Multiplication of numbers near the base

Vedic techniques for multiplying  the number close to the base is atleast 10 times faster than the normal method. The techniques can be used to multiply large numbers such as 999999 x 999998, 10003 x 10004.   We have show the examples along with the steps below

Multiply 88 by 98.

88     12

98     02

86     24

Both 88 and 98 are close to 100. 88 is 12 below 100 and 98 is 2 below 100. (100- 88 = 12 & 100-98 = 02)

As before the 86 comes from subtracting crosswise: 88 - 2 = 86 (or 98 - 12 = 86): you can subtract either way, you will always get the same answer. And the 24 in the answer is just 12 x 2: you multiply vertically. Since our base is 100, so the figure at the right hand side should consist of only two digits.

So 88 x 98 = 8624

Let see how this works in case of bigger numbers (9999 X 9997 ) through examples below

 9999   0001

 9997  0003

  9996 0003

The steps are as follows

1. Write the two numbers to be multiplied above and below.
2. Take a base for the calculation. The base should be that power of 10, which is nearest to the number to be multiplied.
3. Subtract each number from the base and write the remainder with respective plus (+) or minus (-) sign.
4. The product will have two parts left and right.
5. The left hand product is obtained by cross operation of the numbers written diagonally.
6. The right hand product is obtained by multiplying the two digits written at right hand portion.