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Frrraction 101 — The app's main moves

YellowKey is a big deal!

Key idea


information icon InfoTopic:

We now turn our attention to YellowKey—that yellow key over near the right-hand edge — and right beneath it, the little YellowKey status indicator which is usually a white 'W'. What we're getting to is the reason there are both white and yellow labels on the black keys.

To be specific, consider the yellow label M|P on the 1-key. M|P stands for "Mixed or Pure", which are the two ways to display a stacked fraction. That label is yellow to highlight the fact that besides its primary ability to put the digit 1 into a fraction cell, the 1-key has a second function: It can switch the fraction-display mode. The primary functions are shown as white labels on the keys and they are invoked when the little YellowKey status indicator is a white W. (See that little W over there?)

Now. Here's the big deal about YellowKey:
The only way to tap M|P or XCH or APRX or any of the other yellow functions is what we call a ytap:
first tap YellowKey to turn the little status indicator beneath YellowKey into a yellow 'Y' then tap the function key.
As long as that indicator is a white 'W', tapping a key activates the white function of that key: 1 (not M|P) or 2 (not XCH) or 3 (not APRX) or any of the other white functions (not the yellow function mentioned on the same key).

So. From now on when this Guide says to use M|P or to tap M|P or any other yellow function key, it goes without saying that you must first tap YellowKey. That's the only way to tap any yellow function key.
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Summary of the yellow functions, once–over–lightly

information iconInfo


White Label ↔ Yellow Label Yellow Function
1 ↔ M|P Toggles between showing Mixed fractions and showing Pure fractions.
2 ↔ XCH Exchanges F1 with F2.
3 ↔ APRX Approximates the fraction in F1 into a simpler fraction in F2. If F1 is decimal (has a decimal point in F1int, making it "F1intD") the approximation exactly matches all the given digits, accurate within 1 in the last given digit.
4 ↔ DUP Duplicates the active fraction (copies it to the inactive fraction).
5 ↔ MAX Loads the active cell with the largest number that the 32-bit iPhone/iPad system can represent, alternating between pMAX (largest positive) and nMAX (largest negative).
6 ↔ EDIT Brings up the system keyboard so you can type a frrrNote that documents the current screen and contains CF and FILE operations.
7 ↔ CF Performs the Composite Function operation closest to the top in frrrNote.
8 ↔ WEB Opens a web view into Frrraction's website http://www.frrraction.com to keep you up-to-date with the App.
9 ↔ ONE Loads the number one in the pure form 1/1 or in the mixed form 1+0/1 into the active fraction.
0 ↔ RDC Cancels common factors to reduce the active stack to lowest form. Also shows the decimal forms if Frrraction is displaying Mixed fractions.
÷ div ↔ FILE Scans frrrNotes for any of four status-file commands: >|n| (save), <|n| (restore), −|n| (remove), or |?| (list).
× mul ↔ TIK Stops|Restarts the key-click sound. (The sound itself is licensed: http://www.freesound.org/forum/profile.php?mode=register)
− sub ↔ CHS Changes the sign of the integer in the currently active cell.
+ add ↔ STO Stores the active fraction into storage Register Rn with n specified by the next digit-key tapped.
BDel ↔ RCL Recalls a stored fraction from storage register Rn into the currently active fraction.
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M|P — from Pure Fractions to Mixed Fractions

tutorialicon TryIt (with 110/15 already in F1):

Ytap M|P.
(Remember, to do that you must first tap YellowKey — otherwise you'll be tapping the 1-key, not the M|P-key.)
information icon Explanation:

Two M|P things happened: A new cell F1int came into view as the pure fraction 110/15 was replaced by the equivalent mixed fraction: 7+1/3.  Seven is the integer portion of one hundred and ten fifteenths, and 1/3 is the proper part that's left over — 1 in the numerator of the stack portion and 3 in its denominator. The other thing that happened was: The status indicator beneath YellowKey reverted back to a white W, indicating that, once again, the white labels are operational.

The newly uncovered cell of each fraction is called the Integer Part or Fint of the mixed fraction.

Each of the three parts of a mixed fraction can be independently positive or negative, but there is always an implied addition–sign between the integer and the stack. Frrraction's preferred sign combinations are: integer and numerator should have the same sign and the denominator should always be positive. It gets to that condition at its first opportunity—certainly after ytapping M|P or RDC. The only exception is a pathological case called "the Nemesis". More about that fascinating case later.

tutorialicon TryIt (with 7 + 1/3 already in F1):

Tap F1num, then ytap CHS, changing F1 from 7 + 1/3 to 7 + −1/3. Do the same thing to change the sign of F1den, changing F1 from 7 + −1/3 to 7 + −1/−3.
Now the numeric value of F1 is back to the original but its signs are non-standard.

Ytap M|P, notice what you got, then ytap M|P again.
Like we said, Frrraction got back to its preferred signs as soon as it could.

Starting with 7 + −1/−3 in F1, a single ytap of RDC would also set the signs right. Adding or subtracting 0 + 0/1 would also do it. Same as multiplying or dividing by ONE.
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Proper, Improper, and Reduced Fractions

Key ideas: Kinds of fractions


background icon M|P BackgroundTopic:

Actually, M|P did two other things too:
It reduced F1num to make F1's stack into a proper fraction, meaning that its numerator is smaller than its denominator, so the stack became truly a fractional number—less than one. To preserve the value of the number while reducing F1num, M|P made up for the reduction by simultaneously increasing F1int — a nice balancing act.

The website Math is Fun icon and link to adding fractions has a good introduction to the notion of Proper and Improper Fractions.

The other thing M|P did is put the stack into reduced form, which means eliminating all factors shared by the numerator and denominator. Without doing that extra work—something you should usually do when working by hand—F1 would have ended up containing 7+5/15; not wrong, but not the best presentation.
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The HINT gesture

Key idea:
ytap ytap key describes the yellow function of that key


The HINT gesture is: ytap ytap <any key>,
i.e. tap YellowKey twice then some other key.

tutorialicon TryIt:

Tap the Yellow key two times (tapping speed is no issue, this is not intended to be an iPhone-style 'double-tap gesture''). The first tap changes the YellowKey status indicator from a white W into a yellow Y, and the second tap changes that into a yellow H. H stands for Hint. The H is yellow because, like Y, it too is about the yellow functions. While the status is yellow H, tap any of the other keys and Frrraction temporarily covers the Notes area with a hint about the yellow function of that key. For an example of this in action, tap the M|P key while the H is showing and notice the Hint. Notice that the YellowKey status indicator reverts to the white W after the Hint is displayed. The Hint vanishes and the Notes it hid reappear when you do anything else.

You can abort the HINT operation by tapping YellowKey one more time, changing the status back to a white W.

By now you have noticed that every time you tap YellowKey, Frrraction temporarily covers the Notes area with a brief description of what to expect next. Here's welcome news about that:

The three consecutive yTaps that start-then-abort the HINT operation also serve to stop those repeated YellowKey status reminders for the rest of this Frrraction session. (The next time you run Frrraction from a cold start, the reminders will be back.)

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M|P – from Mixed Fractions to Pure Fractions

tutorialicon TryIt (start with 7 + 1/3 in F1):

Before proceeding, yTap M|P again (Remember, that means tap YellowKey then tap the M|P-key) to revert the display to pure fractions. Notice that Frrraction correctly restored F1 to a pure fraction again—albeit in the reduced form 22/3 rather than the original 110/15.

Like several of the other yellow functions, M|P is a  'toggle switch': yTapping it once makes a change, yTapping it again later undoes that change. Taking the stack to reduced form does not get undone by the toggle, however.

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Clr or BDel – Clear whole cell or Backspace–Delete single digit

tutorialicon TryIt (start with 22/3 in F1):

Put the cursor back into F1num and tap the Backspace-Delete BDel key (it's the key below the Yellow key). See what happened in F1num? Tap several digit keys, then tap the BDel key several times. That's what the BDel key does. Finally, notice the Clear or Clr Button in the F1 numerator the odd little white x in a gray circle. Tap several digit keys and then tap the Clr Button. That's what the two delete keys do: One of them back-deletes a single character at a time, the other clears its whole cell to 0.

There. You passed Frrraction 101. You now know the App's basic idioms.

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Contact the Frrraction Development team
Frrraction is a product of GRS Enterprises, NLC,
a Michigan company since 1978
eMail to: theFrrrTeam@frrraction.com
Most recent update of this guide: May 7, 2012, 1800 GMT
Copyright © GRS Enterprises, NLC, 2010-2012
Not void, even where prohibited. Your mileage may vary.