The Speedy 11x Multiplier!

Ever wished you could multiply any two-digit number by 11 in mere seconds, without a calculator? Prepare to impress!

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

The Trick

The 'Sandwich' Rule: To multiply a two-digit number by 11, say $AB$, follow these steps:\n1. Place a space between the digits: $A\_B$.\n2. Add the two digits together: $A+B$.\n3. Place this sum in the middle space. If $A+B$ is a single digit (e.g., $3+4=7$), you're done!\n4. If $A+B$ is a two-digit number (e.g., $6+8=14$), write down the 'ones' digit of the sum in the middle, and 'carry over' the 'tens' digit to the first digit ($A$).\n**Why it works:** This trick stems from the distributive property: $AB \times 11 = (10A + B) \times 11 = 110A + 11B = 100A + 10(A+B) + B$. This structure effectively places the sum of digits in the middle, with $A$ and $B$ at the ends, naturally handling any carry-overs.

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