The Trachtenberg method can be used to easily multiply numbers by 11. Do this to multiply 11 times any number: ex. 11 x 7421 = 81631

-The ones digit of the number being multiplied by 11 is the ones digit of the answer. In the example, the ones digit of 7421 is 1, and this is the ones digit of the answer. _ _ _ _ 1

-Add the last two-digit number pair of the number being multiplied. This yields the tens digit of the answer (there may be a figure to carry). In the example, adding the last digit pair of 7421 gives the tens digit of the answer. 2 + 1 = _ _ _3_

-Add each successive digit pair in the number being multiplied by 11 (plus any carry figures, if any) to give the next successive number of the answer. In the example, adding the next digit pair of 7421 gives the hundreds digit of answer. 4 + 2 = _ _6_ _

-Continue in this manner adding successive digit pairs in the number being multiplied for successive digits of the answer (plus any carry figures, if any). In the example, adding the next digit pair of 7421 gives the thousands digit of the answer. 7 + 4 = _1_ _ _ (carry 1)

-*When there are no more digit pairs possible in the number being multiplied, simply use the left-most digit that is unpaired for the first digit of the answer. In the example, the digit left without a pair for 7421 is 7, and adding the carry figure this gives the first digit of the answer. 7 + (carry figure of 1) = 8_ _ _ _

*I like to consider that the left-most digit having no available pair is paired with 0. This helps me remember to not forget it- I’m not through until I’ve paired a number with 0. Try it with and without pairing the left-most digit with 0, and see which way you prefer.

See how easy these are: 421 x 11 = 4631 295 x 11 = 3245 230 x 11 = 2530

This is an especially easy way to multiply 11 by two digit numbers. The ones digit of the two digit number is the ones digit of the answer. Add the two digits of the two digit number for the tens digit of the answer. (If there is a carry figure, add it to the next step.) Lastly, the tens digit of the two digit number is the hundreds digit of the answer. The carry figure added, if there is one, is always 1 as 9+9 is the highest number pair that can be added.

11 x 23=253

11×17=187

11 x 96 = 1056

11 x 75 = 825

Because 1 is the only carry figure possible, any time you are given a 2-digit figure to multiply by 11, you should instantly recognize if there is a carry figure and automatically bump the first figure of the answer by one as you say the answer. Very quick and easy!