The Speedy 11x Multiplier!

Ever wish you could multiply ANY two-digit number by 11 in seconds, without a calculator? Prepare to amaze yourself!

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

The Trick

To multiply a two-digit number, let's say $AB$ (where $A$ is the tens digit and $B$ is the units digit), by 11: 1. Write down the first digit ($A$) and the second digit ($B$) with a space in between: $A \_ B$. 2. Add the two digits together: $A+B$. 3. Place this sum in the space. If $A+B$ is a single digit, that's your answer: $A(A+B)B$. 4. If $A+B$ is a two-digit number (e.g., 13), write down its units digit in the space and CARRY OVER its tens digit to the first digit $A$. Why it works: Multiplying by 11 is like multiplying by $(10+1)$. So, $AB \times 11 = AB \times 10 + AB \times 1$. In terms of place values, $(10A+B) \times 11 = 110A + 11B = 100A + 10A + 10B + B = 100A + 10(A+B) + B$. This naturally forms the digits $A$, then $(A+B)$, then $B$, handling any carries.

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