There is a trick that is taught to children to help them remember their 9 times tables.
As illustrated below, the digits of the multiplication problem in question can be determined by:
- Splitting the digits
1 to 0(10)by whatever number you are multiplying 9 by.
- The resulting sums of the digits on either side of the split make up the the digits of the answer.
(Feel free to edit this description to make it more mathematically correct and/or intuitive)
How does this work? Why does it only work for the 9 times tables, and not any of the other times tables?
The answer is probably fairly intuitive, but I'd like to hear what math experts have to say about it.