The Speedy 11x Multiplier

Ever wish you could multiply any two-digit number by 11 in seconds, without a calculator? Get ready to impress your friends!

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

The Trick

For any two-digit number $AB$, multiplying it by 11 is super easy! Think of $A$ as the first digit and $B$ as the second. \n\n**Trick:** Place the sum of the digits ($A+B$) between $A$ and $B$. If the sum $A+B$ is a two-digit number (e.g., $10, 11, ...$), write down the units digit of the sum in the middle, and carry over the tens digit to $A$. \n\n**Why it works:** When you multiply $AB \times 11$, it's the same as $AB \times (10+1) = (AB \times 10) + (AB \times 1)$. This expands to $(100A + 10B) + (10A + B) = 100A + 10(A+B) + B$. This structure directly shows how the digits $A$, $(A+B)$, and $B$ form the result, with carries for the sum.

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