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Frrraction 001 — Getting started

Special paragraphs

As part of the presentation, this FrrrGuide has a variety of topic-types scattered through its sections. Plain text such as the present paragraph are simple and direct. Other paragraphs, intended to highlight one aspect or another of a topic, are marked for quick recognition as InfoTopics, TryIt topics, Background topics, KeyIdeas, and SideIssues. Here are examples of each:

information icon InfoTopic:

Topics marked with this open-reference-book icon introduce specific features of the Frrraction app.
tutorialicon TryItTopic:

Topics marked with this iPhone-in-hand icon describe specific hands-on exercises to clarify the section material. They are best read when you can use Frrraction's WEB and Return-To-Frrr buttons to toggle back and forth between the detailed TryIt-guidance and the live frrrApp.
background icon BackgroundTopic:

Topics marked with this scenic-background icon provide background of interest to the section material. Not essential for using Frrraction, they can be skipped until sometime you might feel like reading them.

Key idea

Some topics are side-issues that you might like to know about, but which aren't pressing, and don't need a whole section by themselves. When another topic seems to be a good context, these blue paragraphs serve to describe the side-issue.

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Brief Overview of Frrraction

information icon InfoTopic:

Frrraction displays six integers organized as two fractions F1 and F2 that you directly interact with. It also provides storage registers for ten more fractions, R0 through R9. These support flexible operations, letting you explore the arithmetic of exact numbers—along with their relation to the approximate forms that use a decimal point.

The flexibility allows interesting experiments with numbers. You'll be able to use fundamental formulas to calculate things like square roots or the value of a logarithm accurate to seven or eight digits.

Besides encompassing any integer x (in the form x over 1) and any rational number (as x over y), pure fractions can represent zero and infinity as well as the notion of indeterminate  (which uses the unique form 0 over 0) when there truly is no meaningful numeric value.

A "frrrNotes" area of the screen comments on what the app just did and shows helpful hints about what the app can do next.

You can add your own comments to the frrrNotes area at any time. Combined with the iPhone's ability to take snapshots of its own screen and deliver them to the web or via email, this allows attractive and informative reports.

Frrraction also provides access within the App to this website, www.frrraction.com, to help keep you abreast of developments. Within Frrraction, you can toggle between Frrr Guide and the live App, for convenient hands-on experience with its information, tutorials, and background paragraphs.
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A fractions-math app for iPhone and iPod touch

background topic BackgroundTopic:

Our philosophy is that Math should not be a passive subject. With Frrraction you can explore numbers in the relaxed atmosphere of your own little handheld exploratorium.
  • What's the biggest integer an iPhone can handle?
  • What's the biggest stacked fraction it can handle?
  • What if you add 1 to make the biggest fraction bigger?
  • What if you divide a number by 0?
  • What if you divide 0 by 0?
  • How do you find simple little fractions like 22/7 to replace big awkward fractions like 314159/100000?
  • Given decimal fractions like 3.14159 how do you find cute little pure fractions like 22/7 to stand in their place?
  • Are mixed fractions more general than pure fractions?
  • Integers are not fractions, but can fractions equal integers?
  • How do you know which integers are prime?
  • If an integer is not prime, what are its prime factors?
  • When is 5 + 9 = 3? and 5 * 9 = 1? (Hint: In modular arithmetic when the modulus is 11.)
  • What are "continued fractions"? What are they good for?
All this and more you can find out for yourself with Frrraction. And when you do? Mathematics is a big world. As they say, the sky's the limit!
information icon Fraction representations:

Fractions can be presented in a variety of formats. Foremost in this App are the

pure ratio fraction
(formatted as two integers:
    num and den
separated by a division symbol),
e.g. 456/123

the

mixed ratio fraction
(formatted as three integers:
    integer, num and den
separated by a plus and a division symbol),
e.g. 3 + 58/82

and the

dot fraction
also known rather misleadingly as the decimal fraction
(formatted as two integers:
    integer part and fractional part
separated by a decimal point)
e.g. 3.707317

Two other fraction formats favored by Frrraction are:

continued fraction,
e.g.
Continued Fraction example

and

egyptian fraction,
e.g.
Egyptian Fraction example

Minor point of interest: The five examples just given are different forms of the same fraction. All but the dot-form are exact, while the dot form is an approximation. A more precise dot form is 3.7073170731707317073170731. But even that one is still inexact.

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The very beginning Basics

information icon InfoTopic:

When you start the app your iThing becomes a calculator, and you can refer to the screen as you read this description (tap the yellow key then WEB to toggle between this Guide and the live app):

The opening screen (after removing some explanatory markup) looks like Fig. 1:

Frrraction opening screen
Figure 1
Frrraction's opening screen.

The rectangular cells—one white, three salmonish—are the numerators and denominators for two pure fractions. Both fractions have been initialized to contain zero in the form suitable for fractions:

0 over 1

The numerator of F1 is white and the little waving stroke /|/| is the digit cursor, showing where the next input digit will go.

The app wakes up with the input cursor in the numerator of Fraction F1, which is the reason that cell starts out white instead of salmon. Tapping the other numerator or either of the denominators moves the input cursor to the one you tapped, making it be "the active cell".

The main function of the black keys along the bottom is number entry.
tutorialicon TryIt: (starting with 0/1 in F1):

Tap the key whose label is the digit 1. Tap it again.
See where the 1s went? See where the cursor is now?

The little circled × in the active cell is the cell's "clear button" or "Clr button". Each cell has its own Clr button, visible only when the cell is active. Tapping a cell's Clr clears the cell to zero.

Tap F1num's Clr button.
Now F1 contains 0/1 again.
information icon As shown at the bottom of Fig. 1, the black keys have yellow labels as well as white labels. In cooperation with the yellow key over at the right of the screen, the yellow labels give access to Frrraction's additional functionality.

Likewise, as shown at the right of Fig. 1, the white labels for those black keys are for arithmetic, and the yellow labels are more of Frrraction's functions.

Those yellow functions are a long story that we'll get to in a moment, but first…let's input an actual number:
tutorialicon TryIt: (starting again with 0/1 in F1):

Start by tapping the numerator of F1 if necessary to get the waving cursor into that cell. Then tap 1, then 1 again, then 0.
That action put the numeric value 110 into F1's numerator—or F1num as we will call it from now on.

By the way, "F1num" is pronounced... well, this will tell you:

background icon BackgroundTopic:

a moment of silliness

There was a young number named Fnum,
Who was asked to step out of her room.
She said with a frown,
   "I'd be glad to climb down,
But if I merely stepped out
   I'd fall BOOM."
There was also a fellow named Fden,
Who was asked
   where he'd gone to and when.
He said with a smile,
   I've been gone for a while,
It's down in the basement I've been.
[Well, too silly or not, that's how to pronounce those two words:
rhyme Fnum with 'eff-room'
and Fden with 'eff-when'.
The Integer part Fint is pronounced 'eff-int'.]
tutorialicon TryIt: (starting with 110/1 and the cursor in F1num)

Tap F1den (the salmonish denominator cell of Fraction F1) then tap the 5-key.

Where did the salmon go? And the 5? A 1 was already in F1den so now the denominator is 15. That's what I mean about a  cell becoming active to receive numbers, one cell at a time, at any time. F1 now displays the pure fraction 110 over 15, one hundred and ten fifteenths — 110/15 is the usual notation.
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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: July 24, 2012, 0300 GMT
Copyright © GRS Enterprises, NLC, 2010-2012
Not void, even where prohibited. Your mileage may vary.