The Trachtenberg rule for multiplying by 6 is a simple and elegant process known as the "Add Half the Neighbor" method. It builds the answer digit by digit, making large multiplications manageable.
For each digit, working from right to left:
First, add a leading zero: 0254.
The final answer is 1,524.
Enter any number to see the step-by-step "Add Half the Neighbor" method.
The 'neighbor' is always the digit immediately to the right of the digit you are currently working on. For the rightmost digit of the number, its neighbor is considered to be 0.
This is a clever trick to handle decimals without actually using them. It mathematically compensates for the .5 that is dropped when taking 'half of the neighbor' if the neighbor is odd, along with other factors, to keep the calculation correct.
Yes, this is the most common point of confusion. You always start with the digit you are working on, and then you add the other parts (half the neighbor, 5 for odd digits, and the carry) to it.
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The 'neighbor' is always the digit immediately to the right of the digit you are currently working on. For the rightmost digit of the number, its neighbor is considered to be 0.
This is a clever trick to handle decimals without actually using them. It mathematically compensates for the .5 that is dropped when taking 'half of the neighbor' if the neighbor is odd, along with other factors, to keep the calculation correct.
Yes, this is the most common point of confusion. You always start with the digit you are working on, and then you add the other parts (half the neighbor, 5 for odd digits, and the carry) to it.