Trachtenberg System

The Trachtenberg System is a mental math technique invented by Jakob Trachtenberg to simplify multiplication, especially for the number nine and other challenging calculations. It uses specific shortcuts and patterns—like replacing complex steps with simple addition or subtraction—to speed up calculations and reduce errors. For example, multiplying by nine can be done by multiplying the number by ten and then subtracting the original number. The system emphasizes mental calculations and pattern recognition, making it a practical tool for performing quick, accurate arithmetic without a calculator.