Multiplying by 11

When multiplying by 11, write down the rightmost digit first, then work your way to the left adding pairs of digits, carrying if necessary. When you reach the leftmost digit, write it down, again carrying if necessary.

Example: 4381*11
Solution: work from right to left. write the 1, add 8+1 and write 9, add 3+8 and write 1 (carrying the 1), add 4+3 and write 8 (remembering to add in the carried 1), and finally write 4.
Answer: 48191

Exercises:

This trick generalizes to multiplication by 111, 1111, etc. Start by writing down the rightmost digit, then add the two rightmost digits, then work your way up to n digits where n is the number of repeated 1's.

Example: 2143234*1111
Solution: write the 4, add 3+4 and write 7, add 2+3+4 and write 9, add 3+2+3+4 and write 2 (carrying the 1), add 4+3+2+3 and write 3 (remembering to add in the carried 1 and carrying a new 1), add 1+4+3+2 and write 1, add 2+1+4+3 and write 1, add 2+1+4 and write 8, add 2+1 and write 3, and finally write 2.
Answer: 2381132974

Exercises:

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