# Tutorial del sistema trachtenberg (en ingles)

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Multiplication

well. 3) Last step: once you arrive the last number, reduce it by 2. Add the carried tens and write down the result. Case 8: multiplication by 9 1) First step: subtract the first number of the multiplicand from 10. Writedown the result. 2) Middle steps: subtract each number from 9. Add the whole neighbor. Write down the result. Do this to the left-hand number as well. 3) Last step: say the last number, reduce it by 1. Add “carried tens”. Write down the result.

Two-fingers Method:
Let's say we want to opperate 3112 x 6. The steps to do this with the Units and Tens or the twofingers method is as follows: 1) Westart by placing the U from the UT (Units and Tens) just above the number 2. Multiply 6x2 and place the Units result, carry the tens: UT 3112 x 6 2

→ carry 1

2) Move the UT to the left. That is because the U of the UT is always placed over the position where the next figure of the answer is to appear, that is, where the 7 will be. In this example, the 7 is the pair-product of the units-digitof 06 (from 1 times 6) plus the tens-digit of 12 (from 2 times 6). In the first step, the 2 of 3112 was used as a U. In the second step it was used again, but this time as a T. This always happens. Each figure of the multiplicand is used twice, once under the U of UT and then under the T. UT 3112 x 6 72

→ 6 times 1 = 6 + 1 from the carry = 7

3) Move UT again to the next figure to the left.6 is the pair-product of the units-digit of 06 (1 times 6 is 06), plus the tens-digit of 06 (again 1 times 6 is 6). UT 3112 x 6 672 4) Move UT to the next figure to the left. The 8 is the pair-product of the units-digit of 18 (3 times 6), plus the tens-digit of 06 (1 times 6 is 06). UT 3112 x 6 8672

5) Add a 0 at the end of the multiplicand. Following the same logic, This is the pair-product...