Divide Numbers fast and easy using Vedic Mathematics

 Division also becomes easy using Vedic mathematics techniques. As multiplication can be done easily using Vedic math’s formulae, similarly Division becomes simple using this. Earlier I surprised when I was learning this formulae how this works really right and perfect. But it is true that using this one can do division without much of the paper work. So I have described such a wonderful, magical method to work with numbers speedily. I hope you will find it Easy and simple.

Denominator ending with 9
   
Let try to find 73/139 up to 5 places of decimal. Let us have a look over conventional method:
      
Dividend------- 139) 730 (0.52517------Quotient
  - 695 
  ---------
  350
  - 278  
  --------------
  720
  - 695
  ----------------
  250
  139
  ----------------- 
  1110
  973
  -----------------
  137

  Now let us see magical and easy method. As follows,
73/139=7.3/13.9=7.3/14=0.52517 —Answer
  3 7 2 11 ---Remainder
  If you cross check you will find answer is exactly same. By the conventional method, our answer is 0.52517.
  By the magical method too, our answer is 0.52517. There is no difference in the answers. However, the procedure adopted in both the methods is different. One is more cumbersome than the other. Detail explanation of the steps is as follows.

STEPS:
• 73 is divided by 139 (a digit ending with 9).
• 73/139 is reduced to 7.3/13.9 or 7.3/14.
• Start dividing 73 by 14.
• Put the decimal point first; divide 73 by 14. 
• Then we get 5 as quotient and 3 as a remainder. 5 is written after the decimal and 3 is written in front of 5 as shown below.
• Our next gross number is 35; divide 35 by 14. Quotient = 2 and Remainder=7.
• Q=2 and R=7, Q=2 is written after 5 and R=7 before 2 (below it).
• Our next gross number is 72; divide 72 by 14. Quotient = 5 and Remainder=2
• Q=5 and R=2, Q=5 is written after 2 and R=2 before 5 (below it).
• Our next gross number is 25; divide 25 by 14. Quotient = 1 and Remainder=11.
• Q=1 and R=11, Q=1 is written after 5 and R=11 before 1 (below it).
• We have already found the answer up to four decimal places; our next dividend is 111 which is to be divided by 14. Quotient=7, and thereby we have found the answer up to five places of decimal.
• Repeat the above steps if you want to find the values further.
  
  We have seen the steps required to solve such kind of problems where the denominator ends with 9. Let us look at some more examples.

   
• 75/168=7.5/16.8=75./17= 0. 5 3 9 5 6 8 –Answer
  5 13 7 9 11 --Remainder  
   
• 63/149=6.3/14.9=6.3/15= 0 . 4 2 2 8 1 8 8 7—Answer
  3 4 12 2 13 11 –Remainder 


• 83/189=8.3/19=0. 4 3 9 1 5 3--Answer
  7 17 2 10 6 8-Remainder.


Denominator ending with 8

 You must be thinking weather the process discussed is applicable only if a denominator ends with 9. The answer is no. We can apply this technique to digits that end with 8, 7,6 etc. but with slight change.
Let us see it applied to denominator ending with 8:

  +2+8+9+8
• 73/138=7.3/13.8=7.3/14= 0.5 2 8 9 8--Answer
  3 12 12 10 –Remainder
In case of denominator digits ending with 8 (one less than 9), the steps are as follows:

• Placing of remainder in front of the quotient remains the same as explained in case 73/138 or where the denominator digit ends with 9.
• In the quotient digit, 1 time (9-8) of the quotient digit is added at every step and divided by the divisor for finding out the answer.
As in this case, we found our first Q1=5 and R1=3. our gross dividend comes out to be 35 in which we added 5 to make it 40, then divided it by 14. In the next step Q2=2 and R2=12. Our gross dividend at step 2 becomes 122+Q2=124. divide this by 14. The procedure is repeated to find the solution to the required number of decimal places.
  Let us have a look at few more examples as follows.

  +4+4+6+4+2
• 75/168=7.5/16.8=7.5/17=0. 4 4 6 4 2 8 
  7 10 6 4 14 
   
  +4+6+6+2
• 83/178=8.317.8=8.3/18=0. 4 6 6 2 9
  11 10 4 16
   
  +1+6+4+8
• 31/188=3.1=18.8=3.1=19=0.1 6 4 8 9
  12 8 16 16 

Denominator ending with other digits

  After learning this magical method for denominator digits ending with 8, you would like to learn the same for denominator digits ending with 7.
Let us have a look at following example:

  +10+6+4+16+8
• 73/137=7.3/13.7=7.3/14= 0. 5 3 2 8 4
  3 3 11 4 6  

Once you see operation you know instantaneously that in this case the quotient digit is multiplied by 2 (9-2=2) and added to the quotient. All other operations remain the same as before.