 Hi and welcome to the session. Today we will learn about ratio and proportion. Let us start by comparing two quantities. So here we have a basket A and basket B. The weight of basket A is 17 kgs and the weight of basket B is 22 kgs. Now we want to know that which basket is heavier. So for that we will subtract the weight of basket A from basket B that means this will be equal to 22 minus 17 kgs that is equal to 5 kgs. So this implies that basket B is heavier than basket A by 5 kgs. Two quantities of the same type compared by taking the difference between the two quantities. To compare the two quantities using the concept of ratio to find ratio of two quantities the two quantities are compared by division. Let us take the same example the weight of basket A is 17 kgs and weight of basket B is 22 kgs. So weight of basket A upon weight of basket B is equal to 17 kgs upon 22 kgs that means the ratio of weight of basket A is to weight of basket B is equal to 17 is to 22. So here we have compared the weight of basket A and basket B by division. And this symbol is used for ratio and is written as is to. So ratio is expressed is to be for any two numbers A and B in more points that is to find ratio of any two quantities the two quantities must be in the same unit. In the same unit then before finding ratio we must change them in the same unit. Now let us study the simplest form of the ratio. A ratio is said to be in the simplest form when the two terms of the ratio have no common factor other than one. For example suppose we are given a ratio 36 is to 64 and we need to find its simplest form. So 36 is to 64 can be written as 36 upon 64 which is equal to 9 upon 16. So this is 9 is to 16. So the simplest form of 36 is to 64 is 9 is to 16. And as we can see that both the terms that is 9 and 16 have no common factor other than 1. Now let us learn what are equivalent ratios. Now equivalent ratios can be obtained multiplying or dividing the numerator denominator by the same number. Here is one example for this we have the ratio 2 is to 3. Now 2 is to 3 can be written as 2 upon 3 and we can multiply the numerator by the number 5. So this will be equal to 10 upon 15 which is equal to 10 is to 15. That means the ratio 2 is to 3 is equal to 10 is to 15 and thus these both are equivalent ratios. Now let us move on to proportion. Four numbers a, b, c and d are said to be in proportion if the ratio of first two numbers that is a is to b is equal to the ratio of the third and fourth that is c is to d and this is written as a is to b as c is to d. This is the symbol for proportion and is read as s. Now suppose we are given two ratios 6 is to 18 and 8 is to 24. Now 6 is to 18 is equal to 1 is to 3 in its simplest form. Also a is to 24 is equal to 1 is to 3 in its simplest form. So that means the ratio 6 is to 18 is equal to the ratio 8 is to 24 and in proportion we can write it as 6 is to 18 as 8 is to 24. So from this we can say that these two ratios are in proportion and if two ratios are not equal then we say that the two ratios are not in proportion. Now in the proportion a is to b as c is to d first and the fourth term are known as extreme terms and second and the third term are known as middle terms. The topic of proportion must be clear to you. So now let's move on to next topic that is unitary method. In this method we first find out the value of one unit and then we find the value of required number of let's take one example for this. We are given the cost of 15 oranges as rupees 35 and we need to find the cost of 39 oranges. So here we have cost of 15 oranges equal to rupees 35. Now first of all we will find the value of one unit. So cost of one orange will be equal to rupees 35 upon number of oranges that is 15. Now we will find the value of required number of units that is 39 oranges. So cost of 39 oranges is equal to rupees 35 over 15 that is the cost of one orange into the required number of units that is 39. So this will be equal to rupees 91. Thus the cost of 39 oranges is rupees 91. This is known as unitary method. So with this we finish this session. Hope you must have understood all the concepts. Goodbye, take care and have a nice day.