How to find remainder in Casio fx 991ES PLUS

Question

Disclaimer: This is a highly specific answer for calculators of the casio family that support Pol and Rec functions, which convert cartesian coordinates to polar and vice versa.

Suppose you want to know what A mod B is, you can do the following then:

Pol(-Rec(1/(2π) , 2π×A/B), Y)(π - Y)B

Hereby, Y is an arbitrary constant, e.g. 1.2345, 1337 or -42. It doesn't matter, because the Rec function will overwrite the value.

Calculator usage: division and remainder calculations with the Casio fx-991ES PLUS C

Jack Posted on May 10, 2017 Posted in Calculator Usage, math

Tutoring math, I’m impressed with the functions available on scientific calculators. The tutor shows the division and remainder function on the fantastic Casio fx-991ES PLUS C.

Example: On the Casio fx-991ES PLUS C, find the quotient and remainder of 324 ÷ 15.

Solution:

Key in 324 ALPHA ■/□ (3rd key down from top left)
Key in 15
Press =

Neat, eh?

Source:

Casio fx-991ES PLUS C User’s Guide.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

This calculator does not have any modulo function. However there is quite simple way how to compute modulo using display mode ab/c (instead of traditional d/c).

How to switch display mode to ab/c:

Go to settings (Shift + Mode).
Press arrow down (to view more settings).
Select ab/c (number 1).

Now do your calculation (in comp mode), like 50 / 3 and you will see 16 2/3, thus, mod is 2. Or try 54 / 7 which is 7 5/7 (mod is 5). If you don't see any fraction then the mod is d/c0 like d/c1 (mod is d/c0).

The remainder fraction is shown in reduced form, so d/c3 will result in d/c4. Remainder is d/c5 which is d/c6 so mod is d/c7.

EDIT: As @lawal correctly pointed out, this method is a little bit tricky for negative numbers because the sign of the result would be negative.

For example d/c8, thus, mod is d/c9 which is ab/c0 in mod 26. Alternatively you can add the modulo base to the computation for negative numbers: ab/c1 (mod is ab/c2).

EDIT2: As @simpatico pointed out, this method will not work for numbers that are out of calculator's precision. If you want to compute say ab/c3 then some tricks from algebra are needed. For example, using rule ab/c4 we can write: