NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8 Maths provide comprehensive, step-by-step answers to all questions from all 16 chapters of the NCERT Class 8 Mathematics textbook. These solutions are prepared by expert mathematics teachers and cover every exercise, example, and problem in a clear and structured manner. Whether you are preparing for school exams, olympiads, or simply want to strengthen your mathematical foundation, these NCERT solutions are your most reliable study companion.

Class 8 Maths builds the foundation for higher mathematics. Topics like Linear Equations, Mensuration, Algebraic Identities, Exponents, and Data Handling introduced in Class 8 directly prepare students for Class 9 and Class 10 board-level mathematics. Regular practice with NCERT solutions helps students develop logical thinking, problem-solving skills, and confidence in tackling both simple and complex mathematical problems.

NCERT Solutions for Class 8 Maths

Rational Numbers

Difficult

Q.

Using appropriate properties find:
$\begin{array}{l}\left(\mathrm{i}\right) \frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}\\ \left(\mathrm{ii}\right) \frac{2}{5}\times \left(-\frac{3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}\end{array}$

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Rational Numbers

Easy

Q.

Fill in the blanks.

(i) Zero has ________ reciprocal.
(ii) The numbers ________ and ________ are their own reciprocals.
(iii) The reciprocal of – 5 is ________.
$\left(\mathrm{iv}\right) \mathrm{Reciprocal} \mathrm{of} \frac{1}{\mathrm{x}}, \mathrm{where} \mathrm{x}\ne 0 \mathrm{is}\_\_\_\_\_\_\_\_\_\_.$
(v) The product of two rational numbers is always a _______.
(vi) The reciprocal of a positive rational number is ________.

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Rational Numbers

Easy

Q.

Write five rational numbers greater than –2.

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Rational Numbers

Easy

Q.

$\begin{array}{l}\text{Find five rational numbers between}\\ \left(\mathrm{i}\right)\frac{2}{3} \mathrm{and} \frac{4}{5} \left(\mathrm{ii}\right)\frac{-3}{2} \mathrm{and} \frac{5}{3} \left(\mathrm{iii}\right)\frac{1}{4}\mathrm{and}\frac{1}{2}\end{array}$

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Rational Numbers

Easy

Q.

$\mathrm{Find} \mathrm{ten} \mathrm{rational} \mathrm{numbers} \mathrm{between}\frac{-2}{5}\mathrm{and}\frac{1}{2}.$

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Rational Numbers

Medium

Q.

$\mathrm{Find} \mathrm{ten} \mathrm{rational} \mathrm{numbers} \mathrm{between} \frac{-2}{5} \mathrm{and} \frac{1}{2}.$

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Rational Numbers

Easy

Q.

Write five rational numbers which are smaller than 2.

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Rational Numbers

Medium

Q.

$\mathrm{Represent} \frac{-2}{11},\frac{-5}{11},\frac{-9}{11} \mathrm{on} \mathrm{the} \mathrm{number} \mathrm{line}.$

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Rational Numbers

Medium

Q.

Represent these numbers on the number line.

$\left(\mathrm{i}\right)\frac{7}{4} \left(\mathrm{ii}\right)\frac{-5}{6}$

 

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Rational Numbers

Easy

Q.

Write.
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.

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Rational Numbers

Easy

Q.

Write the additive inverse of each of the following.
$\left(\mathrm{i}\right)\frac{2}{8} \left(\mathrm{ii}\right)\frac{-5}{9} \left(\mathrm{iii}\right)\frac{-6}{-5} \left(\mathrm{iv}\right)\frac{2}{-9} \left(\mathrm{v}\right)\frac{19}{-6}$

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Rational Numbers

Medium

Q.

$\mathrm{Is} 0.3 \mathrm{the} \mathrm{multiplicative} \mathrm{inverse} \mathrm{of} 3\frac{1}{3}?\mathrm{Why} \mathrm{or} \mathrm{why} \mathrm{not}?$

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Rational Numbers

Medium

Q.

$\mathrm{Is} \frac{8}{9} \mathrm{the} \mathrm{multiplicative} \mathrm{inverse} \mathrm{of}-1\frac{1}{8}?\mathrm{Why} \mathrm{or} \mathrm{why} \mathrm{not}?$

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Rational Numbers

Easy

Q.

$\begin{array}{l}\mathrm{Tell} \mathrm{what} \mathrm{property} \mathrm{allows} \mathrm{you} \mathrm{to} \mathrm{compute}\\ \frac{1}{3}\times (6\times \frac{4}{3})\mathrm{as}(\frac{1}{3}\times 6)\times \frac{4}{3}.\end{array}$

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Rational Numbers

Easy

Q.

$\mathrm{Multiply} \frac{6}{13} \mathrm{by} \mathrm{the} \mathrm{reciprocal} \mathrm{of}\frac{-7}{16}.$

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Rational Numbers

Easy

Q.

Name the property under multiplication used in each of the following.

$\begin{array}{l}\left(\mathrm{i}\right)\frac{-4}{5}\times 1=1\times \frac{-4}{5}=\frac{-4}{5}\left(\mathrm{ii}\right)-\frac{13}{17}\times \frac{-2}{7}=\frac{-2}{7}\times \frac{-13}{17}\\ \left(\mathrm{iii}\right)\frac{-19}{29}\times \frac{29}{-19}=1\end{array}$

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Rational Numbers

Easy

Q.

Find the multiplicative inverse of the following.
$\begin{array}{l}\left(\mathrm{i}\right)-13 \left(\mathrm{ii}\right)\frac{-13}{19} \left(\mathrm{iii}\right)\frac{1}{5} \left(\mathrm{iv}\right)\frac{-5}{8}\times \frac{-3}{7}\\ \left(\mathrm{v}\right)-1\times \frac{-2}{5}\left(\mathrm{vi}\right)-1\end{array}$

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Rational Numbers

Easy

Q.

Verify that – (– x) = x for.
$\left(\mathrm{i}\right) \mathrm{x}=\frac{11}{15}\left(\mathrm{ii}\right)\mathrm{x}=-\frac{13}{17}$

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Rational Numbers

Easy

Q.

$\mathrm{Find} \mathrm{ten} \mathrm{rational} \mathrm{numbers} \mathrm{between} \frac{3}{5} \mathrm{and} \frac{3}{4}.$

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Chapter-wise NCERT Solutions for Class 8 Maths

Chapter 1 – Rational Numbers Chapter 1 introduces students to rational numbers and their properties. Students learn about closure, commutativity, associativity, and the role of zero and one as identity elements. The chapter also covers the representation of rational numbers on the number line and finding rational numbers between two given rational numbers.

Chapter 2 – Linear Equations in One Variable Chapter 2 covers linear equations in one variable and their solutions. Students learn to solve equations with variables on both sides, equations reducible to linear form, and applications of linear equations in real-life word problems involving numbers, ages, perimeters, and more.

Chapter 3 – Understanding Quadrilaterals Chapter 3 helps students understand different types of quadrilaterals — parallelograms, rhombuses, rectangles, squares, kites, and trapeziums. The chapter covers the angle sum property of polygons and the properties of each type of quadrilateral in detail.

Chapter 4 – Practical Geometry Chapter 4 teaches students how to construct quadrilaterals when certain measurements are given — such as four sides and one diagonal, two diagonals, three sides and two included angles, and so on. It develops students' geometric construction skills using ruler and compass.

Chapter 5 – Data Handling Chapter 5 introduces students to organising and interpreting data using bar graphs, pie charts, and histograms. It also introduces the concept of probability in a simple and intuitive way, helping students understand the likelihood of events.

Chapter 6 – Squares and Square Roots Chapter 6 covers perfect squares, properties of square numbers, and methods to find square roots — including the prime factorisation method and the long division method. Students also learn to estimate square roots of non-perfect squares.

Chapter 7 – Cubes and Cube Roots Chapter 7 introduces perfect cubes and cube roots. Students learn to find cube roots using the prime factorisation method and understand the properties of cubes of natural numbers. The chapter also covers interesting patterns in cube numbers.

Chapter 8 – Comparing Quantities Chapter 8 is one of the most practically important chapters. It covers ratios, percentages, profit and loss, discount, VAT, simple interest, and compound interest. Students learn to calculate compound interest using the formula and understand its real-life applications in banking and finance.

Chapter 9 – Algebraic Expressions and Identities Chapter 9 covers the addition, subtraction, and multiplication of algebraic expressions. It introduces the four standard algebraic identities — (a+b)², (a-b)², (a+b)(a-b), and (x+a)(x+b) — and their applications in simplifying expressions and solving problems.

Chapter 10 – Visualising Solid Shapes Chapter 10 helps students visualise three-dimensional shapes through 2D representations. It covers views of 3D shapes from different directions, mapping spaces using scale, and introduces the concept of polyhedra, Euler's formula, and nets of solids.

Chapter 11 – Mensuration Chapter 11 is a high-weightage chapter covering the area of trapeziums, quadrilaterals, and polygons, the surface area and volume of cubes, cuboids, cylinders, and other solids. Students apply these concepts to a wide variety of real-life problems.

Chapter 12 – Exponents and Powers Chapter 12 extends students' understanding of exponents to include negative exponents and very large and very small numbers expressed in standard form (scientific notation). Students learn the laws of exponents and apply them to simplify complex expressions.

Chapter 13 – Direct and Inverse Proportions Chapter 13 covers direct proportion — where two quantities increase or decrease together — and inverse proportion — where one quantity increases as the other decreases. Students solve a variety of word problems involving speed, time, work, and other real-life scenarios.

Chapter 14 – Factorisation Chapter 14 teaches students how to factorise algebraic expressions using common factors, grouping, and algebraic identities. It also covers division of algebraic expressions and finding and correcting errors in algebraic manipulations.

Chapter 15 – Introduction to Graphs Chapter 15 introduces students to the Cartesian plane and different types of graphs — bar graphs, pie charts, histograms, and line graphs. Students learn to plot points, read graphs, and understand what different types of graphs convey.

Chapter 16 – Playing with Numbers Chapter 16 covers divisibility tests and the general form of numbers. Students explore interesting properties of numbers written in their generalised forms and solve puzzles and problems involving letters that represent digits.

FAQs – NCERT Solutions for Class 8 Maths

Q1. How are NCERT Solutions for Class 8 Maths helpful for students?

NCERT Solutions for Class 8 Maths provide step-by-step explanations for every question in the textbook. They help students understand the correct method of solving problems, clear their doubts, and practise effectively for school exams. Since CBSE board papers are entirely based on the NCERT curriculum, mastering these solutions gives students a significant advantage in their examinations.

Q2. Which is the most difficult chapter in Class 8 Maths?

Many students find Chapter 8 (Comparing Quantities) and Chapter 11 (Mensuration) relatively challenging due to the variety of formulas and real-life applications involved. Chapter 14 (Factorisation) is also considered tricky because it requires a strong understanding of algebraic identities. However, with regular practice using NCERT solutions, all chapters become manageable.

Q3. Which chapters in Class 8 Maths are most important for exams?

The most important chapters for Class 8 Maths exams are Chapter 2 (Linear Equations), Chapter 6 (Squares and Square Roots), Chapter 8 (Comparing Quantities), Chapter 9 (Algebraic Expressions and Identities), Chapter 11 (Mensuration), Chapter 13 (Direct and Inverse Proportions), and Chapter 14 (Factorisation). These chapters carry the highest weightage in school examinations and form the basis for Class 9 and 10 mathematics.

Q4. When should I start practising NCERT Solutions for Class 8 Maths?

You should start practising NCERT solutions alongside your classroom lessons. After every chapter is taught in school, revisit all the solved examples in the textbook and then attempt every exercise question. Use the NCERT solutions to check your approach and understand alternative methods. Starting early and practising consistently is the most effective strategy.

Q5. What is the best way to use NCERT Solutions for Class 8 Maths effectively?

First, read the theory and solved examples in the NCERT textbook carefully. Then attempt the exercise questions on your own before referring to the solutions. When you check your answers, focus on understanding the method rather than just memorising the answer. Revisit difficult questions regularly and solve the previous year's question papers once all chapters are complete.