Start with a real example.
Watch the digits change in a calculation you can check for yourself.
A guide to mental calculation
The Trachtenberg method, made clear.
A system of small, repeatable rules for working with numbers. See how it works, try a calculation, and learn at your own pace.
Understand the ruleSee it in action
×11 workshopLearn the rule · Practice game
Multiply by 11, in your head.
Try any two-digit number. The answer appears one small step at a time.
Enter a two-digit number to see the rule.
4Keep the first digit
74 + 3
3Keep the last digit
4 + 3 = 7. Put that sum between the two original digits.
Or try
The idea
Big calculations. Smaller moves.
The Trachtenberg method is a system of arithmetic rules developed by Jakow Trachtenberg. Instead of treating a long calculation as one big problem, you work through its digits using a rule for the operation at hand.
The ×11 example above is a simple place to start: keep the outside digits, add neighbouring digits for the middle, and carry when the sum is ten or more. Once that makes sense, other multiplication rules become easier to explore.
Understand each move.
Use a short instruction for each step, including what to do when you need to carry.
Practise until it clicks.
Try different numbers and let the small steps become second nature.
Keep going
Take the next rule with you.
Our companion app turns multiplication rules into short guided lessons, hints, and practice. Start with ×11 for free, then build from there.
Explore the iPhone & iPad appSee what the current app offers →
Build confidence with a clear rule, one calculation at a time.
