Modulo or reminder computation on calculators without the modulo function
12-31-2022, 07:52 PM
Post: #1
 pier4r Senior Member Posts: 2,248 Joined: Nov 2014
Modulo or reminder computation on calculators without the modulo function
I was reading the manual of the Casio 991 DE X (I am not sure which model would be the international one) and I noticed that it had the modulo function. I though "woah, they are really putting more and more functions in good non-programmable and non-graphing calculators".

Then I looked at my trusty sharp el506w (bought in the early 2000), that is very good for many needs, and I thought: "well this model doesn't have a modulo function or a function that can compute the reminder between dividend and divisor".

Or doesn't it?

I noticed that the sharp el506w has the function a b/c, this function transforms the result of a decimal division X/Y in the form: a + b/c . Where a is normally an integer (0 or 1 in most cases), c is equal to Y or a submultiple of it.

Therefore the value of b is the reminder of the formula X mod Y. If c is a submultiple of Y, then one needs to multiply the value b by Y/c . In other words the modulo can be obtained relatively quickly with few operations.

I was thinking: is there a better way (with an handful of operations at most) to compute the modulo on such calculators? Is the same approach working on other calculators or does one need to get creative on other models? (considering models that are meant for scientific usage though and have plenty of functions, not really basic calculators)

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12-31-2022, 08:25 PM
Post: #2
 Steve Simpkin Senior Member Posts: 1,190 Joined: Dec 2013
RE: Modulo or reminder computation on calculators without the modulo function
The closest model to the fx-991DE X in the U.S. is the fx-991EX. They look very similar but the 991EX is missing the modulo function (÷R).
The following YouTube video demonstrates one way (maybe the simplest) to find the remainder on calculator models that do not have the modulo function built-in.

https://youtu.be/AY2vkR38vGI
12-31-2022, 08:46 PM
Post: #3
 pier4r Senior Member Posts: 2,248 Joined: Nov 2014
RE: Modulo or reminder computation on calculators without the modulo function
Thank you for the video and the info. Interesting that the version is not standardized everywhere, that is, beside the language, all the functions should be the same everywhere but seemingly aren't so.

In the video the person says practically:

X/Y = A + B . Where A is an integer and B is the decimal fraction with -1 < B < 1 . Thus it practically equals to b/c on the el506w. If one indeed multiplies b/c per Y it returns the reminder, true.

Well yes then it is pretty doable everywhere.

Wikis are great, Contribute :)
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