 Hello and welcome to the session. In this session we discussed the following question which says arrange the following rational numbers in ascending order. 2 upon 3, 3 upon 4, 4 upon minus 5 and minus 5 upon 6. Let's move on to the solution. The given rational numbers are 2 upon 3, 3 upon 4, 4 upon minus 5 and minus 5 upon 6 and we need to arrange these rational numbers in ascending order. So, first of all we'll express each of these rational numbers with positive denominators. Now the first rational number 2 upon 3 has already a positive denominator. 3 upon 4 also has a positive denominator. Now 4 upon minus 5 has a negative denominator. So, consider the rational number 4 upon minus 5 to make its denominator positive. We will multiply its numerator and denominator by minus 1. So this is equal to minus 4 upon 5. That is we have got 4 upon minus 5 is equal to minus 4 upon 5. So we have expressed the given rational number 4 upon minus 5 with a positive denominator as minus 4 upon 5. Now the next rational number minus 5 upon 6 also has a positive denominator. So now we have the rational numbers 2 upon 3, 3 upon 4, minus 4 upon 5, minus 5 upon 6 and now we will arrange these rational numbers in ascending order. So here again our next step would be to take the LCM of all these positive denominators that is 3, 4, 5 and 6. Let's find out the LCM of 3, 4, 5 and 6. Now 3, 1 times is 3 and 3, 2 times is 6. Then 2, 2 times is 4 and 2, 1 times is 2. Then 2, 1 time is 2 and 5, 1 time is 5. So we get the LCM of 3, 4, 5 and 6 is equal to the product of these numbers. That is 3 multiplied by 2 multiplied by 2 multiplied by 5 which is equal to 16. So we get the LCM of the positive denominators of the given rational numbers is 60. Now in the next step we will express each of these rational numbers with this LCM that is 60 as the common denominator. Now consider the rational number 2 upon 3. To make its denominator 60 we need to multiply its numerator and denominator by 20. So this is equal to 40 upon 60. Next consider the rational number 3 upon 4. To make its denominator 60 we need to multiply its numerator and denominator by 15. So this is equal to 45 upon 60. Then we consider the rational number minus 4 upon 5. To make its denominator 60 we need to multiply its numerator and denominator by 12. So this is equal to minus 48 upon 60. Now our next rational number is minus 5 upon 6. To make its denominator 60 we need to multiply its numerator and denominator by 10. So this is equal to minus 50 upon 60. So we have expressed all the given rational numbers with the LCM that is 60 as the common denominator. Now we need to compare the numerators of the given rational numbers that is the numerators of these rational numbers. So in that case this would be the smallest that is minus 50 upon 60 is less than minus 48 upon 60 and this is less than 40 upon 60 and this is less than 45 upon 60. This is the ascending order or we can write this in the form as minus 50 upon 60 is equal to minus 5 upon 6. So minus 5 upon 6 is less than minus 48 upon 60 is equal to minus 4 upon 5. So minus 5 upon 6 is less than minus 4 upon 5 which is further less than 40 upon 60 which is equal to 2 upon 3. So we write 2 upon 3 here and this is further less than 45 upon 60 which is equal to 3 upon 4. So we get minus 5 upon 6 is less than 4 upon minus 5 since the given rational number was 4 upon minus 5 and we had expressed this with a positive denominator. So minus 4 upon 5 can be written as 4 upon minus 5 this is less than 2 upon 3 this is further less than 3 upon 4. So this is the given ascending order of the given rational numbers. This is our final answer. This completes the session. Hope you have understood the solution for this question.