Core Multiplication Rules
The Rule for 11: Add the Neighbor
Learn the simplest Trachtenberg rule for multiplying any number by 11 with effortless addition.
The Rule for 12: Double and Add Neighbor
Master multiplying by 12 by simply doubling each digit and adding its neighbor.
The Rule for 6: Add Half the Neighbor
A unique method for multiplying by 6 that uses a simple "add half the neighbor" trick.
The Rule for 7: Double and Add Half
A powerful rule for multiplying by 7 by doubling each digit and adding half of its neighbor.
The Rule for 5: Half the Neighbor
An incredibly fast method for multiplying by 5 that relies on just finding half of the next digit.
The Rule for 9: Subtract from 10
A clever subtraction-based method for multiplying by 9 without using multiplication tables.
The Rule for 8: Subtract from 10 and Double
A two-step rule for multiplying by 8 that builds on the rule for 9.
The Rule for 4: Subtract from 10
A simple subtraction rule for multiplying by 4, perfect for mental calculation.
The Rule for 3: A Unique Pattern
Learn the final digit-specific rule for multiplying by 3, which involves doubling and subtracting from 10.
General Methods
General Multiplication (Two-Finger Method)
Learn the core Trachtenberg method for multiplying any two numbers of any length.
Speed Addition: No-Carry Adding
A fast and accurate method for adding long columns of numbers without carrying.
Subtraction: A Different Approach
Explore the Trachtenberg method for subtraction, which simplifies the process.
Division: The Simple Method
Learn the Trachtenberg technique for long division, which aims to reduce mental strain.
Squaring Numbers
A specific application of the Trachtenberg multiplication rules for finding the square of any number.