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NCERT Solutions for Class 8 Maths Exercises - PDF Solutions

Class 8 Maths covers a vivid CBSE syllabus that includes the basic and advanced concepts of arithmetic, geometry and algebra topics. The preparation of these chapters needs the assistance of the complete study material. Add the NCERT Class 8 Maths All Exercises Solutions developed by the experts of Vedantu to learn how the formulas and concepts of these chapters are skillfully used to frame the accurate answers to the exercise questions.

Vedantu is a platform that provides free NCERT Solutions and other study materials for students. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 8 Science , Maths solutions and solutions of other subjects.

Detailed Overview of Class 8 Maths NCERT Solutions

Ncert solutions for class 8 maths - chapter-wise list.

Given below are the chapter-wise NCERT Solutions for Class 8 Maths . These solutions are provided by the Maths experts at Vedantu in a detailed manner. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Download NCERT Solution for Class 8 Maths to help you to revise complete syllabus answers and score more marks in your examinations.

NCERT Solutions for Class 8 Maths Chapter 1

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NCERT Solutions for Class 8 Maths Chapter 2

Ncert solutions for class 8 maths chapter 3, ncert solutions for class 8 maths chapter 4, ncert solutions for class 8 maths chapter 5, ncert solutions for class 8 maths chapter 6, ncert solutions for class 8 maths chapter 7, ncert solutions for class 8 maths chapter 8, ncert solutions for class 8 maths chapter 9, ncert solutions for class 8 maths chapter 10, ncert solutions for class 8 maths chapter 11, ncert solutions for class 8 maths chapter 12, ncert solutions for class 8 maths chapter 13, ncert solutions for class 8 maths chapter 14, ncert solutions for class 8 maths chapter 15, ncert solutions for class 8 maths chapter 16.

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NCERT Solutions for Class 8 Maths - All Exercises

   

Importance of NCERT Maths All Exercises book Class 8 Solutions

The solutions have been framed chapter-wise so that students can find them right away on the list. These solutions contain precise answers to all the fundamental questions asked in the exercises. All these answers have been framed following the latest CBSE syllabus so that students can get accustomed to the best methods of answering such questions to score more.

The exercise solutions will act as the perfect guide for the students to follow during preparing an exam syllabus. They will learn the specific techniques and can even assess their preparation level by comparing their answers to the solutions.

Benefits of Chapter Wise List of Class 8 Maths All Exercises

The 8th Maths All Exercises Book Answers will help you find the right answers and answering methods in no time. You can make your preparation sessions more efficient.

Learn how to solve crucial exercise problems by following the answers in the solutions. Grab hold of the stepwise techniques to keep your answers to the point.

Resolve doubts related to Class 8 Maths exercises and prepare chapters faster.

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Important Related Links for NCERT Class 8

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Important Questions for CBSE Class 8

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NCERT Solutions for Class 8

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NCERT Solutions for Class 8 Maths Free PDF Download

Ncert solutio ns for class 8 maths.

NCERT Solutions for Class 8 Maths will help you to ace the unsolved problems in the maths book prescribed by the CBSE. NCERT Solutions for Class 8 breaks down the solutions into detailed steps to increase your score in exams.

NCERT Solutions are prepared by our team of highly professional, qualified and experienced faculties. These NCERT Solutions for Class 8 Maths helps you to quickly grasp all the concepts and formulas of maths. In case you have a doubt while you are studying NCERT Solutions for Class 8 Maths which we are providing, for this, we have a team of teachers who are just a click away to solve your doubt any time.

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ncert solutions for class 8 maths

NCERT Solutions for Class 8 Maths Chapter-wise

  • Chapter 1- Rational Numbers
  • Chapter 2 – Linear Equations in One Variable
  • Chapter 3 – Understanding Quadrilaterals
  • Chapter 4 – Practical Geometry
  • Chapter 5 – Data Handling
  • Chapter 6 – Square and Square Roots
  • Chapter 7 – Cube and Cube Roots
  • Chapter 8 – Comparing Quantities
  • Chapter 9 – Algebraic Expressions and Identities
  • Chapter 10 – Visualising Solid Shapes
  • Chapter 11- Mensuration
  • Chapter 12 – Exponents and Powers
  • Chapter 13 – Direct and Inverse Proportions
  • Chapter 14 – Factorisation
  • Chapter 15 – Introduction to Graphs
  • Chapter 16 – Playing with Numbers

CBSE Class 8 Maths Chapter-wise NCERT Solutions

Ncert solutions for class 8 maths chapter 1 – rational numbers.

In this chapter will learn the properties of real numbers, rational numbers, representation of a rational number on number line, additive and multiplicative identity.

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

In this chapter you will learn the concept of linear equation and methods to solve them, reducing equations to a simpler form and their applications.

NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals

In this chapter, you will learn the basics of a quadrilateral, polygon, kinds of quadrilateral and polygon, the measure of external angle of polygons.

NCERT Solutions for Class 8 Maths Chapter 4 – Practical Geometry

This chapter includes drawing 4 sides in a quadrilateral with 2 adjacent sides, 3 angles, and 1 diagonal area given.

NCERT Solutions for Class 8 Maths Chapter 5 – Data Handling

In this chapter you will learn to organize the data in a systematic method, represent the data in a pictograph, a bar graph, double bar graph, pie chart, and histogram.

NCERT Solutions for Class 8 Maths Chapter 6 – Square and Square Roots

In this chapter, you will learn about the squares of numbers and their properties, various patterns of squares, and square roots of numbers.

NCERT Solutions for Class 8 Maths Chapter 7 – Cube and Cube Roots

In this you will study about cubes of different numbers, cubes of numbers by adding consecutive odd numbers pattern, cube roots of a number, solving cube roots by prime factorization method.

NCERT Solutions for Class 8 Maths Chapter 8 – Comparing Quantities

In this chapter you will compare quantities, increase or decrease of percentage, discount, profit and loss, vat tax, sales tax, computing interest.

NCERT Solutions for Class 8 Maths Chapter 9 – Algebraic Expressions and Identities

In this chapter, you will learn about the algebraic expressions and their types, like and unlike terms, addition and subtraction, multiplication of algebraic expressions, standard identities and their implementation.

NCERT Solutions for Class 8 Maths Chapter 10 – Visualizing Solid Shapes

In this chapter, you will study the cubes, cuboids, cones, cylinders, spheres, hemispheres and their area, triangular pyramids, triangular and square base prisms, application of Euler’s formula.

NCERT Solutions for Class 8 Maths Chapter 11 – Mensuration

In this chapter, you will learn about the perimeter and areas of plane closed figure and surface area, the volume of a solid figure, transform the quantity into other units.

NCERT Solutions for Class 8 Maths Chapter 12 – Exponents and Powers

In this chapter you will study powers with negative exponents, laws of exponents, express the numbers in standard form and comparison of extremely large numbers.

NCERT Solutions for Class 8 Maths Chapter 13 – Direct and Inverse Proportions

In this chapter, you will solve the problems related to direct and inverse proportion and their identification based on relative increase or decrease of a quantity with respect to the first one.

NCERT Solutions for Class 8 Maths Chapter 14 – Factorization

In this chapter, you will learn methods of factorization, division of algebraic expression, error finding in algebraic equations.

NCERT Solutions for Class 8 Maths Chapter 15 – Introduction to Graphs

In this, you will study the representations of data by a bar graph, histogram, pie chart, line graph, and linear graph, application based on the graph using the dependent & independent variable.

NCERT Solutions for Class 8 Maths Chapter 16: Playing with Numbers

In this chapter, you will deal with numbers in a general form, puzzles related to numbers, divisibility tests.

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Solved Questions For You:

Question 1. For which of these would you use a histogram to show the data? (a) The number of letters for different areas in a postman’s bag. (b) The height of competitors in an athletics meet. (c) The number of cassettes produced by  5  companies. (d) The number of passengers boarding trains from  7 : 0 0  a.m. to  7 : 0 0  p.m. at a station. Give reasons for each.

(a) We can’t use the histogram in this case because we cannot define the class intervals for this data.

(b) We can use histogram here because it will be easy to divide the data into class intervals.

(c) We do not have approximate data we won’t use a histogram. We do not know about the number of cassettes produced by companies.

Question 2. List the outcomes you can see in these experiments.

question

(a) Possible outcomes would be:  A , B , C , D

Question 3. When a die is thrown, list the outcomes of an event of getting

(i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than  5

Possible outcomes:  1 , 2 , 3 , 4 , 5 , 6 (i) (a) Prime numbers:  2 , 3 , 5 It represents the outcomes of Prime numbers (b) Not a prime number:  1 , 4 , 6 It represents the outcomes of not prime numbers. (ii) (a) A number greater than  5 : Only when  6  comes (b) Number not greater than  5 : Only when outcomes:  1 , 2 , 3 , 4  and  5

Question 4. A survey was made to find the type of music that a certain group of young people liked in a city. The adjoining pie chart shows the findings of this survey.

From this pie chart answer the following: (i) If  2 0  people liked classical music, how many young people were surveyed? (ii) Which type of music is liked by the maximum number of people? (iii) If a cassette company were to make  1 0 0 0  CDs, how many of each type would they make?

question

The light chart represents the maximum number as it is  4 0 % of the total.  ∴  Light music is liked by max. people.

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NCERT Solutions for Class 8

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Unit 1: Numbers and operations

Unit 2: solving equations with one unknown, unit 3: linear equations and functions, unit 4: systems of equations, unit 5: geometry, unit 6: geometric transformations, unit 7: data and modeling, review articles.

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Assignments For Class 8 Mathematics

Assignments for Class 8 Mathematics have been developed for Standard 8 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 8 Mathematics from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 8 Mathematics. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics book and get good marks in class 8 exams.

Assignments for Class 8 Mathematics as per CBSE and NCERT pattern

More assignments for class 8 mathematics, assignments for class 8 mathematics as per cbse ncert pattern.

All students studying in Grade 8 Mathematics should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics exam for standard 8. We have made sure that all topics given in your textbook for Mathematics which is suggested in Class 8 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 8 Mathematics

  • Solving Assignments for Mathematics Class 8 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
  • By solving one assignments given in your class by Mathematics teacher for class 8 will help you to keep in touch with the topic thus reducing dependence on last minute studies
  • You will be able to understand the type of questions which are expected in your Mathematics class test
  • You will be able to revise all topics given in the ebook for Class 8 Mathematics as all questions have been provided in the question banks
  • NCERT Class 8 Mathematics Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
  • Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 8 Mathematics teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 8 Mathematics Assignments PDF.

Assignments For Class 8 Mathematics

You can download free assignments for class 8 Mathematics from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 8 Mathematics from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 8, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

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  • NCERT Solutions
  • NCERT Class 8
  • NCERT 8 Maths
  • Chapter 1: Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Ncert solutions class 8 maths chapter 1 – free pdf download.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers are provided here to help the students understand the concepts right from the beginning. The concepts taught in Class 8 are important to be understood as these concepts are continued in Classes 9 and 10. To score good marks in the Class 8 Mathematics examination, it is advised to solve questions provided at the end of each chapter in the NCERT textbook. These NCERT Solutions for Class 8 Maths help the students understand all the concepts in a better way.

Download Exclusively Curated Chapter Notes for Class 8 Maths Chapter – 1 Rational Numbers

Download most important questions for class 8 maths chapter – 1 rational numbers.

Numbers that can be represented in the form of p/q, where q is not equal to zero, are known as Rational Numbers . It is one of the most critical topics in Class 8 Maths. In simpler words, any fraction with a non-zero denominator is said to be a rational number. To represent rational numbers on a number line, we need to simplify them first. Does it sound hard? Not anymore. Students can now access the NCERT Solutions for Class 8 Maths Chapter 1 while solving the exercise problems for any concept clarity and doubt clearance. Try practising these NCERT Solutions to grasp important topics with ease.

NCERT Solutions for Class 8 Maths – Rational Numbers

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ncert solutions for class 8 maths may22 chapter 1 rational numbers 1

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Access Answers to NCERT Class 8 Maths Chapter 1 Rational Numbers

Exercise 1.1 page: 14, 1. using appropriate properties, find:.

(i) -2/3 × 3/5 + 5/2 – 3/5 × 1/6

-2/3 × 3/5 + 5/2 – 3/5 × 1/6

= -2/3 × 3/5– 3/5 × 1/6+ 5/2 (by commutativity)

= 3/5 (-2/3 – 1/6)+ 5/2

= 3/5 ((- 4 – 1)/6)+ 5/2

= 3/5 ((–5)/6)+ 5/2 (by distributivity)

= – 15 /30 + 5/2

= – 1 /2 + 5/2

(ii) 2/5 × (- 3/7) – 1/6 × 3/2 + 1/14 × 2/5

2/5 × (- 3/7) – 1/6 × 3/2 + 1/14 × 2/5

= 2/5 × (- 3/7) + 1/14 × 2/5 – (1/6 × 3/2) (by commutativity)

= 2/5 × (- 3/7 + 1/14) – 3/12

= 2/5 × ((- 6 + 1)/14) – 3/12

= 2/5 × ((- 5)/14)) – 1/4

= (-10/70) – 1/4

= – 1/7 – 1/4

= (– 4– 7)/28

2. Write the additive inverse of each of the following:

The Additive inverse of 2/8 is – 2/8

The additive inverse of -5/9 is 5/9

(iii) -6/-5 = 6/5

The additive inverse of 6/5 is -6/5

(iv) 2/-9 = -2/9

The additive inverse of -2/9 is 2/9

(v) 19/-16 = -19/16

The additive inverse of -19/16 is 19/16

3. Verify that: -(-x) = x for:

(i) x = 11/15

(ii) x = -13/17

We have, x = 11/15

The additive inverse of x is – x (as x + (-x) = 0).

Then, the additive inverse of 11/15 is – 11/15 (as 11/15 + (-11/15) = 0).

The same equality, 11/15 + (-11/15) = 0, shows that the additive inverse of -11/15 is 11/15.

Or, – (-11/15) = 11/15

i.e., -(-x) = x

(ii) -13/17

We have, x = -13/17

Then, the additive inverse of -13/17 is 13/17 (as 13/17 + (-13/17) = 0).

The same equality (-13/17 + 13/17) = 0, shows that the additive inverse of 13/17 is -13/17.

Or, – (13/17) = -13/17,

4. Find the multiplicative inverse of the following:

(i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × (-3/7) (v) -1 × (-2/5) (vi) -1

Multiplicative inverse of -13 is -1/13.

(ii) -13/19

Multiplicative inverse of -13/19 is -19/13.

Multiplicative inverse of 1/5 is 5.

(iv) -5/8 × (-3/7) = 15/56

Multiplicative inverse of 15/56 is 56/15.

(v) -1 × (-2/5) = 2/5

Multiplicative inverse of 2/5 is 5/2.

mathematics assignment class 8

Multiplicative inverse of -1 is -1.

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

(i) -4/5 × 1 = 1 × (-4/5) = -4/5

(ii) -13/17 × (-2/7) = -2/7 × (-13/17)

(iii) -19/29 × 29/-19 = 1

Here 1 is the multiplicative identity.

The property of commutativity is used in the equation.

The multiplicative inverse is the property used in this equation.

6. Multiply 6/13 by the reciprocal of -7/16.

Reciprocal of -7/16 = 16/-7 = -16/7

According to the question,

6/13 × (Reciprocal of -7/16)

6/13 × (-16/7) = -96/91

mathematics assignment class 8

7. Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3.

1/3 × (6 × 4/3) = (1/3 × 6) × 4/3

Here, the way in which factors are grouped in a multiplication problem supposedly does not change the product. Hence, the Associativity Property is used here.

8/9 × (-9/8) = -1 ≠ 1

3/10 × 10/3 = 1

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocals.

(iii) The rational number that is equal to its negative.

(I) The rational number that does not have a reciprocal is 0.

Reciprocal of 0 = 1/0, which is not defined.

mathematics assignment class 8

(ii) The rational numbers that are equal to their reciprocals are 1 and -1.

Reciprocal of 1 = 1/1 = 1, similarly, reciprocal of -1 = – 1

(iii) The rational number that is equal to its negative is 0.

Negative of 0=-0=0

11. Fill in the blanks.

(i) Zero has _______reciprocal.

(ii) The numbers ______and _______are their own reciprocals

(iii) The reciprocal of – 5 is ________.

(iv) Reciprocal of 1/x, where x ≠ 0 is _________.

(v) The product of two rational numbers is always a ________.

(vi) The reciprocal of a positive rational number is _________.

(i) Zero has no reciprocal.

(ii) The numbers -1 and 1 are their own reciprocals

(iii) The reciprocal of – 5 is -1/5 .

(iv) Reciprocal of 1/x, where x ≠ 0 is x .

(v) The product of two rational numbers is always a rational number .

(vi) The reciprocal of a positive rational number is positive .

Exercise 1.2 Page: 20

1. Represent these numbers on the number line.

Divide the line between the whole numbers into 4 parts, i.e. divide the line between 0 and 1 to 4 parts, 1 and 2 to 4 parts, and so on.

Thus, the rational number 7/4 lies at a distance of 7 points away from 0 towards the positive number line.

NCERT Solution For Class 8 Maths Chapter 1 Image 7

Divide the line between the integers into 4 parts, i.e. divide the line between 0 and -1 to 6 parts, -1 and -2 to 6 parts, and so on. Here, since the numerator is less than the denominator, dividing 0 to – 1 into 6 parts is sufficient.

Thus, the rational number -5/6 lies at a distance of 5 points, away from 0, towards the negative number line.

NCERT Solution For Class 8 Maths Chapter 1 Image 8

2. Represent -2/11, -5/11, -9/11 on a number line.

Divide the line between the integers into 11 parts.

Thus, the rational numbers -2/11, -5/11, and -9/11 lie at a distance of 2, 5, and 9 points away from 0, towards the negative number line, respectively.

NCERT Solution For Class 8 Maths Chapter 1 Image 9

3. Write five rational numbers which are smaller than 2.

The number 2 can be written as 20/10

Hence, we can say that the five rational numbers which are smaller than 2 are:

2/10, 5/10, 10/10, 15/10, 19/10

4. Find the rational numbers between -2/5 and ½.

Let us make the denominators the same, say 50.

-2/5 = (-2 × 10)/(5 × 10) = -20/50

½ = (1 × 25)/(2 × 25) = 25/50

Ten rational numbers between -2/5 and ½ = ten rational numbers between -20/50 and 25/50.

Therefore, ten rational numbers between -20/50 and 25/50 = -18/50, -15/50, -5/50, -2/50, 4/50, 5/50, 8/50, 12/50, 15/50, 20/50.

mathematics assignment class 8

5. Find five rational numbers between:

(i) 2/3 and 4/5

(ii) -3/2 and 5/3

(iii) ¼ and ½

Let us make the denominators the same, say 60

i.e., 2/3 and 4/5 can be written as:

2/3 = (2 × 20)/(3 × 20) = 40/60

4/5 = (4 × 12)/(5 × 12) = 48/60

Five rational numbers between 2/3 and 4/5 = five rational numbers between 40/60 and 48/60.

Therefore, five rational numbers between 40/60 and 48/60 = 41/60, 42/60, 43/60, 44/60, 45/60.

mathematics assignment class 8

Let us make the denominators the same, say 6

i.e., -3/2 and 5/3 can be written as:

-3/2 = (-3 × 3)/(2× 3) = -9/6

5/3 = (5 × 2)/(3 × 2) = 10/6

Five rational numbers between -3/2 and 5/3 = five rational numbers between -9/6 and 10/6.

Therefore, five rational numbers between -9/6 and 10/6 = -1/6, 2/6, 3/6, 4/6, 5/6.

Let us make the denominators the same, say 24

i.e., ¼ and ½ can be written as:

¼ = (1 × 6)/(4 × 6) = 6/24

½ = (1 × 12)/(2 × 12) = 12/24

Five rational numbers between ¼ and ½ = five rational numbers between 6/24 and 12/24.

Therefore, five rational numbers between 6/24 and 12/24 = 7/24, 8/24, 9/24, 10/24, 11/24.

6. Write five rational numbers greater than -2.

-2 can be written as – 20/10

Hence, we can say that the five rational numbers greater than -2 are

-10/10, -5/10, -1/10, 5/10, 7/10

7. Find ten rational numbers between 3/5 and ¾.

Let us make the denominators the same, say 80.

3/5 = (3 × 16)/(5× 16) = 48/80

3/4 = (3 × 20)/(4 × 20) = 60/80

Ten rational numbers between 3/5 and ¾ = ten rational numbers between 48/80 and 60/80.

Therefore, ten rational numbers between 48/80 and 60/80 = 49/80, 50/80, 51/80, 52/80, 54/80, 55/80, 56/80, 57/80, 58/80, 59/80.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Summary

Chapter 1, Rational Numbers, contains 2 exercises, and the NCERT Solutions for Class 8 Maths given here contains precise answers for all the questions present in these exercises. Let us have a look at some of the concepts that are being discussed in this chapter.

  • Rational numbers are closed under the operations of addition, subtraction and multiplication.
  • Commutative for rational numbers
  • Associative for rational numbers
  • The rational number 0 is the additive identity for rational numbers.
  • Rational number 1 is the multiplicative identity for rational numbers.
  • Distributivity of rational numbers: For all rational numbers a, b and c, a(b + c) = ab + ac and a(b – c) = ab – ac
  • Rational numbers can be represented on a number line.
  • Between any two given rational numbers, there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.

The main topics covered in this chapter include:

1.1 Introduction

1.2 Properties of Rational Numbers

1.2.1 Closure

1.2.2 Commutativity

1.2.3 Associativity

1.2.4 The Role of Zero

1.2.5 The Role of 1

1.2.6 Negative of a Number

1.2.7 Reciprocal

1.2.8 Distributivity of Multiplication over Addition for Rational Numbers.

1.3 Representation of Rational Numbers on the Number Line

1.4 Rational Numbers between Two Rational Numbers

It’s highly recommended that students utilise the NCERT Solutions for Class 8 to comprehend key concepts in CBSE Class 8 Maths. Unasked doubts can also be clearly instantly when referred to these solutions.

Access Exercise-wise NCERT Solutions Class 8 Maths of Chapter 1:

Exercise 1.1 Solutions 11 Questions (11 Short Answer Questions) Exercise 1.2 Solutions 7 Questions (7 Short Answer Questions)

Numbers are considered to be the most basic block of Mathematics. In lower classes, the students would have learnt the different types of numbers, including natural numbers, whole numbers, integers etc. Chapter 1 of Class 8 Maths  NCERT Solutions takes the students to another set of numbers, the rational numbers.  This chapter explains almost all the concepts that a student of Class 8 has to learn about rational numbers.

Chapter 1 of NCERT Class 8 Maths also describes the method of representing a rational number on a number line as well as the method of finding rational numbers between 2 rational numbers. Read and learn Chapter 1 of the  NCERT textbook to learn more about Rational Numbers and the concepts covered in them. Learn the NCERT Solutions for Class 8 effectively to score high in the annual examination.

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Dropped Topics – 1.2.6 Negative of a number, 1.2.7 Reciprocal, 1.3 Representation of rational numbers on the number line and 1.4 Rational numbers between two rational numbers.

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Category: Assignments Class 8

Assignments Class 8 Mathematics Visualising Solid Shapes PDF Download

Assignments Class 8 Mathematics Visualising Solid Shapes PDF Download

Students can refer to Assignments for Class 8 Mathematics Visualising Solid Shapes available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Visualising Solid Shapes Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your […]

Assignments Class 8 Mathematics Understanding Quadrilaterals PDF Download

Assignments Class 8 Mathematics Understanding Quadrilaterals PDF Download

Students can refer to Assignments for Class 8 Mathematics Understanding Quadrilaterals available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Understanding Quadrilaterals Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest NCERT […]

Assignments Class 8 Mathematics Squares and Square Roots PDF Download

Assignments Class 8 Mathematics Squares and Square Roots PDF Download

Students can refer to Assignments for Class 8 Mathematics Squares and Square Roots available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Squares and Square Roots Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given […]

Assignments Class 8 Mathematics Rational Numbers PDF Download

Assignments Class 8 Mathematics Rational Numbers PDF Download

Students can refer to Assignments for Class 8 Mathematics Rational Numbers available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Rational Numbers Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest NCERT […]

Assignments Class 8 Mathematics Practical Geometry PDF Download

Assignments Class 8 Mathematics Practical Geometry PDF Download

Students can refer to Assignments for Class 8 Mathematics Practical Geometry available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Practical Geometry Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest NCERT […]

Assignments Class 8 Mathematics Playing with Numbers PDF Download

Assignments Class 8 Mathematics Playing with Numbers PDF Download

Students can refer to Assignments for Class 8 Mathematics Playing with Numbers available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Playing with Numbers Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your […]

Assignments Class 8 Mathematics Linear Equations PDF Download

Assignments Class 8 Mathematics Linear Equations PDF Download

Students can refer to Assignments for Class 8 Mathematics Linear Equations available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Linear Equations Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest NCERT […]

Assignments Class 8 Mathematics Mensuration PDF Download

Assignments Class 8 Mathematics Mensuration PDF Download

Students can refer to Assignments for Class 8 Mathematics Mensuration available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Mensuration Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest NCERT Books for […]

Assignments Class 8 Mathematics Introduction to Graphs PDF Download

Assignments Class 8 Mathematics Introduction to Graphs PDF Download

Students can refer to Assignments for Class 8 Mathematics Introduction to Graphs available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Introduction to Graphs Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your […]

Assignments Class 8 Mathematics Factorisation PDF Download

Assignments Class 8 Mathematics Factorisation PDF Download

Students can refer to Assignments for Class 8 Mathematics Factorisation available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Factorisation Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest NCERT Books for […]

Outrage After Class 8 Students In US Asked To Rate Hitler In Assignment

The questions sparked an outrage with some parents expressing concern and questioning if these are anti-semitic in nature.

Outrage After Class 8 Students In US Asked To Rate Hitler In Assignment

Adolf Hitler was the dictator of Nazi Germany from 1933 to 1945.

A private school in the US is making news for giving assignments to Class 8 students on Adolf Hitler, the dictator of Nazi Germany from 1933 to 1945. According to Fox5 Atlanta, the students were given a series of questions asking them to rate some of Hitler's characteristics as a leader. A screenshot of the question-and-answer assignment given by Mount Vernon School in Atlanta to the students has been posted on X by Fox5 reporter, highlighting the sections that are causing controversy.

EXCLUSIVE: An Adolf Hitler themed school assignment is causing controversy at the Mount Vernon School. 8th graders were asked to rate Hitler as a “Solution Seeker” & as an “Ethical Decision maker.” At 5&6pm on @FOX5Atlanta : students & the school respond. pic.twitter.com/sxEJq11mLy — Brittany Edney (@BrittanyEdney) May 14, 2024

In one of the questions, students were asked, "According to the Mount Vernon Mindset rubric, how would you rate Adolf Hitler as a 'solution seeker'?"

Another one asked students to "rate Adolf Hitler as an ethical decision-maker".

Both the questions included options like "Lacks Evidence, Approaching Expectations, Meets Expectations, Exceeds Expectations".

Students too found the questions "troubling" and wondered if the questions glorified the Nazi leader.

"Obviously, that looks horrible in the current context. Knowing Mount Vernon, we do things a little odd around here," one student told Fox5 Atlanta.

One student said he can see the school's intended approach to critical thinking.

"I can definitely see why they'd be upset, but overall, I think it's important to look at both sides of the coin in every situation and I think it's important to be able to compare and contrast everything that's happened in our world history, whether it's been good or bad," said the student.

The outlet also spoke to some former students who said these questions weren't given to them during eighth grade.

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When school officials came to know about the phrasing of the questions, they removed if from the school's curriculum.

The principal of Mount Vernon, Kristy Lundstrom, wrote in a statement that the assignment was "an exploration of World War II designed to boost student knowledge of factual events and understand the manipulation of fear leveraged by Adolf Hitler in connection to the Treaty of Versailles."

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‘It Feels Like I Am Screaming Into the Void With Each Application’

An illustration depicting the orange silhouette of a person sitting down, their arms around their knees as if dejected, wearing a blue mortarboard.

By Peter Coy

Opinion Writer

When I asked new college graduates last month to tell me about their job searches, I got back a ton of heartache. Unanswered applications. Lowered expectations. For some, a sense that college was a waste of time and money.

John York wrote that he was about to earn a master’s degree in mathematics from New York University. “I have submitted close to 400 applications. I have heard back from less than 40, all rejections,” he wrote. “I essentially cannot get any job, because there are no entry-level positions anywhere at all.” He has a patent, he passed the first-level exam for Chartered Financial Analysts and he’s getting his Series 3 license, another financial credential. Nevertheless, he wrote, “It is just so silent, it feels like I am screaming into the void with each application I am filling out.”

Mauricio Naranjo, who is seeking work as a graphic designer, wrote, “Over the past year, I have submitted more than 400 applications and consistently receive a response that appears to be A.I.-generated, stating that unfortunately, they have moved forward with another candidate who better fits their expectations. This is the exact phrasing every time. Very few respond, as most do not reply at all.”

“Exhausting. Utterly demoralizing,” wrote Beth Donnelly, who is graduating this month with a major in linguistics and minors in German and teaching English as a second language. “I’ve been searching since early August for full-time, part-time or internship positions after I graduate. I’ve started putting my ‘desired salary’ at $35,000 in hope that just one person will think, ‘Oh, I won’t have to pay this person a large wage, so they get a leg up in the hiring process.’”

I got some positive responses, too. Lucinda Warnke, who landed a job in journalism as a general assignment reporter, wrote: “I am optimistic and excited! I feel confident in my career trajectory and my ability to build a stable, satisfying career. The job I got out of school comes with a livable wage and benefits, so I can build savings in the event that I am laid off or have some other financially demanding emergency. I feel like I made a good investment in my education because I went to a school that was affordable and studied subjects that balanced my interests with my professional needs.”

A majority of responses were grim, though. That’s not too surprising, given that half of college graduates are underemployed a year after graduation, meaning that they are working in jobs that don’t require the degrees they earned, as I wrote in my April 29 newsletter.

There’s clearly something wrong when young graduates can’t find jobs at the same time that employers complain of not being able to find qualified workers. As of March, there were still fewer unemployed people than job openings, according to the Bureau of Labor Statistics. In April the unemployment rate remained below average at 3.9 percent.

The responses I got aren’t a representative sample of all college graduates. It’s possible that unhappy people were more likely to write in. (I had to leave out some of the angriest and most dejected people because they didn’t want their names to appear.) Separately, my informal impression is that the people who wrote — happy or sad — were more likely to have attended a highly ranked school and to have graduated without student loans than the general student population.

Many students wrote that the jobs they were seeking or secured didn’t draw on what they learned in the classroom. “I will be using the skills I picked up in my data science minor, but nothing from my major (international relations),” Rain Orsi, a 2024 graduate, wrote. “A lot of the educational stuff could’ve been condensed to a 20-page PDF and I probably would be at the same knowledge level,” another student wrote. Jackeline Arcara wrote that if she had it to do over again, “I wouldn’t go to a four-year, fancy-pants school. I would take classes at a local college part-time and see where that takes me.”

Some students said that classroom learning was only part of what made college worthwhile to them. “College gives you four years to grow up — I have the maturity now to handle a full-time job. Before college, not so much,” wrote Caroline Lidz, who got a job in public relations after graduating in December with a degree in media studies and communications and a minor in art history.

Several said internships matter, a lot. “I wish I interned for a company outside of the school instead of being a research/lab assistant,” wrote Roger Vitek, who is graduating in June with a degree in product design and is still job hunting.

Economists have found that what you study in college is at least as important as where you study. As I wrote in my April 29 piece, there’s relatively strong demand for computer science, engineering, mathematics and math-intensive business fields such as finance and accounting.

But as I found out from the people who wrote in, that’s not always the case. Robert Vermeulen, a computer science major, wrote, “Out of the ~155 applications I haven’t had a reference on, I have gotten zero interviews.” Morgan Steckler wrote that he is looking for a software engineering or I.T. administration role paying at least $70,000 a year, but has had no luck so far. He said he’s thinking of bartending while continuing to send out applications. On the positive side, there are people like Warnke, who got a job as a reporter — not exactly a fast-growing profession.

As I read students’ responses, I had to remind myself that this is actually a relatively good year for finding a job. To a lot of members of the class of ’24, it doesn’t feel that way. Julia Brukx, who is graduating with a degree in history and art history, wrote, “I think I hit a new low just this morning when asked to write a cover letter for a retail position.”

Donnelly, the woman who described her job search as demoralizing, wrote: “I was told that if I was involved, active, kind, ready to learn, driven and intelligent, I would end up with a job out of college. This is evidently not true, and few older people seem to understand this.” She added, “I don’t have a backup plan besides working in the service industry.”

Elsewhere: Caps, Not Bans, for Short-Term Rentals

New York City’s Local Law 18, which was passed with the support of the hotel industry, tightens the rules on renting out rooms for less than 30 days. Supporters say renting rooms to tourists raises rents for New Yorkers. But an article published in Harvard Business Review by three scholars — one of whom used to work for Airbnb — calculates that Airbnb caused only about 1 percent of the aggregate increase in rents over the past decade or so. Hosts, guests and the businesses that serve them benefit. To keep certain neighborhoods from being overwhelmed by tourists, the authors recommend caps on how many nights per year a place may be rented out.

Quote of the Day

“The hedonistic conception of man is that of a lightning calculator of pleasures and pains who oscillates like a homogeneous globule of desire of happiness under the impulse of stimuli that shift him about the area, but leave him intact. He has neither antecedent nor consequent.”

— Thorstein Veblen, “Why Is Economics Not an Evolutionary Science?” (1898)

Peter Coy is a writer for the Opinion section of The Times, covering economics and business. Email him at [email protected] . @ petercoy

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Class 8 Mathematics Exponents and Powers Assignments

We have provided below free printable Class 8 Mathematics Exponents and Powers Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 8 Mathematics Exponents and Powers . These Assignments for Grade 8 Mathematics Exponents and Powers cover all important topics which can come in your standard 8 tests and examinations. Free printable Assignments for CBSE Class 8 Mathematics Exponents and Powers , 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 Assignments for Mathematics Exponents and Powers Class 8 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Exponents and Powers Class 8. Students can click on the links below and download all Pdf Assignments for Mathematics Exponents and Powers class 8 for free. All latest Kendriya Vidyalaya Class 8 Mathematics Exponents and Powers Assignments with Answers and test papers are given below.

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We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 8 Mathematics Exponents and Powers . Students and teachers can download and save all free Mathematics Exponents and Powers assignments in Pdf for grade 8th. Our expert faculty have covered Class 8 important questions and answers for Mathematics Exponents and Powers as per the latest syllabus for the current academic year. All test papers and question banks for Class 8 Mathematics Exponents and Powers and CBSE Assignments for Mathematics Exponents and Powers Class 8 will be really helpful for standard 8th students to prepare for the class tests and school examinations. Class 8th students can easily free download in Pdf all printable practice worksheets given below.

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Class 8 Mathematics Exponents and Powers Assignments

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    All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 8. Students can click on the links below and download all Pdf Assignments for Mathematics class 8 for free. All latest Kendriya Vidyalaya Class 8 Mathematics Assignments with Answers and test papers are given below.

  2. NCERT Solutions for Class 8 Maths Updated for 2023-24

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  4. Rational Numbers Class 8 Practice Questions [Solved]

    Practice Questions on Rational Numbers Class 8. 1. State true or false for the following: (i) All integers are rational number. (ii) Multiplicative inverse does not exist for rational numbers. (iii) 1 is the additive identity for rational numbers. (iv) ⅔ lies in between the rational numbers ⅛ and 7/9.

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    NCERT Solutions for Class 8 - Download PDFs. NCERT Solutions for Class 8 is a very crucial study material as it is responsible for laying a strong foundation for your higher classes. However, there is no need to get too stressed or overwhelmed. The best study material any Class 8 student can use is NCERT Books.The textbook explains all the concepts that have to be learned by a Class 8 ...

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    NCERT Solutions for Class 8 Maths Chapter-wise. Chapter 1- Rational Numbers. Chapter 2 - Linear Equations in One Variable. Chapter 3 - Understanding Quadrilaterals. Chapter 4 - Practical Geometry. Chapter 5 - Data Handling. Chapter 6 - Square and Square Roots. Chapter 7 - Cube and Cube Roots. Chapter 8 - Comparing Quantities.

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    According to NCERT Solutions for Class 8 Maths Chapter 1, rational numbers are represented in p/q form where q is not equal to zero. It is also a type of real number. Any fraction with non-zero denominators is a rational number. Hence, we can say that '0' is also a rational number, as we can represent it in many forms, such as 0/1, 0/2, 0/3 ...

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    Students can refer to Assignments for Class 8 Mathematics Factorisation available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Factorisation Class 8 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest ...

  17. Outrage After Class 8 Students In US Asked To Rate Hitler In Assignment

    A private school in the US is making news for giving assignments to Class 8 students on Adolf Hitler, the dictator of Nazi Germany from 1933 to 1945. According to Fox5 Atlanta, the students were ...

  18. Opinion

    John York wrote that he was about to earn a master's degree in mathematics from New York University. "I have submitted close to 400 applications. I have heard back from less than 40, all ...

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