# NCERT Solutions for Class 8 Maths

Here we are providing NCERT Solutions for Class 8 Maths, the solutions are latest and up-to-date. You can download Solution for each and every chapter listed below (Chapterwise).Download Free NCERT Solutions for class 6th to 12th.

## NCERT Solutions for Class 8 Maths â€“ Free PDF Download Chapterwise

### CHAPTER 1: RATIONAL NUMBERS

Properties of Real numbers, integers, whole numbers, rational numbers and natural numbers â€“ Commutative, associative and closure.  Roll of 1 and additive inverse of multiplication and addition. Representation of a rational number on number line and to find rational numbers between any two rational numbers. Additive identity (0) and the multiplicative identity (1).

### CHAPTER 2: LINEAR EQUATIONS IN ONE VARIABLE

The chapter linear equations in one variable deals with linear expression in one variable only. We know that an algebraic equations are equality involving variables. In a linear equations the values of expression on LHS are equal to values on RHS. To solve these equations, we perform the same mathematical operations on both sides of the equation, so that the balance is not disturbed. There are equations in which variable is only one side, variable is on both the side, reducing into simple equation and then to solve and applications based on linear equations.

Understanding quadrilaterals â€“ A simple closed curve made up of only line segments is called polygon and the curves that are not closed are not polygon. Types of polygon â€“ Triangle, quadrilateral, pentagon, hexagon. A diagonal is a line segment connecting two non-consecutive vertices of a polygon. If all sides of a polygon is equal it is a regular polygon. The sum of external angles of any polygon is 360. A parallelogram is a quadrilateral with each pair of opposite sides parallel.

### CHAPTER 4: PRACTICAL GEOMETRY

Practical geometry includes the constructing a quadrilateral four sides and one diagonal are given or when two adjacent sides and three angles are given or when three sides and two included angles are given, etc. Using the given specification, the quadrilateral can be drawn uniquely in this chapter.

### CHAPTER 5: DATA HANDLING

The collection of information to study and analyze it further about any fact/case study is called data. Organize the data in systematic way or in a required manner and then interpret it is called data handling. To get clear idea about any data it is represented graphically as a pictograph, a bar graph, double bar graph, histogram and pie chart. In this chapter, a brief discussion about probability is also given.

### CHAPTER 6: SQUARE AND SQUARE ROOTS

The square and square roots chapter gives an idea about how to find the roots of  a number. If a number, say x can be expressed as the square of any other number, say y, then y is the square root of x. Square root is the inverse operation of square. A natural number is called perfect square if its square root is a natural number. The method of finding square roots of a decimal number is frequently used even in higher classes.

### CHAPTER 7: CUBE AND CUBE ROOTS

In cube and cube roots, there are various methods to find cubes/cube roots of any number. We can get cubes of numbers by adding consecutive odd numbers pattern. Prime factorization method is also used to find cubes or cube roots. In the prime factorisation method, if every factor appears thrice, then the number is perfect cube.

### CHAPTER 8: COMPARING QUANTITIES

Comparing quantities compares the increase or decrease percentages, marked price, sales price, discount, discounted values of the article checking whether profit or loss %. Treatment of additional expense during the purchase of an article. Sales tax and cost including or excluding the tax. Simple interest and compound interest when interest is compounded half yearly, quarterly, monthly or yearly. Comparing simple interest and compound interest on the same amount.

### CHAPTER 9: ALGEBRAIC EXPRESSIONS AND IDENTITIES

This chapter gives a basic idea about algebraic expressions and identities and their implementation. Terms are added to form algebraic expression and these terms themselves can be formed as the product of factors. The numeral factor of a term is called its coefficient.  Monomials, binomials, trinomials and so on, depending the number of terms. Addition of algebraic expression taking like terms together and multiplication of polynomials by polynomials. Standard identities and their uses in solving algebraic expressions.

### CHAPTER 10: VISUALIZING SOLID SHAPES

In visualizing solid shapes, we will study about the solid objects having length, breadth and height that is why it is called 3-D figures. For example cubes, cuboids, cones, cylinders, spheres, hemispheres, etc. are the 3-D figures. In this chapter we will try to find faces, edges and vertices of some solid figures like cuboids, triangular pyramids, triangular and square base prisms. Application of Eulerâ€™s formula F + V â€“ E = 2, where F â€“ Faces, V â€“ Vertices and E â€“ Edges.

### CHAPTER 11: MENSURATION

In mensuration chapter, we will workout the problems based on perimeter & areas of plane closed figure and surface area (sum of area of its all faces) & volume (amount of region occupied by a solid) of some solid figure like cube, cuboid, cylinder, etc. Conversion related to volume as 1 cubic cm = 1 mL, 1 L = 1000 cubic cm and 1 cubic m = 1000000 cubic cm = 1000 L.

### CHAPTER 12: EXPONENTS AND POWERS

Main points â€“ Exponents and Powers: Powers with negative exponents, scientific notation of decimal numbers, questions based on laws of exponents, use of exponents to express the numbers in standard form and comparison of very large numbers to small numbers.

### CHAPTER 13: DIRECT AND INVERSE PROPORTIONS

Questions based on direct proportion ( when the quantity of one value increases the other also increases), inverse proportion ( if one quantity increases, the other quantity decreases and vice versa). Direct and inverse proportion can be identified on the basis of relative increase of decrease of other quantity with respect to first one. Most of the questions on this topic are interesting  and based on daily life.

### CHAPTER 14: FACTORIZATION

Factorization of natural numbers and algebraic expression. These factors may be numbers, algebraic variables or algebraic variables or expressions. Factorization method of common factors, by regrouping terms, using identities and using factors of the form (x + a)(x + b). Division of algebraic expression â€“ monomial by another monomial, polynomial by monomial and polynomial by the polynomial. Error finding in algebraic equations.

### CHAPTER 15: INTRODUCTION TO GRAPHS

Introduction to graphs â€“ The purpose of the graph (visual representations of data collected) is to show numerical facts in visual form so that every one can understand it easily, more clearly and quickly. Types of graphs â€“ Bar graph, histogram, pie chart, line graph and a linear graph (on xy â€“ plane). Application based on graph â€“ Quantity & cost, principal & simple interest and time & distance using dependent variable & independent variable.

### CHAPTER 16: PLAYING WITH NUMBERS

In playing with numbers, we have to go through numbers in general form, fun with games in numbers and puzzles in which letters take the place of digits in an arithmetic problems. Divisibility tests â€“ divisibility by 10, 2, 5, 3 & 9 and 11. Questions based on divisibility test to find the missing term in a number.

Most of the students starts taking tuitionâ€™s from class 8 onwards as plethora of new concepts are introduced in this class. 90% of the students opt for tuitionâ€™s and even after that they score low marks. Reason? Poor concepts and lack of practice. Yes! Maths is a game whose key players are concepts and formulas. If you donâ€™t know the formula then you cannot even go a single step further.

I know you would have always wished that whenever your teacher asks any question, your hand should be raised first. But donâ€™t worry. That can happen. You can also become a maths genius like the toppers of your class. You just need the right study material with apt guidance. There is no second option than to solving NCERT books.

These books are appropriately designed as per the latest CBSE pattern and are in fact prescribed by CBSE as well. A teacher may feel bugged when you keep on pinging her every time for checking the answer. What if you get the complete NCERT Solutions for class 8 Maths? Sounds good?

Yes, here we bring to you the NCERT solutions for class 8 Maths which solves each and every question till the answer giving proper explanations at every step. Chapters such as Algebra, rational numbers, mensuration, etc. need formula memorization. Chapter 6 Square and square roots and chapter 7 cube and cube roots form the base of mathematics. If is advisable to students to keep practicing them every day. Students generally get confused between them and 80% of the students answer it wrongly.

Then comes a similar chapter exponents and powers. Here you need to be very careful regarding the figures. It has been noticed that most of the students often copy wrong figures from the question paper. Stay attentive while solving your mathematics problem. One wrong figure will lead you to a wrong answer, so copy them very carefully.

We recommend the students to make a chart of all the formulas and paste them near the place of your study. This will help them to memorize the formulas in an easy manner without any hassle. www.educationlearnacademy.com visions to make each and every student in India fully equipped with the NCERT study material (textbook + solutions) so that he/she do not face any problem in their preparation for examination.

## CLASS 8 NCERT SOLUTIONS

CBSE NCERT Solutions for class 8 (VIII) Maths, Science, Social Science and Hindi are given in PDF form to free to use online or download.

## Chapter-wise NCERT Solutions for Class 8 Maths

Chapter 1 – Rational Numbers

Learn about the properties of rational numbers in the number system by using our NCERT Class 8 Maths Chapter 1 solutions. This chapter covers topics such as additive inverse, multiplicative inverse, reciprocal inverse, negative of a number and more. In NCERT Maths Class 8 Chapter 1, study the representation of rational numbers on a number line and practise word problems related to rational numbers. Also, understand how you can find a rational number between two rational numbers with our NCERT solutions for Class 8 Maths Chapter 1. While learning the properties of rational numbers, you can boost your knowledge of real numbers, whole numbers, integers and natural numbers with the NCERT Class 8 Maths book solutions.

Chapter 2 – Linear Equations in One Variable

Through the NCERT concise Mathematics Class 8 solutions for this chapter, practise the methods used by experts to solve contextual problems based on the concept of linear equations in one variable. Use our NCERT solutions for Class 8 Maths Chapter 2 to learn concepts such as equations having the variable on both sides, equations reducible to the linear form etc. Knowledge of variables gained from our NCERT Class 8 Maths Chapter 2 solutions will benefit you a lot in higher classes such as Class 9, Class 10, Class 11 and Class 12. So, use TopperLearningâ€™s NCERT Maths Class 8 Chapter 2 solutions and study better with accurate answers to the exercise questions from your Maths textbook.

This chapter gives you a thorough understanding of the properties of quadrilaterals such as the sum of angles of a quadrilateral is equal to 360 degrees. Revise the various types of polygons such as convex, concave, regular and irregular polygons from NCERT Maths Class 8. Also, learn about the properties of parallelograms. Understand the different types of curves by utilising our NCERT solutions for Class 8 Maths Chapter 3. By revising our solutions from NCERT Maths Class 8, youâ€™ll come across several examples of question formats that are likely to appear in your Class 8 Maths exam. Also, learn to calculate the sum of the measure of the exterior angles of a polygon with our NCERT 8 Maths solutions.

Chapter 4 – Practical Geometry

Class 8 Maths Chapter 4 helps you to understand the construction of quadrilaterals, parallelograms, rhombus, squares and rectangles. Learn about the construction of geometric shapes with TopperLearningâ€™s NCERT solutions for Class 8 Maths Chapter 4. This chapter teaches you in detail about the concept of diagonals in shapes. Our CBSE Class 8 Maths solutions will also take you through the properties of geometric shapes. With our NCERT Class 8 Maths book solutions, you can easily learn the role played by angles and sides in different scenarios.

Chapter 5 – Data Handling

In this chapter, read in detail about what is data and what are the ways to present data. With the NCERT solutions for Class 8 Maths Chapter 5, you can learn about the visual representation of different types of data. The solutions in this chapter will teach you to read data in bar graphs and pie charts. Youâ€™ll also learn about circle graphs, pictographs, double bar graphs, histograms and more by studying this chapter. Youâ€™ll also be able to revise probability and chance from the data handling perspective along with real-life applications.

Chapter 6 – Square and Square Roots

In this chapter, learn to find square roots with the help of the division method and the factor method. Practise answers of problems from your NCERT Class 8 Maths book to understand the concept of a perfect square and square roots. With our NCERT solutions for Class 8 Maths Chapter 6, youâ€™ll be able to do your revision of the properties of square numbers. Revise NCERT Maths Class 8 book concepts like square roots of a decimal, square of a number etc. Also, for homework, use our NCERT solutions for Class 8 Mathematics Chapter 6 that are created by some of the best Maths teachers in the country. It will be easy for you to complete assignments related to this chapter.

Chapter 7 – Cube and Cube Roots

Study this interesting chapter on cube and cube roots with TopperLearningâ€™s NCERT solutions for Class 8 Maths Chapter 7. The two key methods for solving problems from this chapter are the estimation method and the prime factorisation method. Our NCERT solutions for CBSE Class 8 Chapter 7 gives you step-wise answers to find cube roots using the factor method. Also, learn the concept of a perfect cube and how to estimate cube roots while understanding the number system. Practise problems related to Chapter 7 effectively by going through the accurate answers by our experts for this chapter.

Chapter 8 – Comparing Quantities

NCERT Class 8 Maths Chapter 8 covers topics such as compound interest, percentages, ratios, sales tax and more. Find solutions on the unitary method and its applications. Also, revise the concept of profit and loss. NCERT Maths Class 8 Chapter 8 is an important chapter because it will present you with the basics of accounting. Youâ€™ll be able to perform complex accounting in the later years if youâ€™ve grasped the concepts in this chapter. With NCERT solutions for Class 8 Maths Chapter 8, you can practise and learn how to calculate interest, tax etc. The application of the concepts learned in this chapter will also help you to understand the basic calculations in day-to-day life.

Chapter 9 – Algebraic Expressions and Identities

Get answers on the addition, subtraction, division and multiplication of algebraic expressions in NCERT Class 8 Maths Chapter 9. Also, study about interpretations of algebraic identities. Take advantage of TopperLearningâ€™s NCERT solutions for Class 8 Maths Chapter 9 Algebraic Expressions to understand the relevance of pure mathematical expressions and how to implement them. Also, revise answers to exercise questions from your NCERT 8th Maths book that are based on terms like polynomials, trinomials, binomials and monomials. Also, find out what is a factor and how coefficients work.

Chapter 10 – Visualising Solid Shapes

Explore the fascinating world of 3D objects and the basics of how to work with them through our NCERT solutions for Class 8 Maths Chapter 10. Learn about ways to view a 3D object such as front view, top view and side view. Get a deeper understanding of 3D objects and how to map 3D objects by revising NCERT Maths Class 8 solutions from this chapter. Understand the importance of vertices, faces and edges in 3D objects such as triangular pyramids, prisms and more. Also, practise the use of Eulerâ€™s formula in solving Maths problems with our NCERT Class 8 Maths solutions.

Chapter 11 – Mensuration

For revision of Chapter 11 Maths Class 8 Mensuration, get Class 8 Maths solutions on finding the area of a polygon and the area of a trapezium. Learn more on the concept of volume of a cube, volume of a cylinder and volume of a cuboid in NCERT Maths Class 8 Chapter 11. Also, find out how to measure the surface area of a cube, cylinder, and cuboid. Get NCERT solutions for Class 8 Maths Chapter 11 to practise the steps to calculate the area of a general quadrilateral. In addition, find out what is the meaning of capacity and what are the properties of solid shapes.

Chapter 12 – Exponents and Powers

In NCERT solutions for Class 8 Maths Chapter 12, you will learn more about the integers in the number system. Revise the laws of exponents that have integral powers. Learn how to utilise exponents for expressing numbers in the standard form. At TopperLearning, qualified Mathematics experts have prepared the solutions for Chapter 12 to assist you with the topic of exponents and powers. With enough practice, you will be able to attempt questions based on laws of exponents and power with negative components. Once you are comfortable with the topic, try solving the problems without referring to the solutions. Use the NCERT solutions to assess yourself and score better marks in your exam.

1. ### Why are NCERT Solutions for Class 8 important?

Learning Maths takes a lot of practice. NCERT solutions for Class 8 helps you to revise concepts such as linear equations, cube roots, square roots and more. These concepts form the foundation of advanced concepts that you will study in higher classes. Also, the knowledge of your Class 8 Maths concepts supports your preparation for competitive exams such as JEE, NEET etc. Our NCERT solutions are freely available as reliable reference material to study the concepts as well as the application of concepts as per the most recentÂ NCERT syllabus for Class 8 Maths.
With expert NCERT solutions for Class 8 within your reach, you can practise solutions as much as you want. The chapter-wise format of NCERT solutions ensures that you can access specific chapters quickly to prepare for mock tests related to the chapter or complete class assignments based on the select chapters. The ease of using the NCERT Class 8 Maths book solutions through your dashboard will also save you time and effort. In this way, you do not have to lose precious time searching for specific solutions from the NCERT Class 8 Maths book. Instead, get all the textbook solutions in one place.

2. ### Where can I find free NCERT solutions for Class 8 Maths?

TopperLearning provides free online solutions for exercise questions from your NCERT Class 8 Maths textbook. You can find them under â€˜textbook solutionsâ€™ in the Class 8 resources section of our study portal.

3. ### Which chapters from Maths Class 8 NCERT are present on TopperLearning?

Solutions for all 16 chapters from the Maths NCERT Class 8 textbook covering topics such as rational numbers, factorisation, practical geometry etc. are available on TopperLearning.

4. ### Will the NCERT Maths book Class 8 solutions be enough for me to score high marks?

NCERT solutions for Class 8 Maths are a great resource for revision. However, for scoring high marks, you should practise more Maths problems by attempting sample papers and previous yearsâ€™ question papers.

5. ### I donâ€™t know which chapter to start for revision using NCERT solutions. What should I do?

First of all, download the latest CBSE NCERT syllabus for Class 8 Maths. Decide whether you want to revise specific chapters or topics from the entire syllabus. Based on your decision, plan your schedule for revising one chapter at a time.

6. ### How to prepare for Class 8 Maths exams?

For Maths preparation tips, you can read our blog on how to prepare for CBSE Class 8 MathsÂ here.

Chapter 13 – Direct and Inverse Proportions

Learn to solve word problems on direct variation and inverse variation in quantities through the NCERT 8 Maths CBSE Board solutions given in this chapter. NCERT solutions for Class 8 Maths Chapter 13 covers all the exercises given in your Maths textbook. Use these NCERT solutions to revise the concept of proportion. Also, learn to solve problems wherein you have to find out about the proportional increase or decrease of given quantities. If you practise the NCERT solutions multiple times, youâ€™ll be able to grasp the topic and remember the ways to tackle the questions related to this topic.

Chapter 14 – Factorisation

This chapter helps you learn the concept of factorisation and algebraic identities. Our NCERT solutions for Class 8 Maths Chapter 14 will support you to understand how the division of an algebraic expression takes place. For example, find out how a polynomial can be divided by a monomial or how a monomial can be divided by a monomial. Practise the different ways to find factors in problem questions. For your exam, the latest NCERT Maths book is the most recommended textbook to prepare for this chapter. Finding the correct solutions for the NCERT Maths Class 8 textbook questions can be difficult. At TopperLearning, we give you free access to the best NCERT solutions for Chapter 14 by some of the qualified and experienced Maths teachers in India.

Chapter 15 – Introduction to Graphs

In this chapter, learn how to plot points in graphs for situations such as multiples of different numbers, perimeter vs. length for squares etc. Understand the different types of graphs such as bar graph, linear graph, histogram, pie chart etc. In our NCERT solutions for Class 8 Maths Chapter 15, youâ€™ll find solutions to study the topic of graphs in detail. Use our NCERT Mathematics Class 8 model answers as a handy e-learning reference source for your Class 8 exam preparation and push your efforts to score top marks in the exams.

Chapter 16 – Playing with numbers

Learn how to write a 2-digit and 3-digit number in the generalised form by solving number puzzles in this chapter. Through our NCERT solutions for Class 8 Maths Chapter 16, learn about divisibility tests, letters for digits and other concepts. Youâ€™ll also enjoy learning the fun number exercises in this chapter.

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