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.

- 2 _ _ 3 (3 digits - put extra 2 blanks in the middle)
- 2 2+4 _ 3 (add the 1st 2 numbers)
- 2 6 4+3 3 (add the last 2 numbers)
- 2 6 7 3

Therefore, 243 x 11 = 2673

**Example 2:**1435 x 11.

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

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

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

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ReplyDelete6*11= 66

ReplyDelete73*0101= 7373

657*001001= 657657

1237*00010001= 12371237

And so on...

kkraghuthaman

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

ReplyDeleteLeading zeros help us to compute mentally.

ReplyDeleteSee 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!