The Speedy 11x Multiplier

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

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

The Trick

To multiply any two-digit number $AB$ by $11$: \n1. Write down the first digit ($A$) as the first digit of your answer.\n2. Write down the second digit ($B$) as the last digit of your answer.\n3. Add the two digits $A+B$. Place this sum between $A$ and $B$. \nIf $A+B$ is a two-digit sum (e.g., $10, 11, ...$), carry over the tens digit of the sum to the first digit ($A$).\n\n**Why it works:** Let the number be $10A + B$. Multiplying by $11$ is $(10A+B) \times (10+1) = (10A+B) \times 10 + (10A+B) \times 1 = 100A + 10B + 10A + B = 100A + 10(A+B) + B$. This structure is $A$ (hundreds) $A+B$ (tens) $B$ (units).

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