The rule for multiplying by 9 is: Subtract the digit from 10 (or 9) and add the neighbor.
Add a leading zero: 0423.
The final answer is 3,807.
Enter any number to see the step-by-step Trachtenberg process for multiplying by 9.
This is a core concept in Trachtenberg's subtraction methods. It's a way to handle 'borrowing' without thinking about it. Subtracting the units digit from 10 is the base operation. Subtracting all subsequent digits from 9 accounts for the 'borrow' that would have occurred from that position in traditional math.
Yes, in a way. Both are based on the mathematical properties of the number 9 in a base-10 system. The fact that 9 is '10 minus 1' is what allows for these kinds of subtraction-based shortcuts.
This is the final step of the algorithm. After adding a leading zero, you apply the 'subtract from 9, add neighbor' rule to it: (9 - 0) + neighbor = 9 + neighbor. This would incorrectly inflate the answer. The 'neighbor - 1' is a simplified and corrected final step that gives the proper leftmost digit of the product.
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This is a core concept in Trachtenberg's subtraction methods. It's a way to handle 'borrowing' without thinking about it. Subtracting the units digit from 10 is the base operation. Subtracting all subsequent digits from 9 accounts for the 'borrow' that would have occurred from that position in traditional math.
Yes, in a way. Both are based on the mathematical properties of the number 9 in a base-10 system. The fact that 9 is '10 minus 1' is what allows for these kinds of subtraction-based shortcuts.
This is the final step of the algorithm. After adding a leading zero, you apply the 'subtract from 9, add neighbor' rule to it: (9 - 0) + neighbor = 9 + neighbor. This would incorrectly inflate the answer. The 'neighbor - 1' is a simplified and corrected final step that gives the proper leftmost digit of the product.