Welcome to the Fractions Calculator help documentation.
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V1.1.2 is -3^2=-9 or 9, you choose.
This version offers the ability to email the calculator tape to someone, if email is supported on the device. It also allows you choose between pure math mode and excel mode where the order of precedence for negation and power is different.
Aug 19th,
v1.0.8 provides faster factorial calculations on the iPhone 3G S.
Fractions unlimited is a calculator that does Fractions, although there are a number of calculators on the App store that do fractions, this application is unique in the way it handles unlimited sized fractions, and factorials as it attempts to preserve numerical accuracy.
We also support brackets, floating point entry, and x raised to y, plus have a “paper tape”. Other calculators on the store lack those features.
For example you can enter
512!/513! which is 1/513, this requires manipulation of a 1,170 and 1,167 digit number. The actual calculation is found below the help text.
“1/1” Mixed Fraction or Fraction key
To Enter 42 3/8 we tap the “1/1” also described as the “/” key
'4' '2' '/' '/' '3' '/' '8'
that gives
42_3/8
Note the tapping of the '/' key twice to indicate you are entering a mixed fraction. Also if you just enter 42_7 that will evaluate to 42+7/1 or 49 because the 7/1 is implied.
Order of Precedence
! Factorial
/ Fraction operator
_ Mixed Fraction operator
^ raise to the power of
- negated
multiply, divide
plus and minus
So 1_1/2^2 is 9/4 because we calculate it as (1+1/2)^2
-3^2 is -9 because it is -(3^2)
-5_3/4^2 is -33_1/16 because it is -((5+3/4)^2)
Huh? isn’t -3^2 = 9?
{ Our Version 1.1.2 will allow you choose between pure math mode and excel mode where the order of precedence for negation and power is different, however read on for the arguments about which is correct}
Check WolfRam Research's Alpha web site:
http://www.wolframalpha.com/input/?i=-3%5E2
It say '-9'
That is our IMPARTIAL reviewer and how we cross checked all our calculations for proper order of operation in our test phase, in fact we have 100's of test cases to confirm our math is correct.
Don't trust WolfRam Research? Can you trust WikipediA?
Then http://en.wikipedia.org/wiki/Order_of_operations
See Examples: Specific cases (5).
Oddly they say -9 too!
But?
We allow for two different orders, a pure math order, and a second order that follows Microsoft Excel concepts.
The pure math order is:
! Factorial
/ Fraction operator
_ Mixed Fraction operator
^ raise to the power of
- negated
multiply, divide
plus and minus
So 1_1/2^2 is 9/4 because we calculate it as (1+1/2)^2
-3^2 is -9 because it is -(3^2)
-5_3/4^2 is -33_1/16 because it is -((5+3/4)^2)
The Microsoft Excel order is:
! Factorial
/ Fraction operator
_ Mixed Fraction operator
- negated
^ raise to the power of
multiply, divide
plus and minus
-3^2 is 9 because it is (-3)^2, and -3^3 is -27.
-5_3/4^2 is 33_1/16 because it is (-(5+3/4)^2)
This order follows the pattern of most calculators. It is set by turning on the -3^2=9 switch in the Settings Application for Fractions, for historical reasons the pure math order is the default.
Fractions versus Divide
“/” is not “÷”
“/” means number/number to make a fraction
“÷” means expression divide by expression.
saying
1 / 3 ÷ 4 / 3 = 1/4
is very different than
1/3 / 4/3 = 1/36
We note because of ambiguity in calculating the above we would calculate it as ((1/3)/4)/3. Therefore you should use the brackets keys if you intend to calculate the value as (1/3) / (4/3). Or obviously it could be better expressed as 1/3 ÷ 4/3 and then no brackets are needed.
! Factorial
The “!” key as you saw indicates factorial. But how big? Well try 5000!, that might take a few seconds and the number is 16,326 digits long. Once a calculation takes more than 2 seconds we put up the swirling wait icon.
Oh and 5000!/4999!= is 5000
The time consuming part of the calculation is expressing large numbers as written decimals in the text area, so asking for 5000! takes a long time, but asking for 5000!/4000!= happens in a few seconds.
^ Raise to the Power of:
The “^” key let’s you perform x^y say for example
2^151 ->
2854495385411919762116571938898990272765493248
Your regular calculator may have problems showing that
Do not forget -3^2 in math terms is -9 not 9, but in Excel mode it is 9. Which mode you pick is a personal decision, but we do note the Apple's calculator mimics Excel.
x<>F mixed fraction/float
Shows the mixed fraction value of the last calculated result, pressing again shows the floating point value.
45÷23=
45/23
x<>F gives
1_22/23
pressing x<>F again gives
1.956521739130435
Obviously the floating point value is an approximation of the fraction as a double precision number, and really large numbers will calculate to float Infinity or -Infinity.
Floating Numbers
Fractions allows you to enter Floating point numbers, these numbers are then converted to approximated fractions. Floating point numbers are double precision based, and they are immediately converted to fractions when entered.
“e” and the “-” keys
The “e” and the “-” keys help you enter the - and e for negative number or negative exponents:
0.3003 -> (3003/10000)
-0.333e-5 -> (-333/100000000)
-0.333e5 -> -33300
or for example
5--3 -> 8 which is 5 minus negative 3
STO
Stores the calculated value or current number into a memory cell.
RCL
Pulls the remembered value into the current calculation, it replaces the current number.
Calculator tape.
As you compute numbers we remember the calculations and store the tape between sessions.
1+2=
3
1/4÷4.332+45/69=
35365/49818
We limit the tape to 8,096 characters and save the tape between sessions, along with the state of the calculator including the memory entry. If the tape is greater than 8096 characters it is truncated to a smaller size on a calculation boundary.
C
You can use the C key to delete the last digit/operator entered. Tap and hold for a second to get a prompt, otherwise quick taps will delete one character backwards.
You can also swipe the calculator tape, left or right to get a dialog asking what you want to delete.
The Mail Button.
The Mail button allows you to email the 'Paper Tape' to someone, or yourself. We write the version number of the Calculator on the tape along with the date and time, and the setting for the order of precedence. When you conclude the email session we write the status of the email processing to the paper tape.
Email must be activated on your device for the Mail button to be enabled.
Example email:
Fractions Calculator Unlimited Tape Version 1.1.0
2009-08-25 10:53:56 -0700
Setting -3^2=9 is OFF, so -3^2=-9
Paper Tape Calculator
5_7/8*3_2/3=
517/24
21_13/24
21.54166666666667
Sent from my iPhone
The Info Button.
Tapping the info button lets you see the help text, and a hyper link to our Web Site.