How to do Vedic Math Division
Now we will look at long division using the Vedic Math division method. Actually the Vedic Math division method looks very similar to short division but incorporates modifying the divisor to round it to the nearest ten to try to simplify the calculations.
How the division will be modified depends on the unit digit of the divisor:
- 1 to 4 : subtract to bring the divisor down to the nearest ten.
- 5 : double both the divisor and the dividend then do the division.
- 6 to 9 : add to round the divisor up to the nearest ten.
Divide 31652 by 77 using Vedic Math Division
We will do a few examples to make it a bit clearer, first we will divide 31652 by 77.
Since the divisor has a 7 for the units we will add to make the divisor up to 80. We now have a divisor of 80 but we ignore the zero and treat the divisor as 8 and to make up for the fact we are dividing by one digit instead of two we will put a slash "/" one digit in from the right of the dividend so we setup the division like this:
We have reduced both the divisor and the dividend by one digit which will have no effect on our answer.
Our first step is to find out how many times 8 goes into 31. In Vedic Math you are expected to do these calculations in your head.
So the 3 goes up over the one of the 31 and the 7, the remainder, is put next to the next digit in the dividend, the 6, as a subscript or superscript. My preference is to use subscripts.
Now we read the "" as then to this we add the 3 multiplied by the we added to the 77.
Now we find how many times 8 goes into 85. Which is 10 times with 5 remainder.
We cannot put 10 above the 5 as part of the answer so we write the unit digit, the 0, above the 6 then write the tens digit, the 1, above the digit to the left in our answer, ie above the 3 from the previous step. We write the remainder, the 5, in front of the next digit to the right in the dividend, the 5.
we read the "" as and we add 10 times the we added to the 77.
Now we find how many times 8 goes into 85. Which as we saw earlier is 10 times with 5 remainder.
Again we cannot put 10 above the 5 as part of the answer as we only have space for one digit so what we do is write the unit digit, the 0, above the 5 then write the tens digit, the 1, above the digit to the left in our answer, ie above the 0 from the second step. We write the remainder, the 5 in front of the next digit to the right in the dividend, the 2.
We are now at the 2 in the dividend so we have crossed the slash that we put in the dividend which means we are now working on the remainder.
We read the "" as 52 to which we have to add .
We have a problem, our remainder of 82 is larger than our divisor of 77, t fix this we will increase our answer by one. To show we have done this we will write a 1 over the zero in the column to the left. Having increased our answer by one we need to now reduce our remainder by 77.
Our remainder is now 5 and our equation now looks like this:
To read our answer when we have one or more numbers above our preliminary answer we simply add up each column to get our final answer.
We have 411 with 5 remainder as our final answer.
Divide 235815 by 64 using Vedic Math Division
This time when dividing by 64 we will subtract 4 from the divisor and use 60 as the new divisor. We ignore the zero and treat the divisor as 6 and to make up for the fact we are dividing by one digit instead of two we will put a slash "/" one digit in from the right of the dividend so we setup the division like this:
Our first step in the division is to find how many times 6 goes into 23.
It is 3 times so we put the 3 up above the 3 of the 23 and the 5 for the remainder we write down next to the next digit of the dividend which is also a 5.
We read as 55. The 3 from our previous calculation we now multiply by which gives us 12. As ww subtracted the 4 from our divisor we must subtract the 12 from 55.
This leaves us with 43 and now the question is how many times does 6 go into 43?
It is 7 times so we write the 7 up over the 5 and put the 1 for the remainder down next to the next digit in the dividend, the 8.
Now we have a problem since is only 18 and we know we need to subtract the result of 7 times which would result in a negative number.
To fix this we need to decrease our result by one so the 7 we just put as the answer we change to a 6 and redo the calculation.
So we have 7 as the remainder now and we put this down next to the 8.
That is better as we now have a larger number to subtract from.
We now have to find how many times 6 goes into 54, which should be 9 times.
If we put the 9 up over the 8 in the dividend and put the 0 in front of the next digit in the dividend we start to see another problem.
We only have 1 from which we must subtract a larger number. To correct this we will reduce our answer by 1 so instead of 9 we make it 8 and then we redo the calculation.
We now put the 8 up over the 8 in the dividend and put the 6 in front of the next digit in the dividend
We multiply the 8 by the and subtract this from the 61.
Now we need to find how many times 6 goes into 29.
We put the 4 up over the 1 in the dividend and we put the 5 down in front of the last digit of the dividend.
We cross over the slash here so we already have our answer and the remaining step is to see if there is any remainder.
We multiply the 4 by the and subtract this from 55.
We have a remainder of 39 so we can write the R39 next to our answer of 3684.
As you can see the Vedic Math division looks very similar to the short division and by adding or subtracting to round the divisor to the nearest ten then adjusting the results with
Next we look at the Trachtenberg System division.