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Multiplication Trick 6



1. Condition :  This trick is used when we multiply quickly two numbers near  a  multiple of a power of 10.
Example.  211×209, 189×191

Illustration 1 :     207×211

Numbers       Working Base       Difference    
 207                    2×100                 +7 
 211                    2×100                 +11 
 Solution: 
1st part / 2nd part(2 digits)
                   
[Number of digits in the 2nd part = Number of 0s in the base]
                          
2×(207+11) / 7×11(2 digits)
      2×218     /    77
         436       /    77
 Answer is   43677

Note: 1st part can either be 207+11 or 211+7 

Illustration 2 :     191×187

Numbers       Working Base       Difference    
 191                    2×100                 -9 
 187                    2×100                 -13 
 Solution: 
1st part / 2nd part(2 digits)
                   
[Number of digits in the 2nd part = Number of 0s in the base]
                          
2×(191-13)    /  9×13(2 digits)
    2×178         /    117
       356          /   117
 356+1(carry)/     17
       357          /    17
 Answer is  35717


Note: 1st part can either be 191-13 or 187-9

Illustration 3 :     2018×2012

Numbers       Working Base       Difference    
 2018                    2×1000                 +18 
 2012                    2×1000                 +12 
 Solution: 
1st part / 2nd part(2 digits)
                 
[Number of digits in the 2nd part = Number of 0s in the base]
                          
2×(2018+12) / 18×12(3 digits)
      2×2030     /     216
         4060       /     216
 Answer is   4060216

Note: 1st part can either be 2018+12 or 2012+18 
Try Now :
1.  205×209
2.  302×303
3.  2014×2016
4.  2025×2050
5.  40063×40003

  

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