The Trachtenberg rule for 12 builds beautifully on the method for 11. It uses the same "neighbor" concept but adds a simple "doubling" step, making it another fast and efficient tool for your mental math toolbox.
To multiply any number by 12, work from right to left. For each digit, you **double it** and then **add its neighbor** to the right.
Add a leading zero: 048.
The final answer is 576.
Enter any number to see the step-by-step "Double and Add Neighbor" method.
Multiplying by 12 is the same as multiplying by 10 and adding the number doubled (12N = 10N + 2N). The Trachtenberg method is a streamlined way of doing this. Adding the 'neighbor' is part of the 'times 10' operation, and 'doubling the digit' handles the 'plus 2N' part.
It's very similar, which makes it easy to learn. The only difference is that for 11, you 'add the neighbor,' while for 12, you 'double the digit *then* add the neighbor.' It's just one extra, simple step.
The neighbor of the leading zero is the first digit of the original number. For example, if you are multiplying 48, you work with 048. The neighbor of the leading 0 is 4. The final step is (0 x 2) + 4 = 4, plus any carry.