The 11x Magic Trick!

Ever wished you could multiply any two-digit number by 11 faster than a calculator? You can! Discover this super speedy mental math hack!

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 $A$. \n2. Write down the second digit $B$. \n3. In the middle, write the sum of the digits, $A+B$. \nSo, $AB \times 11$ becomes $A(A+B)B$. \n**Wait!** If $A+B$ is $\geq 10$, write its unit digit in the middle, and add the tens digit (carry-over) to $A$. \n**Why it works:** A two-digit number $AB$ is $10A+B$. So, $(10A+B) \times 11 = (10A+B) \times (10+1) = 10(10A+B) + (10A+B) = 100A+10B+10A+B = 100A+10(A+B)+B$. This clearly shows $A$ in the hundreds, $A+B$ in the tens, and $B$ in the units place, explaining the trick and carry-overs!

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