The Speedy 11x Multiplier!

Ever wished you could multiply any two-digit number by 11 in seconds, without a calculator? Prepare to amaze your friends and teachers!

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

The Trick

To multiply a two-digit number by 11, follow these steps: \n1. Take the two-digit number, say $AB$. \n2. Separate the digits $A$ and $B$. \n3. Add the two digits together: $A+B$. \n4. Place the sum $A+B$ in between $A$ and $B$. The result is $A(A+B)B$. \n5. If the sum $A+B$ is 10 or greater, write down the units digit of the sum in the middle, and carry over the tens digit to the first digit $A$. \n\n**Why it works:** A two-digit number can be written as $10A + B$. Multiplying by 11 gives $(10A + B) \times 11 = 110A + 11B = 100A + 10A + 10B + B = 100A + 10(A+B) + B$. This structure clearly shows the hundreds digit is $A$, the tens digit is $(A+B)$, and the units digit is $B$. Carry-overs handle sums greater than 9.

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