Magic of Adding Numbers with Anti-Nines

Step 1: Have someone pick a large number with any number of digits.

Step 2: Vertically, have them write down a second and third number with the same number of digits.

Step 3: Now, here is the magic -- you write down two more numbers (so a 4th and 5th number) of the same number of digits and you should act as if your numbers are random; but they are not random. Your two numbers are the anti-nines of the first two numbers (if their first number was 1234, then your 4th number will be 8765, because 8 is the anti-nine of 1, 7 is the anti-nine of 2, 6 is the anti-nine of 3, and 5 is the anti-nine of 4).

anti-nines: 0 & 9; 1 & 8; 2 & 7; 3 & 6; and 4 & 5

Step 4: On another piece of paper, you will write down the answer to this addition problem within a couple of seconds and do not let them see your answer. Now, they start adding the numbers and show you their answer. If they did their addition correctly, it will match your answer.

HOW YOU GET YOUR ANSWER: since you have done nothing with the third number (number in the middle), this is our focus. Subtract 2 from this third number and tac on a 2 in front of the number. For example, if the third number is 1,234, first subtract 2 to get 1,232 and then tac a 2 on the front of the number to get 21,232. Pretty cool!!

You can do this on your own as well to practice your addition and anti-nine skills, but it is more fun doing this with someone else as if you are the mathemagician.

The attached pdf has a color graphic example that makes it clear which number is the anti-nine of the other as well as how to manipulate the middle number to get your answer. There are several pages of practice with five-digit numbers and 20-digit numbers. When you write down your prediction, it is actually like having a calculator since the actual sum will be the same. If you use the 20-digit number pages, there are twenty separate addition problems of five digits, most of which will be in the twenties. If any of your answers do not match the prediction, you either made a mistake in addition or in writing down the anti-nines.