The Magic 11x Multiplier!

Want to impress your friends by multiplying any 2-digit number by 11 in seconds, all in your head?

Subject: mental-calculation • Classes: 6–12 • Difficulty: basic (6-8)

The Trick

Here's how to multiply any 2-digit number by 11 super fast: 1. Take your 2-digit number, say $AB$ (where $A$ is the tens digit and $B$ is the units digit). 2. Add the two digits together: $A + B$. 3. If the sum $A+B$ is a single digit, simply place it between $A$ and $B$. Your answer is $A(A+B)B$. 4. If the sum $A+B$ is a two-digit number (e.g., $10, 11, ...$), place the units digit of the sum between $A$ and $B$. Then, 'carry over' the tens digit of the sum and add it to the first digit $A$. **Why it works**: This trick is based on place value. A 2-digit number $AB$ can be written as $10A + B$. When you multiply it by 11, you get $11(10A + B) = 110A + 11B = 100A + 10A + 10B + B = 100A + 10(A+B) + B$. This shows that the digits are indeed $A$, then $(A+B)$, then $B$. If $(A+B)$ is $\ge 10$, the 'carry over' handles the addition to $100A$.

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