 Hello American to the session. In this session we discussed the following question which says arrange the following rational numbers in ascending order. 4 upon minus 5 minus 6 upon 7 8 upon minus 15 and 3 upon 14. Now let's move on to the solution. The given rational numbers are 4 upon minus 5 minus 6 upon 7 8 upon minus 15 and 3 upon 14. First of all we would make the denominators of all these rational numbers positive. So consider the first rational number given to us 4 upon minus 5. It's denominator as you can see is a negative number so we will make it positive by multiplying its numerator and denominator by minus 1. So this gives us minus 4 upon 5. Now the next rational number is minus 6 upon 7. It already has a positive denominator. So let's move on to the next rational number which is 8 upon minus 15. Its denominator is negative. We make it positive by multiplying its numerator and denominator by minus 1. So this is equal to minus 8 upon 15. Now the next rational number is 3 upon 14. It has a positive denominator. So now the given rational numbers are minus 4 upon 5 minus 6 upon 7 minus 8 upon 15 and 3 upon 14. In all these rational numbers the denominators are positive. Now in the next step we find out the LCM of the positive denominators of these rational numbers. That is we will find the LCM of 5, 7, 15 and 14. Now we have 5, 1 times is 5, 5, 3 times is 15, then 7, 1 times is 7 and 7, 2 times is 14, then 3, 1 times is 3 and 2, 1 times is 2. So we have LCM of the numbers 5, 7, 15 and 14 is equal to the product of these numbers. That is 5 into 7 into 3 into 2 which is equal to 210. Now in the next step we express each of these rational numbers with this LCM that is 210 as the common denominator. So consider the rational number minus 4 upon 5. Now we need to make its denominator 210. So for this we will multiply its numerator and denominator by 42 since 42 5 times is 210. So this would be equal to minus 168 upon 210. Now in the same way consider the next rational number minus 6 upon 7. Here also we will convert its denominator to 210. For this we need to multiply its numerator and denominator by 30 since 37 times is 210. So this would be equal to minus 180 by 210. Now the next rational number is minus 8 upon 15. Here also we will convert its denominator to 210. For this we will multiply its numerator and denominator by 14 since we know like 15 14 times is 210. So this comes out to be equal to minus 112 upon 210. Now the next rational number that we have is 3 upon 14. So we need to make its denominator also 210. For this we will multiply its numerator and denominator by 15 since 15 14 times is 210. And this is equal to 45 upon 210. So we have expressed all the given rational numbers with LCM that is 210 as the common denominator. And now the number having greater numerator would be greater. Now from here we see that minus 180 upon 210 is less than minus 168 upon 210 which is further less than minus 112 upon 210 and this is less than 45 upon 210. Now we can say now since minus 180 upon 210 is equal to minus 6 upon 7. So we say that minus 6 upon 7 is less than. Now minus 168 upon 210 is equal to minus 4 upon 5. So here we write minus 4 upon 5. Now this is less than minus 112 upon 210 which is equal to minus 8 upon 15. And this is less than 45 upon 210 which is equal to 3 upon 14. Or this could also be written as minus 6 upon 7 is less than 4 upon minus 5 is less than 8 upon minus 15 is less than 3 upon 14. So now this is the required ascending order of the given rational numbers. Hence our final answer is minus 6 upon 7 less than 4 upon minus 5 less than 8 upon minus 15 is less than 3 upon 14. So this completes the session. Hope you have understood the solution for this question.