Multiplication of numbers

In VM we use multiplication of two numbers from left to right mentally .

suppose 234 x 3

here you multiply 2 by 3 then 3 by 3then 4 by 3 , but In conventional maths we do it from right to left for that we have to use pen and paper , but in VM if we do from left to right we calculate it mentally.

= 69(1)2                    here (1) is the carry
=702                         1 added to 9 we get 10 , then 6 added to 1 of 10 we get 7
Any number of digits we can do calculate mentally using Left to Right Approach of VM.

One More than the One Before-Sutra of VM

When first digit of two numbers are same and last digits added to 10 of two numbers then we use One more than the one Before sutra of VM.

Multiply 53 x 57
here 1st two digits of two numbers 53 and 57 are same ie 5 .Last digits of two numbersadded to 10 i.e 3 +7 = 10

= 5 x ( 5+1) |   ( 3 x 7)

=(5 x6)  |  ( 3 x 7)

= 3021 
 here next number of 5 is 6 i,e one more of before number 5 is ( 5 +1) i.e 6

First by First and Last by Last - Sutra of Vedic Maths

Multiply 48 x 68
here last digit in both numbers are same. and sum of 1st digits of two numbers is 10 . i.e 4+6=10

= (4 x 6)+8 | (8 x 8)

=3264
This sutra is known as " First by First and Last by Last " of Vedic Maths


 


  

Multiplication of a number with groups of 9's in a easy way...

How to find   multiplication of a number with 9  in a Easy way

Suppose we have to find out Multiplication of 6 with 9

6*9  = 54 everybody knows it from table

but there is a easy method without knowing the table ,

6*9  =  subtract 1 from first number (6-1) is 5   |   subtract the result from 9 i.e.second number

       = 5 | (9 - 5)

       =  54

Now find out 237   *  999

=  236763

h ow it gets lets check out ,     (237  - 1)  |   ( 999  - result of 1st part)

                                              =   236  |  (999  -  236)

                                     =    236763

Now find out a larger number with group of 9's  with in 5 seconds

4674523091  *  9999999999     too many large figures

=   46745230905325476909   

Just check out it !!!!!

This method is known as ONE LESS THAN ONE BEFORE  .. As 1st number is subtracted from 1





  

square of a number ends with 5 in easy method

How to find square of a number ends with 5

 Suppose we have to find out square of 65

square of 65= 4225

now discuss how it find out . In 65, last digit is 5 . take square of 5 i.e 25

and 1st digit is 6, multiply 6 with one more than 6 i.e (6+1) i.e. 6*7=42

then write down the number 4225

Now check for one more number find square of 225

22*23  |  (5*5)

= 2*11*23  |  25

= 2*253 | 25       ( 23*11= 2 | (2+3)  |  3 )

= 50625



Try :  i) square of 95

        ii)  square of 45