Now that you've learned the individual rules, it's time for the main event: the Trachtenberg method for multiplying any two numbers. This technique is systematic and eliminates the need for intermediate rows of calculation.
We build the answer one digit at a time, from right to left. Each step involves multiplying pairs of digits and adding them up with any carry from the previous step.
The final answer is 1,312.
Enter any two numbers to see a step-by-step breakdown using the Trachtenberg pair-product method.
It's the core of Trachtenberg's general multiplication. Instead of multiplying the entire second number by each digit of the first, you build the answer one digit at a time. Each digit is the sum of cross-multiplied pairs of digits from the original numbers.
For many people, yes, once they get the hang of it. It reduces the amount of information you need to hold in your head at one time, replacing it with a consistent, rhythmic process. This can lead to greater speed and fewer errors.
Absolutely. The same principle of summing up pair-products applies whether you're multiplying 2-digit numbers or 5-digit numbers. The number of pairs you need to sum for each step simply increases.