# Ncert Solutions for Class 8 Maths

**CBSE Class 8 Maths Ncert Solutions 2022-23 Edition**

**NCERT Solutions for Class 8 Maths **are available here according to the latest **CBSE Syllabus** Download PDF free**.** These Solutions are prepared by Utopper Subjects experts and will help you in your exam preparation. Practicing **NCERT Solutions** is an absolute necessity for students who wish to perform well on their Maths examination. Students having difficulty solving problems from the **NCERT textbook** for Class 8 can consult the NCERT Solutions listed below.

Students are advised to practise the **Class 8 NCERT Solutions**, which are available in PDF format, as this facilitates their comprehension of fundamental concepts. Utopper has prepared step-by-step solutions with thorough explanations for students who experience anxiety while searching for the most comprehensive and thorough **NCERT Solutions for Class 8 Maths**. Our expert tutors have designed these exercises to aid in your exam preparation and help you earn high marks in the subject.Â

## Ncert Solutions for **Class 8 Maths Latest 2023 – Download Free PDFs**

Our subject experts put together the **NCERT Solutions for Class 8 Maths** to answer all of your questions about every chapter in one place. Students who want to do well on the **CBSE Class 8** Exam will find that these Solutions for **Class 8 NCERT** are a great way to learn all of the Maths, Science, and Social Science concepts on the **syllabus**. The **NCERT Solutions** are clearly explained with clear graphs and worked-out examples that make it easy to learn. It helps students build a strong understanding of ideas, which is a big part of how well they do on competitive exams later on.

**Chapterwise PDF for NCERT Solutions for Class 8 Maths**

Students in 8th grade can access these items according to their needs and preferences. While completing **NCERT books** problems, they can use our solutions manual to obtain the best, most simply comprehended responses. In addition, when preparing for the exam, they can use our **revision notes**, which provide an overview of all the relevant topics. In addition, **the **previous year’s question papers will aid in understanding the exam’s question format and grading method. To have extra practice** sample papers** and critical questions are supplied on **Utopper**. Click on the below links to obtain the necessary materials for Class 8.Â

**NCERT Solutions for Class 8 Maths â€“ All Chapters**

The **NCERT Class 8 Maths Solutions** are given out in a logical way. The solutions are organised by chapter in a way that helps students make good use of their time. The explanations are based on the **NCERT Book of Class 8 Maths** and will help students understand what each topic is about. Even the most complicated problems have been broken down in a way that is easy to understand. Below, students can find all the information they need about the chapters and exercises in Class 8 Maths NCERT Solutions:

If you click on the name of the chapter whose solutions you wish to view, you will be taken to the page for that chapter. Then, you can review the detailed, step-by-step CBSE 8th grade mathematics questions and answers for every single question in that chapter.

In class 8, you must learn **16 chapters** of mathematics. The following are notable chapters and their respective subjects:

**NCERT Solutions for Class 8 Maths Chapter-wise Links :**

- 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 Squares and Square Roots
- Chapter 7 Cubes 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 Indirect proportions
- Chapter 14 Factorisation
- Chapter 15 Introduction to Graphs
- Chapter 16 Playing with Numbers

**Some Important Topics Present in the NCERT Class 8 Maths Solutions**

**NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers**

Students will learn the independent, associative, and closure properties of real numbers, integers, whole numbers, rational numbers, and natural numbers in this chapter. This chapter discusses the significance of zero and one, the superiority of multiplication over addition, the representation of rational numbers on the number line, and the search for rational numbers between two rational numbers. This chapter also covers the topics of additive identity (0) and multiplicative identity (1). This chapter contains two exercises with questions pertaining to all of the chapter’s topics.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Rational Numbers Exercise 1.1
- Class 8 Maths Rational Numbers Exercise 1.2

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

The chapter, Linear Equations in One Variable, focuses exclusively on linear expressions with a single variable. Such equations are known as one-variable linear equations. This chapter contains six exercises with a total of sixty-five questions. Solving linear equations in one variable, its applications, reducing equations to a simpler form, and word problems related to solving linear equations in one variable are covered in this chapter.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Linear Equations in One Variable Exercise 2.1
- Class 8 Maths Linear Equations in One Variable Exercise 2.2
- Class 8 Maths Linear Equations in One Variable Exercise 2.3
- Class 8 Maths Linear Equations in One Variable Exercise 2.4
- Class 8 Maths Linear Equations in One Variable Exercise 2.5
- Class 8 Maths Linear Equations in One Variable Exercise 2.6

**NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals**

The eighth-grade math chapter Understanding Quadrilaterals provides students with a thorough understanding of quadrilaterals. The chapter also discusses various polygon types, such as triangles, quadrilaterals, pentagons, hexagons, etc. The chapter contains four exercises that aid students in their comprehension of these shapes.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Understanding Quadrilaterals Exercise 3.1
- Class 8 Maths Understanding Quadrilaterals Exercise 3.2
- Class 8 Maths Understanding Quadrilaterals Exercise 3.3
- Class 8 Maths Understanding Quadrilaterals Exercise 3.4

**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry**

The chapter Practical Geometry describes how to construct a quadrilateral with specified parameters. Each of the five exercises in this chapter deals with a different method of quadrilateral construction. The first exercise, for instance, involves the construction of quadrilaterals when the lengths of four sides and a diagonal are given; similarly, the second exercise involves the construction of quadrilaterals when two diagonals and three sides are given, and so on. Therefore, we can conclude that learning this chapter will equip students with a thorough understanding of all quadrilateral concepts for future classes.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Practical Geometry Exercise 4.1
- Class 8 Maths Practical Geometry Exercise 4.2
- Class 8 Maths Practical Geometry Exercise 4.3
- Class 8 Maths Practical Geometry Exercise 4.4
- Class 8 Maths Practical Geometry Exercise 4.5

**NCERT Solutions for Class 8 Maths Chapter 5 Data Handling**

Data is the collection of information that can be used for analysis. Students learn about data organization and representation in this chapter. The systematic organization of data is referred to as data handling. This chapter teaches students how to diagrammatically represent these data as a pictograph, bar graph, double bar graph, pie chart, and histogram. In this chapter, students will be introduced to the concepts of probability and likelihood. This chapter contains three exercises that address each of the concepts covered.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Data Handling Exercise 5.1
- Class 8 Maths Data Handling Exercise 5.2
- Class 8 Maths Data Handling Exercise 5.3

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

This chapter, Squares and Square Roots, assists students in understanding the concept of square numbers and square roots. This chapter discusses the properties of square numbers, patterns that can be learned using square numbers, finding the square of a number, Pythagorean triplets, finding square roots using various methods, square roots of decimals, and much more.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Squares and Square Roots Exercise 6.1
- Class 8 Maths Squares and Square Roots Exercise 6.2
- Class 8 Maths Squares and Square Roots Exercise 6.3
- Class 8 Maths Squares and Square Roots Exercise 6.4

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

In the chapter Cubes and Cube Roots, students learn a variety of methods for determining a number’s cubes and cube roots. This chapter explains how to find the cubes of various numbers, as well as some interesting patterns that can be learned using cubes, and how to find the cube roots. Two exercises in the chapter will aid students in gaining a thorough understanding of the fundamentals of cubes and cube roots.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Cubes and Cube Roots Exercise 7.1
- Class 8 Maths Cubes and Cube Roots Exercise 7.2

**Class 8 Maths NCERT Solutions for Chapter 8 Comparing Quantities**

Comparing Quantities is a chapter that teaches students how to compare the increase and decrease of percentages, market value, sales value, discount, etc. This chapter discusses an essential concept applicable to daily life: Interest. Students are instructed on simple interest, compound interest calculated semi-annually, quarterlyly, monthly, or annually, and a great deal more. This chapter contains three exercises that help students understand the concept of comparing quantities.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Comparing Quantities Exercise 8.1
- Class 8 Maths Comparing Quantities Exercise 8.2
- Class 8 Maths Comparing Quantities Exercise 8.3

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

This chapter, Algebraic Expressions and Identities, assists students in comprehending algebraic expressions-related concepts such as terms, factors, and coefficients. The chapter also provides a concise introduction to monomials, binomials, and polynomials. Students are taught to add, subtract, and multiply algebraic expressions. In addition, the concept of identity is discussed in this chapter. The chapter’s five exercises cover all concepts associated with algebraic expressions and identities.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Algebraic Expressions and Identities Exercise 9.1
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.2
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.3
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.4
- Class 8 Maths Algebraic Expressions and Identities Exercise 9.5

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

In this chapter, students learn to visualize three-dimensional solid shapes with the aid of three exercises. This chapter is extremely interesting because it discusses viewing three-dimensional shapes, mapping the space around us, and learning about faces, edges, and vertices. In addition, the chapter discusses Euler’s formula, which states that F + V â€“ E = 2, where F represents Faces, V represents Vertices, and E represents Edges, as well as its application.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Visualising Solid Shapes Exercise 10.1
- Class 8 Maths Visualising Solid Shapes Exercise 10.2
- Class 8 Maths Visualising Solid Shapes Exercise 10.3

**NCERT Solutions for Class 8 Maths Chapter 11 Mensuration**

Area and perimeter of various closed plane figures, such as triangles, rectangles, circles, etc., must have been taught to students in lower grades. In this chapter, Measurement, students will learn how to solve problems involving the perimeter and area of quadrilaterals and other closed plane figures. Students will eventually learn about the surface area and volume of various solid shapes, including a cube, cuboids, and cylinders. There are a total of four exercises in this chapter.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Mensuration Exercise 11.1
- Class 8 Maths Mensuration Exercise 11.2
- Class 8 Maths Mensuration Exercise 11.3
- Class 8 Maths Mensuration Exercise 11.4

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

In the chapter Exponents and Powers, students are introduced to various mathematical concepts, such as powers with negative exponents, the laws of exponents, the use of exponents to express numbers in standard form, and the comparison of extremely large and small numbers. The chapter contains two exercises to assist students in learning about exponents and powers.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Exponents and Powers Exercise 12.1
- Class 8 Maths Exponents and Powers Exercise 12.2

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

This chapter contains two exercises based on the concepts of direct and inverse proportion. Two quantities x and y are in direct proportion if they increase (decrease) in tandem such that the ratio between their respective values remains constant. Alternatively, two quantities x and y are said to be in inverse proportion if an increase in x results in a proportional decrease in y (and vice versa) such that the product of their respective values remains constant.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Direct and Inverse Proportions Exercise 13.1
- Class 8 Maths Direct and Inverse Proportions Exercise 13.2

**Class 8 Maths NCERT Solutions for Chapter 14 Factorization**

Students learn how to perform Factorization in this chapter. This chapter covers the factors of natural numbers and algebraic expressions, factorization by regrouping terms, and factorization with identities. This chapter also covers the division of algebraic expressions, such as the division of a monomial by another monomial, the division of a polynomial by a monomial, etc. This chapter contains four exercises containing questions covering all of the chapter’s topics.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Factorisation Exercise 14.1
- Class 8 Maths Factorisation Exercise 14.2
- Class 8 Maths Factorisation Exercise 14.3
- Class 8 Maths Factorisation Exercise 14.4

**Class 8 Maths NCERT Solutions for Chapter 15: Introduction to Graphs**

In the chapter titled “Introduction to Graphs,” students learn how to represent various types of data using a variety of graph types. Bar graphs, pie graphs, line graphs, and linear graphs are the various graph types. Students will learn how to locate a point and its coordinates on a graph with the aid of this chapter. The chapter contains a total of three exercises that will aid students in comprehending the concepts of Graphs.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Introduction to Graphs Exercise 15.1
- Class 8 Maths Introduction to Graphs Exercise 15.2
- Class 8 Maths Introduction to Graphs Exercise 15.3

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

Students have studied a variety of number types, including natural numbers, whole numbers, integers, and rational numbers. They may have also investigated a variety of fascinating properties of these numbers, such as their factors, multiples, and relationships. Similarly, in this chapter, students can investigate the diverse types of numbers in depth. These concepts can aid students in justifying divisibility tests. This chapter includes 2 exercises on the topic of playing with numbers.

**Links to exercise solutions for the topics covered in this chapter can be found here.**

- Class 8 Maths Playing with Numbers Exercise 16.1
- Class 8 Maths Playing with Numbers Exercise 16.2

NCERT Solutions Class 8 Maths Chapter-wise List |

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 Squares and Square Roots |

Chapter 7 Cubes 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 Indirect proportions |

Chapter 14 Factorisation |

Chapter 15 Introduction to Graphs |

Chapter 16 Playing with Numbers |

**Benefits of NCERT Solution of Class 8 Maths**

NCERT solutions for Class 8 are the key to success for every student because they help them build on their core knowledge and become experts in every subject. Some of the good things about the Class 8 Ncert solutions are as follows:

- The answers are made according to the rules and format set by the CBSE board. This gives the students an idea of how the questions will be set up on the final exams.
- Some expert teachers with years of experience in this field put together the solutions, so you can be sure that there are no mistakes in them. The students can be sure that the solutions are good.
- The answers are given to the questions that are most likely to show up on the tests. This helps the students prepare well.

**Key features of NCERT Solutions for Class 8**

Here are a few advantages of referring to Utopperâ€™s **NCERT Solutions**:

- These solutions are grade-appropriate and use easily-understood language so that children can comprehend them without difficulty.
- These solutions have been produced by the nation’s leading specialists, allowing you to study from highly qualified instructors with minimal effort.
- All solutions are crafted with the most recent recommendations in mind.
- The PDF will serve as a one-stop shop for all of your educational needs.
- It will assist you in establishing a solid basis for higher study.
- You will receive practice tests to evaluate your knowledge and learning.
- These solutions have been created by a group of Utopper specialists who have taken into account the grade level of the pupils. Students should not worry about the accuracy of the solutions because they will receive the most accurate responses to the problems.
- If students practice these solutions beforehand, they will be able to complete the curriculum well ahead of schedule. In addition, the Class 8 All Subject Question Answer PDF will assist students to have a deeper understanding of questions that may be asked in final exams.

**Class 8 NCERT Solutions – Marks Weightage**

All topics in Class 8 are worth a total of 100 marks, 20 of which come from an internal evaluation and 80 from the summative assessment administered at the conclusion of the school year by schools in accordance with the requirements of the CBSE. The internal evaluation consists of a weighted average of the grades earned on examinations, projects, and other assignments. The final examination for each subject is worth 80 marks and is weighted differently for each chapter and topic. A student’s ability to intelligently judge their readiness for tests might be aided by adhering to suitable plans.

Internal Assessment | Summative Assessment | Total |

20 | 80 | 100 |

**Other Related Study Material for Class 8 :**

- NCERT Class 8 Maths Solutions
- Ncert Class Science Solutions
- NCERT Class 8 Textbooks
- NCERT Class 8 Science Book
- NCERT Class 8 Maths Book
- NCERT Syllabus

**Importance of Class 8 NCERT Solutions for All Subjects**

Class 8 students have a great deal of homework to complete. Their curriculum comprises of numerous subjects, including mathematics, physics, English grammar, Hindi composition, and social studies. In order to outperform the rest of the class, pupils must have a solid understanding of these disciplines. After finishing the chapters, students might seek out extra study materials to further their understanding. Choosing **Utopper’s NCERT solutions** will assist students to solve difficult questions and gain an understanding of the curriculum. In addition, students will be able to comprehend the essential concepts taught in **Class 8 NCERT Solutions**. Thus, individuals can develop a study plan that will aid them throughout their final exams.

These **NCERT solutions** are unquestionable of great assistance to students who wish to complete the Class 8 curriculum and do well on their tests. These solutions were developed by subject matter specialists at Utopper in accordance with CBSE guidelines. Therefore, students can utilize these solutions as references to enhance their own skills in order to perform well on exams.Â

**Frequently Asked Questions on NCERT Solutions for Class 8 Maths**

**Frequently Asked Questions on NCERT Solutions for Class 8 Maths**

**Q.1 What are the benefits of using Utopper’s NCERT Solutions for Grade 8?**

**Q.1 What are the benefits of using Utopper’s NCERT Solutions for Grade 8?**

The NCERT Solutions for Class 8 on Utopper are written with great care by experts in the field. Easy-to-understand language is used to help students easily pass the test. Diagrams are used wherever they are needed to give students a visual way to learn. The answers are in PDF format, and you can get them by clicking on the links given. Students can trust these answers because they are based on the CBSE’s curriculum and rules for the year.

**Q.2 Why is it important to have NCERT solutions Class 8 Maths Pdf?**

**Q.2 Why is it important to have NCERT solutions Class 8 Maths Pdf?**

Having the NCERT solutions for Class 8 Maths in pdf format helps students learn well and get the best preparation. The PDF format of the solutions makes it easy to download them at any time and from anywhere, and it’s also easy to use them on any device. The pdf versions of the solutions also have questions and statements of the problem. It makes sure that the students don’t have to carry the whole books around with them. Students can get good grades if they use them.

**Q.3 How do I make a plan for studying for Class 8?**

The steps for making a good study plan for Class 8 are-

First, you should figure out what’s wrong with your current plan. You need to change your schedule so that you do the most important things first. For example, getting ready for class tests, homework, etc.

Find out when you work best. No matter if you prefer to study in the morning or at night. Just check the time and get to work.

Make sure to take short breaks every one to two hours. You can stop for 5 to 10 minutes and then start again.

Try to spend at least an hour on each subject to review what you’ve learned. You can, however, make the time longer or shorter based on your preferences and plans.

**Q.4 Can I do well on my exam if I study with Utopper NCERT Solutions for Class 8?**

**Q.4 Can I do well on my exam if I study with Utopper NCERT Solutions for Class 8?**

Students will find answers to questions about English, Science, Social Science, and Math in NCERT Class 8 Solutions. The solutions at Utopper are made by teachers with a lot of experience based on the questions in the most recent NCERT textbook. Students who don’t understand the ideas in class can look at these solutions to learn more about the big picture. Step-by-step explanations are given in the solutions to help students easily grasp the idea.

**Q.5 How hard or easy are the subjects in Class 8?**

Well, the answer to this question depends on how smart the student is. Some students who are good at school may find this class easy to pass. At the same time, there are some students who aren’t good at school and will find this class hard. Students in this situation should start studying as soon as possible so that they can finish their coursework on time and fully understand the ideas. They can also look at the NCERT Solutions for all subjects and chapters to help them understand better. All of the study materials are free to use and can be found on the Utopper website.Â