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The 11 Trick: A Shortcut to Multiplication
Multiplying by 11 can seem daunting, especially for larger numbers. But fear not! There's a handy trick that can make this task a breeze, even without a calculator. This method is perfect for sharpening your mental math skills and impressing your friends.
The 11 Trick Explained
The trick lies in breaking down the multiplication into simpler steps. Let's take an example: 23 x 11.
- Separate the digits: Write down the digits of the number you're multiplying by 11. In our example, we have 2 and 3.
- Add the digits: Add the digits together (2 + 3 = 5). If the sum is a single digit, write it down between the original digits.
- Carry over if needed: If the sum is a two-digit number, write the second digit between the original digits and carry over the first digit to the leftmost position.
Let's see how this works in our example:
23 x 11 = 2 (2+3) 3 = 253
Examples
Here are a few more examples to illustrate the 11 trick:
| Multiplication | Trick Breakdown | Result |
|---|---|---|
| 45 x 11 | 4 (4+5) 5 | 495 |
| 72 x 11 | 7 (7+2) 2 | 792 |
| 89 x 11 | 8 (8+9) 9 | 979 |
The 11 Trick with Carrying Over
Let's look at an example where we need to carry over:
67 x 11 = 6 (6+7) 7 = 6 (13) 7. Since 13 is a two-digit number, we carry over the 1 and write down the 3 between the digits. The final result is 737.
The 11 Trick with Larger Numbers
The 11 trick works for larger numbers as well. Just follow the same steps, remembering to carry over when necessary.
Example: 345 x 11
3 (3+4) (4+5) 5 = 3 (7) (9) 5 = 3795
Why Does This Trick Work?
This trick is essentially a visual representation of the distributive property of multiplication. When you multiply by 11, you're essentially adding the original number to itself ten times. The trick breaks down this addition into simpler steps, making it easier to visualize and calculate.
Practice Makes Perfect
With a little practice, you'll master the 11 trick and be able to impress your friends and teachers with your mental math skills. So, grab a pen and paper and start practicing!