The Instant 11x Multiplier!
Ever wished you could multiply any number by 11 in seconds, without a calculator? Unleash your inner math wizard!
Subject: mental-calculation • Classes: 6–12 • Difficulty: basic
The Trick
To multiply any number by 11: 1. Write the last digit of the original number as the last digit of your answer. 2. Starting from the right, add each pair of adjacent digits in the original number. Write down the sum. If the sum is $10$ or more, write only the units digit of the sum and carry over the tens digit to the next sum. 3. Write the first digit of the original number as the first digit of your answer, adding any final carry-over. Why it works: Multiplying by $11$ is equivalent to multiplying by $(10 + 1)$. So, $N \times 11 = N \times 10 + N \times 1$. Each digit of $N$ effectively gets shifted one place to the left (multiplied by 10) and then added to its original position. For a number like $abc$, $abc \times 11 = (100a + 10b + c) \times 10 + (100a + 10b + c) \times 1 = 1000a + 100b + 10c + 100a + 10b + c = 1000a + 100(a+b) + 10(b+c) + c$. This structure reveals the sum-of-adjacent-digits pattern with carries.
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