Number Magic

Here is the example about mathemagic tricks taken from Mathemagic Website

Squaring a 2-digit number ending in 1

* Take a 2-digit number ending in 1.
* Subtract 1 from the number.
* Square the difference.
* Add the difference twice to its square.
* Add 1.

Example:

1. If the number is 61, subtract 1: 61 - 1 = 60.
2. 60 × 60 = 3600 (square the difference).
3. 3600 + 60 + 60 = 3720 (add the difference twice to its square).
4. 3720 + 1 = 3721 (add 1).
5. So 61 × 61 = 3721.

Pretty Cool Huh? Mental math shortcuts can benefit students in elementary, middle, high school and beyond!

Here's another:

1. For 81 × 81, subtract 1: 81 - 1 = 80. 2. 80 × 80 = 6400 (square the difference). 3. 6400 + 80 + 80 = 6560 (add the difference twice to its square). 4. 6560 + 1 = 6561 (add 1) 5. So 81 × 81 = 6561.

Multiplying by 111