NCERT Solutions for Class 6 Maths Chapter 11 – Algebra

NCERT Solutions for Class 6 Maths Chapter 11 Algebra consist of exercise-wise solutions to all the questions available. CBSE NCERT Solutions for Class 6 Maths Chapter 11 comprises a total of 5 exercises encompassing all the topics given in the Chapter- ‘Algebra’. Some important topics covered in this chapter are variables, uses of variables, expressions with variables, practical use of expressions, the meaning of an equation and solution of an equation.

Algebra introduces the concept of Algebra to you. These solutions have been compiled according to the guidelines of CBSE. These solutions are formulated by our subject-matter experts in such a way that you will find them very easy to grasp. Through NCERT Solutions, you can easily develop an in-depth understanding of all the topics covered in Chapter 11 of CBSE Class 6 Maths.

NCERT Solutions of Maths Chapter ‘Algebra’ has been framed in a comprehensive manner to cover the different types of questions important from exam standpoint. NCERT Solutions for Class 6 Maths Chapter 11 Algebra clarifies your concepts and makes you ready for higher-level classes. NCERT Solutions for Class 6 Maths Chapter 11 Algebra gives you enough practice and prepares you for examination very well. They are extremely helpful and handy for effective revision during exams and enable you to score more marks.

NCERT Solutions for CBSE Class 6 Maths Chapter 11: Important Topics

NCERT Solutions of Class 6 Maths Chapter 11 comprises a variety of fundamental algebraic topics that you need to understand clearly in order to build a strong conceptual foundation for learning advanced algebra in higher classes. Some of the important concepts covered in this chapter have been listed below.

  • Introduction

Algebra is studying mathematics through the formation of equations consisting of several variables. These variables are generally denoted through various alphabets or letters. It tells us that we can develop powerful tools for solving mathematical problems with algebra.

It teaches you about other important concepts such as constant, terms of expression, factors of a term, like and unlike terms, Monomial terms, binomial terms, trinomial terms, and polynomial terms.

  • Matchstick Patterns

This part of the chapter introduces the idea of making a mathematical formula built on the repetition of certain patterns based on numbers. The formula was created using the letter ‘n’ to fit into all the situations.

  • The Idea of a Variable

This portion of the chapter introduces the important term ‘variable’ to you. A variable refers to something which can vary, and its value is not fixed. It can take any value like 1,2,3,4,5 and 6 etc. It is an unknown quantity that is prone to change with the context of a situation.

For example, in the expression 3x+7, x is the variable. It also tells you that a variable allows us to express relations in any practical situation.

  • More Matchstick Patterns

This part gives you the idea of how you can formulate more problems, rules for them and their solutions by making more combinations of given resources in order to learn the concept well.

  • More Examples of Variables

This section of the chapter introduces you to the idea that we can choose any letter like x, y or z, n, l, m, p to depict a variable for defining our pattern or problem. It teaches you that the variables are nothing but a number and are not fixed and that they can take any number. This portion also tells you how you can perform all the mathematical operations such as addition and subtraction, on these variables to formulate a particular situation as a mathematical expression.

Examples: x-3, y+4, 6n, 5m/2. These are the simplest expressions, and you must carefully see the mathematical operators used like x + 3 and 3x are not the same and how they hold a different meaning.

  • Use of Variables in Common Rules

This part of the chapter teaches you to express the common rules of geometry and arithmetic using variables in a general way.

For example, the rule that the sum of two numbers remains the same if the order in which the numbers are taken is reversed. It can be expressed as a + b = b + a. Here, the variables a and b stand for any number. This portion also teaches you that variables of any expression can take on values independent of each other. i.e. the value one variable takes, does not depend on what value the other variable has taken.

  • Formation of Algebraic Expressions

This portion of the chapter makes you understand the meanings of expressions in words which lets you understand the relation between a variable and a number in expression joined by mathematical operations like addition, subtraction, multiplication and division. This chapter further encourages you to form some expressions on your own to gain a better understanding. It also teaches you about addition and subtraction of like terms and addition and subtraction of unlike terms.

  • Using Expressions Practically

This part of the chapter gives you an idea about converting day to day practical situations into mathematical expressions.

  • What is the Equation?

This portion of the chapter introduces you to the concept of mathematical ‘equations’ and how to form the same using the given information in words. It teaches you that an equation is a condition on a variable and it is satisfied for a definite value of a variable. The condition says that the expression with a variable is equal to a certain number.

For example: x – 3 = 10. You also come to know here that, every equation has LHS (left-hand side) and RHS (right-hand side) and both the sides are equal to each other, i.e. LHS = RHS for a definite value of the variable in the equation. This value is actually the ‘solution of the equation’ or the value of the variable.

  • The Solution of an Equation

The last part of Class 6 Maths Algebra chapter tells you that the value of the variable in an equation which satisfies the equation is called a solution to the equation. It teaches you that one of the methods to solve equations is ‘trial and error method’ where some values to the variables are given to check whether it satisfies the equation.

NCERT CBSE Class 6 Maths Chapter 11: Exercises Discussion

NCERT Solutions for Class 6 Maths Chapter 11- Algebra comprises a total of 5 exercises. The list of exercises given in CBSE NCERT Class 6 Maths book and their components are as follows –

Exercise 11.1

This exercise consists of 11 questions. Question no. 1 to 7 ask you to write mathematical rules for simple situations, enabling you to understand and practice the concept of variables. Question no. 8 to 11 ask you to introduce some mathematical operators in relation to the variables used to make an expression. 

Exercise 11.2 

This exercise consists of 5 questions. Question no. 1 to 4 deal with writing a mathematical expression for a given situation utilizing the rules of geometry. This utilizes your knowledge of the rules given in topic mensuration. Question no. 5 asks you to apply the arithmetic property associativity of the addition of numbers in a general way by using variables a, b and c

Exercise 11.3 

This exercise consists of 6 questions. First two questions let you understand about the expressions formed with numbers only. Question no. 3 asks you to identify the mathematical operators used in each case. Question no. 4 to 6 ask you to convert situations given in words to mathematical expressions which utilize the relation of variable and number. 

Exercise 11.4 

This exercise consists of 3 questions, where each of the questions has several subparts. Question 1 (a) to (e) asks you to convert the various practical situations to mathematical expressions using more than one variable. This gives you a good amount of practice regarding how to manipulate the relation given between the different variables of a particular situation. Question no. 2 and 3 ask you to convert word problems with expression to ordinary statements. 

Exercise 11.5

Consists of 5 questions with several subparts. The first question asks you to identify the proper equations among the given ones and also to identify the variables in the equations containing the variable. Question no. 2 to 4 ask you to solve the given equation using trial and error method. The last question asks you to write meaningful equations utilizing the information given in the riddles.

All questions from the above exercises have been solved using the best-solving methods in a step-by-step manner to help score better.