Vedic Multiplication

Intro

To learn this little bit of Vedic multiplication you must be become familiar with the idea of a "Significant Digit" and the Idea of a "Base 10 number"

"Significant Digit"-usually the first digit of any number...but if you comfortable with larger numbers you can take the first few digits as the significant digit. for Example:

27: the 2 is the significant digit

300054: the 3 is the significant digit, or if you prefer it could be 30 or 300 or 3000. It all depends on how you're willing to look at it.

"Base 10" any number comprised only of 10's as it's only factors.

for Example:

10 is base ten it's just 1x10 (I know I said just tens but every number has 1 as one of it's factors)

so are

100

1000

1000000000000000000.

what's 9x9?

If you remember your grade school multiplication tables then you know it's 81 but suppose I said phooey to your multiplication tables and said try this instead:

write down the numbers and next to them write down how far they are away from the nearest base 10 number. For example:

9   1

9    1

Now to get the "significant digit" of your answer just SUBTRACT crosswise.

Crosswise is VERY important don't subtract the one from the nine in it's own row you subtract the one from the other row.

9      -     1    =8 (this is the first digit of our answer)

and to get the last digit(s) of our answer we multiply the last digits in each row by each other (also known as vertically)

1   =  1(this is the last digit of our answer)

so we get 81

9         1

8         2

No matter which way you subtract crosswise you'll get the same first digit 7

and multiply the 1x2 to get the last digit of your answer thus we have:

72

I know I know you learned these answers from your grade school times tables but that's where the handy dandy "Base 10" numbers come in:

what's 99x99

Hah!!! I bet your times tables didn't go that high!

well 100 is a base 10 number too, so we can use this method with it:

99      1

99      1

cross subtracting gives us 98 as our significant digit and the 1x1 gives us our last digit but we have to be careful here because a two digit number times another two digit number usually gives us a four digit number so we write the 1 as 01.

98x98?

98     2

98     2

cross subtraction gives us 96 as the significant digit of our answer and 2x2 gives us 04 so we know the answer is

9604

try a few:

 9x6 98x97 89x91 94x94 86x86 7x8 7x6 89x90 92x97 80x80

Now with some of these above example you realize you may have to carry for example 80x80

80     20

80      20

cross subtraction gives us 60 as our first digit, we know the answer should be 4 digits long and multiplying 20x20 gives us 400 which is three digits so we write the for in the zero after 60 thus

6400

well 1000 is base 10   so,

999     1

998     2

cross subtraction tells us the significant digit of our answer will be 997 but we also know a three digit number times another three digit number of this size should give us a 6 digit number so we write the 1x2 as 002

997002

Some teachers will swear by the times tables but if you get used to this method soon you should be able to multiply PHONE numbers together or even credit card size numbers.

Well that's a long ways off from the nearest base 10 number but lets use 50 and see how it comes out.

Remember 50 is HALF our base ten number so we must remember to HALF the significant digit of our answer also. (Just the significant digit only nothing else)

49     1

47     3

cross subtraction tells us that our significant digit is going to be

46

BUT we must HALF it before we write it down as our final answer thus

it becomes

23

1x3 gives us 03

2303

well the nearest base 10 number is 1000 but what if we used 200 instead?

Well 200 is DOUBLE the base 10 number 100, so we must remember to DOUBLE the significant digit of our answer.

199     1

197     3

cross subtraction shows our significant digit to be 196 but we must double that so we get

392_ _ _

1x3 gives us 3 but we write it as 03

39203

try a few:

 197x197 298x298 999x997 396x390

be sure to be careful where you put the digits. Practice Practice Practice.

Another Vedic Multiplication trick:

crosswise and vertical multiplication:

51x41

write down the digits like so

1

4     1

to get the significant digit of our answer just multiply the significant digits (blue) 5x4

so we get 20, then the next digit of our answer will be the sum of cross multiplying (blue 5 x red 1)+(blue 4 x other red 1)= 5+4=9.

so far we have 209_

we get the last digit by multiplying the 1's vertically (red x red) which is 1

2091

This method is useful but it involves a lot of carrying over into the next digits place so be careful.

more to come ;-)