Sunday, February 21, 2021

TI-84 Plus CE and HP 17BII+: Euclidian Divison

 TI-84 Plus CE and HP 17BII+: Euclidian Division


What is the ├ symbol on the calculator?

(├ the symbol is a vertical line with a horizontal line coming from the center to the right)


In several scientific calculators sold in Europe such as the Texas Instruments TI-40 Galaxy:


http://www.datamath.org/Sci/Galaxy/TI40_Galaxy.htm


and the current TI-Primaire Plus, which is sold in France, 


http://www.datamath.org/Sci/Modern/TI-PrimairePlus.htm


There is a key marked [ ├ ].  Going through the manual for the TI-40 Galaxy, this is the Euclidean Division key, which returns the quotient and remainder of the division.


x ├ y returns two results:

Q = int(x/y)   (quotient)

R = x - frac(x/y) * y   (remainder)


The TI-84 Plus family has the remainder function (I think it is OS 2.5 and later).  Here are several ways to emulate the Euclidian Division function:


TI-84 Plus CE Program:  EUCDIV


Prompt X,Y

{int(X/Y),remainder(X,Y)}


HP 17BII+ Formula:


EUCDIV: 0=IF(S(Q): IP(X÷Y)-Q: MOD(X:Y)-R)


Inputs: X,Y

Outputs:  Q (quotient), R (remainder)


Examples:


25 ├ 7 ->  Q = 3, R = 4

77 ├ 6 ->  Q = 12, R = 5


Can we use the [ a b/c ] fraction key?  


Calculators such as the Casio fx-260 Solar II calculator could be used to simulate the Euclidean division with the [ a b/c ] key.  The fraction would be illustrated in the mixed fraction format.  Let us illustrate:


56 [ a b/c ] 5 [ = ]   11 _ 1 / 5    

(Q = 11,  R = 1, divisor = 5)


125 [ a b/c ] 14 [ = ]  8 _ 13 / 14

(Q = 8,  R = 14, divisor = 14)


So far so good, but...


9314 [ a b/c ] 60 [ = ]  155 _ 7 / 30

Look at the denominator:  it is 30 not in 60, the fraction has been simplified.   Of course, we know that 7/30 = 14/60, hence Q = 155, R = 14. 


Note:  if you use the [ a b/c ] key, be sure to look at the resulting denominator is not the same,  it is not in the Q _ R / D form.  


Eddie


All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


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