# NCERT Solutions for Class 8 Maths

Share**NCERT Solutions for Class 8 Maths **cover all the back-exercise questions that are present in Class 8 Maths NCERT book. These solutions have been prepared by our expert teachers having a thorough knowledge of Maths subject. Our maths experts do extensive research to come up with clear and well-explained solutions for NCERT Class 8 Maths Book.

Our NCERT Maths Class 8 Solutions include clear explanations of complex Maths topics which can help you better your performance in the exam. In any case, you can check out the chapter-wise solutions for CBSE Class 8th Maths Textbook below.

## NCERT Class 8 Maths Solutions - All Chapters

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Our NCERT Class 8 Maths Book Solutions include answers and explanations for all the questions given in the NCERT Maths Textbook. These solutions will help students understand complex Maths topics and questions properly and solve them easily. The CBSE 8th Class Maths Solutions provided by us are based on the latest curriculum.

## NCERT Solutions for Class 8 Maths (Chapter-wise description)

**Chapter 1: Rational Numbers**

**Introduction: **Let us first recall real numbers from earlier classes. Real numbers consist of natural numbers, whole numbers, and integers. In Class 7 NCERT Maths textbook, you first came across the concept of rational numbers. You learnt that these are also part of real numbers.

To define, rational numbers can be expressed in the form of p/q, where q cannot be equal to zero. In NCERT Class 8 Maths, you will learn to work out with rational numbers. You will also study how these numbers can be closed under the operations of addition, subtraction and multiplication.

In the latter half of this chapter, you will get to understand how rational numbers are represented on a number line. This chapter consists of 2 exercises and 18 questions based on the following concepts.

**Topics**

1. Properties of Rational Numbers

(a). Closure

(b). Commutativity

(c). Associativity

(d). The role of zero

(e). The role of 1

(f). Negative of a number

(g). Reciprocal

(h). Distributivity of multiplication over addition for rational numbers

2. Representation of Rational Numbers on the Number Line

3. Rational Numbers between Two Rational Numbers

**Chapter 2: Linear Equations in One Variable**

**Introduction: **In the last two grades, you were taught that an algebraic equation is equality that involves variables. So far, you have only covered linear equations in one variable. An equation is said to be linear when its highest power of the variable is 1.

This year, you will learn to transpose variables from one side of the equation to the other. In an equation, the expression on the left-hand side is always equal to the expression on the right-hand side.

The utility of linear equations is in various applications such as the combination of currency notes, different problems on numbers, ages, perimeters etc. Initially, you may find some word problems tricky. However, you can verify or rectify your answers by looking at our NCERT Solutions for Class 8 Maths Chapter 2.

**Topics**

1. Equations With Linear Expressions On One Side And The Numbers On The Other Side

2. Some Applications

3. Solving Equations Having The Variable On Both Sides

4. Applications Of Linear Equations

5. Reducing Equations To Simpler Form

6. Equations Reducible To The Linear Form

**Chapter 3: Understanding Quadrilaterals**

**Introduction: **Before you understand quadrilaterals, try to recall different varieties of curves such as plane curve, simple curve, simple closed curve etc. In NCERT Class 8 Maths Chapter-3, our topic of concern is a simple closed curve made up of line segments, which is called a polygon.

Based on the number of sides or vertices, polygons can be classified as a triangle (3 sides), quadrilateral (4 sides), pentagon (5 sides) and so on. After completing this chapter, you will have a clear understanding of properties of different types of quadrilaterals such as parallelogram, rhombus, rectangle, square and kite.

There are a total of 33 questions in 4 exercises based on the following concepts.

**Topics**

1. Polygons

(a). Classification Of Polygons

(b). Convex And Concave Polygons

(c). Regular And Irregular Polygons

(d). Angle Sum Property

2. Sum of the Measures of the Exterior Angles of a Polygon

3. Types of Quadrilaterals

(a). Trapezium

(b). Kite

(c). Parallelogram

(d). Elements of a Parallelogram

(e). Angles of a Parallelogram

(f). Diagonals of a Parallelogram

4. Some Special Parallelograms

(a). Rhombus

(b). Rectangle

(c). Square

**Important Concepts of Understanding Quadrilaterals**

**1. Properties of Parallelogram**

- Opposite sides are equal
- Opposite angles are equal
- Diagonals bisect each other

**2. Properties of Rhombus**

- Opposite sides are equal
- Opposite angles are equal
- Diagonals bisect each other
- Diagonals are perpendicular to each other

**3. Properties of Rectangle**

- Opposite sides are equal
- Opposite angles are equal
- Diagonals bisect each other
- Each of the angle is a right angle
- Diagonals are equal

**4. Properties of Square**

It includes all the properties of a parallelogram, rhombus and a rectangle.

**5. Properties of Kite**

- The diagonals are perpendicular to one another
- Diagonals bisect each other

Chapter 4: Practical Geometry

Chapter 4: Practical Geometry

**Introduction: **In the previous edition of NCERT Maths textbook, you have learnt how to draw triangles. It took three measurements to draw a unique triangle. Having understood the properties of different types of quadrilaterals, we will now proceed with the construction of quadrilaterals.

In this chapter, you will come across five different known conditions for the construction of a unique quadrilateral. These conditions are mentioned below.

**Topics**

A quadrilateral can be constructed when-

- Four sides and one diagonal are given
- Two diagonals and three sides are given
- Two adjacent sides and three angles are given
- Three sides and two included angles are given
- When other special properties are known

Chapter 5: Data Handling

Chapter 5: Data Handling

**Introduction: **When we extract data from sources, it is available in an unorganized form, also called raw data. In this chapter, you will learn to draw meaningful inferences and organize the data systematically. As studied earlier in pictograph, a frequency gives the number of times a particular entry occurs.

With the help of grouped frequency distribution, raw data can be grouped and presented systematically. Grouped data can be represented in various ways, including histograms, pie charts, bar graphs, etc.

As you proceed further, you will study about random experiments and the probability of an event. Check out the complete list of topics covered in NCERT Class 8th Maths Chapter- 5.

**Topics**

1. Organizing Data

2. Grouping Data

(a). Bars with a Difference

3. Circle Graph on Pie Chart

4. Chance and Probability

(a). Getting a Result

(b). Equally Likely Outcomes

(c). Linking Chances to Probability

(d). Outcomes as Events

(e). Chance and Probability

**Important Formulas of “Probability”**

Probability of an event (P) = Number of outcomes that make an event/ Total number of outcomes of the experiment

Chapter 6: Squares and Square Roots

Chapter 6: Squares and Square Roots

**Introduction: **Suppose, a natural number *m *can be expressed as *n**2*, where *n* is a natural number, then *m* is a square number. One can identify a square number by observing its unit place. Numbers that end with 0,1, 4, 5, 6 or 9 are called square numbers.

Another way to identify a square number is by counting the number of zeros at the end. Numbers that have an even number of zeros at the end are called square numbers. The square root is the inverse operation of the square.

This chapter is divided into four exercises, with a total of 31 questions. By the end of the chapter, you will have a clear understanding of the following topics.

**Topics**

- Properties of Square Numbers
- Finding the Square of a Number
- Square Roots
- Finding Square Root by Division Method
- Square Roots of Decimals
- Estimating Square Root

Chapter 7: Cubes & Cube Roots

Chapter 7: Cubes & Cube Roots

**Introduction: **S.Ramanujan, who is regarded as one of the finest mathematical geniuses, came out with a unique concept when he met Prof. G.H. Hardy. Professor came to visit him in a taxi whose number was 1729. While talking to each other, Ramanujan suddenly thought of it as the smallest number that can be expressed as a sum of two cubes.

Similarly, there are infinitely many such numbers such as 4104, 13832 etc. These numbers are known as Hardy-Ramanujan Numbers. Cube numbers such as 8, 27, 64, 125 etc. can be obtained when 2, 3, 4, 5 etc. are multiplied by themselves three times respectively.

Cube root is the inverse operation of the cube. For example ∛27 = 3. When doing prime factorisation of any number, if you find each factor appearing three times, then the number is a perfect cube.

**Topics**

1. Cubes

2. Cube Roots

(a). Cube root through prime factorisation method

(b). Cube root of a cube number

**Chapter 8: Comparing Quantities**

**Introduction: **Before you start-off this chapter, it is recommended that you revisit ratios and percentages. In the first exercise of this chapter, you can strengthen your previous concepts related to ratios and percentages. While the second exercise of the chapter will include questions based on the increase or decrease percent, discounts, profit and loss, and goods and services tax.

In the last exercise, you will deal with word problems involving the use of compound interest annually or half-yearly. A few questions will be based on the applications of compound interest formula.

This chapter requires you to have utmost accuracy that can only come with regular practice. When you are practising questions, it is important that you cross-check your answers from our NCERT Class 8 Maths Chapter-8 Solutions. In total, there are 28 questions across 3 exercises based on the following concepts.

**Topics**

1. Ratios and Percentages

2. Finding the Increase or Decrease Percent

3. Finding Discounts

4. Prices Related to Buying and Selling

5. Sales Tax/ Value Added Tax/ Goods and Services Tax

6. Compound Interest

7. Deducing a Formula for Compound Interest

8. Rate Compounded Annually or Half Yearly

9. Applications of Compound Interest Formula

**Important Formulas of “Comparing Quantities”**

1. Discount = Marked price - Sale price

2. Discount = Discount % of the marked price

3. Cost Price = Buying price + Overhead expenses

4. Compound Interest (A) = Principal amount + Interest

5. Compound Interest when interest is compounded annually

= P (1 + R/100)^{n}, where P is principal, R is the rate of interest, *n* is time period

6. Compound Interest when interest is compounded half-yearly

= P (1 + R/200)^{2n}, where R/2 is half yearly rate, 2n = number of half-years

Chapter 9: Algebraic Expressions and Identities

Chapter 9: Algebraic Expressions and Identities

**Introduction: **In earlier editions of NCERT Maths textbook, you learnt that terms are formed from variables and constants. When you add or subtract these terms, you will get an expression. Expressions that contain exactly one, two and three terms are called monomials, binomials and trinomials, respectively.

In general, a polynomial can be termed as an expression with one or more terms having non-zero coefficients.

When we speak of Like and Unlike terms, like terms are formed from the same variables having a similar degree. However, coefficients of Like terms need not be the same.

Later in the chapter, you will be introduced to three standard identities and an additional identity. These identities will be useful in solving squares and products of algebraic expressions. Check out the topics and identities of this chapter below.

**Topics**

- Expressions
- Terms, Factors and Coefficients
- Monomials, Binomials and Polynomials
- Like and Unlike Terms
- Addition and Subtraction of Algebraic Expressions
- Multiplication of Algebraic Expressions
- Multiplying a Monomial by a Monomial
- Multiplying a Monomial by a Polynomial
- Multiplying a Polynomial by a Polynomial
- What is Identity?
- Standard Identities
- Applying Identities

**Important Identities of “Algebraic Expressions and Identities”**

- (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a - b)
^{2}= a^{2}- 2ab + b^{2} - (a + b) (a - b) = a
^{2}- b^{2} - (x + a) (x + b) = x
^{2}+ (a + b)x + ab

**Chapter 10: Visualising Solid Shapes**

**Introduction: **In class 7, you have learnt about two-dimensional (plane) shapes and three-dimensional (solid) shapes. You may recall that circle, rectangle, triangle etc. are classified under 2-D figures while cubes, cylinders, cones, spheres etc. are 3-D figures.

This year, you will study 3D objects that have different views from different positions. The main highlight of this chapter is Euler’s formula, in which you will get to understand the relationship between faces, vertices, and edges.

**Topics**

1. Views of 3D-Shapes

2. Mapping Space Around Us

3. Faces, Edges and Vertices

**Euler’s Formula**

F + V - E = 2, where

‘F’ stands for the number of faces

‘V’ stands for the number of vertices

‘E’ stands for the number of edges

Chapter 11: Mensuration

Chapter 11: Mensuration

**Introduction: **In the previous edition of NCERT Maths, you have learnt to find the area and perimeter of various plane figures such as triangles, rectangles, circles, etc. Now, your next task will be to solve problems related to perimeter and area of various plane closed figures.

While the last exercise of this chapter will include word problems based on surface area and volume of solids such as a cube, cuboid and cylinder. With the help of NCERT Solutions for Class 8 Maths Chapter 11, you will get to practice 34 questions across 4 exercises. These solutions will enable you to grasp the following concepts.

**Topics**

- Area and Perimeter of Rectangle, Square, Triangle, Parallelogram, Circle
- Area of Trapezium
- Area of a General Quadrilateral
- Area of a Polygon
- Solid Shapes
- Surface Area of Cube, Cuboid and Cylinder
- Volume of Cube, Cuboid and Cylinder
- Volume & Capacity

**Important Formulas of “Mensuration”**

1. Area of Trapezium = ½ x (Sum of the length of parallel sides) x Distance between them

2. Area of Rhombus = ½ x Product of its diagonals

3. Total Surface Area of a Cuboid = 2(lb + bh + hl)

4. Total Surface Area of a Cube = 6l^{2}

5. Total Surface Area of a Cylinder = 2πr (r + h)

6. Volume of a Cuboid = l x b x h

7. Volume of a Cube = l^{3}

8. Volume of a Cylinder = πr^{2}h

9. Some Important Conversions

(a). 1 cm^{3} = 1 mL

(b). 1 L = 1000 cm^{3}

(c). 1 m^{3} = 1000000 cm^{3} = 1000 L

**Chapter 12: Exponents and Powers**

**Introduction: **You should be well-versed with the laws of exponents before you start solving questions of chapter-12. Earlier, you dealt with only positive exponents, but now you will extend your knowledge to negative exponents. The laws of exponents are applicable for numbers with negative exponents.

Basic laws of exponents and important topics of this chapter are given below.

**Topics**

2. Laws of Exponents

3. Use of Exponents to Express Small Numbers in Standard Form

**Important Formulas/ laws of “Exponents and Powers”**

(a). a^{m} x a^{n} = a^{m+n}

(b). a^{m} ÷ a^{n} = a^{m-n}

(c). (a^{m})^{n} = a^{mn}

(d). a^{m} x b^{m} = (ab)^{m}

(e). a^{0} = 1

(f). a^{m}/ b^{m} = (a/b)^{m}

**Chapter 13: Direct and Inverse Proportions**

**Introduction: **Direct and inverse proportion is one of the most important chapters of NCERT Class 8 Maths as it will come to play in higher classes**, **especially in Physics and Chemistry. Two variables x and y are said to be in direct proportion when the value of y increases with respect to increase in the value of x such that the ratio x/y does not change.

On the other hand, two variables x and y are said to be in inverse proportion, when x increases y decreases and vice-versa. This chapter features 21 questions in its 2 exercises.

**Topics**

1. Direct Proportion

2. Inverse Proportion

**Formulas of Direct and Indirect Proportion**

1. Direct Proportion

x_{1}/y_{1} = x_{2}/y_{2}

2. Indirect Proportion

x_{1}/ x_{2} = y_{2}/ y_{1}

**Chapter 14: Factorisation**

**Introduction: **Previously, we learnt to obtain factors using the prime factorisation method. When we factorise an algebraic expression, we represent it in the form of the product of factors. In NCERT Solutions for Class 8 Maths Chapter- 14, you will study four different methods of factorisation given below in the list of topics.

In the latter half of this chapter, you will study division of a polynomial by a monomial. You can carry out the division either by dividing each term of the polynomial by a monomial or by the common factor method.

In the last exercise of this chapter, your task will be to spot errors in algebraic equations. In total, there are 34 questions across its 4 exercises.

**Topics**

1. Factorization

(a). Method of Common Factors

(b). Regrouping Terms

(c). Using Identities

(d). Factors of the Form (x + a) (x + b)

2. Division of Algebraic Expressions

(a). Division of a Monomial by Another Monomial

(b). Division of a Polynomial by a Monomial

3. Division of Algebraic Expressions

4. Error Spotting

Chapter 15: Introduction to Graphs

Chapter 15: Introduction to Graphs

**Introduction: **Graphical representation of data is carried out after collecting raw data from the authentic sources. Three basic methods of graphical representation include a bar graph, a pie chart and a histogram.

Further, you will learn to display data using a line graph. A line graph is alternatively called a linear graph. To locate a point on the graph sheet we need, x-coordinate and y-coordinate. This chapter consists of 13 questions.

**Topics**

1. Bar Graph

2. Pie Chart

3. Histogram

4. Line Graph

5. Linear Graphs

(a). Location of a Point

(b). Coordinates

6. Applications of Graphs

## Benefits of studying with NCERT Class 8 Maths Book Solutions

There are several benefits that you can experience by studying maths with the help of NCERT Solutions. To begin with, you can practise each topic and question by following a detailed and meticulous approach. Moreover, you get the opportunity to learn the topics and concepts sitting at your home with the help of the Internet. Continue to read below, to learn about additional benefits that you can get by relying on CBSE Class 8 Maths Solutions from Goprep.

- Well researched and easy to understand solutions
- Accurate and Reliable explanations of questions
- Exercise and topic-based solutions covering the majority of questions
- Available for free and easy to download
- Based on the latest curriculum released by the CBSE
- Step by step solutions for a better understanding of the topics
- Help to score better marks in the exam.
- These solutions can be accessed at anytime of the day anywhere

## FAQs | NCERT Class 8 Maths Textbook

Students looking to study with the help of NCERT Solutions for Class 8 often come up with some doubts regarding the applicability and reliability of these solutions. Therefore, to address the concern of students, we have compiled a few questions that are frequently asked by them.

### Can I score more marks by studying NCERT Solutions for class 8?

Obviously, you can score more marks by relying on NCERT Solutions for Class 8 Maths Textbook. However, for that to happen, you need to practise important questions regularly. Our NCERT Solutions cover explanations for all topics and questions, and thus by practising them, you can definitely score better marks.

### Are CBSE NCERT Class 8 Maths Solutions reliable?

Since these solutions are prepared by qualified and expert teachers of Goprep, they are 100% reliable. Moreover, the solutions are based on the curriculum of CBSE for Class 8, which further confirms their validity and reliability.

### Can I get NCERT Solutions for Class 8 Maths for Free?

Yes, NCERT Solutions for 8th Class Maths are made available by us for free of cost. You can access and download these solutions at anytime and anywhere for practice purpose.

### How long will it take to practise all the questions in CBSE 8th Class Maths Solutions?

It entirely depends upon you and the amount of time you are willing to devote to practise these solutions. You can practise these solutions simultaneously with your NCERT Maths Textbook questions, or you can use them at the time of examination for supplementing your preparation.

Given the fact that Maths is always a tough subject to prepare and you cannot rely on your class textbook only to score good marks in the exam. NCERT Solutions provided by Goprep can go a long way in helping you clear your doubts and understand the complex concepts thoroughly. This would certainly enable you to perform better in the exam and secure more marks.