9 -A Magic Number

9 is the largest 1-digit number and it has many unique properties.

We have already studied Nine Point Circle and it’s benefits in finding the digit sum.

  • The digit sum does not change by adding  9 or subtracting 9 from it. 
  • The digit sum of any multiple of 9 is always 9.

Look at the table of 9:

9 × 1   =      9
9 × 2   =   1 8
9 × 3   =   2 7
9 × 4   =   3 6
9 × 5   =   4 5
9 × 6   =   5 4
9 × 7   =   6 3
9 × 8   =   7 2
9 × 9   =   8 1
9 × 10 =   9 0
9 × 11 =   9 9
9 × 12 = 10 8

On the right side of all products in every case, the digit sum is 9.
There is a unique observation in the above products. If you read the answers as two columns the left column goes up (1, 2, 3, . . .) and the right column goes down
(9, 8, 7, . . .).
This makes it easy to get the answers in the table of 9.

There is no need to remember the table of 9. We can use our fingers to multiply by nine.
Suppose the fingers of your hands are numbered as shown below:

table-9
For example, multiply 3 by 9, simply fold down the 3rd finger.
You will find 2 fingers to the left of the folded finger and 7 fingers to the right.
So 3 × 9 = 27.

Why don’t you practice with your fingers and have fun!