How to calculate a Mod b in Casio fx-991ES calculator

Does anyone know how to calculate a Mod b in Casio fx-991ES Calculator. Thanks

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 0 like 50 / 5 = 10 (mod is 0).

The remainder fraction is shown in reduced form, so 60 / 8 will result in 7 1/2. Remainder is 1/2 which is 4/8 so mod is 4.

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 -121 / 26 = -4 17/26, thus, mod is -17 which is +9 in mod 26. Alternatively you can add the modulo base to the computation for negative numbers: -121 / 26 + 26 = 21 9/26 (mod is 9).

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 200^5 mod 391 then some tricks from algebra are needed. For example, using rule (A * B) mod C = ((A mod C) * B) mod C we can write:

200^5 mod 391 = (200^3 * 200^2) mod 391 = ((200^3 mod 391) * 200^2) mod 391 = 98

As far as I know, that calculator does not offer mod functions. You can however computer it by hand in a fairly straightforward manner. Ex.

(1)50 mod 3

(2)50/3 = 16.66666667

(3)16.66666667 - 16 = 0.66666667

(4)0.66666667 * 3 = 2

Therefore 50 mod 3 = 2

Things to Note: On line 3, we got the "minus 16" by looking at the result from line (2) and ignoring everything after the decimal. The 3 in line (4) is the same 3 from line (1).

Hope that Helped.

Edit As a result of some trials you may get x.99991 which you will then round up to the number x+1.

You need 10 ÷R 3 = 1 This will display both the reminder and the quoitent

---

÷R

There is a switch a^b/c

If you want to calculate

491 mod 12

then enter 491 press a^b/c then enter 12. Then you will get 40, 11, 12. Here the middle one will be the answer that is 11.

Similarly if you want to calculate 41 mod 12 then find 41 a^b/c 12. You will get 3, 5, 12 and the answer is 5 (the middle one). The mod is always the middle value.

You can calculate A mod B (for positive numbers) using this:

Pol( -Rec( ¹/_2π^r , 2π^r × ^A/_B ) , Y ) ( π^r - Y ) B

Then press [CALC], and enter your values for A and B, and any value for Y.

/ indicates using the fraction key, and ^r means radians ( [SHIFT] [Ans] [2] )

Here's how I usually do it. For example, to calculate 1717 mod 2:

• Take 1717 / 2. The answer is 858.5
• Now take 858 and multiply it by the mod (2) to get 1716
• Finally, subtract the original number (1717) minus the number you got from the previous step (1716) -- 1717-1716=1.

So 1717 mod 2 is 1.

To sum this up all you have to do is multiply the numbers before the decimal point with the mod then subtract it from the original number.

type normal division first and then type shift + S->d

Note: Math error means a mod m = 0

It all falls back to the definition of modulus: It is the remainder, for example, 7 mod 3 = 1. This because 7 = 3(2) + 1, in which 1 is the remainder.

To do this process on a simple calculator do the following: Take the dividend (7) and divide by the divisor (3), note the answer and discard all the decimals -> example 7/3 = 2.3333333, only worry about the 2. Now multiply this number by the divisor (3) and subtract the resulting number from the original dividend.

so 2*3 = 6, and 7 - 6 = 1, thus 1 is 7mod3

Calculate x/y (your actual numbers here), and press a b/c key, which is 3rd one below Shift key.

Simply just divide the numbers, it gives yuh the decimal format and even the numerical format. using S<->D

For example: 11/3 gives you 3.666667 and 3 2/3 (Swap using S<->D). Here the '2' from 2/3 is your mod value.

Similarly 18/6 gives you 14.833333 and 14 5/6 (Swap using S<->D). Here the '5' from 5/6 is your mod value.