NCERT Solutions for Class 8 Maths  

NCERT Solutions for Class 8 Maths help you find how to solve every exercise question step by step. Now, every Class 8 student can enhance their understanding of Maths concepts and prepare well for their exams with askIITians NCERT Solutions. Our Maths experts have prepared these solutions in a detailed manner so that every student can learn how to solve questions in exams. The solutions that we have prepared are based on the CBSE syllabus and the latest exam pattern. Students can download these solutions and refer to them at any time. 

askIITians NCERT Solutions for Class 8 Maths help you in various ways such as:

• Preparing for term exams, unit tests, and final examination
• Understanding Class 8 Maths concepts 
• Preparing for competitive exams and olympiads
• Ensuring a solid foundation for Class 9 Maths syllabus 
• Increasing theoretical and practical knowledge of concepts 

Free NCERT Solutions for Class 8 Maths 

NCERT Class 8 Maths includes topics like linear equations in one variable, data handling, rational numbers, geometry, squares and square roots, algebraic expressions and identities, mensuration, exponents, factorisation and more. We have provided chapter-wise Solutions for the Class 8 Maths NCERT textbook so that you face no issues in finding help. The best thing is that you do not have to pay anything for these solutions. Yes, the NCERT Solutions for Class 8 Maths Chapter 1 to 16 are available for free to every student. So why wait? Start downloading them right now and begin your learning. 

NCERT Solutions for Class 8 Maths | Chapter 1 to 16

Download NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers 

NCERT Class 8 Maths Chapter 1 Rational Numbers includes topics like closure property of rational numbers, commutative property of rational numbers, distributive property, negative of a number, representing rational numbers on a number line, and rational numbers between two rational numbers. There are just 2 exercises in this chapter that we have solved step by step in our NCERT exercises. Important points about this chapter are: 

• Rational numbers are closed under the operations of addition, subtraction and multiplication. 
• Rational numbers are commutative and associative for the operations of multiplication and division.
• The additive inverse of the rational number a/b is -a/b and vice-versa.
• Distributivity of rational numbers is given by:
  • a(b+c)=ab+ac and 
  • a(b–c)=ab–ac

For all rational numbers a, b and c

• The additive identity for rational numbers is the rational number 0. 
• The multiplicative identity for rational numbers is the rational number 1. 

Class 8 Maths NCERT Solutions for Chapter 1

Chapter 1 Class 8 NCERT Maths Ex 1.1 Solutions - 11 Questions Chapter 1 Class 8 NCERT Maths Ex 1.2 Solutions - 7 Questions

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

Linear Equations with One Variable Chapter includes 6 exercises based on topics like what is an algebraic equation, what is a linear equation in one variable, the solution of a linear equation, and applications of linear equations. Download our stepwise NCERT solutions for this chapter and start practising right now. Here are some important points about this chapter:

• An Algebraic Expression involves a constant, variable and some operations like addition, multiplication etc. For example, 2x + 3 is an algebraic expression. 
• An equation is a statement that has two expressions. For example, 2x = 2, x2 + x = 8 is an equation. 
• A linear expression is an expression whose highest power of the variable is 3 9one only. For example, 4x + 1 = ⅖ is a linear equation. 
• An equation of the form ax + b = c, where a, b and c are real numbers and a ≠ 0 is called a linear equation in one variable. 

Class 8 Maths NCERT Solutions for Chapter 2

Chapter 2 Class 8 Maths NCERT Ex 2.1 Solutions - 12 Questions Chapter 2 Class 8 Maths NCERT Ex 2.2 Solutions - 16 Questions Chapter 2 Class 8 Maths NCERT Ex 2.3 Solutions - 10 Questions Chapter 2 Class 8 Maths NCERT Ex 2.4 Solutions - 10 Questions Chapter 2 Class 8 Maths NCERT Ex 2.5 Solutions - 10 Questions Chapter 2 Class 8 Maths NCERT Ex 2.6 Solutions - 7 Questions

Download NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

Chapter 3 Understanding Quadrilaterals of Class 8 Maths NCERT book has 4 exercises. This chapter includes the understanding of the properties of various quadrilaterals such as parallelogram, rhombus, rectangle, square and kite. There are short answer and long answer questions in this chapter. You must remember the following points before solving NCERT questions for this chapter:

• A parallelogram is a quadrilateral with each pair of opposite sides parallel to each other. 
• A rhombus is a parallelogram with sides of equal length.
• A rectangle is a parallelogram with a right angle.
• A square is a rectangle with sides of equal length.
• A kite is a quadrilateral with exactly two pairs of equal consecutive sides.

Class 8 Maths NCERT Solutions for Chapter 3

Chapter 3 Class 8 Maths NCERT Ex 3.1 Solutions  - 7 Questions Chapter 3 Class 8 Maths NCERT Ex 3.2  Solutions - 6 Questions Chapter 3 Class 8 Maths NCERT Ex 3.3  Solutions - 12 Questions Chapter 3 Class 8 Maths NCERT Ex 3.4  Solutions - 6 Questions

Download NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry 

Chapter 4 Practical Geometry of Class 8 NCERT Maths book includes 5 exercises based on the construction of quadrilaterals. In this chapter, you study four different ways of constructing a quadrilateral as given below:

• Constructing a quadrilateral uniquely if the lengths of its four sides and a diagonal are given.
• Constructing a quadrilateral uniquely if its two diagonals and three sides are known.
• Constructing a quadrilateral uniquely if its two adjacent sides and three angles are known.
• Constructing a quadrilateral uniquely if its three sides and two included angles are given.

Class 8 Maths NCERT Solutions Chapter 4

Chapter 4 Class 8 Maths Ex 4.1 - 1 Question Chapter 4 Class 8 Maths Ex 4.2 - 1 Question Chapter 4 Class 8 Maths Ex 4.3 - 1 Questions Chapter 4 Class 8 Maths Ex 4.4 - 1 Questions Chapter 4 Class 8 Maths Ex 4.5 - 4 Questions

Download NCERT Solutions for Class 8 Maths Chapter 5 Data Handling 

Chapter 5 Data Handling in Class 8 Maths is the foundation of Statistics. In this chapter, you study different ways of organising and grouping data. You learn about grouped frequency distributions, histograms, circle graphs, random experiments, probability and more. There are 3 exercises in this chapter. Important points to remember in this chapter are:

• Unorganised data is also known as raw data. 
• The number of times any data item occurs is called its frequency. For example, the frequency of 2 in the data set “3, 5, 6, 2, 1, 0, 7, 8, 2, 3, 2” is 3.
• A histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval.
•  A circle graph shows the relationship between a whole and its part.
• Probability is calculated by:Number of outcomes that make an eventTotal number of outcomes of the experiment 

Class 8 Maths NCERT Solutions for Chapter 5

Chapter 5 Class 8 Maths NCERT Ex 5.1 Solutions - 5 Questions Chapter 5 Class 8 Maths NCERT Ex Solutions 5.2 - 5 Questions Chapter 5 Class 8 Maths NCERT Solutions Ex 5.3 - 6 Questions

Download NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots 

Learn what a square of a number is, properties of a square number, and interesting patterns based on applications of squares of a number in the Chapter Squares and Square Roots. The chapter includes 4 exercises based on the following points:

• If a natural number m can be expressed as n2, where n is also a natural number, then m is a square number.
• The square root is the inverse operation of the square.

Class 8 Maths NCERT Solutions for Chapter 6

Chapter 6 Class 8 Maths NCERT Ex 6.1 Solutions - 9 Questions Chapter 6 Class 8 Maths NCERT Ex 6.2 Solutions - 2 Questions Chapter 6 Class 8 Maths NCERT Ex 6.3 Solutions - 10 Questions Chapter 6 Class 8 Maths NCERT Ex 6.4 Solutions - 9 Questions

Download NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots 

Cubes and Cube Roots Chapter of Class 8 Maths NCERT book includes 2 exercises based on the understanding of cube numbers, perfect cube and cube roots. Here are some important points about this chapter:

• Numbers obtained when a number is multiplied by itself three times are known as cube numbers. For example 1, 8, 27, ... etc.
• If in the prime factorisation of any number each factor appears three times, then the number is a perfect cube.
• The symbol3denotes cube root. 

Class 8 Maths NCERT Solutions Chapter 7

Chapter 7 Class 8 Maths NCERT Ex 7.1 Solutions  - 4 Questions Chapter 7 Class 8 Maths NCERT Ex 7.2 Solutions - 3 Questions

Download NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities 

In this chapter, you learn about various ways you can compare different quantities such as ratios and percentages, increase and decrease per cent, discounts, estimation of percentages, profit and loss, tax, and compound interest and its applications. There are 3 exercises in this chapter and all are very important from the examination point of view. Some important formulae related to this chapter are:

• Cost Price = Buying price + Overhead expenses
• Discount = Marked Price - Sale Price
• Sales tax = Tax% of Bill Amount
• Annually Compounded Interest = P(1 + R/100)n
• Semi-annually Compounded Interest = P(1 + R/200)2n

Class 8 Maths NCERT Solutions for Chapter 8

Chapter 8 Class 8 Maths NCERT Ex 8.1 Solutions - 6 Questions Chapter 8 Class 8 Maths NCERT Ex 8.2 Solutions - 11 Questions Chapter 8 Class 8 Maths NCERT Ex 8.3 Solutions - 12 Questions

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

Chapter 9 Algebraic Expressions and Identities includes important topics that will form a solid foundation for algebra. The chapter includes basic definitions of expressions, terms, variables and coefficients. You will study different types of polynomial expressions such as monomials, binomials, trinomials, along with like terms, unlike terms, and addition, subtraction and multiplication of algebraic expressions. There are 5 exercises in this chapter. Some important formulae used in this chapter include:

• (a + b) (a - b) = a2 - b2
• (a - b)2 = a2 - 2ab + b2
• (a + b)2 = a2 + 2ab + b2
• (x + a) (x + b) = x2 + (a + b)x + ab

Class 8 Maths NCERT Solutions for Chapter 9

Chapter 9 Class 8 Maths NCERT Ex 9.1 Solutions - 4 Questions Chapter 9 Class 8 Maths NCERT Ex 9.2 Solutions - 5 Questions Chapter 9 Class 8 Maths NCERT Ex 9.3 Solutions - 5 Questions Chapter 9 Class 8 Maths NCERT Ex 9.4 Solutions - 3 Questions Chapter 9 Class 8 Maths NCERT Ex 9.5 Solutions - 8 Questions

Download NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes 

In this chapter, you learn how different 2-dimensional shapes can be visualised in the 3-dimension space as 3-dimensional shapes. It includes topics like mapping, faces, edges, and vertices of shapes. There are 3 exercises in this chapter based on important points like:

• 3D objects have different views from different positions.
• A map depicts the location of a particular object/place in relation to other objects/places.
• Symbols are used to depict the different objects/places on a map. 
• Euler’s formula: For any polyhedron, F + V - E = 2,

where ‘F’ stands for the number of faces, V stands for the number of vertices and E stands for the number of edges. 

Class 8 Maths NCERT Solutions NCERT Chapter 10

Chapter 10 Class 8 Maths NCERT Ex 10.1 Solutions - 3 Questions Chapter 10 Class 8 Maths NCERT Ex 10.2 Solutions - 4 Questions Chapter 10 Class 8 Maths NCERT Ex 10.3 Solutions - 8 Questions

Download NCERT Solutions for Class 8 Maths Chapter 11 Mensuration 

In Chapter 11 of NCERT Class 8 Maths book, you study how to find the surface area and volume of different three-dimensional shapes like cubes, cuboids, and cylinders. This chapter involves complex calculations and so you must remember the formulae for finding area and volume distinctly. Some important formulae used in this chapter are:

• Area of a trapezium = half of the sum of the lengths of parallel sides × perpendicular distance between them
• Area of a rhombus = half the product of its diagonals
• Area of  cuboid = 2(lb + bh + hl)
• Area of a cube = 6l2
• Area of a cylinder = 2πr(r + h)
• The Volume of a cuboid = l × b × h 
• The volume of a cube = l3
• The Volume a cylinder = πr2h

Class 8 Maths NCERT Solutions for Chapter 11

Chapter 11 Class 8 Maths NCERT Ex 11.1 Solutions - 5 Questions Chapter 11 Class 8 Maths NCERT Ex 11.2 Solutions- 11 Questions Chapter 11 Class 8 Maths NCERT Ex 11.3 Solutions - 10 Questions Chapter 11 Class 8 Maths NCERT Ex 11.4 Solutions - 8 Questions

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

Chapter 12 Exponents and Powers of Class 8 Maths NCERT book is about powers with negative numbers, laws of exponents, using exponents to represent small numbers in standard form and comparing very large and very small numbers. There are just 2 exercises in this chapter that we have solved comprehensively for your understanding. Take note of some important formulae of this chapter:

• am × an = am+n
• am ÷ an = am-n
• (am)n = amn
• a0 = 1
• am ×bm =(ab)m

Class 8 Maths NCERT Solutions for Chapter 12

Chapter 12 Class 8 NCERT Maths Ex 12.1 Solutions - 7 Questions Chapter 12 Class 8 NCERT Maths Ex 12.2 Solutions - 2 Questions

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

In this chapter, you will learn how values are directly and indirectly proportional to each other which means how an increase or decrease in one value affects the other. There are 2 exercises in this chapter and both of them are solved by our experts for your reference. Download our online NCERT solutions right away. 

• Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant. 
• Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. 

Class 8 Maths NCERT Solutions for Chapter 13

Chapter 13 Class 8 NCERT Maths Ex 13.1 Solutions - 10 Questions Chapter 13 Class 8 NCERT Maths Ex 13.2 Solutions - 11 Questions

Download NCERT Solutions for Class 8 Maths Chapter 14 Factorisation 

The main topics included in this chapter are factors of a natural number, factors of algebraic expressions, finding common factors, regrouping terms to factorise expressions, using identities to factorise expressions and division of algebraic expressions. The chapter has 4 exercises, each of which is solved step by step by our experts. Some important points to note about this chapter include:

• Factors of a number are numbers that divide it evenly. For example, 2 and 3 are factors of 6. 
• Factorization writes a number as the product of smaller numbers. For example, 6 can be factored as 2 * 3. 
• Identities that can be used in factorisation:
  • (a + b)2 = a2 + 2ab + b2
  • (a - b)2 = a2 - 2ab + b2
  • (a + b)(a - b) = a2 – b2
  • (x + a)(x + b) = x2 + (a + b)x + ab

Class 8 Maths NCERT Solutions for Chapter 14

Chapter 14 Class 8 Maths NCERT Ex 14.1 Solutions - 3 Questions Chapter 14 Class 8 Maths NCERT Ex 14.2 Solutions - 3 Questions Chapter 14 Class 8 Maths NCERT Ex 14.3 Solutions - 5 Questions Chapter 14 Class 8 Maths NCERT Ex 14.4 Solutions - 20 Questions

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

In Chapter 15 of Class 8 Maths NCERT book, you study topics like bar graphs, pie charts, histograms, line graphs, linear graphs, and their plotting on a graph paper. This chapter is important for higher classes and you must solve all of its 3 exercises carefully. Some important points for solving NCERT exercises of this chapter include:

• A bar graph is used to show comparisons among different categories or data items. 
• A pie graph is used to compare parts of a whole.
• A histogram is a bar graph that shows data intervals.
• A line graph displays data that changes continuously over periods of time.
• A line graph which is a whole unbroken line is called a linear graph.
• For fixing a point on the graph sheet we need its x-coordinate and y-coordinate.

Class 8 Maths NCERT Solutions for Chapter 15

Chapter 15 Class 8 NCERT Maths Ex 15.1 Solutions - 7 Questions Chapter 15 Class 8 NCERT Maths Ex 15.2 Solutions - 4 Questions Chapter 15 Class 8 NCERT Maths Ex 15.3 Solutions - 2 Questions

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

The last chapter of the Class 8 Maths NCERT book includes topics like representation of numbers in general form, two-digit numbers, three-digit numbers, using letters for digits and test of divisibility (divisibility by 10, 5, 2, 9, 3). There are 2 exercises in this chapter. Take note of the important points about this chapter:

• Numbers can be written in a general form. Thus, a two-digit number ab will be written as ab = 10a + b.
• The general form of numbers helps solve puzzles or number games.

Class 8 Maths NCERT Solutions Chapter 16 Exercises

Chapter 16 Class 8 NCERT Maths Ex 16.1 Solutions - 10 Questions Chapter 16 Class 8 NCERT Maths Ex 16.2 Solutions - 4 Questions

NCERT Class 8 Maths Solutions FAQs

1. Why should I download the NCERT Solutions for Class 8 Maths? 

The NCERT Solutions for Class 8 Maths will help you prepare for your term-end and final examination. You can understand how to solve questions step by step in the examination and secure full marks in every chapter. Our NCERT solutions also help in solidifying your conceptual understanding of the chapters so that you can solve any kind of questions without any trouble. 

2. Do I need to practice all the exercises given in the NCERT Class 8 Maths book?

Yes, solving every exercise is a must for better exam preparation and understanding of the concepts. CBSE papers are generally based on NCERT problems only so if you practice all the exercises thoroughly, it is likely that you can achieve full marks in Maths. 

3. How often do I need to practice NCERT Class 8 Maths exercises? 

You must practice a few questions every day. Our NCERT solutions help you learn the concepts at your own pace. They are self-explanatory and include easy to understand explanations. Practising a few questions every day helps you complete the syllabus on time.