◀ ▲ ▶Branches / Fun / Tricks / Example: Multiplying small numbers by 9
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 \(n\)thfinger, and mentally split your 10 fingers into two groups:
 first group being on the left side of your \(n\)thfinger (can be none, if \(n=1\)),
 second group being on the right side of your \(n\)thfinger (can be none, if \(n=10\)).
The following figures demonstrate this principle for \(n=1,2,3\) and \(4\), respectively:
As you can see, the bluemarked fingers are the ones of the result, the orangemarked fingers are the tenner part of the result. The results above are:
 \(1\times 9=9\Rightarrow\) zero tenner and nine ones in the leftupper figure,
 \(2\times 9=18\Rightarrow\) one tenner and eight ones in the rightupper figure,
 \(3\times 9=27\Rightarrow\) two tenner and seven ones in the leftbottom figure,
 \(4\times 9=36\Rightarrow\) three tenner and six ones in the rightbottom figure.
 ...
 \(n\times 9\Rightarrow\) \(n1\) tenner and \(10n\) ones
Why does it work?
This works, since \(n1\) tenner and \(10n\) ones means:
\[(n1)\times 10 + (10n)=10n  10 + 10  n=n\times 9. \]
Thank you to the contributors under CC BYSA 4.0!
 Github:
