NCERT Book Class 6 Maths Algebra

11.1 Introduction

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.

The main feature of the new branch which we are going to study is the use of letters. Use of letters will allow us to write rules and formulas in a general way. By using letters, we can talk about any number and not just a particular number. Secondly, letters may stand for unknown quantities. By learning methods of determining unknowns, we develop powerful tools for solving puzzles and many problems from daily life. Thirdly, since letters stand for numbers, operations can be performed on them as on numbers. This leads to the study of algebraic expressions and their properties.

You will find algebra interesting and useful. It is very useful in solving problems. Let us begin our study with simple examples.

11.2 Matchstick Patterns

Ameena and Sarita are making patterns with matchsticks. They decide to make simple patterns of the letters of the English alphabet. Ameena takes two matchsticks and forms the letter L as shown in Fig 11.1 (a). 

Then Sarita also picks two sticks, forms another letter L and puts it next to the one made by Ameena [Fig 11.1 (b)].

Then Ameena adds one more L and this goes on as shown by the dots in Fig 11.1 (c).

Their friend Appu comes in. He looks at the pattern. Appu always asks questions. He asks the girls, “How many matchsticks will be required to make seven Ls”? Ameena and Sarita are systematic. They go on forming the patterns with 1L, 2Ls, 3Ls, and so on and prepare a table. Appu gets the answer to his question from the Table 1; 7Ls require 14 matchsticks.

While writing the table, Ameena realises that the number of matchsticks required is twice the number of Ls formed. Number of matchsticks required = 2 × number of Ls. For convenience, let us write the letter n for the number of Ls. If one L is made, n = 1; if two Ls are made, n = 2 and so on; thus, n can be any natural number 1, 2, 3, 4, 5, .... We then write, Number of matchsticks required = 2 × n. Instead of writing 2 × n, we write 2n. Note that 2n is same as 2 × n. Ameena tells her friends that her rule gives the number of matchsticks required for forming any number of Ls.

Thus, For n = 1, the number of matchsticks required = 2 × 1 = 2

For n = 2, the number of matchsticks required = 2 × 2 = 4

For n = 3, the number of matchsticks required = 2 × 3 = 6 etc.

These numbers agree with those from Table 1.

Sarita says, “The rule is very powerful! Using the rule, I can say how many matchsticks are required to form even 100 Ls. I do not need to draw the pattern or make a table, once the rule is known”. Do you agree with Sarita?

11.3 The Idea of a Variable

In the above example, 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,.... Let us look at Table 1 once again. In the table, the value of n goes on changing (increasing). As a result, the number of matchsticks required also goes on changing (increasing). 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. We shall look at another example of matchstick patterns to learn more about variables

Please refer to attached file for NCERT Class 6 Maths Algebra