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From the Fun Fact files, here is a Fun Fact at the Medium level:

Multiplication by 111

If you liked the Fun Fact Multiplication by 11, you'll enjoy seeing how to take that idea one step farther. Here's a quick way to multiply by 111.

To multiply a two-digit number by 111, add the two digits and if the sum is a single digit, write this digit TWO TIMES in between the original digits of the number. Some examples:


23x111= 2553
41x111= 4551

The same idea works if the sum of the two digits is not a single digit, but you should write down the last digit of the sum twice, but remember to carry if needed. So

57x111= 6327

because 5+7=12, but then you have to carry the one twice.

If the number you are multiplying by 111 is a three-digit number, say ABC, then the answer will have five digits (though it may be six if there is a carry involved):
the first digit is A,
the second digit is A+B,
the third digit is A+B+C,
the fourth digit is B+C,
the fifth digit is C.
Again, you must remember to carry if any of these sums is more than one digit. Thus 123x111=13653, 241x111=26751, and for an example where carrying is needed, 352x111=39072. (Because of the carries, it may be easier to do the sums and write the answer down from right to left.)

Presentation Suggestions:
Do the Multiplication by 11 Fun Fact first.

The Math Behind the Fact:
Multiply using the traditional (long) method for multiplication, and you will find that the above shortcut works because it is doing exactly the same sums that you would have to do using the traditional method for multiplication.

See some of the other Fun Facts on lightning arithmetic.

How to Cite this Page:
Su, Francis E., et al. "Multiplication by 111." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

References:
Subjects:    algebra
Level:    Medium
Fun Fact suggested by:   Francis Su
Suggestions? Use this form.
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