The Speedy 11x Multiplier!

Tired of long multiplication for 11? What if you could multiply ANY two-digit number by 11 in seconds, without a calculator?

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

The Trick

Here's the trick: Take any two-digit number, say $AB$. Sum its two digits: $A+B$. Now, place this sum in between the original two digits. If the sum $A+B$ is 10 or more, write down the units digit of the sum, and carry over the 1 to the first digit ($A$). \n\nWHY it works: Consider a number $10A + B$. Multiplying by 11 gives $11(10A + B) = 110A + 11B = 100A + 10A + 10B + B = 100A + 10(A+B) + B$. This clearly shows the units digit is $B$, the tens digit is $(A+B)$, and the hundreds digit is $A$. Any carry-over from $(A+B)$ adds to $A$.

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