TO CALCULATE THE PRODUCT OF NOs. Ending with 5

           Here we discuss the multiplication of two numbers ending with 5 ie 25x25 ,25x45 35 x75
             we cover  three types of problems under this heading
           1. 25x25   both nos are same no difference ie difference is 0(25-25 =0)
           2. 25x35  45x75  difference of  first digits (35-25) is odd like 10 ,30 ,70,90 ,110
           3. 25x45 45 x65  difference of  first digits (45-25 ) is even like 20, 60 ,40 ,120

            Let us take first case when there is no difference

75x75 = 5625

The answer is in two parts: 56 and 25.
The last part is always 25.
The first part is the first number, 7, multiplied by the number "one more", which is 8:
so 7 x 8 = 56

Similarly 85x85 = 7225 because 8 x 9 = 72.

Now we take both cases where difference of  first  digit is either even or odd
When  difference of first digit is odd our last part of answer is 75  and in the case of even it is 25
you can remember  it by this way  - difference of  first digits is odd , take 75 having  first digit odd
                                                       difference of first digist is even, take 25  having first digit  even

 Now Learn How to calculate first part

               See this example 25x45 =??????        45 -25 =20  

                  Because first digit's difference  is even ,our   second part of answer is 25
                  Multiply 2 to 4   ie 2x4 =8,  take average of first digit of both numbers  (2+4) /2 = 6/2=3
                   this 3 also add to 8 ie 8+3 =11   It  is first part of our answer . Now our required answer is 1125

                See one more example  45 x85 =???        Difference is  even  8-4 =4   second part is 25

               
                8x4 =32          (8+4)/2 =12 /2=6       32 +6 =38

                             Required answer is 3825

               Now see the odd difference example  45 x55=???           5-4  =1, difference is odd so second part is 75
                       Multiply 5x4  = 20   now take average of both first  digits  numbers after deducting  1
                       (5+4-1)/2 =8/2=4   add this one to multiplication of 5and 4 ie 20 +4 =24
                        It is our first part Now  answer is 2475

                        Required answer is 2475

            See one more example    65 x95 =?????

                Difference is odd 9-6 = 3  so second part is 75
                 6x9 = 54 ,  ( 6+9-1)/2   =(15-1 )/2 = 14/2  =7  54 +7 = 61

                             Required answer is 6175

                                                                                                  

Back

Home

Next