The rule for multiplying by 4 is: Subtract the digit from 10 (or 9) and add half the neighbor.
Add a leading zero: 0324.
The final answer is 1,296.
Enter any number to see the step-by-step Trachtenberg process for multiplying by 4.
This is a clever way to handle the 'borrowing' that happens in traditional subtraction. Subtracting the first digit from 10 accounts for the units place, while subtracting subsequent digits from 9 accounts for the fact that we have already 'borrowed' from them.
This rule, like in the rule for 3, is a correction factor. It compensates for the decimal part that is dropped when taking 'half of the neighbor,' ensuring the calculation remains accurate without needing to work with fractions.
The final step of taking half the neighbor and subtracting 1 is the last part of the subtraction algorithm. It finalizes the calculation by accounting for the last 'borrow' from the leftmost position of the number.
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This is a clever way to handle the 'borrowing' that happens in traditional subtraction. Subtracting the first digit from 10 accounts for the units place, while subtracting subsequent digits from 9 accounts for the fact that we have already 'borrowed' from them.
This rule, like in the rule for 3, is a correction factor. It compensates for the decimal part that is dropped when taking 'half of the neighbor,' ensuring the calculation remains accurate without needing to work with fractions.
The final step of taking half the neighbor and subtracting 1 is the last part of the subtraction algorithm. It finalizes the calculation by accounting for the last 'borrow' from the leftmost position of the number.