# NCERT Solutions for Class 8 Math

NCERT Solutions are considered an extremely helpful resource for exam preparation. Meritnation.com gives its users access to a profuse supply of NCERT questions and their solutions. CBSE Class 8 Math NCERT Solutions are created by experts of the subject, hence, sure to prepare students to score well. The questions provided in NCERT Books are prepared in accordance with CBSE, thus holding higher chances of appearing on CBSE question papers. Not only do these NCERT Solutions for Class 8 Math strengthen studentsâ€™ foundation in the subject, but also give them the ability to tackle different types of questions easily.

Our Class 8 Math textbook solutions give students an advantage with practical questions. These textbook solutions help students in exams as well as their daily homework routine. The solutions included are easy to understand, and each step in the solution is described to match the studentsâ€™ understanding.

## Math - NCERT Solutions for class 8

- NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers
Mathematics NCERT Grade 8, Chapter 1:

**Rational Numbers**- Basic operations on**natural numbers, integers**and**rational numbers**are already discussed.

In this chapter, students will try to explore some**properties of rational numbers**like closure, commutativity, associativity.

Solved examples are given to make the students understand the topic.

After that, the**role of zero (0)**and the**role of 1**is made clear by giving a short description of the same including**additive**and**multiplicative identity**.

This is followed by the topics**Negative of a number**or**additive inverse**and**Reciprocal**or**multiplicative inverse**. Further in this chapter**distributivity of multiplication over addition**for**rational numbers**are explained.

Exercise 1.1 has 11 questions.

Next exercise 1.2 is based on the topics-**Representation of Rational Numbers on the Number Line**and**Rational Numbers between Two Rational Numbers**. Some solved examples are given in the chapter. Following those examples students can solve the problems of exercises easily.

In the end key points of chapter are given. - NCERT Solutions for Class 8 Maths Chapter 2 - Linear Equations in One Variable
Mathematics NCERT Grade 8, Chapter 2:

**Linear Equations in One Variable**- In this chapter students will get to know about**linear equations in one variable**. A short revision of previously discussed topics is done in the beginning.

In this chapter, one can study how to solve**linear equations**which may be in one of the given forms:**Equations having a linear expression on one side and numbers on the other side****Equations having the variable on both sides****Equations reducible to linear form**

**left hand side**and**right hand side, transposing.**This is followed by**applications of linear equations in one variable**. This involves problems on various topics like**age, money, dimensions of given figures, numbers**etc.

Lot of solved examples and exercise questions are given for better clarity of the topic. For conclusion, a recap of a few important points is discussed. - NCERT Solutions for Class 8 Maths Chapter 3 - Understanding Quadrilaterals
Mathematics NCERT Grade 8, Chapter 3:

**Understanding Quadrilaterals**- Different varieties of**curves**have already been discussed in earlier classes. Starting with**polygons**chapter moves to the topic-**classification of polygons**.

After that**Convex and concave polygon**are discussed. Before moving to**angle sum property**students will learn about**regular and irregular****polygons**. After going through the introductory section students need to solve the problems of exercise 3.1.

**Sum of the measure of the exterior angles of a polygon**is another topic that will be discussed in this chapter.

Various kinds of**quadrilaterals**are explained.**Angles of parallelogram**and**some special parallelograms**are also discussed.

A total of 4 exercises are there in this chapter.

In the end, Topic What we have discussed so far is given in that topic all-important key points of the chapter are discussed. - NCERT Solutions for Class 8 Maths Chapter 4 - Practical Geometry
Mathematics NCERT Grade 8, Chapter 4:

**Practical Geometry**- To start with, a brief introduction is given. In the first part of the chapter, students will learn how to**construct**a unique**quadrilateral.**Different cases are listed and every case is explained in a step wise manner. Cases of**construction**which are explained in this chapter are as follows:- When four
**sides**and one**diagonal**are given. - When
**diagonals**and three**sides**are given. - When two adjacent
**sides**and three**angles**are given. - When three
**sides**and two included**angles**are given. - When other special
**properties**are known.

**construction**of the cases listed above, some special cases are also taken.

This chapter contains a total of 5 unsolved exercises and a summary of the chapter is also given in the end. - When four
- NCERT Solutions for Class 8 Maths Chapter 5 - Data Handling
Mathematics NCERT Grade 8, Chapter 5:

**Data Handling**- Ever wondered what is data?**Collection**of any**specific information**is called**data.**It is usually collected in the context of a situation that we want.

**Data**is sometimes represented**graphically**. Students have already studied different types of**graphs**in earlier classes like**pictographs**,**bar****graphs, double bar graphs**. The section 5.2 is about**organising data**in the form of**frequency distribution table**followed by**grouping data**into**class intervals with upper and lower limits**. The next topic is**Bars with a difference**where one studies**histograms**. Exercise 5.1 is based on the same concepts.**Circle graph or pie chart**is also discussed in this chapter. Students will learn about**chance and probability**. In this section following topics will be discussed:

1.**Getting a result**

2.**Equally likely outcomes**

3.**Linking chances to probability**

4.**Outcomes as events**

5.**Chance and probability related to real life**

Keypoints are listed in the end. - NCERT Solutions for Class 8 Maths Chapter 6 - Squares and Square Roots
Mathematics NCERT Grade 8, Chapter 6:

**Squares and Square roots**- Numbers like 1, 4, 16, 36 are known as**square numbers**.

In this chapter, students will learn to**find squares and square roots of any number.**The chapter will be fun to study as students will get to experiment more with the numbers.- In general,
**if a natural number m can be expressed as**.*n*^{2}, where*n*is also a natural number, then*m*is a square number

**square numbers**will be explained in this chapter.

**Some more interesting patterns**are also discussed. Section 6.4 deals with the topic-**Finding the square of a number**. The section is subdivided into the following points:

1.**Other patterns in squares**

2.**Pythagorean triplets**

Another section gives details about**Square Roots**. Different methods of**Finding Square Roots**are discussed.

After that**Square Roots of Decimal**is discussed and the concept of**Estimating Square Roots**is also explained.

To make the content more interesting, different types of solved, unsolved exercises, activities are given in the chapter.

At last, the key points of the chapter are discussed. - In general,
- NCERT Solutions for Class 8 Maths Chapter 7 - Cubes and Cube Roots
Mathematics NCERT Grade 8, Chapter 7: Cube and Cube Roots- The chapter starts with an interesting story about India's great mathematician

**S.Ramanujan.**In this chapter, students will learn about**cube**,**cube roots**and many interesting facts about them.

The first section is about**cubes**.**Perfect cubes**or**cube numbers**are explained. This section is further divided into sub-parts. One will come across**interesting patterns related to cubes**. Not only this cubes and their**prime factors**will be taught followed by**smallest multiple**which is a**perfect cube**. Exercise 7.1 is based on the concept of**cubes**.

Moving further students will learn about**cube roots**in the next section. This includes methods like**prime factorisation**and**estimation method.**

The last exercise is 7.2 which is based on the concept of**cube roots**. The chapter ends with a summary. - NCERT Solutions for Class 8 Maths Chapter 8 - Comparing Quantities
Mathematics NCERT Grade 8, Chapter 8:

**Comparing Quantities**- Section 8.1 is about**Recalling Ratios and Percentages.**Solved examples are given in the chapter for a better explanation.

The next section is about**Finding the Increase or Decrease Percent**.

After that,**Finding discounts**will be explained. Moving on to the next section, section 8.4 discusses**Prices Related to Buying and Selling**(**Profit and Loss**).

The section is further divided into subsection which explains about**Finding cost price/selling price, profit%/loss%**.

After solving the questions of exercise 8.2 students will learn about**Compound Interest**.**Deducing a Formula for Compound Interest**is also explained.

Section 8.8 lays emphasis on**Rate Compound Annually or Half Yearly(Semi-Annually)**.

After that,**Applications of Compound Interest**Formula is given in section 8.9. The last exercise is 8.3 which contains 12 questions.

In the end, the key points of the chapter is explained. - NCERT Solutions for Class 8 Maths Chapter 9 - Algebraic Expressions and Identities
Mathematics NCERT Grade 8, Chapter 9:

**Algebraic Expressions and Identities**- The chapter gives an insight into concepts related to**algebraic****expressions**. Section 9.2 gives details about**terms, factors,**and**coefficients.**

Terms like**monomials, binomials,****trinomials**and**polynomials**are discussed in detail. Emphasis is given to important topics like**Addition and subtraction of algebraic expressions. Like**and**unlike terms**are discussed under section 9.4.

The discussion moves further to the next topic-**multiplication of algebraic expressions**. This topic contains various subparts. All subparts are explained in great detail.

Ever wondered what is an**identity**? This chapter will clear all doubts of students relating to the same concept-**Identity**. The chapter also discusses**Standard identities.**

Unsolved exercises, questions in different patterns will make the chapter more comprehensible to students.

All important points of the chapter are cited in the end under the title-**What Have We Discussed**? - NCERT Solutions for Class 8 Maths Chapter 10 - Visualising Solid Shapes
Mathematics NCERT Grade 8 Chapter 10:

**Visualising Solid Objects**- The chapter puts focus on different**solid shapes**. Ever wondered difference between**2D**and**3D****shapes**. Students will get all answers about the same. In the first half of the chapter,**Views of****3D shapes**where**front view, side view**and**top view**are explained. Also,**maps, scale**and depicting location of a particular objects or place is taught in this chapter. Moving towards end of the chapter**, polyhedron, prism, pyramid, convex and regular polyhedrons,**concept of**faces**,**edges**and**vertices**will be discussed. Not only this,**Euler's formula**relating**faces, edges and vertices of a polyhedron**is an important topic to be studied in this chapter. Total 3 unsolved exercises are given in this chapter. Each exercise is enriched with adequate number of questions for practice. All the sections of chapter are explained in great detail.

9 points are listed in the summary of chapter in the end. - NCERT Solutions for Class 8 Maths Chapter 11 - Mensuration
Mathematics NCERT Grade 8, Chapter 11:

**Mensuration**- This chapter will cover all the**concepts of perimeter and area**of other plane figures such as**quadrilaterals, rhombus, polygons**etc. Also, emphasis will be laid upon the concept of**surface area**and**volume of solids**such as**cube, cuboid,**and**cylinder.**The first half of the chapter covers the following topics:**Area of Trapezium****Area of General Quadrilateral: Area of special quadrilaterals**are discussed in brief in this section.**Area of polygon**

In the other half of the chapter,**solid shapes**,**surface area of cube**,**cuboid,**and**cylinder**are discussed.

The**volume of cube, cuboid,**and the**cylinder**is also explained in the next section.

Assessment of these concepts can be done by solving exercises 11.3 and 11.4.

Solved examples are covered in the chapter to make the students understand each topic in a crystal clear way.

Summarization of all important points is done in the end. - NCERT Solutions for Class 8 Maths Chapter 12 - Exponents and Powers
Mathematics NCERT Grade 8, Chapter 12:

**Exponents and Powers**- This chapter highlights all the concepts related to**exponents and****powers**. Initially,**Power with Negative Exponents**and**Laws of Exponents**will be discussed.

The other portion of the chapter gives insight about**Use of Exponents to Express Small Numbers in Standard Form**. Once the**standard notation**is understood, its application is given in the form of comparison of**very small and large numbers.**The chapter includes two unsolved exercises and various solved examples.

Students will get to learn about some new concepts and this chapter will further strengthen their base of the concept**exponents and powers.**

The chapter comprises a summary in which all the important concepts of the chapter-**Exponents and Powers**are mentioned. - NCERT Solutions for Class 8 Maths Chapter 13 - Direct and Inverse Proportions
Mathematics NCERT Grade 8, Chapter 13:

**Direct and inverse proportion**- In this chapter, the emphasis is laid on the concept of**direct proportions**and**inverse proportion**.

First of all, the**direct proportion**followed by**inverse proportion**.- Two quantities
and*x*are said to be in*y***direct proportion**if they**increase or decrease**together in such a manner that the**ratio**of their**corresponding values remains constant.** - Two quantities are said to be in
**inverse proportion**if an**increase in**in such a way that the*x*causes a proportional decrease in*y*and vice - versa**product**of their corresponding values remains**constant**.

For the purpose of better learning, some questions are also given in the form of '**Try These**'.

Two important points are cited in the box which is titled '**What Have We Discussed.**' - Two quantities
- NCERT Solutions for Class 8 Maths Chapter 14 - Factorisation
Mathematics NCERT Grade 8, Chapter 14: Factorisation- The chapter explains how to express

**algebraic expressions**as the**products of****their factors**. The chapter gives detail about the following topics:- What is
**Factorisation?** - Division of
**Algebraic Expressions** - Division of
**algebraic expressions continued ( Polynomial $\xf7$ Polynomial)** - Can You Find the Error?

These topics are divided into sub-sections. All the topics are supplemented with examples and some short questions.

To make the content of the chapter-**Factorisation**more interesting some fun facts are also discussed in the chapter.

Recaptulisation of all important points is done at the end. - What is
- NCERT Solutions for Class 8 Maths Chapter 15 - Introduction to Graphs
Mathematics NCERT Grade 8, Chapter 15:

**Introduction to Graphs**- The chapter includes a sectional explanation of the concepts related to**graphs**.

In this chapter we shall study different types of graphs like**Bar graph****Pie graph(or circle graph)****Histogram****Line graph**

**Linear graphs**. In this section, one can study how to**locate a point**on**graph sheet**through the coordinate points likeand*x*-coordinate.*y*-coordinate

The concept of**dependent**and**independent variables**is also stated in this chapter-**Introduction to Graphs**.

Understanding of each topic of the chapter,**Introduction to Graphs**is made easier by adding examples, activities, and diagrams.

In addition to this, the topic-wise assessment of the understanding is done with the help of questions provided at the end of each topic.

A summary of all the important points of the chapter,**Introduction to Graphs**is provided at the end followed by a set of exercises that tests the overall understanding of concepts mentioned in the chapter. - NCERT Solutions for Class 8 Maths Chapter 16 - Playing with Numbers
Mathematics NCERT Grade 8, Chapter 16:

**Playing with Numbers**- This chapter throws light on the concepts like**Numbers in General****Form**,**Letters for Digits**and various**divisibility tests**. The chapter also contains an interesting topic-**Games with Numbers**. To make the content more attractive and interesting some**games**related to**numbers**are given. These**games**will be fun to play and will also clear the concepts of students. Students will find the chapter very interesting to read and solve.**Divisibility tests**explained in this chapter are as follows:**Divisibility by 10****Divisibility by 5****Divisibility by 2****Divisibility by 9 and 3****Divisibility by 11**