MEW3.com [ Main Page ] [ Products ] [ News ] [ Support ] [ Contact Us ] [ Links ] [ Search MEW3.com ]

Fraction! Documentation

Fraction! is a multi-function RPN (Reverse Polish Notation) Fraction calculator for Palm OS. Features RPN entry and operation Add, Subtract, Multiply and Divide fractions Use mixed and/or improper form for entry and display of fractions Reduce fractions, or put fractions in improper form Forty (40) number stack for saving intermediate results Ten (10) memories for storing results until later Undo feature for undoing a prior operation Built in functions for taking the reciprocal or squaring fractions Stack manipulation functions: swap, drop, duplicate, rotate and over Extended stack element display for high resolution devices Shareware Limitations The shareware version is fully operational for 31 days, after which you must register to continue using the product.

Operation

Fraction! is used like any ordinary RPN style calculator (What is RPN?). You enter fractions (operands) onto the stack and perform operations on the entered numbers. For ease of entry the whole part, numerator and denominator are entered with periods separating the parts. For example, 2/3rds would be entered as 2.3, 1 and 2/3rds would be entered as 1.2.3

Understanding the Fraction! display

Although Fraction! has a 40 number stack, only the top four numbers are displayed. They are displayed, from top of the screen down towards the keyboard in descending order. Several RPN calculators only have a 4 number stack. For consistency with these calculators, the four numbers displayed can be referred to as the T Register, Z Register (just below the T register), Y Register and X Register (just above the numeric keypad). Normally Fraction! will show the X Register in the large number font. For the sample display on the right, the T (4) Register = 1 & 2/3, Z (3) = 4/5, Y (2) = 2/3, and finally X (1) = 1/6 The value in the X Register is the top most value on the stack. When this manual refers to the current number on the stack, or top of stack, it is referring to the value in the X Register.

Let's start by adding two simple fractions:

Example 1: Add 1/3 and 4/5

Press the following keys: 1 . 3 <ENTER> (the stack will show 1.3)
Then press: 4 . 5 <+> (the stack will show 1.2.15, which is read 1 and 2/15ths)

To show the answer in improper numerator over denomitator form (or non reduced form) press the <IMP> button. The display should then show: 17.15 which is read 17/15ths).

Now for something more complex, such as adding and multiplying several numbers which affects the order of operations. RPN calculators do not require the use of parentheses. For example, when calculating the answer to: 1 + 3 * 4 you typically multiply 3 * 4 for 12 and then add the 1 giving the result 13. This is because we are taught that multiplication and division have a higher precedence than addition and subtraction.

Non algebraic calculators, like the typical four fuction calculator, do not understand algebraic precedence and when you enter 1 + 3 * 4 and press = you will get the answer 16. A typical scientific calculator is usually programmed with precedence rules and pressing 1 + 3 * 4 = would generate the result 13.

Using an RPN calculator, you can calculate the answer either way because you control the order of operations, or precedence.

Method 1 - Non Algebraic (type the following):

1 <ENTER> (the stack will show 1)
3 + (the stack will show 4; Note that pressing an operator such as +, -, /, *, etc. automatically presses the <ENTER> key for you) 4 * (the stack will show 16)

Method 2 - Applying precedence or correct order of operations:

1 <ENTER> (the stack will show 1)
3 <ENTER> (the stack will show a 1 and a 3)
4 * + (the calculator first multiplies the 4 by the 3 and then adds the 1; the stack will show 13)

Advantages of RPN:

• No parenthetical calculations
• User controlled operator precedence and/or order of operations
• No equals key is necessary generally resulting in fewer keystrokes
• RPN coupled with a stack for intermediate results gives you a convenient way to see intermediate results while performing more complex calculations

Disadvantages of RPN:

• Some of the advantages are also disadvantages especially if you don't want to think about parenthetical expressions or order of operations

Computing the answer to a parenthetical expression:

Find the answer to the expression: (1/2 + 1/5) * 4/6

Since we've learned to group operations in parentheses over operations outside of parentheses, we solve the expression inside the parentheses first. Type:
1.2 <ENTER> 1.5 + (the stack will show 7.10)
4.6 * (the stack will show 7.15)

In it's normal configuration, Fraction! will reduce and place in mixed proper form fractions as they are entered. For example, pressing 4.6 <ENTER> results in 2.3 being displayed on the stack.

Entering 1.10.5, i.e. 1 and 10/5ths results in the value 3 being displayed on the stack.

Fractions entered in improper form, such as 7/3rds, will be shown as 2.1.3. Automatic reduction can be turned off in the preferences screen so that calculated or entered fractions remain unreduced.

Additional references are available below, and are suggested reading!

Function Reference

Function	Name	Description	Required numbers on stack
*	Multiplication	Multiply two numbers on the stack leaving the result on the stack	2
/	Division	Divide two numbers	2
+	Addition	Add two numbers	2
-	Subtraction	Subtract two numbers	2
x<>y	Swap X and Y	Exchange X and Y on the display	2
+/-	Change Sign	Change the sign of the current number on the stack	1
Red	Reduce	Reduce a fraction to mixed or proper form	1
Imp	Improper	Put a fraction in improper form	1
1/x	Reciprocal	Calculate the reciprocal of the current number on the stack	1
x^2	Square X	Square the current number on the stack	1
P	Put	Put the current number on the stack in a memory location. P is followed by pressing 0 through 9. Once a number is put into a memory location, it is removed from the stack	1
S	Save	Save the current number on the stack in a memory location. S is followed by pressing 0 through 9. Saving a number remove it from the stack	1
R	Recall	Recall a value from a memory location and put it on the stack. R is followed by pressing 0 through 9.	1
Over	Over	Bring a copy of the Y register over the X register putting it on the top of the stack	2
Rot	Rotate	Rotate X, Y and Z. Z gets moved to the top of the stack, X gets moved to Y and Y gets moved to Z.	3

Preferences

Automatic Reduce When this option is checked, calculated and entered numbers and fractions are automatically reduced. For example, entering 4.2 on the stack gets automatically reduced to the value 2. To leave numbers unreduced or improper form when entered, uncheck this setting. Default Value: Checked Show & and / When checked, this option shows fractions or numbers in the Y, Z and T registers with & and / characters in the appropriate locations instead of periods (.). Default Value: NOT Checked Always Show Large Number This value works in conjunction with Show & and / above. Due to a font limitation in Palm OS, when the Show option is checked the X register gets shown as a small font so that the & and / characters can be displayed. However, you can check this box to leave the X register displayed with large numbers and the period character separating the whole, numerator and denominator parts. Default Value: Checked Show Warnings When enabled, you'll be prompted to confirm deleting the entire stack contents or memory registers when those functions are used. Otherwise, they'll be executed without confirmation (fast and dangerous mode). Default Value: Checked Show Extended Stack When enabled on high resolution devices stack elements 5 through 10 are displayed in a small font on the right hand side of the Fraction! display. On low resolution devices this checkbox has no function.

Known Issues and Limitations

• Addition and subtraction of very large (or small) numbers can result in incorrect results being displayed since there is no over or underflow detection currently implemented on addition and subtraction.

RPN References

• Reverse Polish Notation -- RPN facts
• hpmuseum.org's RPN - What is RPN?
• The Evolution of RPN and Numeric Entry
• Fraction Calculator v1.0 for Palm OS 2.x through 4.x

Release History

• Version 1.1 - 2003 October 27
  • Extended stack display is now available for High Resolution devices.
  • Stack elements are numbered.
• Version 1.0 - 2003 June 1
  • Initial release