The rule for 7 is one of the most powerful in the Trachtenberg System. It brilliantly combines several ideas we've seen before—doubling, adding half the neighbor, and adding 5 for odd digits—into one seamless process.
For each digit, working from right to left:
First, add a leading zero: 0342.
The final answer is 2,394.
Enter any number to see the step-by-step Trachtenberg process for multiplying by 7.
Multiplying by 7 is the same as multiplying by 5 and then adding the number doubled (7N = 5N + 2N). The Trachtenberg System combines the simple rule for 5 ('half the neighbor, +5 if odd') with the rule for 2 ('double the digit') into this single, efficient process.
Yes, exactly! It's a brilliant combination of the techniques used for multiplying by 2, 5, and 6. It takes 'doubling' from the rule for 2 and 'add half the neighbor, plus 5 if odd' from the rules for 5 and 6, merging them into one powerful rule.
The most common challenge is simply remembering all the parts of the calculation for each digit: double, add half the neighbor, add 5 if odd, and add the carry. However, once you practice it a few times, the rhythm becomes second nature.