NCERT 6TH CLASS MATHEMATICS CHAPTER INTRODUCTION TO ALGEBRA
In Arithmetic, numerals 1, 2, 3, 4,..... etc. and four fundamental operation : addition, subtraction, multiplication and division are used to deal with various problems. In Algebra, in addition to numerals, we use letters such as x, y, z in various situations to solve the problems.
Salman and Aamir are making pattern with matchsticks. They decide to make simple patterns of the letters of the english alphabet. Salman takes two matchsticks and form the letter L as shown in figure 1. The Aamir also picks two sticks form another letter L and puts it next to the one made by salman as shown in figure 2. The Salman adds one more L and this goes on as shown in figure 3.
If we tabulate this result we obtained the following table as given below
Here we observe that number of matchstick required is twice the number's of L
So, we can say number of matchstick required = 2 × n, where n represent the number of L's
Consider the following statements :
I think of a number and when I subtract 9 from it the result is 23.
If is used to represent the number I think of, then the above statement using mathematical symbols, is simply written as – 9 = 23.
Ex. Use , D etc. and mathematical symbols and rewrite the following statements :
(a) I think of a number, subtract 3 from it and the result is 34.
(b) I think of two numbers, add these numbers, multiply the result by 2 to get the final answer as 14.
(c) I think of two numbers. Twice difference is added by 3 gives result 15.
Sol. (a) – 3 = 34
(b) 2 × ( + D) = 14
(c) 2 × ( – D) + 3 = 15
Ex. Rewrite each of the following statements without using symbols, beginning each statement with : I think of .....
(a) + 9 = 28
(b) 2 × – 23 < 25
(c) ( + D) ¸ 5 = 25
Sol. (a) I think of a number, when 9 is added to it gives result 28.
(b) I think of a number, when 23 is subtracted from the twice the number gives the result is less than 25.
(c) I think of two numbers, when their sum is divided by 5 gives quotient 25.