Example: Multiplying small numbers by 9

(related to Part: Tricks for Mental Maths)

If you want to multiply \(n\times 9\), \(n\in\{1,2,\ldots,10\}\), you do not have to memorize all 10 results. The trick is to look at your hands, find the \(n\)th-finger, and mentally split your 10 fingers into two groups:

The following figures demonstrate this principle for \(n=1,2,3\) and \(4\), respectively:

recon1 recon2

recon3 recon4

As you can see, the blue-marked fingers are the ones of the result, the orange-marked fingers are the tenner part of the result. The results above are:

Why does it work?

This works, since \(n-1\) tenner and \(10-n\) ones means: \[(n-1)\times 10 + (10-n)=10n - 10 + 10 - n=n\times 9. \]

Thank you to the contributors under CC BY-SA 4.0!