 Hello and welcome to the session. In this session we will learn about Algebra which is a very important branch of mathematics. The main feature of Algebra is the use of letters. Algebra is very interesting and useful. It is very useful in solving the problems. Next we discuss about the idea of a variable. Variable means something that can vary or you can say that can change. The value of the variable is not fixed. It can take different values. Let's consider this triangle. In this we have three angles. So the number of angles of a triangle is fixed. Hence it is not a variable but the length of the sides of the triangle can take any values. So it is the variable. Let's consider an expression 2n. In this expression the numerical value 2 is obviously fixed but this letter n can take any value. So it is called the variable in this expression. n can take any value be it 0, 1, 2, 3 and so on. As in this expression we have used the letter n to show a variable but we should know that we can use any letter be it n, l, m, p, q, r, x, y, z and so on to show a variable. Now we should discuss about the use of variables in common rules. Variables allow us to express many common rules in both geometry and arithmetic in a general way. First let's discuss about rules from geometry. Let's see how we express the perimeter of a square in terms of variables. Consider the square with each side equal to l. So the perimeter of the square would be equal to sum of the length of the sides of square and that would be equal to l plus l plus l plus l. That is that becomes 4l. If we denote the perimeter of the square by the variable p we get this expression which is used to express the perimeter of the square. Where we letters p and l are the variables where p is the perimeter and l is the length of the side of the square which can take any values. In this way we can obtain various formulas and rules for the parameters and areas of plane figures using the concept of variables. Now we discuss about the rules from arithmetic. Here we shall discuss about the commutativity of addition of two numbers. Suppose we are given two numbers their sum in this order would be equal to this. Now commuting basically means interchanging. So let's interchange the digits and add the numbers. Let's see what is the sum. We see that the sum is same in both the cases. So commuting the order of numbers in addition does not change the sum. With the help of variables let's express the generality of this property in a concise way. Like if we have two variables a and b then according to this property we have a plus v would be equal to b plus a. Where these a and b are the variables and they can take any values. So the different properties of numbers like the distributivity of numbers commutativity of multiplication of numbers etc can be expressed in a more general and concise way using the variables. Now we shall discuss about the expressions with variables. Expressions can be formed from variables. Expressions with variables are obtained by operations of addition, subtraction, multiplication and division on variables. Since we know that variables are basically the numbers but their values are not fixed it can vary. So that is why we can perform these operations of addition, subtraction, multiplication and division on variables. Let's consider the expression 2n again. In this expression the letter n is a variable and the number 2 obviously is fixed. So this expression is formed by 2 multiplied by the variable n that is we have applied the operation of multiplication on the number 2 and the variable n. So we get the expression 2n and using different operations we can form various expressions with variables. So this completes our session hope you have understood the concept of variables.