Fun with Math

[fuzzygeek]

So I ran across this video Egyptian Maths, and its followup Part 2.

Basically, how to multiply and divide numbers using powers of 2. Since I didn't feel like doing anything useful this afternoon I learned the methodology, which is rather neat -- especially for doing long division by hand. Not that it really matters since mobile phones and computers have calculator apps, and in the event of a zombie apocalypse and phones and computers stop working we'll be too busy to be doing long division anyway.

In any case, I'm going to teach this to our younger child when he has to start doing long division because, well, it's cool. And precise. This got me to thinking: how else does one learn how to do long division, other than the "guess-and-check" method?

[Fivelives]

I learned via multiplication tables. From 1x1 all the way up to 12x12.

[Levantine]

I learned via multiplication tables. From 1x1 all the way up to 12x12.

This. I actually said 'the fuck' when you mentioned manual long division being guess and check. :/

[Fenrìr]

As much as I hate my stepdad, this is one thing he did do right for me. I was doing 4 digit multiplication and long division by 2nd grade.

He started out with simple stuff, such as 1x1, and once every two weeks, he tacked on another digit.

[fuzzygeek]

I learned via multiplication tables. From 1x1 all the way up to 12x12.

This. I actually said 'the fuck' when you mentioned manual long division being guess and check. :/

Hmm. We grew up memorizing the multiplication tables up to 12, and they still had us guess and check. Sure, the guess is an estimate based on the significant digits, but there's still some multiplication being done on the side. I asked both our college-bound son and my wife to do an arbitrary long division problem, and they both had some additional scratch math going on the side. I did the same, but I haven't done long division by hand in decades. When figuring factors I generally take three digits into account, which knowing up to 12x12 didn't help with.

Are you guys just able to infallibly pick factors when dealing with multi-digit numerators?

I've been poking around to see if there's another methodology we weren't taught, and I'm not really finding anything; mostly variations of



or http://www.mathpath.org/concepts/divisionalgo.htm . Does anyone have a resource?

[aureon]

using powers of 2 gets problematic quickly.
You're gonna need long division for polynoms anyway.
exact results on big divisions are useless, too. approximate and be happy with it - or get out a calculator.

[fuzzygeek]

You can get precision to whatever level you want by decimal shifting.

My question was whether people know a way to do long division without figuring approximations in their head. Using powers of 2 does not require any approximations, and can be calculated out using nothing by addition and subtraction. I guess the method the animated gif is stepping through is also technically just adding to find the factor, but it requires a loop.

Levantine's "the fuck" suggests that he knows some other method than approximations that knowing basic times tables helps with; I didn't find anything new when I looked around.

[aureon]

well, the method this guy is using is not "division" per se, it's converting to binary, and then doing operations in binary.
I mean, doing 16x25 is still a multiplication, even if you do it by the way of 25x2x2x2x2.