MULTIPLICATION TRICK-3

In the last post we had discussed about NIKHILAM NABATAH CHARAMAM DASATAHA

 Now we will be discussing about ANURUPYENA , which is a corollary of  that.

Anurupyena(corollary):

If the numbers to be multiplied are far from these bases,then we can take the working base as 40,50,200,300 etc.

 

                                            49  -1

                                          ×44  -6

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                 {(49-06)or(44-01)}x5 / (-6)x(-1)  =   43x5  /  6

                                         = 2156

Here the sub base is 50 BUT base is 10 as only one digit appear in the right(for e.g.-6 if base is 100 it would be -06). So  44 is lesser than 50 by 6 and 49 is lesser than 50 by1

//step-1  :(-6)x(-1)=6

//step-2  : {(49-06)or(44-01)}x5 

 Here,It is Multiplied by 5 .As 50 is 5 times 10.

                                                63 +3

                                          × 57 -3

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      {(63-03)or(57+03)}x6/ (-3)x(+3)  =360 / -9  = 360-1/10-9

                                                                                                                           =3591

Here the sub base is 60 BUT base is 10 as only one digit appear in the right. So  63 is greater than 60 by 3 and 57 is lesser than 60 by 3

//step-1  :(3)x(-3)=-9

//step-2  : (63-03)or(57+03)}x6

Here,It is Multiplied by 6 .As 60 is 6 times 10.

//step-3  : As -9 is -ve,So We Subtract it from ten.& Making 360-1

                            195 -05

                                                ×196 -04

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                  {(195-04)or(196-05)}x2 / (-05)x(-04) =   

                                       189x2 / 20  =37820  

Here the sub base is 200 BUT base is 100 as two digits appear in the right. 

Rest of Steps are same as First Example.

Thank you.............