Division using paravartya sutra 19 mathematics Tricks and Fun

Division using paravartya sutra 19 mathematics

 Tricks and Fun 

Hello friends, we are going to continue studying 

 division. This is the 19th lesson of mathematics

 tricks and fun tutorial I am Dr Prema B Sejekan. We studied in the earlier class , Nikhilam sutra which is 

used when dividing with big digits like 6,7,8,9 . Since 

the complement of these digits are small, the division becomes easier. Now how will we divide with small

 digit numbers?

Here comes the paravartya sutrafor our help. 

Paravartya yojayet means transpose and apply.we 

use this when divisors are with small digit numbers.

we have to change the sign with change of side I have shown here. Plus becomes minus,and vice versa, and divide becomes multiply and vice versversa, with 

change of side.

 Here I have given 3 examples. One in Nikhilam 

method and the same how to do in paravartya. Now

 we have to divide 1234 by 112. In Nikhilam method 

we take the complement and since 112 is small digit number, the complement is big digit number and 

makes the procedure long and cumbersome as shown 

it goes on and on

But in paravartya you take the number only of the divisor.omit the first digit and bring down the

 remaining digits after changing sign as said earlier. 

Now Start dividing into two groups acc. to the number

 of digits in the new divisor so here mark line between 

12 and 34. Bring down the first digit of the dividend multiply it with divisor so 1×12 gives 12 write below 2 

and 3 as shown with their (-) signs subtract.since

 balance 1 is there again multiply and as shown below

 3&4 subract .so the quotient is 11 and Remainder

 is 02. Carry on the other example in the same way.

Here we have two examples with the little variation . 

1234 to be divided by 160.we write12 then gap 34 and write -6-0 below 160 as shown .Bring down 1 to quotient side then 1× 60 =60which is written below2 & 3.now

-6+2 gives -4 . Now -6-0× -4 gives +240.taken to the

 other side and 240+34 gives 274. Since 274 is more 

than 160 we will divide 274 by 160 which gives 1

 added to original quotient (10-4)=6+1 gives 7 and remainder 114.

Divide 13905 by 113, we write 139 gap 05 and -1-3

 below 113.Bring down 1 to the quotient side and 1×13= 14 we write with their respective signs below39now 3-1=2take to quotient side 2×13=26written below 90

Now 9-2-3 gives 4 4× 13 gives -4-12 written below 0

 and 5. So -6-4 gives -10 and -12+5 gives -7 so since 

-107 we borrow one ie 113 from 124and deduct -107 

from 113 which gives 06 as remainder and quotient

 123.

 In these two examples we are using vinculum and paravartya .

we have to divide with bigger digits, take vinculum.

then using paravartya divide.

First example 39999÷ 9819.now vinculum of 9819 

gives 100-2=9820-1=19, 10-22-1.. making it paravartya omit 1 and write 0+2-2+1 now start division.bring 

down 3 to quotient side, 3×0221 gives 0+6-6+3now

 adding 06-63+9999 gives 10542so dividing 10542 by 9819 gives Q1 with R 723finalQis 3+1=4.

1111÷839 Vinculum of 8=10-2 and 39= 40-1 Gives 

1-2+4-1, so paravartya becomes +2-4+1.now dividing

 1 111/+2-4+1 .quotient 1 brought down and multiply

 1× 2-41 written below 111 gives 272 as remainder.

 In this example , We are using vinculum and Nikhilam sutra in division.39 893÷829and complement being 

171 and vinculum of which is 2-3+1.bring down 3 and

 3×2-31 gives 6-9+3.now 9+6=15 so bring 15 to quotient and multiply 2-3+1 with 15 gives 30-45 and 15.so 

adding 30+15 gives 45 remainder side 15+3= 18 now (9+3)-5=7 which when 1 from is added gives 8 .

(30+8)-(-9-4) gives 25 so 2 carried over to other side

 gives 45+2= 47 and remainder 588 now 2 is carried

 over equals 4-62 added to 588 gives 930 since 930 is bigger than 829 divide 930÷ 829 gives 1 as quotient

 to be added to original quotient 47 gives 48.

remainder. 101.

 Here anurupya andparavartya sutra used in division. 

This is useful when you have mixed is big and small

 digits as divisor.in the first example divisor182 by vinculum it is equal to 2-2+2by anurupya we can

 convert it to smaller digit .dividing 222by 2 gives

 1-1+1 and by paravartya Finally you get 1-1since 2

 digits here we write 13 gap 56 nowbring down 1, 

1× 11 gives 1-1written below 3 and 5.now 3+1 is 4 

written on the quotient side and 4×11 is 4-4 written

 below 5&6. Now adding gives Quotient 14 R 82 to 

be divide by 2 gives Q7 and R 82

(Remainder should not be divided)

Similarly other example is done.

In the coming class we will study straight division

 using deanjanga sutra.Thank you.

Please subscribe to my channel .