The Trachtenberg rule for multiplying by 5 is one of the fastest in the system. It turns multiplication into simpler operations like halving a number.
For each digit of the answer, working from right to left:
Add a leading zero: 0436.
The final answer is 2,180.
Enter any number to see the step-by-step "Half the Neighbor" method.
It's based on the fact that multiplying by 5 is the same as multiplying by 10 and then dividing by 2 (e.g., N x 5 = N x 10 / 2). The Trachtenberg method cleverly turns this into a single pass. Taking 'half the neighbor' is part of the division by 2, and adding 5 for odd digits handles the remainders.
Correct! This is what makes the rule for 5 so fast and simple. Each digit of the answer is calculated independently without affecting the next digit. This reduces the mental load significantly compared to traditional multiplication.
A common shortcut is to note that if the last digit of the original number is even, the answer will end in 0, and if it's odd, the answer will end in 5. Our general rule handles this automatically: the 'neighbor' of the last digit is 0, so its half is 0. You then add 5 only if the last digit is odd, giving you a final digit of 0 or 5.