Multiplication by 11

H.D. Motiramani

Multiplication of any number with 11 is very easy. Here is a simple technique. It is in two steps.

1)      First and last digit of the number to be multiplied by 11 remains same in answer.

2)      Middle number of the answer is obtained by adding the two adjacent numbers.

The process will become easier if we see some examples.

Example1:      35*11

In the answer, first digit will be 3, last digit will be 5 and middle digit will be 3+5 that is 8.  So the answer will be 3         8          5          = 385

Example 2:     96*11

9First digit                  (9+6) Sum of the two              6 the Last digit

Here, Middle digit is 9+6 that is 15. Therefore, 5 will be retained in the middle and 1 will get carried to its left to get added to 9. Therefore, the answer will become 10 5 6 that is 1056.

Example3:      254*11

            2first digit       (2+5)   (5+4)   4 Last digit

            2                      7          9          4          =          2794

Example 4:     598*11

            5 first digit      (5+9)   (9+8)   8          =          5          14        17        8

Here, middle digits are to be made single digit by carrying 1 from 17 to it’s left where 14 will become 15. Likewise 15 will have 1 carry to its left to get added in 5 that will become 6. So, next step will be

            5+1      5          7          8          =          6578

Example5:      6576*11

            6 first digit      (6+5)   (5+7)   (7+6)   6 last digit

            6          11        12        13        6          =          6+1      2          3          3          6

Going from right to left the rightmost digit is 6,  then 3 and 1 carry, then 12+1=13 that is 3 again and 1 carry, then 11+1=12 that is 2 and 1 carry, then 6+1 that is 7 So the answer is 72336

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