Multiplying by 11: The Art of Quick Calculation
One clever yet highly effective method of quick calculation is multiplying by 11. This straightforward trick significantly speeds up operations, even with larger numbers.
To multiply a two-digit number by 11, there’s a simple trick. Just write down the digits of the number and insert the sum of those digits in between. For example, multiplying 23 by 11 gives us 253, since 2 and 3 add up to 5. We represent this as 2, (2 + 3) 5, 3, resulting in 253.
But what if the sum of the digits exceeds 10? In that case, you need to follow a specific process: place the units of the sum between the original digits, and add the tens to the first digit. For instance, when multiplying 67 by 11, the answer is 737 because 6 + 7 = 13. Here, we write the 7 in the center and add 1 to the 6, giving us a starting digit of 7. The final result is 737.
This method also works for larger numbers. You’ll write the first and last digits of the number and insert the sequential sums of the digits in between. For example, multiplying 345 by 11 follows the same principle: 3 (3 + 4) (4 + 5) 5. The sums in the parentheses are 7 and 9, so the final result is 3795.
If the sums of the digits exceed 9, the carry-over principle we discussed earlier applies. For example, 789 * 11 equals 8 (15) (17) 9. Here, 15 and 17 break down into 1 and 5, and 1 and 7, respectively. We then add the corresponding digits: 8 + 1 = 9, with 5 remaining, and the 1 carrying over to the next digit, and so on. The final answer is 8679.
To easily find products of larger numbers by 11, it’s best to have the original number in front of you. Keeping track of the order of operations is crucial to avoid mistakes. This method is just one of many included in the Trachtenberg speed calculation system. If you’re interested in learning more about this unique system, I highly recommend exploring specialized resources.
For those looking to master multiplication by 11, it’s beneficial to delve into both the theory and hands-on practice with real examples. If you prefer video materials, check out the instructional videos on the website успехвшколе.рф. Immerse yourself in a world of mathematical tricks and discover new horizons for effective learning!
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