Question

How would we multiply the numbers 13680347, 35702369 and 25692359 with 9 mentally ? What is the pattern that emerges.

Answer 1

To multiply a number with $9$ we use the following trick:- The number $x(10-1)$

$13680347\times 9=\left(13680347\right)\times (10-1)=136803470-13600347$

$=123123123$

$35702369\times 9=35702369\times (10-1)=357023690-35702369$

$=321321321$

$25692359\times 9=25692359(10-1)=256923590-25692359$

$=231231231$

These results repeat the digits $1,2$ & $3$ in a cyclic pattern.