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