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Multiplication Trick 5



1. Condition :  This trick is used when we multiply quickly three numbers near  a  same power of 10.
Example.  103×112×108 


Illustration 1 :     107×102×105

Numbers       Base       Difference    
 107               100        +7 (let a=7)
 102               100        +2 (let b=2)
 105               100        +5 (let c=5)
Solution: 
1st part / 2nd part / 3rd part 
                     
(Number of digits in the 2nd and 3nd part =Number of 0s in the base)
                          
formula:
107+b+c / a×b+b×c+c×a / a×b×c
107+2+5 / 7×2+2×5+5×7 / 7×2×5
      114    /    14+10+35    /   70
      114    /           59          /   70

 Answer is   1145970   

 Note: 1st part can either be  107+b+c  or  102+a+c  or   105+a+b



Illustration 2 :     102×109×106

 Numbers            Base            Difference    
  102                    100                  +2 (let a=2)
  109                    100                  +9 (let b=9)
  106                    100                  +6 (let c=6)
Solution:     
1st part / 2nd part / 3rd part 
                     
(Number of digits in the 2nd and 3nd part =Number of 0s in the base)
                          
formula:       
102+b+c / a×b+b×c+c×a / a×b×c 
102+9+6 / 2×9+9×6+6×2 / 2×9×6
     117     /     18+54+1      /   108
     117     /           84          /   108
     117     /   84+1(carry)   /    08
     117     /         85            /    08

      Answer is       1178508 

Note: 1st part can either be  102+b+c  or  109+a+c  or   106+a+b
Try Now :
1.  12×13×11
2.  102×103×104
3.  104×108×113
4.  1002×1005×1006
5.  1003×1007×1011






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