How to Multiply Any 3-or-More-Digit Number by 11
Multiply faster!
Jason Marshall, PhD
To multiply any 3-or-more-digit number by 11, add up the various pairs of neighboring numbers in the original number, and then stick the results between the 2 outside digits of the original number while removing the inside number(s). This is quite a mouthful, I know, so the easiest way to see how it works is with an example. Let’s try the problem 1,523 x 11. Start by adding up all the pairs of neighboring numbers: 1+5=6, 5+2=7, 2+3=5. Now put these three numbers in order between the outside pair of digits from 1,523. This gives 1-6-7-5-3 or 16,753…which is the answer to the problem!
If any of the pairs of numbers add up to a number that’s 10 or greater, you must remember to carry the tens to the next highest digit. For example, if the problem had instead been 1,529 x 11, we would have again started by adding the neighboring pairs of digits: 1+5=6, 5+2=7, 2+9=11. Now place these digits between the two original outside digits to get: 1-6-7-11-9. What do we do with the 11? Simply send the 1 from the tens column to the left and add it to the 7 to get the final answer: 1-6-8-1-9 = 16,819.
For more, see 2 Tips for Multiplying by 11
Eleven image courtesy of Shutterstock
About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.