Multiplication by 11

Multiplication by 11 is easy! To multiply by a 2-digit number add the two digits and place the sum in between!

25 x 11 = 275 
31 x 11 = 341 
57 x 11 = 627 <– you need to carry the 1!

What about a 3-digit number? Can you figure out what’s going on here?

253 x 11 = 2783 
117 x 11 = 1287 
532 x 11 = 5852 
267 x 11 = 2937

Presentation Suggestions:
Do examples! What you notice is that multiplication by 11 can be done quickly with numbers of any length by starting with the first and last digits (they remain the same, unless there is a carry) and then inserting the sums of adjacent pairs of digits sequentially in between. For example, 253 x 11 begins with a 2 (like 253 does), then the next digit is 2+5=7, the next digit is 5+3=8, and the last digit is 3 (like 253 has). So the product is 2783. Remember to carry if necessary. So 267 x 11 starts with a 2 (like 267 does), the next digit is 2+6=8, the next digit is 6+7=13 (oops! carry the 1 back to the previous digit, leaving a 3 in this place), then the last digit is 7 (just like 267 has). Thus the product is 2937.

The Math Behind the Fact:
Long multiplication reveals why the trick works… you end up adding adjacent digits. Based on this, can you figure out a snappy rule for Multiplication by 111? The reference has more tricks for doing lightning arithmetic.

How to Cite this Page: 
Su, Francis E., et al. “Multiplication by 11.” Math Fun Facts. <https://www.math.hmc.edu/funfacts>.

References:
A. Benjamin and M. Shermer, Secrets of Mental Math, Three Rivers Press, 2006.

Fun Fact suggested by:
Francis Su

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