 Hello and welcome to the session. In this session we will discuss a question which says that simplify the following fractions. The first one is 15 is 2, 1 and 2 by 3, second part, 3914 is to 6 by 7, third part, 6 is to 1.2. Now before starting the solution of this question we should know some results. First one is any ratio in the division form like 2 is to 3 can be written as and to simplify ratio we reduce its fraction. First form let us see an example for this to 4 upon 4 since both numerator and denominator are divisible by 2 so we write it as 1 by 2 its lowest form which is 1 by 2. And the second result will be 4 upon c upon d 1 by 3. Now we will see for the numerator we will multiply at 1 to it so it will become 2 into 3 that is 6 plus 1 which is 3. So on simplifying the next section 2 and 1 by 3 we get 7 by 3 for solving the given question. Now we will start the solution of the given question. With the first part we have to simplify 1 and 2 by 3. Now we know that every number is divisible by 1 so we can write any number x in the form. We can write fifth of the key idea. We can write can be written as 15 by 1 1 and 2 by 3 section. So here this will be equal to 15 upon 1 whole upon. Now the next section 1 and 2 by 3 will be equal to 3 into 1 plus 2 which will be equal to 5 which is the numerator and the denominator will be 3 so the next section will become 5 which is given in the key idea. This will be equal to 15 into 3 upon 1 into 5. Now 5 and 15 so dividing the numerator and denominator by 5 we get into 3. 1 into 5 into 3 is 15 and 5 into 1 is 5 3 into 3 whole upon 1 which is equal to we can write it as 9. Now let us start with the second part. In the second part we have to simplify the ratio which is 3 upon 14 is 2 upon 14 which can be further written as 3 into 7 upon 3 into 2 is 6. So 3 is the common factor of 3 and 6 so we divide numerator and denominator by 3 and we get 3 into 7 upon 3 into 6 upon 3. Now 3 into 1 is 3 and 3 into 2 7 upon 14 into 2 numerator and denominator by 7 upon 7 whole upon 14 into 2 upon 7. Now 7 into 1 is 7 and 7 into 2 is 14 which is equal to 1 upon 4 plus 1 is 2. Now in the third part we have to simplify which is given as 6 is 2 1.2. Now this can be written as 6 upon 1.2 so in the numerator we can write 6 as 6 upon 1 whole upon in the denominator we can write 1.2 as into 10 whole upon 1 into 12. Common factor of 6 and 12 so we are writing the numerator and denominator by 6 we get 6 into 10 upon 1 into 12 now 6 into 1 is 6 and 6 into 2 into 10 whole upon 1 and denominator by 2. This will be equal to 1 into 10 upon 2 whole upon 1 into 2 upon 2 now 2 into 5 is 10 and 2 into 1 is 2 so this is equal to and 1 into 1 is 1. So this is equal to 5 upon 1 or you can write it as 5 ratio of the given question time for the session hope you all have enjoyed the session.