As the students rise to higher grades in school, the level of complexity of subjects goes on increasing though the syllabus is designed to suit the average student. Based on the learning streams, the portion changes a little bit without disturbing the basics of the subjects. A subject is well understood if the basic is right and the concepts are clear. These two things must be worked upon hard because the whole capability of learning and grasping power depends on these two factors.

When a student says he is not able to understand a particular portion means that his basics must be worked on. It is nothing but to let the student understand the purpose of this subject and study and the principles of the theorems. **R D Sharma Solutions for Class 8** helps the students to understand Maths to a greater extent by learning them along with textbooks. Students need to read the chapters and try to answer questions by studying solutions. Reading and writing practice are very important factors in the study as it helps to memorize better.

Table of Contents

**Mathematics**

**Chapter-wise Summary**

**Chapter 1 – Rational Numbers**

Rational numbers are involved in many mathematical applications such as addition, subtraction, and multiplication. In this chapter, the students will learn about the introduction to rational numbers, whole numbers & natural numbers, properties of natural & whole numbers, integers & their properties, properties of rational numbers (closure, commutative, distributive, & associative), negatives & reciprocals, and rational numbers between two rational numbers.

**Chapter 2 – Powers**

This chapter consists of an introduction to powers & exponents, powers with negative exponents, visualizing powers & exponents, expanding a rational number using power, exponents with like bases, power of a power, exponents with unlike bases & same exponent, interconversion between the standard & normal forms, and comparison of quantities using exponents.

**Chapter 3 – Squares and Square Roots**

From this chapter, the students will learn about perfect squares, properties of square numbers, finding the square of a number with unit’s place 5, square roots, square root of a number, estimating the number of digits, in the square root of a number, estimating the square root, introduction to square numbers, finding the square of a number, finding the square of a number using identity, interesting patterns, adding triangular numbers, numbers between square numbers, the addition of odd numbers, the square of an odd number as a sum, product of two consecutive even or odd natural numbers, random interesting patterns followed by square numbers, Pythagorean triplets, finding square roots through repeated subtraction, finding square root by long division method, and finding Pythagorean triplets for any given number.

**Chapter 4 – Cubes and Cubes Roots**

The chapter will teach the students about cube numbers, cubes relation with cube numbers, units digit in cube numbers, adding consecutive odd numbers, prime factorization method to find a cube, cube roots, cube root using prime factorization, cube root of a cube number using estimation, and differences of squares of triangular numbers and converse.

**Chapter 5 – Playing With Numbers**

From this chapter, the students will learn about numbers in general form, reversing the 2-digit numbers and adding them, reversing the 2-digit numbers and subtracting them, reversing the 3-digit numbers and subtracting them, taking all the combinations of 3-digit numbers and adding them, letters for digits, and divisibility rule.

**Chapter 6 – Algebraic Expressions and Identities**

This chapter explains the introduction to algebraic expressions and identities, terms, factors, coefficients, like terms, monomial, binomial, polynomial, algebraic identities, addition & subtraction of algebraic expressions, multiplication of monomials, distributive property of multiplication, and multiplication of any polynomial.

**Chapter 7 – Factorization**

This chapter will help the students clear the concepts of factors, division of a monomial by another monomial, division of a polynomial by a monomial, division of a polynomial by a polynomial, factors of natural numbers, algebraic expressions, method of a common factor, method of identities, factorization using algebraic identities, and visualization of factorization.

**Chapter 8 – Division of Algebraic Expressions**

In this chapter, the students will do six exercises as follows –

- Division of a monomial by a monomial
- Polynomials and degree of a polynomial in two variables
- Division of polynomials in one variable
- Division of a polynomial by a monomial
- Division of polynomials by using factorization.

**Chapter 9 – Linear Equations in One Variable**

From this chapter, the students will know the concept of linear equations in one variable, variables & constants, algebraic equations, performing mathematical operations on equations, solving equations with the linear expression on one side and numbers on the other side, solving equations with variables on both sides, applications, equations reducible to the linear form, and reducing equations to aa simpler form.

**Chapter 10 – Direct and Inverse Variations**

When the two variables change in the same sense, they are called directly proportional. From this chapter, the students will know inverse proportion, relation for inverse proportion, time & work, direct proportion, and relation for direct proportion.

**Chapter 11 – Time and Work**

This chapter will help the students to understand the concepts of time and work. Here, the students will learn to find the time required to complete work and find the work done in a given period of time. This is illustrated through various examples in the chapter.

**Chapter 12 – Percentage**

In this chapter, the next level of the previous class is explained. Here, the students can read and solve more problems on percentages. This chapter contains two exercises and the concepts discussed are percent as a fraction, percent as a ratio, and percent in decimal form, and finding the percent of a number.

**Chapter 13 – Profit, Loss, Discount, and Value Added Tax (VAT)**

Students learned about profit, loss, and the calculation of percentages in the previous class. In this chapter, they will find more problems with profit and loss. They will also know the concept of discount in buying and selling the goods along with the Value Added Tax (VAT). This chapter consists of three exercises and can be learned from the review of concepts – cost price, selling price, profit, & loss, problems based on discount, and problems based on value-added tax.

**Chapter 14 – Compound Interest**

This chapter consists of five exercises and can be understood with the help of the following concepts; computation of compound interest – compounded annually, half-yearly, & quarterly, computation of compound interest by using formulae, inverse problems on compound interest, population growth problems, and depreciation related problems.

**Chapter 15 – Understanding Shapes (Polygons, Quadrilaterals, and special quadrilaterals)**

In this chapter, the students will learn about introduction to quadrilaterals, what are quadrilaterals, types of quadrilaterals, revisiting geometry, introduction to curves, polygons, classification of polygons on the basis of a number of sides/vertices, diagonals, polygons on the basis of shape & regularity, angle sum property of polygons, properties of a parallelogram, elements of a parallelogram, angles of a parallelogram, diagonals of a parallelogram, and properties of special parallelograms.

**Chapter 16 – Practical Geometry (Constructions)**

In this chapter of practical geometry, the students can know the construction of a quadrilateral, construction of a quadrilateral when different measures of sides and angles are given, SSS construction, construction of a quadrilateral when four sides and one diagonal are given, construction of a quadrilateral when two diagonals and three sides are given, construction of a quadrilateral when two adjacent sides and three angles are given, construction of a quadrilateral when three sides and two included angles are given, construction of a quadrilateral when other special properties are known, and the number of measurements necessary for the construction of a unique quadrilateral.

**Chapter 17 – Visualizing Shapes**

From this chapter, the students will learn two-dimensional object, area, volume, three-dimensional object, formation of solid solids, solids & their classification, hexagon, non-polyhedrons, polyhedrons, solid cuboid, solid triangular prism, solid hexagonal prism, solid cylinder, solid sphere, solid cone, formation of hollow solids, pyramids, and types of polyhedrons.

**Chapter 18 – Mensuration – I (Area of Trapezium and a Polygon)**

In this portion, the students will know the area of the trapezium by division into shapes to known area and area of trapezium by finding the area of a triangle of the same area.

**Chapter 19 – Mensuration – II (Volumes and Surface Areas of a Cuboid and a Cube)**

Here, the students will know about the solids with a pair or more identical faces, the surface area of solid shapes, the surface area of a cuboid, and the surface area of a cube.

**Chapter 20 – Mensuration – III (Surface Area and Volume of a Right Circular Cylinder)**

In this portion the detail about the surface area of a cylinder, and the relation between the volume and capacity of a right circular cylinder.

**Chapter 21 – Data Handling – I (Classification and Tabulation of Data)**

In this chapter, the organization of data is explained. The students will know what the raw data is, introduction to data handling, and organization of raw data, grouped data, grouped frequency distribution, and tally marks.

**Chapter 22 – Data Handling – II (Graphical Representation of Data as Histograms)**

In this chapter, the students will learn the presentation of data in the form of histograms, equally likely outcomes, random experiment, experiment & outcomes, equally likely outcomes, probability of an event, and experimental probability.

**Chapter 23 – Data Handling – III (Pictorial Presentation of Data as Pie Charts)**

This chapter explains how the data can be organized in bar charts. The students will learn about the scale factor, bar graphs, and multiple bar graphs.

**Chapter 24 – Data Handling – IV (Probability)**

This chapter teaches students to judge the probability of an event under given circumstances, the chances of the event, and the percentage of probability.

**Chapter 25 – Introduction to Graphs**

This chapter will teach students the different types of graphical representations of data, bar graphs, Pie charts, histograms, and linear graphs, application of graphs, Cartesian plane & coordinate axes, and representation of a point on the plane.

**Importance of Mathematics**

Important of learning Mathematics is always highlighted in our life. Learning maths will not only provide a boost in the study but also wiseness in real life. Knowledge of sufficient Maths will help a person to sustain and maintain his position in his job and reality. This is all supported by the **R D Sharma Solutions for Class 8**. The following reasons will an idea why Maths is important in daily life: –

- It provides kids an effective power to analyze, describe, and change things.
- Maths can be applied in each aspect of life. That is why it is regarded as an important subject.
- It is seen that Mathematics supports the development of critical and logical thinking.
- Most importantly, Mathematics is considered the language of Science.

## Maths in Daily Life

Here we can see the 10 important uses of Mathematics in daily life –

- Math is good for the brain
- Math helps you with your finances
- Math makes you a better cook
- Better pattern-solving skill
- Every career uses Math
- Great career options
- Math for fitness
- Helps you understand the world better
- Time management
- To save money

**Conclusion**

Class 8 is the step of education from where the difficulty level of the subjects starts increasing. Hence it is imperative to get the basics right and develop a strong foundation in the early years. Knowing the concept of any subject makes it comparatively easy for students to understand. **R D Sharma Solution for Class 8 **makes it easier Maths for the students. The answers are designed in a descriptive way and cover all syllabuses.

All the chapters and the answers are within the syllabus and cover the topics in a better way. The solutions also provide the revision notes, most important questions, and paper set for students to practice the exam. Thus R D Sharma gives you very reliable study material.

## FAQs

**Is R D Sharma’s solution good for study?**

R D Sharma’s solutions give the students a combination of easy answers and good language. T covers all topics and suggested important questions.

**Why Maths is an important subject?**

Maths can help to improve career and it also helps to improve people’s routine life. It is a very important subject as it relates to the financial and banking sectors.

**Can I get full marks in Maths class 8?**

Yes, students can learn properly and get full marks in Maths.

**What is the job opportunity for Maths graduates?**

Every field needs maths hence there are a lot of job opportunities for a maths student, especially in the finance and banking sectors.

**Why do most students fear maths?**

Maths is a subject with less scope of error. The answer is either right or wrong so there is no half marks distribution for trying to answer. This makes the students worry about maths.

**Who can perform well in maths?**

Statistically, all students are capable to perform well in maths but most students cannot due to the fear in their minds.