The Trachtenberg method can be used to multiply 12 times any number, similar to the process for multiplying 11 times any number. The answer can be written quickly and directly for large numbers. Doing this mentally can be done for smaller numbers with practice. This is the process: Starting with the ones digit, double each digit in turn, and add its right hand neighbor. (Remember to add carry figures when necessary. Here we take the example 12 x 123 = 1476.

In this example, double the 3 (the ones digit). Having no right hand neighbor to add, this is the ones digit of the answer. (2 x 3) + 0 = ___6

Double the next digit (the tens digit). To this add its right hand neighbor for the tens digit of the answer. (2 x 2) + 3 = __7_

Double the next digit (the hundreds digit). To this add its right hand neighbor for the hundreds digit of the answer. (2 x 1) + 2 = _4__

Having no next digit to double (the thousands digit), the right hand neighbor is the thousands digit of the answer. (2 x 0) + 1 = 1___

After seeing this, you probably are figuring that multiplying by 13 should be a similar process. You are right. Triple each number in turn and add its right hand neighbor.

This process may be used for multiplying by any number having 1 as the tens digit, such as 14, 15, 16, …19. The value is not only added quickness, but accuracy. Decreasing the number of steps in a math operation helps lower the possibility of simple math errors. See the problem, write the answer directly.

Try these: 12 x 13 = 156 12 x 461 = 5532 13 x 15 = 195 14 x 44 = 616 16 x 333 = 5328

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