 Hello and welcome to the session. In this session we will learn how to rewrite an expression in different forms and method of evaluating an expression. Now expressions are of two types numerical and algebraic. Now a numerical expression contains only numbers and operations whereas algebraic expression contains numbers, operations and variables. Now consider an expression 5 plus 3 into 2 minus 7. Now in this expression we have the numbers 5, 3, 2 and 7 and also we have the operations of addition, multiplication and suppression. So this expression contains only numbers and operations. So it is called a numerical expression. Now consider another expression that is 2x plus 5. Now if any number and a variable are in multiplication with each other then we can write it as 4 dot x. Here dot represents the operation of multiplication and also we can write it as 4x. Now this expression contains the numbers 2 and 5 and it contains the operation of addition and the operation of multiplication and also it contains an unknown variable. Now this expression contains numbers, operations and a variable. So it is called an algebraic expression. Now an algebraic expression may contain 1, 2 or more variables. For example 2x plus 1, x plus 2y, x plus y plus 3z and so on where 2x plus 1 is an algebraic expression in one variable, x plus 2y is an algebraic expression in two variables and x plus y plus 3z is again an algebraic expression with three variables. Now here variable is a value that varies and variables are denoted by any alphabet. Now let us see how to evaluate an algebraic expression. Now to evaluate an algebraic expression first of all we substitute the appropriate values to the variables in the expression. Then this converts the algebraic expression into a numerical expression. Then in the next step we use the operations in order and evaluate the value of the expression. For this let us see an example. In this we have to evaluate 20s plus 50t for s is equal to 2 and t is equal to 3. Now let us start with its solution. In the first step we will substitute s is equal to 2 and t is equal to 3 in the given expression that is 20s plus 50t. So 20s plus 50t will be equal to 20 into s that is 2 plus 50 into t that is 3. Now here for multiplication we can use the sign of multiplication or dot or brackets. All of them means multiplication. So here first of all we will solve multiplication. Now 20 into 2 is 40 plus 50 into 3 is 150. So this is equal to 190. Hence for s is equal to 2, t is equal to 3 this expression is equal to 190. Now we can also formulate an algebraic expression from a given statement. Now there are some phrases in the given statement that imply addition, subtraction, multiplication and division that help us form expressions from words. For example whenever the phrase increased by is given in the statement then we have to add a number whenever decreased by is given then we have to subtract the number. Now in this table some of the phrases and the operations related to it are given. From here you can see that which type of phrases are used in the statements for the operation of addition, subtraction, multiplication and division. For example a statement is given to us that is 5 is added to a number x. Now we can formulate an algebraic expression from this statement and it will be x plus 5 and here the phrase added to represents the operation of addition. Similarly for this statement that is 5 is subtracted from a number x. The algebraic expression will be x minus 5 as here the phrase subtracted from represents the operation of subtraction. Now here 5 times x can be written as 5x as here the phrase times represents the operation of multiplication and x divided by 5 can be written as x upon 5 as the phrase divided by represents the operation of division. Now consider an equation in this equation we have a plus 0.04 a is equal to 1.04 a. Now the left hand side means increase of a number a by 4 percent which means a plus 0.04 a and right hand side means multiply a number a by 4 percent which means a plus 1.04. So here the whole equation says if we increase a number a by 4 percent it is same as multiplying this number by 1.04. Now suppose a subtraction costs 10 dollars and x on its cost is 5 percent. Now first of all let us find the x. Now x is equal to 5 percent of the cost which is 10 dollars. So this is equal to 5 upon 100 into 10 which is equal to 0.5 dollars. So total cost of the sweater will be equal to 0.5 dollars. So total cost which is 10 dollars plus the tax which is 0.5 dollars. So this is equal to 10.5 dollars. Now this is a two step equation we can also evaluate this in one step. Now if a is the cost of the sweater then the total cost of the sweater including tax will be equal to a plus 5 percent of a. Now 5 percent of a means 0.05 a. So this is equal to a plus 0.05 a and now adding these two terms this will be equal to 1.05 a. Now if the cost of the sweater is 10 dollars then the total cost including tax will be equal to 1.05 a. Now here a is 10 dollars. So it will be 1.05 into 10 which is equal to 1.05 into 10 which is equal to 10.5 dollars. So we can find the total cost of the sweater by using the two step equation or directly we can find it in one step. So an expression can be rewritten in many forms to understand and evaluate a problem in a particular context. Now suppose if cost of an item is given as x dollars and discount percent is given as 20 percent. Now suppose we have to find the total cost of an item after discount. So the cost after discount is equal to 1.05 will be equal to the actual cost which is x dollars minus the discount which will be 20 percent of the actual cost that is 20 percent of x. Now x minus 20 percent of x on calculating will be same as 80 percent of x. So directly we can calculate the cost after discount by calculating 80 percent of x. Now suppose a person buys 3 peanut butter cookies, 3 sugar cookies and 1 chocolate cookie and the cost of each cookie is 2 dollars then the total cost of 3 peanut butter cookies will be 2 into 3 that is 6 dollars for sugar cookies it will be again 6 dollars and for 1 chocolate cookie it will be 2 dollars. Now to calculate the total cost of all these cookies we have to add these costs which we have calculated separately. So the total cost of all the cookies is equal to 6 dollars plus 6 dollars plus 2 dollars which is equal to 14 dollars. Now instead of this we can calculate the total cost of all these cookies by adding the quantities of 3 cookies that is 3 peanut butter cookies plus 3 sugar cookies plus 1 chocolate cookie and then multiplying this total with the cost of each cookie that is 2 dollars. So from here we get the total cost equal to 14 dollars so in this session we have learnt how to evaluate an expression by using different forms of the expression and this completes our session hope you all have enjoyed the session.