Test: Multiplication - Class 1 MCQ

The "Amazing Facts of Nine" Trick Explained

The "Amazing Facts of Nine" trick is a fascinating mathematical phenomenon that showcases the unique properties of the number nine in multiplication. When you multiply any number by nine and then sum the digits of the result, you'll invariably come back to nine. This trick also reveals an interesting aspect about the tens digit of the answer, which we'll explore here.

- Understanding the Trick
- When you multiply a number by nine, the product has a special relationship with the original number.
- For example, if you multiply 2 by 9, you get 18. If you multiply 3 by 9, you get 27, and so on.

- The Tens Digit of the Answer
- Upon closely examining the results of multiplying numbers by 9, you'll notice a pattern in the tens digit of the answer.
- The tens digit increases by one as the original number is incremented by one.
- This pattern leads to a common misconception that the tens digit represents "one more than the original number" or "one less than the original number". However, the correct interpretation is more nuanced.

- Correct Interpretation
- The correct answer to the question of what the tens digit represents is: C) The original number.
- This is because the tens digit effectively mirrors the progression of the original number, with a slight adjustment. When multiplying a single-digit number by nine, the tens digit of the product is always one less than the original number, which might seem counterintuitive but follows from how the multiplication works.

- Illustration of the Concept
- Suppose you choose 5 as your original number and multiply it by 9, resulting in 45.
- Here, the tens digit is 4, which is one less than the original number, 5. However, the total sum of the digits (4 + 5) equals 9, demonstrating the unique relationship with nine.
- This pattern holds true for any single-digit number multiplied by 9, resulting in products that, when their digits are summed, equal to 9, and where the tens digit reflects the original number adjusted by one.

- Conclusion
- The "Amazing Facts of Nine" trick encapsulates the intriguing properties of the number nine within the realm of multiplication.
- It reveals a consistent pattern in the tens digit of the product, which, upon initial observation, illustrates the original number in a slightly modified form.
- To delve deeper into this and other mathematical wonders, exploring educational resources like those available on EduRev can provide further insight and enrichment.