
Arundeep
 
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 righthand 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 :
Step II: Each successive figure of 5892 is added to its righthand 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.
Step III: The first figure of 5892, 5 plus 1, becomes the lefthand figure of the answer:
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 :
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  