Multiplying by nine with your fingers

There's a groovy trick or multiplying a single digit number by 9. Suppose you want to compute 9n, where n is one of 1,2,3,...,9. Counting from the left, hover your mouse over the nth stick below. The digit in the 10s place is the number of sticks to the left and the digit in the 1s place is the number of sticks to the right.

10 × (n-1) + (10-n) =

Figuring out why the trick works is even more fun than using trick in the first place! Ultimately, it boils down to the fact that

9×n = 10 × (n-1) + (10-n).

When we write 9×n this way, we see clearly that n-1 is the digit in the 10s place and 10-n is the digit in the ones place. When we block out the nth stick, though, n-1 is also the number of sticks to the left and 10-n is the number of sticks to the right.