# NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8 Maths consists of the chapter-wise solutions of all the problems provided in the NCERT textbook for Class 8 Mathematics. GeeksforGeeks has created a detailed chapter-wise solution for the NCERT book of class 8 that contains problems on various topics like Rational Numbers, Linear Equations, Quadrilaterals, Data Handling, and many more. Each chapter in this solution thoroughly covers every exercise along with a detailed step-by-step explanation of the solutions.

### Chapter 1: Rational Numbers

The chapter Rational numbers mainly discuss the characteristics of all the real numbers, integers, whole numbers, rational numbers, and natural numbers. This chapter consists of two exercises only in which the problems in Exercise 1.1 are related to the properties of the rational numbers (closure, commutativity, associativity, etc). However, in Exercise 1.2 the problems are related to the advanced concepts of the rational number like the representation of rational numbers on a number line and to determine any numbers of rational number between any two rational numbers.

### Chapter 2: Linear Equations in One Variable

The linear equations in one variable deal with the expression defined in one variable only and its algebraic operations. This chapter contains six different exercises that have problems based on the linear equations in one variable and its application.Exercises 2.1, 2.2, 2.3, and 2.4 are designed to determine the solution of the linear equation. However, Exercises 2.5 and 2.6 are based on the topic equations reducible to the linear form.

### Chapter 3: Understanding Quadrilaterals

This chapter covers all types of quadrilaterals such as polygonal shapes like square, rectangle, triangle, pentagon, hexagon, etc. In total, this chapter contains four exercises in which Exercise 3.1 covers the problems on the definition of various polygons and their properties, Exercise 3.2 is based on the concept of the Angle sum property of a polygon. However, Exercise 3.3 covers the elements and the properties of quadrilaterals like trapezium, kite, and parallelogram, and Exercise 3.4 is designed to learn some special types of parallelogram like square, rectangle, and rhombus.

### Chapter 4: Practical Geometry

The chapter practical geometry helps to learn the construction of quadrilateral when different parameters of it are known. This chapter contains a total of five exercises only in which Exercise 4.1 covers the problem for the case when the lengths of four sides and a diagonal are given. Similarly, Exercises 4.2, 4.3,and 4.4 are based on the topics when two diagonals and three sides are known, two adjacent sides and three angles are given and three sides and two included angles are provided. However, Exercise 4.5 contains problems based on some special cases.

### Chapter 5: Data Handling

Data handling is a method of organizing data or information systematically using diagrams like bar graphs, pictographs, pie charts, and histograms. This chapter consists of only three exercises. Exercise 5.1 is based on the basic concept of representing, organizing, and grouping the data provided while Exercise 5.2 helps to make a pie chart for the given data. Moreover, Exercise 5.3 coves the topic that helps to understand the basic concept of probability.

### Chapter 6: Squares and Square Roots

As the name of the chapter says, Squares and square roots this chapter gives the knowledge of the concept to determine the squares and square root of a number. The different properties and the pattern followed to find a square number are discussed in four exercises. Exercises 6.1 and 6.2 are based on the basic idea of the square numbers and different ways to determine them. Though Exercises 6.4 and 6.5 are focused on the concept of the determination of the square root of a number.

### Chapter 7: Cubes and Cube roots

Again, as the title of the chapter suggest that Cubes and Cube roots this chapter helps to understand the concept to determine the cubes and cube root of a number. The different patterns followed to find a cube and cube root of a number are discussed in only two exercises. Exercises 7.1 contains the problem to determine whether the given number is a perfect cube or not. And Exercises 7.2 focused on the idea of the cube root and the determination of the cube root of a number.

### Chapter 8: Comparing Quantities

This chapter gives a basic understanding of the topics such as increased and decreased percentage, market price, selling price, cost price, discount, and discount price, profit or loss, interest, etc. Total there are three exercises in this chapter, Exercise 8.1 based on the topics ratios and percentage, and Exercises 8.2 and 8.3 covers a wide range of concepts such as percentage, profit or loss, tax, and compound interest.

### Chapter 9: Algebraic Expressions and Identities

The chapter Algebraic Expressions and Identities briefs the basics of monomials, binomials, and polynomials in an algebraic expression. The problems in this chapter are discussed in five exercises, Exercises 9.1 and 9.2 covers the basic concepts of terms related to polynomials and operations on the expressions. Exercise 9.3 and 9.4 are based on the multiplications of polynomials while Exercise 9.5 discussed the standard algebraic identities.

- Exercise 9.1
- Exercise 9.2
- Exercise 9.3
- Exercise 9.4
- Exercise 9.5 Set 1, Set 2

### Chapter 10: Visualising Solid Shapes

This chapter provides the understanding of different solids shapes when visualized in different dimensions and various terms used to describe their properties. The chapter explains this in three different exercises. Here exercises 10.1 and 10.2 are based on the concept of the visualisation of different solid shapes at different positions and the mapping spaces around the observer. Though, Exercise 10.3 discussed the terms like faces, edges, vertices, and relation between them, related to a solid shape.

### Chapter 11: Mensuration

Mensuration is the chapter that deals with the measurement or the calculations related to determine the area, perimeter, volume of various geometrical figures like square, cube, rectangle, cuboid, cylinder, and triangle, etc. This chapter consists of only four exercises in which Exercises 11.1 and 11.2 deal with problems related to the areas of different geometrical shapes, combination of shapes, and every-day life examples. However, Exercises 11.3 and 11.4 discussed the terminology related to 3-Dimensional shapes.

### Chapter 12: Exponents and Powers

The chapter Exponents and powers cover the primary concepts such as laws of exponents and their applications. This chapter consists of only two exercises, Exercise 12.1 is specifically based on the laws of exponents, and Exercise 12.2 deals with the problems using the applications of power to write large numbers in exponents and vice-versa.

### Chapter 13: Direct and Inverse Proportions

This chapter gives a detailed explanation of inverse and direct proportions through problems discussed in two exercises. In which Exercise 13.1 contains problems to determine the direct proportions between any quantity and Exercise 13.2 deals with the questions from the indirect inverse.

### Chapter 14: Factorisation

This chapter comprises the problems on the factors of natural numbers and algebraic expressions, factorisation by regrouping terms, factorisation using identities, division of algebraic expressions. The chapter includes four exercises out of which exercises 14.1 and 14.2 are based on the topic factorisations and their application while exercises 14.3 and 14.4 emphasize the division of algebraic expressions.

### Chapter 15: Introduction to Graphs

This chapter is all about the basic understanding of the graphs, kinds of graphs, etc. It is mainly explained using three exercises, Exercise 15.1 deals with problems from introduction to graphs and terminology related to it while, problems in Exercises 15.2 and 15.3 provided emphasis on the construction of different types of graphs and their applications.

### Chapter 16: Playing with Numbers

All the above-mentioned chapters basically helped to learn about various kinds of numbers and their different properties likewise in this chapter the concept of numbers is discussed in a more general way. This chapter includes two exercises only, Exercise 16.1 and 16.2 which contains fun activities, puzzles, etc. such as divisibility tests to determine any missing number in a series of numbers.