Multiplication and Division with a Comptometer

How to do fast multiplication and division on a comptometer.
This is a bonus episode of my video series about calculating devices. The Comptometer model F was episode 11 of that series.
Arithmetic tests from "The Comptometer Course in Business Arithmetic" here: cstaecker.fairfield.edu/~cstae...
My video about the model F: • Comptometer Model F Ad...
End song inspired by "Hotter than a Molotov" by The Coup.
Chris Staecker webarea: cstaecker.fairfield.edu/~cstae...

[@Lendorien]

Thank you so much for posting this. I have a model similar to yours. Your explanation of how to do the more complicated arithmetic was very useful. I'd figured out how to do subtraction and 1 digit multiplication, but I hadn't quite figured out how to go beyond that. Your explanation was very helpful.

[@alanesq1]

I just got myself a comptometer and had to re-watch this video about 6 times before I got the right result. I then tried approximating Pi with 355 / 113, this took me about 30 mins Could be a while before I qualify - lol

[@BokBarber]

For division, I find it easier to just subtract the whole number (with leading zero if necessary.) It works well enough, plus it's more intuitive to see the repeated subtraction in action. You do lose a position of precision, which might be a limitation on 8 column machines.

[@erlgro]

Just love this! :D

[@xRussianbishop]

Wife: Why are you watching a video about a …. what the fuck is that. Me : Its a Comptometer its a mechanical Calculator. Ex Wife: I want a divorce

[@ChrisStaecker]

i got a guest room

[@xRussianbishop]

@@ChrisStaecker If you keep making videos about past devices I am going to need it. I am about 30 videos in on a binge of your channel

[@someonespadre]

I found a Monroe K model in a thrift store. Carry the 28lb behemoth over to my wife. Why do you want that? Why do you want 5000 books? Now if I’m in my office after hours she says “were you playing with your machine?” Meanwhile sister says she doesn’t get the fascination. I mean free range organic gluten free numbers, what’s not to like? I figured out the Monroe method to extract a square root, I’m up there doing square roots. I can do them in a millisecond on my calculator but this is way more fun.

[@haramanggapuja]

Does the remainder hint number for the next subtraction also work on a pinwheel machine? That'd make it easier to know you were going to ring the bell, seems to me. Nice video. Hope I can remember what I just learned ;-)

[@robertlozyniak3661]

I was thinking about it, and I think I figured out why this method of division works. Suppose you want to divide 90 by 15. Let x=90/15. Multiply both sides by x to get 15x=90. Then, add 85x to both sides. This gets you 100x=90+85x. The Comptometer method of division is nothing more than brute-force checking x=1, x=2, x=3, ..., until a solution is found.

[@lauramartin7883]

What?? I'm sorry, but I'm not following you here. "Let x=90/15." (ok.) Then, "Multiply both sides by x...", (So written out, wouldn't that be: X x X = 90X/15X ? But, why would you multiply both sides by X in the first place? ). Then you completely lost me with you next instruction: "Then, add 85x to both sides." Again, why do this sum? The rest, from "This gets you 100x=90+85x...." well, if I don't understand the first part of the math you're doing, then needless to say, I'm completely lost with the rest of it. Could you please explain? I'd appreciate it because I'd like to understand this.

[@robertlozyniak3661]

@@lauramartin7883 You're right. I made a mistake. Instead of "Multiply both sides by x ...", I meant "Multiply both sides by 15 ..." The reason for adding 85x to both sides is to get 100x by itself on one side. The reason you want 100x by itself on one side is that multiplication by 100 is easy to do in your head. On the Comptometer, it is easy to calculate 90+(85×1), 90+(85×2), 90+(85×3), etc., very quickly. You just start with the number 90 and then keep adding 85. At the same time, you are looking at the Comptometer's display, checking to see if the result matches 100×1, 100×2, 100×3, etc. When you get to 90+(85×6), you will see that it equals 100×6, and thus you will have found that x=6 in the equation 100x=90+85x, and therefore x also equals 6 in the equation x=90/15.

[@amoledzeppelin]

I'm wondering, if you find an *approximation* of the division result on a slide rule first, can the process on such machine be made easier by pre-entering that approximation somehow?

[@axdrome]

I'm trying to get my head around using the leftmost digit as well (and whether that matters). for 15632/85 (=183.90588..), you could also repeat add 915 (9-c of 85, plus one) to use that leftmost digit: 183.9058_03 (if going for as much digits as possible) or 183.905_075 (when 915 cannot be completely added - your intermediate result was 183.9057_0) (compare to your final result: 183.9058_3) I use the symbol '_' to separate computed digits from the remainder, which should not be part of the solution.

[@ChrisStaecker]

Not sure I follow, but I think you're saying I could've gotten one more digit in my answer by starting off one more position to the left. I agree- Typing in that leftmost 1 at the beginning is awkward since there's no keys in that spot, but not so bad since it's just a 1. Then I would've done the same process and gotten an extra digit out of the answer.

[@axdrome]

in the method in the video, '15' (9c+1 of 85) gets added across the columns (in this case starting from the second left column), and the result appears in the second digit onwards (the first digit should always remain zero). but the other way is to add '915' (9c+1 of 085) across the columns (starting from the /first/ column), and the result appears as from the /first/ digit (which has no entry column). but I need some math insight to find out if there is a real difference: because the extra digit in "915", might cause a problem in the extreme right position instead, so I suspect the actual precision could be the same.

[@robertlozyniak3661]

Sometimes the remainder *is* part of the solution: for example, in converting a large number of minutes into hours and minutes, or in conversting a large number of inches into feet and inches.

[@CaribouDataScience]

How would you like to have to use the 8 hours a day😮

[@shedactivist]

I just got my Comptometer 993e working and was wondering how division worked. And now I know, but for how long. It is weird

[@mwichary]

You meant a PDF one could download (multiplication tests), but I don’t see a link - is that still available anywhere?

[@ChrisStaecker]

Sorry- I forgot to post the link. I just added it to the video description. Enjoy!

[@someonespadre]

I’m not a mathematician and I want to know why it works.

[@seanewing204]

Robert Lozyniac above you explained it.

[@aaronrodgers2092]

Super upset I can't find that song anywhere... You know what comes up when I search for hotter then a molotov by the coup..... YOUR VIDEOS.

[@ChrisStaecker]

Ha! Maybe this'll finally make them release a proper recording.

[@keyboard_g]

@5:16 Ahh, I see now.

[@jphili]

It looks waaay easier, faster, and less likely to make a mistake to just work out the problem with a pencil and paper.

[@ChrisStaecker]

For me it's much easier on paper. But for somebody trained and with a lot of practice this thing is a lot faster and more reliable.

[@robertlozyniak3661]

@@ChrisStaecker I can't help but wonder why not just use a Chinese or Japanese abacus instead. After all, if you are going to send your people to learn to use a Comptometer, why not instead send them to learn to use an abacus, and not have to shell out big bucks for those big machines?

[@ChrisStaecker]

@@robertlozyniak3661 I'm not an expert on either, but it seems to me that good (fast) abacus use requires good mental dexterity, while the compometer is more about physical dexterity. I'd bet that a trained comptometer operator could do big multi-digit multiplications faster, but a trained abacus user could probably keep up pretty well. You're right of course- the abacus is much much cheaper, much more portable, less likely to break, etc.

[@robertlozyniak3661]

@@ChrisStaecker It seems to me that just about anyone could learn to add on a comptometer within a minute or two. However, that would be using the "hunt and peck" method of keying numbers, in which the full nine keys in each column would be available for use. I would guess that multiplication could be learned within, say, 5 or 10 minutes, and proficiency achieved within 30 minutes. Subtraction is a bit tricky, so it would probably require a bit longer to learn, but not _too_ long; and again, one could achieve proficiency quickly. Division would (as you already know) be the most complicated and therefore hardest to learn, but still, one could learn it within a day, or even half a day, I would think. It seems to me that a comptometer is like an typewriter in that, with either machine, one could learn to work the machine within a minute or two; however, to work the machine quickly and efficiently requires training and practice. This probably explains the main "advantage" of a comptometer over an abacus. If it is the late 19th or early 20th century and you are in the business of selling office machines, you could demonstrate to an office manager how to type a few words on a typewriter, and also how to add a short column of figures on the comptometer. You might let the manager try his hand at working the machines, just to let him see for himself that the machines do exactly what they are claimed to do, in the way that they are claimed to do it. He would understand that the machines are not a "humbug" or a hoax, and would likely be willing to pay, not only for the machines, but also for training for his employees in how to use them. Compare this to if you were trying to sell abaci. It might well tax the manager's patience to learn how to represent numbers on an abacus, let alone how to add them; and even if he were willing to take the time to learn how to add numbers on an abacus, he would probably see no advantage over traditional pencil-and-paper arithmetic.

[@BokBarber]

@@robertlozyniak3661 Comptometers were used primarily for back office tallying of totals on spreadsheets, which means that 80% of their operations were addition. Comptemeters excel at addition; you simply key the numbers in and they're added to the total as you go. Trained operators could do this as fast or faster than a modern calculator. Division and more complicated operations would've been less frequent, so their relative slowness and clunkiness wasn't too much of an issue to a workflow given the intended use case of the machine. The fact that the machine could do these calculations was sort of a "bonus." Nice that it could be done and that you could hand such calculations off to your Comptometer operators and get results, but the real benefit was always the speed of addition (and multiplication.) Finally. businesses didn't send anyone to learn on the Comptometer. The schools were maintained by the Felt & Tarrant company as a private trade school system at their own expense; people were enticed to attend these schools at the high school level to learn a potential job skill, and they then applied to companies looking for Comptometer operators. This was heavily advertised as an advantage to businesses; trained professionals are just waiting to fill the need if you simply buy our fancy machines and the service contracts to keep them well maintained.

[@ct92404]

Yikes. Thank goodness for modern electronic calculators!

[@ChrisStaecker]

True- they never would've happend though, without lots of machines like this one coming first.