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Home->Vedic / Quicker Math-> Multiplication by 11

Vedic Math / Quicker Math / Math Tricks :-


MULTIPLICATION BY 11 :

Ex. I Solve 5892 x 11 =?
Step I: Start from right, write down first digit 2
Step II: Add first pair 9 + 2 = 11, write down 1 and carry 1
Step III: Add next pair 8 + 9 = 17 and add carry 1 say 17 + 1 = 18
            write down 8 and carry 1
Step III: Add next pair 8 + 5 = 13 and add carry 1 say 13 + 1 = 14,
            write down 4 and carry 1
Step IV: As there is no more pair so add carry in last digit 5 + 1 = 6, write down 6
Step V: Combine step IV + III + II + I =64812

Detail explanation :
Step I: The last digit of the multiplicand (number multiplied) is put down as the right-hand figure of the answer.
Step II: Each successive digit of the multiplicand is added to its neighbour at the right.
Ex. I Solve 5892 x 11 =?
Soln: Step I: Put down the last figure of 5892 as the right hand figure of the answer :
5892 X 11
2

Step II: Each successive figure of 5892 is added to its right-hand neighbour. 9 plus 2 is 11, put 1 below the line and carry over 1. 8 plus 9 plus 1 is 18, put 8 below the line and carry over 1. 5 plus 8 plus 1 is 14, put 4 below the line and carry over 1.
5892 X 11
12
(9+2 = 11, put 1 below the line and carry over 1)

5892 X 11
812
(8+9+1 =18, put 8 below the line and carry over 1)

5892 X 11
4812
(5+8+1 = 14, put 4 below the line and carry over 1)

Step III: The first figure of 5892, 5 plus 1, becomes the left-hand figure of the answer:
5892 X 11
64812
So the answer is : 64812

As you see, each figure of the long number is used twice. It is first used as a "number", and then, at the next step, it is used as a neighbour. Looking carefully, we can use just one rule instead of three mles, And this only rule can be called as "add the right neighbour" rule.
We must first write a zero in front of the given number, or at least imagine a zero there.
Then we apply the idea of adding the neighbour to every figure of the given number in turn :
5892 X 11
2
As there is no neighbour on the right, so we add nothing.

5892 X 11
4812
As we did earlier

5892 X 11
64812
zero plus 5 plus carried-over lis 6 This example shows why we need the zero in front of the multiplicand. It is to remind us not to stop too soon. Without the zero in front, we might have neglected the last 6, and we might then have thought that the answer was only 4812. The answer is longer than the given number by one digit, and the zero in front takes care of that.

Sample Problems : Solve the following
(1)111111 X 11 (2) 23145 X 11 (3) 89067 X 11 (4) 5776800 X 11 (5)1122332608 X 11
Ans : 1) 1222221 2) 254595 3) 979737 4) 63544800 5) 12345658688
Do it in your mind

MULTIPLICATION BY 111 :

Ex. I Solve 1361 x 111 =?
Step I: Start from right, write down first digit 1
Step II: Add first pair 6 + 1 = 7, write down 7 (and no carry )
Step III: Add next pair 3 + 6 = 9 now add right neighbour digit(1)
            say 9 + 1 = 10 and write down 0 and carry 1
Step IV: Add next pair 1 + 3 = 4 now add right neighbour digit(6)
   say 4 + 6 = 10 and also add carry 1 say 10 + 1 = 11, write down 1 and carry 1
Step IV: As there is no more pair 1 + 3 = 4 , write down 4 and also add carry 1 say 4 + 1 = 5
Step V: At the end combine last digit(1) with equation, write down 1
Step VI: Combine step V + IV + III + II + I = 151071




Share new methods & leave your comments below...

Raghu said on : 2015-09-04 07:40:47
9999*111
just do 111*10000 and then substract 111 from the answer
i.e., 1110000-111=1109889




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