Sunday, November 1, 2009

9 is a Magic Number


When it came to learning my multiplication tables back in grade school, rote memorization was the method most often employed. Multiples of 9, however, are quite magical and to this day, I still use a version of the following algorithm to determine and verify multiples of 9.

Solve for y
Where n = integers 1 through 10,
x = 9 + (1 - n)
y = (n - 1)10 + x

In other words, for every product of the nine multiplication table, the sum of the digits in the product adds up to 9. For example, if you are trying to find the multiple of 9 x 6, take 6 and subtract 1 so it becomes 5. This will be the first number in your answer, so place it in the tens place.

5_

Now ask yourself what number added to 5 equals 9? 4 of course! Put this number in the ones place and you have your answer.

54

9 x 6 = 54

Try it with other integers! I only ever use this method for simple multiplication, but 9 really is a magic number so you should read up on it. And I know what you're thinking: wouldn't it just be easier to memorize the answers? Well hey, do I look like someone who likes to do things the easy way?

Any other readers enjoy using the 9 trick or some variant?

1 comments:

Daniel said...

Well ask any 7 year old and they'll tell you to hold your hands up and place down whatever digit you want to multiply by 9. The number of fingers to the left is the first digit and the number of digits to the right is your second digit. It's the exact same thing you're doing here, only you've expressed it with variables.

In closing, please don't substitute teach math to elementary school children.