Pan Balance 2: Fractions Scroll (Fulcrum And Lever)

The Well-sorted Irreducible Fractions

After the development of the MathCats balance and the Balance of Fractions, I realized that the new fulcrum of the MathCats Balance had not been sufficiently exploited.
The fulcrum of the MathCats Scale was passive. Was expressing only the result of the supposed slope of the balance. It was not really interactive.

In the new Android program, Fractions Scroll, the fulcrum of MathCats is already interactive. It responds to the touch, being able to move the fractions with the finger. From left to right (swipe)

This causes the slope indicator corresponding to the chosen fraction (on the right) to be tilted,

Scrolling up and down widens or reduces the range of fractions used in the program: Increases or decreases the maximum denominator and numerator used.

Fractions Scroll Video: https://www.youtube.com/watch?v=bQbdxCfAPEc

Fractions Scroll App: https://play.google.com/store/apps/details?id=com.nummolt.slope.tap

In the paid version: "Fractions Scroll Gravity Lever" this interaction can also be obtained by tilting the device during the fifteen seconds of use of the accelerometers after pressing the corresponding button.
 
In this version, when the accelerometers are running, the bar that indicates the slope corresponding to the chosen fraction always remains horizontal.

Fractions Scroll Gravity Lever Video: https://www.youtube.com/watch?v=F_fH5XMlIRI

Fractions Scroll Gravity Lever App: https://play.google.com/store/apps/details?id=com.nummolt.slope.gravity  

Fractions Scroll Gravity Lever: Also available at Amazon:

https://www.amazon.com/nummolt-apps-Fractions-Scroll-Gravity/dp/B01MZ18BZP/ref=sr_1_1 

Blog about MathCats Balance and Fractions Balance:

http://nummolt.blogspot.com.es/2016/10/pan-balance-cats-and-fractions.html

 

Pan Balance 1: Cats and fractions

Usually in elementary mathematics, teaching pan scale balances are used only for display them at the time of equilibrium, to verify that two quantities are equivalent.

In this case, apart of this use, it is also useful imbalance in the balance. 

Many years ago (2003), Wendy Petti of MathCats.com and me, we developed the "MathCats Balance":


" choose from a wide range of objects to place on this scale - from electrons to galaxies! " 
" So how can we balance thin cats with fat cats? You might try multiplying each side by the number shown on the opposite side of the balance. Will 2 x 6 thin cats balance with 5 fat cats? Yes, 12 thin cats do balance with 5 fat cats".

MathCats balance: Android version (youtube)

MathCats Balance App (Google Play)

MathCats Balance (Amazon) 

Many years after this, I developed under the same idea a pan balance of fractions.
Inspired in a old photograph of Maria Montessori and his son Mario:

 ( from Getty Images: www.gettyimages.es/fotos/maria-montessori )

Pan balance to weigh fractions:

This imbalance, when the imbalance ratio under certain conditions is proportional to the ratio of content of the dishes, is also the result of the division. The slope of a straight line. In this case, the result of the division of fractions.

To view it, you can multiply the contents of each dish, until the balance is obtained, the numbers for which has multiplied each dish are in turn the result  fraction of the division.
The program only multiply by prime numbers, because any number can be built with them.

 This is the "Fractions Balance" Android App:

 Fractions Balance (Youtube) promotional video

 Fractions Balance App (Google Play)
Fractions Balance App (Amazon)

Comparing: 
1/2 + 1/3 + 1/6 
with: 1/3 + 1/5 + 1/6 + 1/8 + 1/10 + 1/12
And with: 1/3 + 1/4 + 1/5 + 1/8 + 1/12

 Comparing very near fractions addition (youtube)

I hope it helps on teaching division of fractions.

Touch Fraction ℚ (1.4.x)

New version of Android App "Touch Fraction ℚ"  (version 1.4.x and up)
https://play.google.com/store/apps/details?id=nummolt.touch.fraction


Evolution of the app over the years: (1993-2015)
In 1993 I developed the first executable (for Windows 3.1) of Touch Fraction ℚ (Racional.exe):

http://www.nummolt.com/rebost/index.html

It was my first attempt of to show an interactive representation of Rational numbers as fibres in (Z * Z {0}) and arrangement in Q.
As the Rational representation in Wikipedia:  Rational Numbers:

 https://en.wikipedia.org/wiki/Rational_number

In 2013 I made the new version of the app: The translation of the original executable to the Android OS.

The interaction became extended to the fraction:

The pie fraction to navigate across the fractions, and the rational representation to navigate across the equivalent fractions. (and select the range of available denominators)

In 2015 after the development of Touch Integers ℤ (+ - × ÷) (https://play.google.com/store/apps/details?id=com.nummolt.touch.integers)

This time, I was able to afford the next step:

Explain fractions and rational numbers as the prime factorization of its members: numerator and denominator.

This is the new version of Touch Fraction ℚ:

https://play.google.com/store/apps/details?id=nummolt.touch.fraction

Interact with the fraction, build fractions adding or removing prime factors in the numerator or in the denominator.

Simplify fractions dragging common prime fractions to the "common" zone, and invert fractions with the "^-1" button.  

Touch Fraction ℚ is a complete tool to understand positive fractions, negative fractions, positive and negative numerators, positive and negative denominators, equivalent fractions, and inverted fraction.

(Video of the app, at: Google Play)