NCERT Solutions for Class 6 Maths, Chapter 11 - Algebra

Our study so far has been with numbers and shapes. We have learnt numbers, operations on numbers and properties of numbers. We applied our knowledge of numbers to various problems in our life. The branch of mathematics in which we studied numbers is arithmetic. We have also learnt about figures in two and three dimensions and their properties. The branch of mathematics in which we studied shapes is geometry. Now we begin the study of another branch of mathematics. It is called algebra.

In NCERT Maths Book Class 6, Chapter 11 Solutions, as you progress through the chapter you will learn mensuration. You will look at patterns of making letters and other shapes using matchsticks. You will learn how to write the general relation between the number of matchsticks required for repeating a given shape. The number of times a given shape is repeated varies; it takes on values 1,2,3,… It is a variable, denoted by a letter such as ‘n’. As you move further in this chapter you will study the idea of a variable, some more matchstick patterns, examples of variables, use of variables in common rules. Further, you will learn how to use expressions with variables. Towards the end of this chapter, the concept of equation will be introduced and you will also learn how to solve an equation.

Let’s take a look at topics and sub-topics of Class 6 Maths Chapter 11, Algebra

11.1 Introduction

11.2 Matchstick Patterns

11.3 The Idea Of A Variable

11.4 More Matchstick Patterns

11.5 More Examples Of Variables

11.6 Use Of Variables In Common Rules

11.7 Expressions With Variables

11.8 Using Expressions Practically

11.9 What Is An Equation?

11.10 Solution Of An Equation

In Class 6 Maths NCERT Solutions Chapter 11, you will learn –

Section 11.2 – In this section, you will study matchstick patterns to learn the concept of algebra. Take two matchsticks and make the letter L. Take two more matchsticks and make another L alongside the previous one. We observe that each L requires two matchsticks. Now, how many matchsticks will be required to make 100 L’? We can say that for the formation of a single L, 2 matchsticks are required thus, for 100 L’s, 100 x 2 = 200 matchsticks will be required.

Section 11.3 – This section will teach you the idea of a variable. In the example discussed in the previous section, we found a rule to give the number of matchsticks required to make a pattern of Ls. The rule was: Number of matchsticks required = 2n Here, n is the number of Ls in the pattern, and n takes values 1, 2, 3, 4,… n is an example of a variable. Its value is not fixed; it can take any value 1, 2, 3, 4,… We wrote the rule for the number of matchsticks required using the variable n. The word ‘variable’ means something that can vary, i.e. change. The value of a variable is not fixed. It can take different values.

Section 11.4 – Now you will study more about matchstick patterns. Instead of making L’s we can also make different letters like C. To make a C three matchsticks will be required. So we can come up with the rule that the number of matchsticks required = 3n. The letter n is used for the number of Cs; n is a variable taking on values 1, 2, 3, 4, … The pattern of F’s can also be made. It will require 4 matchsticks. So we can come up with the rule that the number of matchsticks required = 4n and so on.

Section 11.5 – This section will brief you about some more examples of variables. One may use any letter as m, l, p, x, y, z etc. to show a variable. Remember, a variable is a number which does not have a fixed value. For example, the number 5 or the number 100 or any other given number is not a variable. They have fixed values. Similarly, the number of angles of a triangle has a fixed value i.e. 3. It is not a variable. The number of corners of a quadrilateral (4) is fixed; it is also not a variable. But n in the examples we have looked is a variable. It takes on various values 1, 2, 3, 4,… A variable allows us to express relations in any practical situation. As you move further in this section you will see some interesting examples that will help you in understanding the concepts of variables which is an essential topic of algebra.

Section 11.6 – In this section, you will study how to use variables in common rules. Variables are numbers, although their value is not fixed. We can do the operations of addition, subtraction, multiplication and division on them just as in the case of fixed numbers. Using different operations we can form expressions with variables like x – 3, x + 3, 2n, 5m, 3/p , 2y + 3, 3l – 5, etc. Variables allow us to express many common rules in both geometry and arithmetic 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 can be expressed as a + b = b + a. Here, the variables a and b stand for any number, 1, 32, 1000 – 7, – 20, etc.

Section 11.7 – This section will teach you more about expressions with variables. We know that variables can take different values; they have no fixed value. But they are numbers. That is why, in the case of numbers, operations of addition, subtraction, multiplication and division can be done on them. One important point must be noted regarding the expressions containing variables. A number expression like (4 × 3) + 5 can be immediately evaluated as (4 × 3) + 5 = 12 + 5 = 17. But an expression like (4x + 5), which contains the variable x, cannot be evaluated. Only if x is given some value, an expression like (4x + 5) can be evaluated. For example, when x = 3, 4x + 5 = (4 × 3) + 5 = 17 as found above.

Section 11.8 – Now you will study how to use expressions practically. We have already come across practical situations in which expressions are useful. At the beginning of this chapter, you have studied that expressions can be used to calculate the total number of matchsticks required to make 100 L’s. Here the variable is n, the number of matchsticks. As you move further in this section you will see some more examples of variables that can be used practically. Speed, the quantity of rice, age, the number of questions solved, the number of sections studied are some examples of variables that can be used in expressions practically.

Section 11.9 – Towards the end of this chapter, you will learn the equation. An equation is a condition on a variable. It is expressed by saying that expression with a variable is equal to a fixed number, e.g. x – 3 = 10. An equation has two sides, LHS and RHS, between them is the equal (=) sign. For example, The statement 2n is greater than 10, i.e. 2n > 10 is not an equation. Similarly, the statement 2n is smaller than 10 i.e. 2n < 10 is not an equation. Also, the statements (x – 3) > 11 or (x – 3) < 11 are not equations. Now, let us consider 8 – 3 = 5 There is an equal sign between the LHS and RHS. Neither of the two sides contains a variable. Both contain numbers. We may call this a numerical equation. Usually, the word equation is used only for equations with one or more variables.

Section 11.10 – Now you will learn how to solve an equation. The LHS of an equation is equal to its RHS only for a definite value of the variable in the equation. We say that this definite value of the variable satisfies the equation. This value itself is called the solution of the equation. For getting the solution of an equation, one method is the trial and error method. In this method, we give some value to the variable and check whether it satisfies the equation. We go on giving this way different values to the variable` until we find the right value which satisfies the equation.  Thus, n = 5 is a solution to the equation 2 n = 10. Note, n = 6 is not a solution to the equation 2n = 10; because for n = 6, 2n = 2 × 6 = 12 and not 10.

In this chapter, you are provided with several examples along with their solutions for a clear understanding of algebra. To know more about NCERT Solutions for Class 6 Maths Chapter 11 Algebra, you should explore the exercises below. You can also download the algebra Class 6 NCERT Solutions PDF, solved by expert maths trainers. You can also refer online to Class 6 Maths Chapter 11 Worksheet PDF.