FracEx Calc App - Functionality and Features

FracEx Calc is the abbraviation for the Calculation of Fractions and arithmetic Expressions. 

The App resolves simple calculation with fractions as well as complex calculations of arithmetic expressions including a step by step resolution path.

FracEx Calc deals with common calculations  of arithmetic expressions for fractions, integers and floating point numbers, such as 

• Shorten
• Conversion of „false fractions“ into „mixed fractions“ (e.g. 11/4 into 2 3/4) 
• Conversion into floating point  numbers with up to 5,000 digital places (e.g. 11/4 into 2.75)
• Conversion of floating point numbers into fractions
• Display of periods for floating point numbers
• display of details about floating point numbers such as count of digital places or length of a period
• Calculation of the result for arithmetic  expressions with the basic operations and for parenthetical expressions
• display of a step by step resolution path for arithmetic expressions
• Exercise mode with different difficulty levels.

Users of common electronic calculators can continue as usual by using the Calculator-Mode and can switch to the more comfortable Expression-Mode if necessary for the calculation of more complex expressions.

Furthermore, FracEx Calc is implementied to support multi-language capabilities  (actually supported languages: German and English) and it supports Light-/Dark-Mode.

FracEx Calc supports generally three modes, 

• the Expression-Mode,  
• the Calculator-Mode and
• the Exercises-Mode.

The App requires at minimum:

• iPhone 8 / iPhone SE or higher  
• iOS 16.1 or higher
• macOS 13.1 or higher; both are supported mouse and/or keyboard

General Features:

• Number entry in form of a fraction with numerator and denominator, as integer or as floating point number
• Supports big numbers with 19 digits
• Comfortable entry that helps to prevent false entries
• Removal of last digit in current number entry 
• Basic arithmetic operations : addition (+), subtraction (-), multiplication (*) and division (:)
• Shortening fractions
• Conversion of floating point numbers into fractions
• Conversion of fractions into „mixed fractions“ as well as into  floating point numbers
• Configurable maximum number of digits for displaying floating point numbers (up to  5,000)
• For floating point numbers that contain more than the maximum number of digits, it is possible to display the digits at the end (up to 5)
• Display of the period in floating point numbers 
• Details about floating point numbers such as count of digits before and after the decimal point, length of a period (if periodic)
• Warning and Error messages
• Multi-language capable (actually supported: English, German and French)
• Light- and Dark-Schema support

Additional features in the Expressin-Mode:

• Consideration of proirity rules for arithmetic operations, i.e. (1) resolution of sub-expressions in parentheses, (2) point operations und (3) dash operations
• Almost any nesting depth levels for sub-expressions (parentheses), such as
  (((2+3)*(5+4)-9)*5 -7)*8
• Removal of the last element in an arithmetic expression, i.e. operand, operator or parenthesis  
• Continuous validation of expressions during entry and display of intermediate results for any valid expression
• Step by step resolution path for valid expressions  

Additional features in Calculator-Mode:

• Calculations - as using common electronic calculator - in the order of entry
• Display of the Calculation-Register with representation of results as fraction, „mixed fraction“ and floating point number (optionally)
• Memory-Register as storage for intermediate results

The Exercises-Mode:

• creates exercises of varying complexity,
• checks your result and
• shows the correct result including the resolution path.

FracEx Calc goes far beyond the usual requirements , especially in the space of education but also others.  

However, there exist technical restrictions but also for  the stake of usability and robustness, there are  some limitations that shouldn’t harm too much in the practical, common use of the app.  

Those limitations mainly belong to:

• Integer numbers are limited  to maximum number of 19 digits -  also as numerator and denominator of a fraction. 
• Floating point numbers are displayed with a precision of up to 5,000  digits - this is the maximum that can be shown at one line on iPhone.
• The number of digits for a period gets determined only if the period starts before the 10,000th decimal place and ends before the  500,000th decimal place.
  Practically, this shouldn’t cause limitations.

Due to the limited size of  iPhone 8 / iPhone SE there are specific minor limitations on them:

• The screen title will not be displayed. However, the actual mode can be still determined by the color at the icon on the Navigation Tab Bar at lower end of the display.
• The additional information about floating point numbers, such as the number of digits before and after the separator and the length of a period, are displayed in the Expression Mode only. At the Calculator-Mode these are displayed for the Calc-Register only in case that the  Memory-Register is disabled.