Multiplication simplified

I was stumbling today like always and I came across a nice article which might be useful to all of us. So I am writing it here. I hope you like this.

It's always easy to multiply  numbers with  multiple of 10. That is exactly what this algorithm uses for simplified multiplication.

The algorithm is called “Nikhilam Navatascaramam Dasata.” It is part of a system of algorithms and mnemonics to remember them, collectively known as “Vedic Math”, that was developed by Jagadguru Swami Bharati Krishna Tirthaji Maharaj in the early 20th century.


Lets start with a simple example.

                  7 
                 x8
                

First find a suitable multiple of 10 for both of the numbers. In this case the suitable multiple is 10. Then write the difference between the numbers to be muliplied, and the multiple, off to the right:

multiple 10

                  7     | -3
                x 8     | -2

Multiply the differences. -3 x -2 = 6. The number of digits in the product and number of zeros in our multiple(1 in our case) should be equal; if we don't have enough, we should add leading zeros(we don't need to that here). Write the product on the right side of the answer:

multiple 10

                 7     | -3
               x 8     | -2
              ________

                       | 6  

Now add the difference between the one number to be multiplied and 10, to the other number to be multiplied. Pick either combination, because you will get the same result

8 + (– 3) = 5  OR  7 + (– 2) = 5

Put the result on the left side of the answer:

multiple 10

                7     | -3
              x 8     | -2            7 x 8 = 56            
             ________

                   5  |  6   
                  

Now let's try it with significantly bigger numbers, to see why this is such an advantage.

                98     
              x 89
              ____

Since both numbers are close to 100, we will use 100 as our multiple. Write the difference between the numbers to be muliplied, and the multiple, off to the right. Because 100 has two zeroes, we need two digits on the right hand side.

multiple 100

                98     | (-2)    
              x 89     | (-11)             98 x 89 = 8722
            ___________
                  87   |  22

The 87 comes from either 89 + (-2), or 98 + (-11). The 22 comes from (-2) x (-11). You can do this problem in your head. Let's try another one, to show when you need to add leading zeros to the right side:

multiple 100

               98      (-2)    
             x 97      (-3)              98 x 97 = 9506
            ___________
                  95 | 06

The 95 comes from either 97 + (-2) or 98 + (-3). The 06 comes from (-2) x (-3). We need to add a leading zero, because the multiple is 100 so we need two digits on the right-hand side.

Let's try another example where the numbers to be multiplied are on either side of a multiple of 10(here 100):

                 104     (+4)
               x  98     (-2)
             __________
                   102 | -08

we have a negative on the right! Add it to the left hand side:

              10200 + (-08) = 10192

              104 x 98 = 10192

Let's try bigger numbers.

Multiple 1000

                       995     (-5)
                      x998     (-2)
                    __________
                         993  | 010

993 = 995 + (-2) OR 993 = 998 + (-5). 010 comes from (-5) x (-2) = 10, then one leading zero is added because we need 3 digits because our multiple is 1000.


This is all I have for this post, I hope you found it interesting.......