Friday, September 12, 2008

Multiply a number by 11

Multiplying a one digit number by 11, is easy. For example, 2 x 11 = 22. We just repeat the number back twice.

What if we have 1334 x 11? This strategy could help us to multiply any greater than 2 digits number by 11.



The best way to explain this strategy is by using examples.

Example 1: 243 x 11.

  1. 2 _ _ 3   (3 digits - put extra 2 blanks in the middle)

  2. 2 2+4 _ 3   (add the 1st 2 numbers)

  3. 2 6 4+3 3   (add the last 2 numbers)

  4. 2 6 7 3


Therefore, 243 x 11 = 2673

Example 2: 1435 x 11.

  1. 1 _ _ _ 5  (4 digits - put extra 3 blanks in the middle)

  2. 1 1+4 4+3 3+5 5 = 15785


Therefore, 1435 x 11 = 15785

Note:

If the addition of the 2 numbers would gives 2 digits number, add that number's left digit to the left digit of the original number.

Example 3: 99x 11.

Wrong: 99 x 11 = 9 9+9 9 = 9189

Note that 9 + 9 = 18 (a 2 digits number).

  1. 9 _ 9

  2. 9 9+9 9

  3. 9 18 9 ---> 9 + 1 8 9

  4. 1089


Example 4: 46 x 11.

46 x 11 = 4 4+6 6 = 4 10 6 = 4 +1 0 6 = 506

As a conclusion, to multiply a number by 11, add the digits of a 2 digits number, and place the sum between them. If the addition produce a more than 1 digit number, carry the tens column to the left.

10 comments :

  1. very interesting indeed. just curious to know, are you a mathematician? :wink:

    Ai-Lings last blog post..Into the wild: AdSense for feeds

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  2. uhhh.... kak jie yg tak sekolah tinggi ni faham
    tapi nk kena buka mata luas2 sikit..
    ambil masa :lol:

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  3. nak kena master dulu, pas tu boleh ajar anak2 @pp. Timetable 1-12 pun merangkak2 tu..

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  4. @k@kPOKPEK: OK slow2. Nanti akan dibawakan tips yang lain pula.

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  5. aku nampak bintang2 berputar....

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  6. 6*11= 66
    73*0101= 7373
    657*001001= 657657
    1237*00010001= 12371237
    And so on...
    kkraghuthaman

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  7. @kkraghuthaman: Interesting. But, what is the purpose of the extra leading zeroes?

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  8. Leading zeros help us to compute mentally.
    See an example

    65783 *999 999 999
    Make both factors as 'equal-digit' numbers.

    000065783*999999999. By adding leading zeros it is done!
    Factor(1)*Factor(2)
    How to compute mentally?
    000065782<-- Factor (1) is made one less than 000065783
    999934217<-- 'Vertically each sum of digits'is made 9.
    000065782999934217 is a merged answer
    65782999934217 is final answer (without leading zeros)!

    This manner of computing helps us to "accurately set" billions of trillions digits answers in your own mind!

    It is answer to your question!

    It is an ancient Indian manner to mental compute, which later came to know as "Vedic Mathematics"!

    Step-1 is to make equal-digits in both factors

    A related explanation is simpler in this case(9 based). So I chose this reply. your question related 11, 0101, 001001... too relates similar matrix-position relations.Just by looking at each number we can fix that 'row number' and 'column number' are equal, which means it is a diagonal position-number, which are very easy to relate with mental computing in'entire range of numbers'.

    "Orkut forum" 'NUMBER ZERO'discloses many related computing manners which has been iriginally revealed by shri Jagadguru Sankaracharya (1884-1960)in a book VEDIC MATHEMATICS!

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