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Multiplication by 11

The basis is the following observation: To multiply 11 times a 2-digit number add its first and second digits and place the result between them. For instance, . If the sum of digits is 10 or greater carry over the one  .  

The proof is straightforward .

If the second factor has more digits, follow this rule from right to left and add the digit to that one which stands before it (and take the carries into account if necessary). For example

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