Science to help you to revise the complete syllabus and score more marks in your examinations.

Rational Numbers Class 8 Notes

Before getting to the revision notes, let us first understand the topics covered in Chapter 1 Rational Numbers. 

Topics Covered in NCERT Maths Class 8 Chapter 1 Rational Numbers   

These all topics are discussed below in a concise way for easy and quick understanding. Introduction to rational numbers includes the topics such as what rational numbers is, how to write rational numbers in standard form and what are the types of rational numbers.

Download CBSE Class 8 Maths Revision Notes 2024-25 PDF

Also, check CBSE Class 8 Maths revision notes for All chapters:

Access Class 8 Maths Chapter 1 – Rational Numbers Notes

1. Rational Numbers are numbers in the form of $\dfrac{p}{q}$ such that $q>0$. It is denoted by “Q”.

3. 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 negative. Ex: $\dfrac{2}{3},\dfrac{-7}{-8},...$

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, the denominator is negative. Ex: $\dfrac{2}{-3},\dfrac{-7}{8},...$

iii. Zero Rational Numbers: The numerator is always zero. Ex: $\dfrac{0}{3},\dfrac{0}{8},...$

4. 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. 

Ex: $\dfrac{2}{3}+\dfrac{4}{8}=\dfrac{4}{8}+\dfrac{2}{3},...$

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. Ex: $\dfrac{8}{9}+\left( \dfrac{4}{5}+\dfrac{6}{7} \right)=\left( \dfrac{8}{9}+\dfrac{4}{5} \right)+\dfrac{6}{7}$

iv. Distributive Property: The rational numbers are distributed in the following way:

$a\left( b+c \right)=ab+ac$

$a\left( b-c \right)=ab-ac$

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.

5. 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 $a+0=0+a=a$

6. 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 $a\times 1=1\times a=a$

7. Additive Inverse:

The Additive Inverse of any rational number is the same rational number with the opposite sign. The additive inverse of $\dfrac{a}{b}$ is $-\dfrac{a}{b}$. Similarly, the additive inverse of $-\dfrac{a}{b}$ is $\dfrac{a}{b}$, where $\dfrac{a}{b}$ is the rational number.

8. Multiplicative Inverse: Also known as the Reciprocal.

The Multiplicative Inverse of any rational number is the inverse of the same rational number. The multiplicative inverse of $\dfrac{a}{b}$ is $\dfrac{b}{a}$. Similarly, the multiplicative inverse of $\dfrac{b}{a}$ is $\dfrac{a}{b}$, where $\dfrac{a}{b}$ and $\dfrac{b}{a}$ is any rational number.

A Comprehensive Guide from Vedantu for Effective Learning and Exam Success

Revision notes play a vital role in the preparation of exams. we, at vedantu, realize the value of revision notes and try to cover all the important concepts included in the syllabus. the students are advised to plan their revision strategy well in advance so that the important concepts from the examination viewpoint are not missed. some of the salient features of vedantu are: the vedantu revision notes are very easy to understand and grasp. studying from vedantu revision notes will save a lot of time as they are stepwise and concise. the revision notes contain all the important concepts, formulas, and properties which are given in ncert books. it will help in proper preparation for your exam. the notes are prepared by collecting extracts from ncert books as well as some standard books strictly based on the cbse pattern. all the diagrams and other reference illustrations are also provided. studying from revision notes will help you write any answer in the exam. the vedantu revision notes will make you confident and you will feel well acquainted with it. you can easily revise it, again and again, that too at any time and anywhere as vedantu revision notes are free to download., chapter wise revision notes for class 8 maths, chapter 2 - linear equations in one variable notes chapter 3 - understanding quadrilaterals notes chapter 4 - practical geometry notes chapter 5 - data handling notes chapter 6 - squares and square roots notes chapter 7 - cubes and cube roots notes chapter 8 - comparing quantities notes chapter 9 - algebraic expressions and identities notes chapter 10 - visualising solid shapes notes chapter 11 - mensuration notes chapter 12 - exponents and powers notes chapter 13 - direct and inverse proportions notes chapter 14 - factorisation notes chapter 15 - introduction to graphs notes chapter 16 - playing with numbers notes revision notes of class 8 chapter 1 rational numbers are very useful for the students. students can easily download the pdf and revise the complete chapter anywhere and anytime. also, this easily self-explanatory content help students to understand complex topics easily.  students can also download the other study materials such as solutions to ncert exercises for all subjects, and important questions of each chapter. they can also download practice question papers for the preparation for their exams. this question answers pdf is very useful for the students as they help them to write the clear and conceptual answer in the examination. you just need to visit our website and download the desired pdf.  so, waiting for what download the pdf now and start your preparation., conclusion:, the comprehensive revision notes for cbse class 8 maths chapter 1: rational numbers provide students with a concise yet thorough recap of the chapter's key concepts. these notes serve as a valuable resource for revision, enabling students to reinforce their understanding, practice problem-solving techniques and prepare effectively for exams. by utilizing these revision notes, students can enhance their mathematical skills, build confidence and achieve success in their academic journey..

FAQs on Rational Numbers Class 8 Notes CBSE Maths Chapter 1 (Free PDF Download)

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Rational number Class 8 notes include diagrams, solved examples, formulas, and important terms that enable you to quickly revise the chapter easily at no time. Class 8 Maths rational notes are prepared by the subject experts as per the latest exam pattern issued by the CBSE board. It includes all the additional details that students might require to prepare for school exams and other competitive exams like the Olympiad.

2. From Where can Students Download CBSE Class 8 Maths Rational Numbers Notes PDF?

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3. Why should I choose Vedantu for Chapter 13 of Class 8 Maths?

As a high school student, you should consider 8th-grade Maths to be a crucial subject for your future. In this class, you'll learn concepts and chapters that will be extremely useful for your future studies and even for competitive exams. Understanding the basics from the beginning is important for students. And to cater for this need of the students, Vedantu provides free NCERT solutions, revision notes, important questions, sample papers, etc. that every student can avail.

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Previous years question papers with solutions.

Mock papers with solutions 

NCERT Solutions for Class 8 Maths by Vedantu

Sample papers for Class 8 Maths

5. What is the importance of rational numbers?

Rational numbers hold significant importance in mathematics and practical applications. They allow precise representation of fractions, measurements, and ratios, enabling accurate calculations and comparisons. Rational numbers are essential in fields such as science, engineering, finance, and everyday life, where precise quantities and proportions are crucial. Understanding rational numbers helps develop critical thinking, problem-solving skills, and logical reasoning. It lays the foundation for advanced mathematical concepts and enables students to make informed decisions based on quantitative analysis.

NCERT Solutions

Study materials for class 8.

CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 8 Mathematics Rational Numbers Worksheets

We have provided below free printable  Class 8 Mathematics Rational Numbers Worksheets  for Download in PDF. The worksheets have been designed based on the latest  NCERT Book for Class 8 Mathematics Rational Numbers . These Worksheets for Grade 8 Mathematics Rational Numbers  cover all important topics which can come in your standard 8 tests and examinations.  Free worksheets for CBSE Class 8 Mathematics Rational Numbers , school and class assignments, and practice test papers have been designed by our highly experienced class 8 faculty. You can free download CBSE NCERT printable worksheets for Mathematics Rational Numbers Class 8 with solutions and answers. All worksheets and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Rational Numbers Class 8. Students can click on the links below and download all Pdf  worksheets for Algebraic Expressions and Identities class 8  for free. All latest Kendriya Vidyalaya  Class 8 Mathematics Rational Numbers Worksheets  with Answers and test papers are given below.

Mathematics Rational Numbers Class 8 Worksheets Pdf Download

Here we have the biggest database of free  CBSE NCERT KVS  Worksheets for Class 8  Mathematics Rational Numbers . You can download all free Mathematics Rational Numbers worksheets in Pdf for standard 8th. Our teachers have covered Class 8 important questions and answers  for Mathematics Rational Numbers as per the latest curriculum for the current academic year. All test sheets question banks for Class 8 Mathematics Rational Numbers and  CBSE Worksheets for Mathematics Rational Numbers Class 8  will be really useful for Class 8 students to properly prepare for the upcoming tests and examinations. Class 8th students are advised to free download in Pdf all printable workbooks given below.

Topicwise Worksheets for Class 8 Mathematics Rational Numbers Download in Pdf

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Class viii math, class-8 rational numbers.

Introduction to Rational Number

Facts of Rational Numbers

Addition of rational numbers, addition properties of rational numbers, subtraction of rational number, subtraction properties of rational number, multiplication of rational numbers, multiplication properties of rational number, division of rational number, division properties of rational number, rational number between any two given rational numbers.

Rational Numbers Test

Rational Number Worksheet

Answer Sheet

Introduction to rational numbers.

• Define rational number
• Number line representation of rational numbers
• Comparison of rational numbers
• Operation like addition, subtraction, multiplication, and division

Numbers in form of a ⁄ b where 'a' and 'b' are integer. Here, 'b' is not equal to zero, known as rational numbers. some examples are 5 ⁄ 9 , -6 ⁄ 11 , 9, -3, 0, 3 ⁄ -11 etc.

Every integer is a rational number, but every rational number is not an integer. It is because, every integer 'i' can be written as i ⁄ 1 which is in fraction form. For example, -3 ⁄ 8 is a rational number but not an integer.

Every rational number is not a fraction, but every fraction is a rational number. For example, -5 ⁄ 9 is a rational number but not a fraction.

The rational number -a ⁄ b is same as − a ⁄ b .

Every rational number should be written with positive integer as denominator.

Two rational numbers a ⁄ b = c ⁄ d , if a × d = b × c .

Rational number is positive if both numerator and denominator are positive integers, or both are negative integers. If one is positive integer and other is negative integer then rational number is said to be negative.

All finite decimal numbers are rational numbers. Let's see some examples 0.5 = 1 ⁄ 2 , 0.26 = 13 ⁄ 50 and 0.625 = 5 ⁄ 8 .

When we add two rational numbers, first convert each rational number with positive denominator. Rational Numbers with same denominator If a ⁄ b and c ⁄ d are two rational numbers, then ( a ⁄ b ) + ( c ⁄ b ) = (a+c) ⁄ b .

Example 1. Add 6 ⁄ 9 and 8 ⁄ -9 . Solution. 6 ⁄ 9 + 8 ⁄ -9 Here, first convert 8 ⁄ -9 into positive denominator. 8 ⁄ -9 = {8×(-1)} ⁄ {-9×(-1)}       = -8 ⁄ 9 Then, 6 ⁄ 9 + (- 8 ⁄ 9 ) = 6 ⁄ 9 − 8 ⁄ 9 = (6-8) ⁄ 9 = -2 ⁄ 9 .

Rational Numbers With Different Denominator Here we first find LCM of denominators of two rational numbers. Then we covert the denominator of each rational number to have same value as LCM. At last, add the rational numbers following the process of same denominator.

Example 1. Add -5 ⁄ 7 + 7 ⁄ 3 . Solution. LCM of 7 and 3 = 21 -5 ⁄ 7 = (-5×3) ⁄ (7×3) = -15 ⁄ 21 7 ⁄ 3 = (7×7) ⁄ (3×7) = 49 ⁄ 21 Then, -15 ⁄ 21 + 49 ⁄ 21 = (-15+49) ⁄ 21 = 34 ⁄ 21 .

• Closure property

Commutative

Associative.

• Special properties

Closure Property

Example 1. Add 1 ⁄ 2 and 2 ⁄ 5 . Solution. 1 ⁄ 2 + 2 ⁄ 5 = (5+4) ⁄ 10 = 9 ⁄ 10 So, 9 ⁄ 10 is a rational number.

Example 2. Add -5 ⁄ 9 and -2 ⁄ 3 Solution. -5 ⁄ 9 + -2 ⁄ 3 = {-5+(-6)} ⁄ 9 = -11 ⁄ 9

Example 3. Add -6 ⁄ 5 and 1 ⁄ 4 . Solution. -6 ⁄ 5 + 1 ⁄ 4 = (-6×4+1×5) ⁄ 20 = (-24+5) ⁄ 20 = -19 ⁄ 20

Example 1. -5 ⁄ 7 + 3 ⁄ 5 = 3 ⁄ 5 + -5 ⁄ 7 Solution. We have to prove LHS = RHS LHS = -5 ⁄ 7 + 3 ⁄ 5 = (-25+21) ⁄ 35 = -4 ⁄ 35 RHS = 3 ⁄ 5 + -5 ⁄ 7 = {21+(-25)} ⁄ 35 = -4 ⁄ 35 LHS = RHS. So, it is following commutative properties.

Example 1. ( 1 ⁄ 2 + 2 ⁄ 3 ) + -3 ⁄ 5 = 1 ⁄ 2 + ( 2 ⁄ 3 + -3 ⁄ 5 ). Solution. We have to prove LHS = RHS LHS = ( 1 ⁄ 2 + 2 ⁄ 3 ) + -3 ⁄ 5 = (3+4) ⁄ 6 + ( -3 ⁄ 5 ) = 7 ⁄ 6 - 3 ⁄ 5 = (35−18) ⁄ 30 = 17 ⁄ 30 RHS = 1 ⁄ 2 + ( 2 ⁄ 3 + -3 ⁄ 5 ) = 1 ⁄ 2 + {10+(-9)} ⁄ 15 = 1 ⁄ 2 + 1 ⁄ 15 = (15+2) ⁄ 30 = 17 ⁄ 30 LHS = RHS, hence it is proved that it follows associative property.

Special Properties of Rational Numbers

Example 1. Additive inverse of -3 ⁄ 5 = −( -3 ⁄ 5 ) = 3 ⁄ 5 .

Example 2. Additive inverse of -4 ⁄ -9 = −( -4 ⁄ -9 ) = -4 ⁄ 9 .

Subtraction of rational numbers can be done by adding additive inverse of subtrahend with minuend. That is, a ⁄ b − c ⁄ d = a ⁄ b + ( -c ⁄ d ) .here -c ⁄ d is additive inverse of c ⁄ d .

Example 1. Subtract 5 ⁄ 9 from -3 ⁄ 7 . Solution. -3 ⁄ 7 − 5 ⁄ 9         = -3 ⁄ 7 + additive inverse of 5 ⁄ 9         = -3 ⁄ 7 + ( -5 ⁄ 9 )         = (-3×9−5×7) ⁄ 63         = {-27+(-35} ⁄ 63         = -62 ⁄ 63

Example 2. subtract -3 ⁄ 25 from 3 1 ⁄ 5 . Solution. 3 1 ⁄ 5 − ( -3 ⁄ 25 )         = 16 ⁄ 5 + additive inverse of ( -3 ⁄ 25 )         = 16 ⁄ 5 + 3 ⁄ 25         = (80+3) ⁄ 25         = 83 ⁄ 25         = 3 8 ⁄ 25

Not Commutative

Not associative.

Example 1. 6 ⁄ 9 − 3 ⁄ 4 = (24-27) ⁄ 36 = -3 ⁄ 36 = -1 ⁄ 12 -1 ⁄ 12 is a rational number. Example 2. -7 ⁄ 9 − 4 ⁄ 3 = (-7-12) ⁄ 9 = -19 ⁄ 9 = −2 1 ⁄ 9 −2 1 ⁄ 9 is a rational number.

Example 1. Prove 1 ⁄ 3 − 5 ⁄ 6 ≠ 5 ⁄ 6 − 1 ⁄ 3 . Solution. LHS = 1 ⁄ 3 − 5 ⁄ 6 = (2-5) ⁄ 6 = -1 ⁄ 2 RHS = 5 ⁄ 6 − 1 ⁄ 3 = (5-2) ⁄ 6 = 1 ⁄ 2 LHS ≠ RHS i.e. -1 ⁄ 2 ≠ 1 ⁄ 2 Hence it is proved that 1 ⁄ 3 − 5 ⁄ 6 ≠ 5 ⁄ 6 − 1 ⁄ 3 .

Example 1. prove ( -3 ⁄ 5 − 2 ⁄ 7 ) − ( -1 ⁄ 5 ) ≠ -3 ⁄ 5 − ( 2 ⁄ 7 − -1 ⁄ 5 ). Solution. LHS = ( -3 ⁄ 5 − 2 ⁄ 7 ) − ( -1 ⁄ 5 )         = (-21-10) ⁄ 35 + 1 ⁄ 5         = (-31) ⁄ 35 + 1 ⁄ 5         = (-31+7) ⁄ 35 = -24 ⁄ 35 RHS = -3 ⁄ 5 − ( 2 ⁄ 7 − -1 ⁄ 5 )         = -3 ⁄ 5 − ( 2 ⁄ 7 + 1 ⁄ 5 )         = -3 ⁄ 5 − (10+7) ⁄ 35         = -3 ⁄ 5 − 17 ⁄ 35         = (-21-17) ⁄ 35 = -38 ⁄ 35 -24 ⁄ 35 ≠ -38 ⁄ 35 i.e. LHS ≠ RHS Hence, it is proved that subtraction does not follow associative property.

To get the product of two rational number, numerators are multiplied, and denominators are multiplied. Let's see some examples.

Example 1. Multiply -3 ⁄ 7 and 8 ⁄ 9 Solution. -3 ⁄ 7 × 8 ⁄ 9         = (-3×8) ⁄ 7×9         = -8 ⁄ 21

Example 2. Multiply 3 1 ⁄ 7 and -4 3 ⁄ 4 Solution. 3 1 ⁄ 7 × (-4 3 ⁄ 4 )         = 22 ⁄ 7 × ( -19 ⁄ 4 )         = {22×(-19)} ⁄ 7×4         = -418 ⁄ 28         = -14 26 ⁄ 28

Commutative Property

Associative property.

• Distributive Properties

Multiplicative Identity

Multiplicative inverse.

Example 1. 2 ⁄ 5 × 7 ⁄ 9 = 2×7 ⁄ 5×9 = 14 ⁄ 45 14 ⁄ 45 is a rational number. Example 2. 3 ⁄ 4 × 1 ⁄ 6 = 3×1 ⁄ 4×6 = 3 ⁄ 24 = 1 ⁄ 8 1 ⁄ 8 is a rational number. Example 3. 4 ⁄ 7 × 5 ⁄ 8 = 4×5 ⁄ 7×8 = 5 ⁄ 14 5 ⁄ 14 is a rational number.

Example 1. Prove 2 ⁄ 3 × ( -4 ⁄ 5 ) = ( -4 ⁄ 5 ) × 2 ⁄ 3 . Solution. LHS = 2 ⁄ 3 × ( -4 ⁄ 5 ) = {2×(-4)} ⁄ (3×5) = -8 ⁄ 15 RHS = -4 ⁄ 5 × 2 ⁄ 3 = (-4×2) ⁄ 5×3 = -8 ⁄ 15 LHS = RHS i.e. 2 ⁄ 3 × ( -4 ⁄ 5 ) = ( -4 ⁄ 5 ) × 2 ⁄ 3 Hence, it is proved that multiplication of rational number is commutative.

Example 1. Prove ( 5 ⁄ 7 × -3 ⁄ 2 ) × -1 ⁄ 7 = 5 ⁄ 7 × ( -3 ⁄ 2 × -1 ⁄ 7 ) Solution. LHS = ( 5 ⁄ 7 × -3 ⁄ 2 ) × -1 ⁄ 7 = -15 ⁄ 14 × -1 ⁄ 7 = 15 ⁄ 98 RHS = 5 ⁄ 7 × ( -3 ⁄ 2 × -1 ⁄ 7 ) = 5 ⁄ 7 × 3 ⁄ 14 = 15 ⁄ 98 LHS = RHS i.e. ( 5 ⁄ 7 × -3 ⁄ 2 ) × -1 ⁄ 7 = 5 ⁄ 7 × ( -3 ⁄ 2 × -1 ⁄ 7 ) Hence, multiplication of fraction is associative.

Distributive Property

Example 1. Find multiplicative invers of 7 ⁄ 9 × 10 ⁄ 7 . Solution. First, we multiply 7 ⁄ 9 and 10 ⁄ 7 , then convert into its reciprocal          7 ⁄ 9 × 10 ⁄ 7         = (7×10) ⁄ (9×7)         = 70 ⁄ 63 = 10 ⁄ 9 Multiplicative invers of 10 ⁄ 9 = 9 ⁄ 10

When two rational numbers are divided, first we find out reciprocal of the divisor, then it is multiplied with the dividend. In other words, if a ⁄ b and c ⁄ d are rational numbers ,then a ⁄ b ÷ c ⁄ d = a ⁄ b × d ⁄ c (reciprocal of c ⁄ d ) = a×d ⁄ b×c . Let's see some examples.

Example 1. 2 1 ⁄ 5 ÷ ( -1 ⁄ 3 ). Solution. 2 1 ⁄ 5 ÷ ( -1 ⁄ 3 )         = 11 ⁄ 5 ÷ ( -1 ⁄ 3 ) Reciprocal of -1 ⁄ 3 is equal to -3.         = 11 ⁄ 5 × (-3)         = -33 ⁄ 5

Example 2. Divide the sum of 1 ⁄ 7 and 1 ⁄ 2 by the product of 9 ⁄ 2 and 3 ⁄ 7 Solution. ( 1 ⁄ 7 + 1 ⁄ 2 ) ÷ ( 9 ⁄ 2 × 3 ⁄ 7 )          = (2+7) ⁄ 14 ÷ (9×3) ⁄ (2×7)          = 9 ⁄ 14 ÷ 27 ⁄ 14 Reciprocal of 27 ⁄ 14 is 14 ⁄ 27          = 9 ⁄ 14 × 14 ⁄ 27          = (9×14) ⁄ (14×27)          = 9 ⁄ 27          = 1 ⁄ 3

Division is Non-commutative

Division is non-associative.

In order to know rational number between two rational numbers, we have to calculate the mean of two given rational numbers. If a ⁄ b and c ⁄ d are two rational numbers. Then mean of a ⁄ b and c ⁄ d is written as ( a ⁄ b + c ⁄ d ) ⁄ 2 .

Example 1. Find a rational number between -4 ⁄ 5 and 5 ⁄ 6 . Solution. First, we calculate mean of ( -4 ⁄ 5 + 5 ⁄ 6 ) ÷ 2         = (-24+25) ⁄ 30 ÷ 2         = 1 ⁄ 30 × 1 ⁄ 2 = 1 ⁄ 60 So, 1 ⁄ 60 is a rational number between -4 ⁄ 5 and 5 ⁄ 6 .

Class-8 Rational Numbers Test

Rational Numbers - 1

Rational Numbers - 2

Rational Numbers - 3

Class-8 Rational Numbers Worksheet

Rational Numbers Worksheet - 1

Rational Numbers Worksheet - 2

Rational Numbers Worksheet - 3

Rational Numbers Worksheet - 4

Rational-Numbers-Answer Download the pdf

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• Class 8 Maths MCQs
• Chapter 1 Rational Numbers

Class 8 Maths Chapter 1 Rational Numbers MCQs

Class 8 Maths Chapter 1-Rational Numbers MCQs (Questions and Answers) are provided here online for students. These questions are prepared as per the CBSE board syllabus (2022-2023) and NCERT guidelines. The chapter-wise objective questions are given to students to make them understand each concept and help them to score good marks in exams. Also, learn important questions for class 8 Maths here, at BYJU’S.

Practice more and test your skills on Class 8 Maths Chapter 1 Rational numbers MCQs with the given PDF here. 

MCQs on Class 8 Rational Numbers

Multiple choice questions are available for Class 8 Rational numbers with each question consisting of four answers, out of which one is correct. Students have to solve the question and choose the correct answer. They can also check their solutions here.

1. An integer can be:

A. Only Positive

B. Only Negative

C. Both positive and negative

D. None of the above

Explanation: An integer can be both positive and negative as well as zero.

i.e. …-3, -2, -1, 0, 1, 2, 3,….

2. A rational number can be represented in the form of:

Explanation: A rational number can be represented in the form p/q where p and q are integers and q is not equal to zero.

3. The value of ½ x ⅗ is equal to:

Explanation: ½ x ⅗ = (1 x 3)/(2 x 5) = 3/10

4. The value of (½) ÷ (⅗) is equal to:

Explanation: (½) ÷ (⅗) = (½) x (5/3) = (1 x 5)/(2 x 3) = ⅚

5. The value of ½ + ¼ is equal to:

Explanation: ½ + ¼

Making the denominator equal:

2/4 + ¼ = (2 + 1)/4 = ¾

6. The value of (5/4) – (8/3) is:

Explanation: 5/4 – 8/3

= (15/12) – (32/12)

= (15 – 32)/12

7. The associative property is applicable to:

A. Addition and subtraction

B. Multiplication and division

C. Addition and Multiplication

D. Subtraction and Division

Explanation: As per associative property:

A + (B + C) = (A + B) + C

A × (B × C) = (A × B) × C

8. The value of (-10/3) x (-15/2) x (17/19) x 0 is:

Explanation: Any number multiplied by zero is equal to zero.

9. The additive identity of rational numbers is:

Explanation: Any number added to zero is equal to the number itself.

Ex: 5+0 = 5

Therefore, 0 is the additive identity of rational numbers.

10. The multiplicative identity of rational numbers is:

Explanation: Any number multiplied by 1 is equal to the number itself.

Ex: 5 x 1 = 5

Therefore, 1 is the multiplicative identity of rational numbers.

11. What is the sum of ⅔ and 4/9?

Answer: C.10/9

Solution: ⅔ + 4/9

⇒ ⅔ x (3/3) + 4/9

⇒ 6/9 + 4/9

12. What is the product of 2/9 and ¾?

Answer: A. ⅙

Solution: The product of 2/9 and ¾:

⇒ (2 x 3)/(9 x 4)

⇒ (2 x 3)/(3 x 3 x 2 x 2)

By cancelling the common terms from numerator and denominator, we get;

⇒ 1/(3×2)

13. What is the reciprocal of 1/9?

Answer: A. 9

1/9 x 9 = 1

14. What is the value of 100 divided by 0?

D. Undefined

Answer: D. Undefined

100/0 = undefined

15. Which of the following is commutative for rational numbers?

B. Addition and multiplication

C. Multiplication and division

D. Subtraction and division

Answer: B. Addition and multiplication

16. Division of rational numbers is associative.

Answer: B. False.

Explanation: Division of rational numbers is not associative.

For example, 

2/5 ÷ (1/2 ÷ 1/4) =  0.2

(2/5 ÷ 1/2) ÷ 1/4 = 3.2

Hence, 2/5 ÷ (1/2 ÷ 1/4) ≠ (2/5 ÷ 1/2) ÷ 1/4

17. What is the value of ¾ + ⅚ + 2/7?

Answer: C. 157/84

Solution: Given,

LCM of 4, 6 and 7 = 84

Now, making the denominators the same and adding the given rational numbers, we get;

⇒ 63/84 + 70/84 + 24/84

18. Find the additive inverse of 11/7?

Answer: D. -11/7

Explanation: When a number is added to its additive inverse, then the result is zero,

11/7 – 11/7 = 0

19. How many rational numbers are there in between ¾ and 1?

D. Countless

Answer: D. Countless

Explanation: We can write ¾ as 30/40 and 1 as 40/40.

Hence the rational numbers between them are:

31/40, 32/40, 33/40, 34/40,35/40,36/40, 37/40, 38/40, 39/40.

Note: There are countless rational numbers between any two rational numbers.

20. What should be subtracted from -⅔ to get -1?

Answer: A. ⅓

Solution: Let x is subtracted from -⅔.

-⅔ – x = -1

-x = -1 + ⅔

Video Lesson on Rational Numbers

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For division, identity is 1 and for subtraction, identity is 0. If we divide any number by 1, the number remains the same. Similarly, if we subtract 0 from any number, the number remains the same.

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Rational Numbers Assignment Worksheet Class 8 PDF with Answers

These Rational Numbers Assignment worksheet PDF can be helpful for both teachers and students. Teachers can track their student’s performance in the chapter Rational Numbers Assignment. Students can easily identify their strong points and weak points by solving questions from the worksheet. Accordingly, students can work on both weak points and strong points. 

All students studying in CBSE class 8th, need to practise a lot of questions for the chapter Rational Numbers Assignment. Students can easily practise questions from the Rational Numbers Assignment problems worksheet PDF. By practising a lot of questions, students can improve their confidence level. With the help of confidence level, students can easily cover all the concepts included in the chapter Rational Numbers Assignment. 

Rational Numbers Assignment Worksheets with Solutions

Solutions is the written reply for all questions included in the worksheet. With the help of Rational Numbers Assignment worksheets with solutions, students can solve all doubts regarding questions. Students can have deep learning in the chapter Rational Numbers Assignment by solving all their doubts. By solving doubts, students can also score well in the chapter Rational Numbers Assignment. 

Rational Numbers Assignment Worksheet PDF

Worksheet is a sheet which includes many questions to solve for class 8th students. The Rational Numbers Assignment worksheet PDF provides an opportunity for students to enhance their learning skills. Through these skills, students can easily score well in the chapter Rational Numbers Assignment. Students can solve the portable document format (PDF) of the worksheet from their own comfort zone. 

How to Download the Rational Numbers Assignment Worksheet PDF? 

To solve questions from the Rational Numbers Assignment worksheet PDF, students can easily go through the given steps. Those steps are- 

• Open Selfstudys website.

• Bring the arrow towards CBSE which can be seen in the navigation bar. 

• Drop down menu will appear, select KVS NCERT CBSE Worksheet. 

• A new page will appear, select class 8th from the given list of classes. 
• Select Mathematics from the given list of subjects. Now click the chapter’s name that is Rational Numbers Assignment. 

Features of the Rational Numbers Assignment Worksheet PDF

Before starting to solve questions from the Rational Numbers Assignment problems worksheet PDF, students need to know everything about the worksheet. Those features are- 

• Variety of questions are included:  The Rational Numbers Assignment Maths Worksheet for Class 8 includes varieties of questions. Those varieties of questions are- one mark questions, two mark questions, three mark questions, etc. 
• Solutions are provided:  Doubts regarding each question can be easily solved through the solutions given. Through solving questions, a student's comprehensive skill can be increased. 
• All concepts are covered:  By solving questions from the Rational Numbers Assignment problems worksheet, students can easily cover all the concepts included in the chapter.  
• Created by Expert:  These worksheets are personally created by the subject experts. These Rational Numbers Assignment worksheet pdf are created with proper research. 
• Provides plenty of questions:  The Rational Numbers Assignment worksheet provides plenty of questions to practise. Through good practice, students can get engaged in the learning process. 

Benefits of the Rational Numbers Assignment Worksheet PDF

With the help of Rational Numbers Assignment problems worksheet PDF, students can easily track their performance. This is the most crucial benefit, other than this there are more benefits. Those benefits are- 

• Builds a strong foundation:  Regular solving questions from the worksheet can help students to build a strong foundation. Through the strong foundation, students can score well in the chapter Rational Numbers Assignment. 
• Improves speed and accuracy:  While solving questions from the chapter Rational Numbers Assignment, students need to maintain the speed and accuracy. Speed and accuracy can be easily maintained and improved by solving questions from the Rational Numbers Assignment worksheet PDF. 
• Acts as a guide:  Rational Numbers Assignment worksheets with solutions acts as guide for both the teachers and students. Through the worksheet, teachers can guide their students according to the answers given by them. Students can also analyse themselves with the help of answers and can improve accordingly. 
• Enhances the learning process:  Regular solving of questions from the worksheet can help students enhance their learning process. According to the learning skills, students can easily understand all topics and concepts included in the chapter Rational Numbers Assignment.  
• Improvisation of grades:  Regular solving of questions from the worksheet can help students to improve their marks and grades. With the help of good marks and good grades, students can select their desired field further. 

Tips to Score Good Marks in Rational Numbers Assignment Worksheet

Students are requested to follow some tips to score good marks in the Rational Numbers Assignment worksheet. Those tips are-

• Complete all the concepts:  First and the most crucial step is to understand all the concepts included in the chapter Rational Numbers Assignment.  
• Practise questions:  Next step is to practise questions from the Rational Numbers Assignment problems worksheet. Through this students can identify all types of questions: easy, moderate, difficult, etc.  
• Note down the mistakes:  After practising questions, students need to note down the wrong sums that have been done earlier. 
• Rectify the mistakes:  After noting down the mistakes, students need to rectify all the mistakes made. 
• Maintain a positive attitude:  Students are requested to maintain a positive attitude while solving worksheets. By maintaining a positive attitude, students can improve speed and accuracy while solving the worksheets. 
• Remain focused:  Students need to remain focused while solving questions from the Rational Numbers Assignment problems worksheet pdf. As it helps students to solve the questions as fast as possible. 

When should a student start solving the Rational Numbers Assignment Worksheet PDF?

Students studying in class 8 should start solving worksheets after covering each and every concept included in the chapter. Regular solving questions from the Rational Numbers Assignment worksheet PDF, can help students to have a better understanding of the chapter. Better understanding of the chapter Rational Numbers Assignment can help students to score well in the class 8th board exam. 

Regular solving questions from the Rational Numbers Assignment Worksheet PDF can help students to build a strong foundation for the chapter Rational Numbers Assignment. Strong foundation of the chapter Rational Numbers Assignment can help students to understand further chapters. 

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