Why? The objective is understanding, not getting the rightsl answer, because you will never do a long multiplication in your life since a 3$ chip does it in a tenth of a microsecond
> The objective is understanding, not getting the rightsl answer
I would argue that if your "understanding" doesn't actually enable you to get the right answer, you don't really understand.
> you will never do a long multiplication in your life since a 3$ chip does it in a tenth of a microsecond
And how do you know the chip's answers are accurate?
Or what if you want to design the chip?
Or what if there's an EMP and all of the chips are fried?
More generally, if you're satisfied with just some conceptual-level "understanding" of anything that doesn't actually enable you to tell right answers from wrong, you are setting yourself up to be manipulated, misled, conned, etc. Critical thinking is a valuable life skill, and it requires you to be able to tell right from wrong answers.
I’m probably not going to multiply two 5 digit numbers together on paper much less do long division but I certainly do smaller scale mental arithmetic all the time.
