## 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:

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

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

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