 We are going to learn about a method of division where the base is less than the divisor and this is known as Paravarthya Yojai method. We can take an example of such a kind where we will solve 126 divided by 12 and as you can see here the divisor which is 12 is greater than the base. So basically 12 is greater than 10 because 10 is the base which is a power of 10 which is nearer to 12. And now what we need to find out is a supplement divisor. So supplement divisor as we know is the base minus the divisor which is minus 2. And we can write this minus 2 as a bar over 2. Let's see how we can solve this using Paravarthya Yojai. This is just an extension of Nicolam method. So we again make three parts of the page like this and then we want to write the divisor first which is 12 and below that we will write our supplement divisor which is minus 2. Now we will reserve one place for the remainder because our base is 10 and there is 10 in 10. So only one place for the remainder so let's keep 6 of 126 here and then we can write 1 and 2 like this. Now we can simply take this one which is the first digit of 126 or the dividend note that this is a dividend and now we will write this one here and then we will multiply the supplement divisor minus 2 with this one here and this gives us the result minus 2. We will write minus 2 below the second digit of the dividend and then find the result below which is 0 because 2 minus 2 is 0 and then we use this 0 and multiply the supplement divisor again which actually gives us 0 and then we put 0 in the last column and the result that we get is 6 and now we stop our division process because we have received a one digit remainder which is less than the divisor and we can quickly verify that this is a quotient and this is a remainder. If we verify we get quotient times the divisor which is 10 times 12 plus the remainder is equal to the dividend which is 126 and this is how we can perform para varte uj wherein the base is less than divisor and the supplement divisor is negative and this is an important point with para varte uj. Now let us take different example where we will learn some new concept with different base. We have 24312 divided by 113 and here the base is going to be 100 so base is 100 and so our supplement divisor is going to be 100 minus 113 which is minus 13 and we will write it as bar over 1 and bar over 3 and we will write the supplement divisor like this. Let's go to the next step by dividing the page in three parts and on the left most side we will write our divisor which is 113 and below that let us write the supplement divisor bar over 1 and bar over 3. Now that just means minus 1 and minus 3. Now let's write the dividend our base is 100 and it has two zero so we will reserve two places on the right most side so we will write 1 and 2 out of 24312 and rest of the digits like this the right most part will be for remainder and middle part will give us the quotient. Now let us start our procedure so let's pull down this two at the bottom and then we will multiply this two with the first digit of the supplement divisor which is minus 1. Let me just write it here at the top left minus 1 times the 2 which gives us minus 2 and we will write it as a bar over 2 and we will start writing the result from the second digit of the dividend. Now we will multiply this two with the second digit of the divisor which is minus 3 so we will have negative 3 times 2 which gives us minus 6 and we will write minus 6 below the third digit of the dividend. Now let's combine 4 and minus 2 this gives us 2 and now with the obtained result here we can again multiply with minus 1 and minus 3 and we will again get minus 2 and minus 6 but we will write minus 2 below the third digit of the dividend again and minus 6 below the fourth digit of the dividend. Now we will combine the result of the third column and we get 3 minus 2 minus 6 which is minus 5 and now we will use this minus 5 to multiply this supplement divisor digits so let's just write it here minus 5 times minus 1 which is 5 and minus 3 times minus 5 is 15. So let's write the result minus 5 times minus 1 below the fourth digit of the dividend which is going to be 5 and 15 below the last digit. Now we have reached the last digit that we have written the number below the last digit of the dividend so now we can stop doing our procedure here and we can sum up this column now this gives us 0 and this will give us 17 or this one will flow as a carry towards left and this will basically be 17. Now we will just ensure whether this number that we have got is less than the divisor yes and it is also a 2 digit positive number and so our division is finished. So our quotient is 2 to 5 but 5 has a negative sign so basically this is nothing but 220 minus 5 right because 5 has a negative sign so this basically is 215 and this is 17 so this is a quotient and this is a remainder.