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Multiplication Trick 4


 Condition :  This trick is used when we multiply quickly two  numbers with 5 as the unit digit.       Example.  75×95 , 95×85 ,115×145 , 125×105


Illustration 1 :   
75×95

Solution:   
Numbers                 Split   as
     75                       7    /    5
 × 95                       9    /    5

[Split the numbers keeping the last digit (5) aside]
                       
1st part / 2nd part 

Product +Sum ÷ 2 / 25       
[Product and Sum of no. other then unit digits]

[The 2nd part would be 25 as the sum 7+9=16 is even, if sum is odd , it would have become 75].
                         
step 1→     7×9 +16÷2 /  25
step 2→     63+8          /  25
step 3→     71              /  25
Answer is 7125



Illustration 2 :   
175×105

Solution:   
Numbers              Split as
    175                   17  /  5
× 105                   10  /  5

[Split the numbers keeping the last digit (5) aside]
                       
1st part / 2nd part 

Product +Sum ÷ 2 / 75     
[Product and Sum of no. other then unit digits]

[The 2nd part would be 75 as the sum 17+10=27 is odd, if sum is even , it would have become 25].
                         
step 1→     17×10+(27-1)÷2 /  75  (Subtract 1 if sum is odd)
step 2→     170+13                /  75
step 3→     183                      /  75
Answer is  18375

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