Special Multiplication

As always I think about  shortcuts to perform multiplication easily.
   Many love to learn new tricks , shortcuts to enhance their speed in problem solving.

Let me share one of the trick today .

” Multiplication of two 2 – digit numbers , both ending in 5 ”

#Case_1 : When the tens digits are of  same kind ; are either both odd or even.

      Answer would always end with 25 , that it is the last two digits of result. Now we are left with the first two digits of results. This can be obtained by
    
    Multiplying the tens digit + adding half of sum of tens digits of the two given numbers

   Let’s take one example to understand it
  
     25 ×45 =?
  
   First part : (2)(4) +(2+4)/2 =11
   Second part: 25
  Therefore , 25×45 =1125

    Both odd :
       35 ×55 =?
    First part : (3)(5) +(3+5)/2 = 19
   Second part: 25
  Therefore , 25×45 =1925

#Case_2 : When the tens digits are of  different kind ; one is  odd , other is  even.

      Answer would always end with 75 , that it is the last two digits of result. Now we are left with the first two digits of results. This can be obtained by
    
    Multiplying the tens digit + adding half of sum of tens digits of the two given numbers .
( Neglecting the decimal part ).

   Let’s take one example to understand it
  
     25 ×75 =?
  
   First part : (2)(7) +(2+7)/2 =18
   Second part: 75
  Therefore , 25×75 =1875

    One more example :

       65 ×95 =?
    First part : (6)(9) +(6+9)/2 = 61
   Second part: 75
  Therefore , 65×95  = 6175