Multiplication tables are the most lucid way to explain long division. In order to get from 5 to 40, you need to keep adding 5s until you can't. So to divide 40 by 5, keep subtracting 5s until you can't any longer.

Exactly, I find it far easier to explain LD as just fast subtraction combined with multiplication to my kid than common core methods which I had to stare at for a while. The most critical method here is how to break up components of a number into addition "parts" as well as decimal positions.

You're never going to find 100 people who can perform long division.

Sure you can! Just look at a typical fifth- or sixth-grade classroom. Most of them can perform long division, briefly, before the test. They may even remember it for several days after the test.

What none of them can tell you is why they've been taught long division, when short division is faster.

And it's because you need long division to do division in algebra

What is short division? I only remember being taught long division and having a calculator. Is there another method?

Fascinating. I didn't know, either.

After looking at the English Wikipedia I found that

a) what I learned in school is long division

b) the notation with the dividend and the divisor separated by a parenthesis and the result on top of a horizontal bar is totally alien to me

c) I've never seen short division before

d) the German Wikipedia doesn't even have an article about short division

Thanks! What you said, except my own point d) that Swedish Wikipedia tells that apparently short division is also used in Swedish elementary schools now.

I went to elementary school in the 90s and we were taught both long and short.

Interesting, I'll start using that short version now. I always hated the long version because it took up a ton of vertical space and I didn't need the extra verbosity. In fact, I'll probably teach me kid that method when he gets to division in school.

Holy shit, I didn’t realize the shorter way of writing long division that I invented in early elementary school because I got sick of taking up so much space and introducing copying error potential had a name!

From my quick google it's arriving at the answer, without the step by step process of calculating each division.

Edit: although if someone else can explain it better I'd really like to know.

From what I have searched,(quickly mind you), it seems to be a mind set.

Probably is that New Math that Tom Lehrer warned us about.

https://www.youtube.com/watch?v=UIKGV2cTgqA

I've looked at both Wikipedia pages and still can't really understand the difference. Is it anything more than notational? Either way, you're calculating divisors for each component of the problem, and it only seems to matter whether you calculate it on paper or in your head.

the way I learned it, it's just a notational difference. either way, you are dividing the divisor into each place of the dividend (starting with the most significant digit) and carrying over the divisor to the next place. short division is just a more implicit way of doing this that saves space. the shorthand version doesn't really work for divisors with more than one digit though.

What doesn't work with short division and multi-digit divisors?

it's not that the algorithm "breaks"; it's just that it stops being a convenient notation for humans.

the "short" notation relies on the ability to squeeze the remainder in between the digits of the dividend. if you have a divisor greater than ten, it's possible to have a remainder with more than one digit. two or more remainder digits is a lot harder to write legibly between the digits of the dividend. you also end up subtracting larger numbers in your head, which is error prone. finally, most people only memorize the multiplication table up to 12x12 or so. once they can't simply do a lookup into their memorized table, they switch to more of a "guess and check" approach, where they will inevitably have to cross out or erase their previous work.

in the end, it introduces a lot of unnecessary opportunities to make mistakes and hides stuff that people can't do reliably in their heads.

It’s notation only. I “invented” it as a kid to save space on division problems and reduce the chance of copying errors. It’s the same method as long division (and TIL it already existed!)

It definitely looks nice, and I'll probably start using it. If something is too inconvenient to use short division for (e.g. large divisors), I'll probably just use a calculator.

Yeah, when we were taught short and long division I had the same question and it was not until quite late in high school we got the explanation.

I went to school in Sweden where we do teach all this things, but in a strange order.

Went to school in Sweden too in the 90-00s. I wasn't taught long division until I had to divide polynomials in my last year of high school, and that course was an elective.

Apart from the long division method pointing out that division is just repeated subtraction, that's the only reason to use it.

I think I've only briefly seen short division once. It was long division until fractions here.

Because knowing both helps realise how it works. Yes it's faster to use short division, but long helps you se the step by step process, giving a better understanding.

OK millennial