The Trachtenberg Speed System: Multiply Any Number Without Memorizing Tables

The Trachtenberg Speed System

The Trachtenberg System is a method of rapid mental calculation developed by the Russian engineer Jakow Trachtenberg during World War II. While imprisoned in a concentration camp, Trachtenberg kept his mind sharp by developing new ways to perform arithmetic.

How It Works

Unlike traditional multiplication that relies on memorized times tables, the Trachtenberg System uses a set of rules based on the digit you're multiplying by. Each multiplier (2 through 12) has its own simple procedure.

Multiplying by 11

The simplest Trachtenberg rule — and a great starting point:

Rule: Write the last digit. For each subsequent digit, add it to its right neighbor. Write the first digit.

Example: 3,241 × 11

• Write last digit: 1
• 4 + 1 = 5
• 2 + 4 = 6
• 3 + 2 = 5
• Write first digit: 3
• Answer: 35,651 ✓

Multiplying by 12

Rule: Double each digit and add its right neighbor.

Example: 312 × 12

• (2 × 2) + 0 = 4
• (1 × 2) + 2 = 4
• (3 × 2) + 1 = 7
• 3 → 3
• Answer: 3,744 ✓

Why It's Powerful

• No memorization required — Just follow the rules for each multiplier
• Systematic — Works the same way every time, reducing errors
• Scalable — Works on numbers of any length
• Builds confidence — Students who struggle with memorization excel with this system

Practice on NumDojo

Our Trachtenberg lessons start with multiplying by 11 and progressively teach each multiplier. Each lesson includes step-by-step visual breakdowns and timed practice.