Other people don't have the mental computing power to easily deal with larger numbers and would rather work with smaller ones. Such shortcuts are not necessary anymore for practicing engineers such as myself and for other people who have a knack for numbers (presumably you), but for the benefit of everyone, these small tricks may help them mentally compute for stuff through easy-to-follow steps. Maybe you can share some of your math tricks as well so that you can actually contribute to this thread

Point is, some "short-cuts" are not really shortcuts. In the x11 example, it's actually longer. You have to test the digits if they fall within a certain criterion. If yes, then do one thing. If not, do another thing (which consists of several iterations).

A "simpler shortcut" for x11 is multiply by 10 and add the same number. Thus 45 x 11 = 450+45 = 495. No if-then-else statement.

And just for argument's sake, people who have a "knack for numbers" may not be necessarily good in mathematics. They may be good in arithmetic, but not in the other branches of mathematics, which require logic and analysis.

Which brings me to your "contributing to this thread" statement. I've been "contributing to this thread" by verifying and analyzing the logic of the "math tricks". That is the essence of mathematics, after all.