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.
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)
And now we eat cookies.
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:
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 x 1 = 1(this is the last digit of our answer)
so we get 81
how about 9x8
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:
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:
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:
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.
So our answer is 9801
Easy as eating cookies.
cross subtraction gives us 96 as the significant digit of our answer and 2x2 gives us 04 so we know the answer is
try a few:
Now with some of these above example you realize you may have to carry for example 80x80
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
what about 999x998
well 1000 is base 10 so,
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
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.
What about 49x47?
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)
cross subtraction tells us that our significant digit is going to be
BUT we must HALF it before we write it down as our final answer thus
1x3 gives us 03
so the answer is
How about 199x197?
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.
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
try a few:
be sure to be careful where you put the digits. Practice Practice Practice.
Another Vedic Multiplication trick:
crosswise and vertical multiplication:
write down the digits like so
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
This method is useful but it involves a lot of carrying over into the next digits place so be careful.
more to come ;-)