** 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

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