MULTIPLICATION TRICK - 4

uurdhva-tiryagbhyam

     By this method you can multiply any number having any number of digits easily.

Example 1:

  67

× 78 

---------------------------------------------------------------------------------------------

6x7 / (6x8)+(7x7) / 7x8 

    =    2 7 6

 + 4 9 5 

----------------

=     5 2 2 6 

=  5226

Here step-1 : 7x8 = multiplication of unit digits of the number

                    (6x8)+(7x7)= cross multiplication between the digits of two places and adding them.

                     6x7 = multiplication of last digits of the number

         step-2: writing the result of above step part wise i.e here three parts and carrying the 2nd digit to next  part as one part can contain only one digit.

         step-3: summing them up and writing the final answer .

               IS NOT IT SO SIMPLE !!!!!

Example 2:

    408

 x 512

---------------------------------------------------------------------------------------------

4x5 / (4x1)+(5x0) / (4x2)+(0x1)+(8x5) / (1x8)+(2x0) / 8x2 

=       0 4 8 8 6

+  2 0 4 0 1 

--------------------

=    2 0 8 8 9 6 

=  208896

       Here also the same procedure.But only in

       step-1 :           8x2= multiplication of unit digits 

                 (1x8)+(2x0)= cross multiplication between the digits of first two places and adding them.

       (4x2)+(0x1)+(8x5)=cross multiplication between the digits of three places and adding them.

                 (4x1)+(5x0)=cross multiplication between the digits of last two places and adding them.

                              4x5= multiplication of last digits of the number  

then step-2 & step-3 are same as Example 1. 

Example 3:

    2186
×  4534 

          --------------------------------------------------------------------------------------------

4x2 / (4x1)+(5x2) / (2x3)+(8x4)+(5x1)/(2x4)+(6x4)+(1x3)+(8x5) / (4x1)+(8x3)+(6x5) / (4x8)+(3x6) / 6x4
= 8 4 3 5 8 0 4
 1 4 7 5 5 2

--------------------------------
= 9 9 1 1 3 2 4 = 9911324

Here also same procedure .Only during 1st step, steps will be                                       multiplication of unit digits.                                                                                             cross multiplication of first 2 digits                                                                                   cross multiplication of first 3 digits                                                                                   cross multiplication of 4 digits                                                                                         cross multiplication of last 3 digits                                                                               cross multiplication of last 2 digits                                                                                       multiplication of last digits                                                                                                                       Then step-2 and step-3 are same .