Magic of 9

The “Magic of 9” is a fascinating mathematical trick related to the properties of the number 9. This trick allows you to quickly check the multiplication of any number by 9 and observe a pattern in the results.

Here’s how the magic of 9 works:

1. Choose any number. For example, let’s use 7.
2. Multiply that number by 9:
   • 7 \times 9 = 63 7×9=63
3. Now, look at the result (63) and add the digits together:
   • 6 + 3 = 9 6+3=9

You’ll notice that the sum of the digits is always 9! This phenomenon holds true for any number you choose and multiply by 9.

Let’s try another example with a different number, say 8:

1. Choose the number 8.
2. Multiply 8 by 9:
   • 8 \times 9 = 72 8×9=72
3. Add the digits of the result:
   • 7 + 2 = 97+2=9

Again, the sum of the digits is 9.

This magic trick works because of the way our number system is structured. When you multiply a single-digit number by 9, the sum of the digits in the result will always be 9. This property holds true for higher digits as well.

The pattern becomes even more interesting when you consider two-digit or three-digit numbers:

1. Choose a two-digit number, such as 45.
2. Multiply 45 by 9:
   • 45 \times 9 = 405 45×9=405
3. Add the digits of the result:
   • 4 + 0 + 5 = 94+0+5=9

The magic of 9 persists!

This trick can be a fun and engaging way to introduce patterns in multiplication to students. It’s a simple yet intriguing concept that showcases the beauty of mathematical properties.