# Description

Interactive fraction.

About fractions, and the construction of the rational numbers: ℚ set.

To play with proper and improper fractions, positive and negative also.

About fractions, and the construction of the rational numbers: ℚ set.

To play with proper and improper fractions, positive and negative also.

All fractions in order from least to greatest. You can increase or decrease the fractions included in the app, increasing or decreasing the density of lines in the lower graph framework. The accuracy of the application depends on the capabilities of the device.

The application provides two representations: a circle and a straight line whose has the slope of chosen fraction

Spin the fraction: You can choose different fractions in order from low to high within the possibilities included in the grid at the bottom formed by pairs of integers.

Select equivalent fractions with the rational representation diagram (the lower grid).

Change range of fractions affordable with a "pinch zoom" on the lower grid.

In the vertical strip of the grid graph goes from 0 to 1 you can see the number of units containing the selected improper fraction: Each unit is a black square.

The program is useful to learn about fractions, coordinate geometry, rational numbers, cartesian plane, slope, and the equivalent classes of pairs of integers.

Nummolt construction toys:

http://www.nummolt.com

MathTools reference:

Math 1, 2, 3, 4, 5 Fractions

Math 6 All previous and Rect coordinate geometry

Math 7 All previous and Rational numbers, Linear relationships, Ratio and proportion

Geometry Points and lines, Cartesian plane, Slope

Algebra Whole, Rational

# Reviews

# What's New

v1.3 optimized for 10 in. tablets

v1.2 minor improvements.

v1.1 interaction improved.

v1.0 first version

# Similar

# nummolt

## Time Calculator

Time Elapsed / Time Countdown Time Calculator

With the Time Calculator you can calculate the subtraction between 2 dates:

You can fix a date in the past and subtract it from the present time: You get the elapsed time.

You can fix a date in the future and subtract the present time: You get the countdown to the fixed date.

(Light gray dates are in the past; Light green dates are in the future)

Don't work for dates earlier than 1582.

(Because the Gregorian Calendar)

Android version of:

http://www.mathcats.com/explore/elapsedtime.html

and:

http://www.nummolt.com/obbl/time/calculator.html

A work in collaboration www.mathcats.com and www.nummolt.com

(Wendy Petti and Maurici Carbó)

Practical applications proposed by users:

-. Useful to calculate demurrage. (http://en.wikipedia.org/wiki/Demurrage)

-. To calculate amount of pills of a medical treatment.

-. Calculate the number of days, or hours, or minutes, or seconds, remaining until retirement.

-. How old am I?

-. How old are you?

-. How many months, or weeks, or days, or hours, or minutes, or seconds are there in 1000 years?

-. Estimate the number of heartbeats throughout life at this time.

- multiplying lived minutes by a number between 60 and 100 for human beings.

- minutes, multiplied by 500 in the case of mice.

- minutes, multiplied by 28 in the case of elephants.

- minutes, multiplied by 6 in the case of the giant Galapagos tortoise.

-. Estimate the number of breaths made throughout life at this time: (for human beings)

- birth to 6 weeks: 30–60 breaths per minute

- 6 months: 25–40 breaths per minute

- 3 years: 20–30 breaths per minute

- 6 years: 18–25 breaths per minute

- 10 years: 15–20 breaths per minute

- adults: 12–20 breaths per minute

Developed by: http://www.nummolt.com

Nummolt Blog: Mathematical engine mill: http://nummolt.blogspot.com/

## Touch decimals Place value ±

Touch decimal:

Double interactive place value chart, with up to 40 decimal columns.

Mathematical analogy with positive and negative tokens.

Wireless abacus.

Designed to:

- Show and experience the addition and addition with carry.

- Show and experience the subtraction and subtraction with borrowing.

- Zero as "nothing" in a place value place, or as an undetermined number of negative-positive pairs of particles with sign.

MAIN ELEMENTS:

Two charts.

Each chart with a variable number of places.

In the places, a variable number of tokens with positive or negative value

TOKENS:

The life of tokens:

A token can be positive or negative.

A positive token is born with the tap of a finger on the screen

A pair of positive-negative tokens is born with a tap of two fingers on the screen

A token disappears if it crosses the top or bottom border.

The behavior of tokens:

Positive and negative tokens have the same behavior:

A token can cross at will the intermediate horizontal border

When a token crosses the border on the right, it becomes 10 tokens.

A token need 9 companions from the old place to cross the border to the left.

Positive and negative tokens may be in the same place.

But if two tokens of different signs meet, they cancel each other.

PLACES:

A place is a rectangle.

A place can contain tokens of the same or different sign.

A rectangle has 4 borders.

The upper and the lower borders can be the external border or the intermediate border.

Tokens can cross freely the intermediate border.

If a token cross the external border, disappears.

To get the permission to cross left borders, a token needs 9 companions of the same sign.

A token recovers 9 companions if cross the right borders.

GENERAL:

Chart:

A chart is the horizontal row of places.

There are two charts: The upper chart and the lower chart.

There is a button in each chart to change the sign of all its tokens.

Control:

In the 'settings' option, there is an option to erase all tokens of each chart, or to erase all tokens and refresh all to start again from scratch.

* * * * * * *

Touch decimals Place value ±

The behavior of places and tokens of this app describes the behavior of the numbers in the decimal system.

Courses:

Math 1, 2, 3, 4 Number sense: Place value.

Math 5, 6, 7 Number sense: Base Ten:

*** COMMON CORE State standards initiative:

**Grade 1:

Understand place value:

CCSS.MATH.CONTENT.1.NBT.B.2

Use place value understanding and properties of operations to add and subtract: CCSS.MATH.CONTENT.1.NBT.C.4; CCSS.MATH.CONTENT.1.NBT.C.5; CCSS.MATH.CONTENT.1.NBT.C.6

** Grade 2:

Understand place value:

CCSS.MATH.CONTENT.2.NBT.A.1

Use place value understanding and properties of operations to add and subtract:

CCSS.MATH.CONTENT.2.NBT.B.5; CCSS.MATH.CONTENT.2.NBT.B.6; CCSS.MATH.CONTENT.2.NBT.B.7; CCSS.MATH.CONTENT.2.NBT.B.9

** Grade 3:

Use place value understanding and properties of operations to perform multi-digit arithmetic.

CCSS.MATH.CONTENT.3.NBT.A.2; CCSS.MATH.CONTENT.3.NBT.A.3

** Grade 4:

CCSS.MATH.CONTENT.4.NBT.B.4;

Developed by: http://www.nummolt.com

Nummolt Blog: Mathematical engine mill:

http://nummolt.blogspot.com.es/2015/07/touch-decimals-chapter-i-introduction.html

## Adding apples and oranges

Educational app about adding apples and oranges.

To calculate the value of an apple and an orange from 2 purchases.

(Assuming that all apples are equal and that all oranges are equal)

About mental arithmetic with a pre-algebra tool, introducing the Gaussian elimination. ( Gauss - Jordan )

From http://www.nummolt.com/obbl/appleorange/index.html

nummolt - Obbl - Math Toys collection - Mathcats.

To calculate the value of an apple and an orange from 2 purchases.

(Assuming that all apples are equal and that all oranges are equal)

About mental arithmetic with a pre-algebra tool, introducing the Gaussian elimination. ( Gauss - Jordan )

From http://www.nummolt.com/obbl/appleorange/index.html

nummolt - Obbl - Math Toys collection - Mathcats.

MathTools reference:

http://mathforum.org/mathtools/tool/178345/

Algebra Linear Systems

Algebra II Solving systems of equations, Elimination

PreCalculus Solving systems of linear equations, Gauss-Jordan Method, determinants

We recommend the paid 'Apples and Oranges 1 Decimal':

http://play.google.com/store/apps/details?id=com.appleorange.firstdecimal

(http://mathforum.org/mathtools/tool/219536/)

Math 7: Linear relationships, Find slope, Slope-intercept form, Equation of the line, Rect coordinate geometry, First quadrant, Geometry in the plane

Algebra: Linear Equations, Slope Between Points, Finding Intercepts, Slope - Intercept Form, Point - Slope Form, Graphing, Parallel Lines, Perpendicular Lines, Linear Formulas, Analyzing Linear Data, Is It Linear?, Writing an Equation, Line of Best Fit, Linear Systems, Solve by graphing, Solve by substitution, Solve by combination, Inconsistent System, Applications

Algebra II: Solving systems of equations, Cramer's rule, Matrices, Elimination, Substitution

NOTE:

'Adding apples and oranges' app free, is a simplified version of the first part of the nummolt's paid app: 'Apples and oranges 1 decimal place'. (the Gauss-Jordan elimination)

All options "Apples and oranges first decimal":

( 1: Gauss-Jordan elimination; 2: Graphic; 3: Substitution; 4: Cramer's rule; 5: Inverse matrix )

Credits:

Feature graphic by: http://photo-lgz.blogspot.com/

## Reading fractions

Read fractions - Reading fractions

Basic tool for to experiment with fractions:

The app lets you view the fractions represented in the form of overlapping circles and bars.

The two graphs are interactive. They can be changed by dragging on the screen.

Graphically, fractions are always shown in simplified form.

There are two spinners to select fractions: one for the numerator and one for the denominator.

At the right there are two lock buttons:

The top button locks the numerator when the graph is modified.

The lower button locks the denominator when the graph is modified.

When both buttons are unlocked, the fractions are formed from the denominator 360 (the maximum allowed in the program) when the graph is modified.

When the two buttons are locked, the program always remains under the same fraction, but expresses its equivalent fractions in the spinners.

When the fraction expressed in the spinners is not in its simplified form, can be simplified by clicking on the simplified expression on his left.

Basic tool for to experiment with fractions:

The app lets you view the fractions represented in the form of overlapping circles and bars.

The two graphs are interactive. They can be changed by dragging on the screen.

Graphically, fractions are always shown in simplified form.

There are two spinners to select fractions: one for the numerator and one for the denominator.

At the right there are two lock buttons:

The top button locks the numerator when the graph is modified.

The lower button locks the denominator when the graph is modified.

When both buttons are unlocked, the fractions are formed from the denominator 360 (the maximum allowed in the program) when the graph is modified.

When the two buttons are locked, the program always remains under the same fraction, but expresses its equivalent fractions in the spinners.

When the fraction expressed in the spinners is not in its simplified form, can be simplified by clicking on the simplified expression on his left.

Additionally fractions are shown in written words, mixed fractions (if needed) as a percentage and as a decimal number with dot.

Fractions in words: Available in English, Catalan, Castilian (spanish), and French.

From www.nummolt.com

## ninedigits workshop

The game is about to find solutions ordering the digits from 1 to 9 in a square of 3 * 3 where the sum of the numbers of the two top rows is equal to the bottom row.

This program is aimed at reflecting on the addition. The goal is to find results that meet the primary condition. We must be aware that after obtaining a correct result can be achieved more easily results having in mind the properties of the sum.

Interaction:

To swap two digits must be done tap on each digit, then the digits change the color, and the exchange occurs.

From:

http://www.nummolt.com/obbl/ninedigits/ninedigitsbasic.html

nummolt - Obbl - Math Toys collection - Mathcats.

Ninedigits has 336 solutions. If the program would be easy for someone, then the goal could be to find valid solutions in which a lady could travel chess boxes 1 to 9 making right moves to this tab. According to our analysis, there are 3 solutions of this type. You can also look under the same condition, but with the tower of chess. This combination of conditions has only one solution. The program clearly shows the production of these special results.

As a safety mechanism, the delete button only works when the program displays a correct solution of the problem.

Registered in Math Tools (MathForum):

http://mathforum.org/mathtools/tool/234619/

Classified for courses:

Math 2 Addition

Math 3 Addition, Mental math

Math 4 Addition, Mental math

Math 5 Addition, Mental math, Commutative

Math 6 Addition, Mental math, Commutative

Math 7 Mental math, Commutative

Aligned with Common Core Math:

Grade 3 and up:

Grade 3 » Number & Operations in Base Ten

CCSS.Math.Content.3.NBT.A.2

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Origin of the game:

The ninedigits is based on an idea described in the book: "New Mathematical Diversions" by Martin Gardner published in 1966.

## Touch Natural Numbers

Small laboratory of Natural Numbers:

The Prime numbers are the building blocks of the numbers.

With this app you can:

Analyze the factors of a Composite number.

( Prime factorization of all the composite numbers between 1 and 28181 ).

Build a Composite number from its factors. (multiplication and division of Natural Numbers)

Localize or select a number in the Ulam Spiral.

(Only the Prime Numbers have a color in this spiral).

Verify all the possible products between Primes in a composite number with the Parabolic Sieve (Yuri Matiyasevich & Boris Stechkin).

Analyze or build a number with the Place Value activity (Addition and Subtraction of Natural Numbers)

Understand the Modulo of a number.

Know about the polygonal numbers and the numbers as the sum of two prime numbers, and as the sum of three Prime Numbers.

The Prime numbers are the building blocks of the numbers.

With this app you can:

Analyze the factors of a Composite number.

( Prime factorization of all the composite numbers between 1 and 28181 ).

Build a Composite number from its factors. (multiplication and division of Natural Numbers)

Localize or select a number in the Ulam Spiral.

(Only the Prime Numbers have a color in this spiral).

Verify all the possible products between Primes in a composite number with the Parabolic Sieve (Yuri Matiyasevich & Boris Stechkin).

Analyze or build a number with the Place Value activity (Addition and Subtraction of Natural Numbers)

Understand the Modulo of a number.

Know about the polygonal numbers and the numbers as the sum of two prime numbers, and as the sum of three Prime Numbers.

What is all this about? Read the nummolt blog post:

http://nummolt.blogspot.com.es/2014/06/touch-natural-numbers.html

Touch Math Apps:

http://www.nummolt.com

Registered at MathTools ( MathForum )

http://mathforum.org/mathtools/tool/240793/

Courses:

* Math 1 - Place value

* Math 2 - Place value

* Math 3 - Addition, Subtraction, Multiplication, Division, Whole numbers, Place value, Prime, Composite, Factor, Prime factorization, Divisibility tests, Multiple

* Math 4 - Addition, Subtraction, Multiplication, Division, Whole numbers, Place value, Prime, Composite, Factor, Prime factorization, Divisibility tests, Multiple

* Math 5 - Addition, Subtraction, Multiplication, Division, Whole numbers, Properties of numbers, Prime, Composite, Factor, Prime factorization, Divisibility tests, Multiple

* Math 6 - Addition, Subtraction, Multiplication, Division, Properties of numbers, Exponents, Prime, Composite, Factor, Prime factorization, Divisibility tests, Multiple

* Math 7 - Properties of numbers, Roots/radicals, Writing square roots, Prime, Composite, Factor, Prime factorization, Multiple

Developed by: http://www.nummolt.com

Nummolt Blog: Mathematical engine mill: http://nummolt.blogspot.com/

## How much pizza to order?

Android version of the "How Much Pizza to order?

http://www.nummolt.com/obbl/howmuchpizza/index.html

http://www.nummolt.com/obbl/howmuchpizza/index.html

"How much pizza...?" About adding fractions: Working with Improper fractions and Mixed fractions. The program build the problem, and you can solve filling the textboxes containing question marks. There's a tool that helps you find the common denominator.

Inspired by the works of Cynthia Lanius ("Who wants pizza?")

Nummolt - OBBL Math Toys

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

MathTools reference:

http://mathforum.org/mathtools/tool/186520/

Math 3 Equivalent fractions

Math 4 Equivalent fractions, Simplifying fractions, Adding fractions, Fractions <--> decimals

Math 5, 6, 7 Equivalent fractions, Simplifying fractions, Adding fractions, Multiplying fractions, Writing decimals, Fractions <--> decimals

For more difficult exercises on fractions, we recommend:

Mathcats: "Old Egyptian Fractions":

http://play.google.com/store/apps/details?id=mathcats.oldegyptian.fractions

## Circadian clock

The mechanism :

The green outer ring with 5 primary partitions and and 300 smaller partitions gives 59/300 turns per minute counterclockwise: 11.8 turns per hour.

The planetary gear of the seconds, in green color, is driven by the outer ring and gives 59 rph counterclockwise. And in turn, the axis makes a complete turn clockwise, rolling on the inside of the crown of the minutes, by hour.

The hand of the minutes, in blue color, turning on the central axis and linked to the axis of the planetary gear of the seconds, makes a complete turn every hour.

The wheel that rotates clockwise integrally with its base and with the hand of the minutes, make to spin counterclockwise two blue planetary wheels. These two planetary wheels spins counterclockwise a third planetary gear.

The third planetary wheel rotates one turn per hour clockwise and transmits the rotation to the fourth planetary wheel. The fourth planetary wheel spins counterclockwise and progresses clockwise.

The fourth blue planetary wheel gives 2 turns on itself and its axis gives the entire turn around the sphere of the clock every 12 hours.

On the four planetary wheels is mounted the hour hand: a big red triangle, giving rigidity to the structure and indicating the hours and rotating clockwise.

The big red triangle, linked to a freewheel on the central axis, drives the rotation of the three static planetary yellow wheels of the day. Turning counterclockwise about its fixed axis, rotates counterclockwise the yellow big crown that distinguishes the day light hours, of the darkness of the night and makes a complete turn every 24 hours.

The big red triangle, also linked to another freewheel on the central axis, drives the rotation of three static planetary wheels magenta of the week, much bigger than those for the day. Turning counterclockwise about its fixed axis, and spinning counterclockwise the crown magenta indicating the day of the week, and makes a complete turn every week.

Interaction:

Buttons:

The buttons are used to toggle the different layers of the watch:

-. Blue hand of minutes, and the green planetary gear of the seconds

-. Green crown of the seconds.

-. Static blue sphere of the hours and the minutes.

-. Planetary gear set and red triangle of the hours.

-. Planetary gear set in yellow color, and yellow crown of the day and the night

-. Planetary gear set in magenta color, and yellow crown of weekday.

-. Clock base body.

Dragging:

-. Dragging a finger, you can move the clock from its initial position.

-. Joining or separating and sliding two fingers on the screen, reduce or increase the size of the watch.

-. Dragging and rotating about the central axis with the finger on the red triangle of the hours, you can change the time. After removing the finger, the 'circadian clock', will slowly readjusting to redial the actual system time.

Circadian Clock:

www.nummolt.com

Technical drawings for the Circadian Clock:

http://www.nummolt.com/CircadianClock/

© 2014 Maurici Carbó, architect.

http://nummolt.blogspot.com/2014/03/posted-new-circadian-clock-at-google.html

Notes from developer:

The term 'circadian' comes from the Latin 'circa', meaning "around" (or "approximately"), and 'diem' or 'dies', meaning "day".

This app is only a clock, with many layers, showing many overlapped mechanisms, with zoom. The triangle of the hours is manually adjustable, and has an algorithm to reset the clock to the system time after any adjustment.

Nothing concerning the biological circadian cycle.

But one of the layers of the clock represents daylight.

There's a version in live wallpaper format.

Is a paid version:

At: https://play.google.com/store/apps/details?id=com.nummolt.circadian.clock.wallpaper

## Adding unit fractions

The app proposes 21 challenges to overcome.

Obtaining the proper fractions listed at the top of the application, adding two or three unit fractions.

Obtaining the proper fractions listed at the top of the application, adding two or three unit fractions.

Each proposed proper fraction has a variable number of solutions.

And different levels of difficulty

You can not repeat unit fractions with the same value.

In the app you'll find a button to delete all the solutions found in the current problem, and to start from scratch.

The littlest unit fraction used in this app is 1/28.

The program is designed to show the usefulness of the subtraction of fractions in solving such problems.

From www.nummolt.com

This is an evolution of the "Old Egyptian Fractions" made in collaboration with www.mathcats.com

Hint:

In the Rhind Mathematical Papyrus (RMP) in 1650 BC the scribe Ahmes copied the now-lost test from the reign of the king Amenemamhat III .

The first part of the papyrus is taken up by the 2/n table. The fractions 2/n for odd n ranging from 3 to 101 are expressed as sums of unit fractions.

In this app you can build some of the Ahmes decompositions ( 2/3 , 2/5, 2/7, 2/9 ) and the discarded ones by him also.

The app allow to decompose also: 3/4 , 3/5 , 4/5 , 5/6 , 3/7 , 4/7 , 5/7 , 3/8 , 5/8 , 7/8 , 4/9 , 5/9 , 7/9 , 8/9 , 3/10 , 7/10 , 9/10.

You can use the knowledge acquired solving the 2/n decompositions to solve the rest of the problems.

More: http://nummolt.blogspot.com/2014/12/adding-unit-fractions.html

Math Tools reference of this app:

http://mathforum.org/mathtools/tool/260740/

Courses:

Math 1, 2 and 3: Fractions

Math 4: Writing fractions, Equivalent fractions, Comparing and ordering, Simplifying fractions, Adding fractions, Subtracting fractions

Math 5, 6 and 7: Writing fractions, Equivalent fractions, Comparing & ordering, Simplifying fractions, Adding fractions, Subtracting fractions, Multiplying fractions, Dividing fractions

## Circadian clock live wallpaper

Version of the free nummolt's Circadian Clock, as a Live Wallpaper.

This time, the buttons of the original app, are in the preferences checkboxes of the installer.

This time, the buttons of the original app, are in the preferences checkboxes of the installer.

What is the Circadian Clock?

Here: http://nummolt.blogspot.com.es/2014/03/posted-new-circadian-clock-at-google.html

Buy this app to support the development work of educational software that makes nummolt.com

## Adding unit fractions +

The app proposes 31 challenges to overcome.

Build the proper fractions listed at the top of the application, adding two, three or four unit fractions.

Build the proper fractions listed at the top of the application, adding two, three or four unit fractions.

Each proposed proper faction has a variable number of solutions.

And different levels of difficulty

You can not repeat unit fractions with the same value.

In the app you'll find a button to delete all the solutions found in the current problem, and to start from scratch.

The littlest unit fraction used in this app is 1/66.

The program is designed to show the usefulness of the subtraction of fractions in solving such problems.

From www.nummolt.com

This is an evolution of the "Old Egyptian Fractions" made in collaboration with www.mathcats.com

Hint:

In the Rhind Mathematical Papyrus (RMP) in 1650 BC the scribe Ahmes copied the now-lost test from the reign of the king Amenemamhat III .

The first part of the papyrus is taken up by the 2/n table. The fractions 2/n for odd n ranging from 3 to 101 are expressed as sums of unit fractions.

In this app you can build some of the Ahmes decompositions ( 2/3 , 2/5, 2/7, 2/9, 2/11 ) and the discarded ones by him also.

The app allow to decompose also: 3/4 , 3/5 , 4/5 , 5/6 , 3/7 , 4/7 , 5/7 , 6/7 , 3/8 , 5/8 , 7/8 , 4/9 , 5/9 , 7/9 , 8/9 , 3/10 , 7/10 , 9/10, 3/11, 4/11, 5/11, 6/11, 7/11, 8/11, 9/11, and 10/11.

You can use the knowledge acquired solving the 2/n decompositions to solve the rest of the problems.

The app warns of obtaining the best solution (the one with the lowest denominators)

If it's one of the problems appearing in the Rhind Mathematical Papyrus table, the app warns of coincidence with the solution written in the Rhind 2/n table.

More: http://nummolt.blogspot.com/2014/12/adding-unit-fractions.html

## Jujol arq.

Review and locate the Josep Maria Jujol main architectural works:

Casa Bofarull Els Pallaresos.

Església del Sagrat Cor de Vistabella

Teatre del Patronat Obrer de Tarragona

Casa Ximenis de Tarragona

Can Negre de Sant Joan Despí

Casa Sansalvador de Barcelona

Casa Planells de Barcelona

......

He worked with Antoni Gaudí on many of his most famous works: Casa Batlló (facade cladding), Casa Milà (balcony railings and ceiling), Park Güell (Roofing and continuous bench)

Casa Bofarull Els Pallaresos.

Església del Sagrat Cor de Vistabella

Teatre del Patronat Obrer de Tarragona

Casa Ximenis de Tarragona

Can Negre de Sant Joan Despí

Casa Sansalvador de Barcelona

Casa Planells de Barcelona

......

He worked with Antoni Gaudí on many of his most famous works: Casa Batlló (facade cladding), Casa Milà (balcony railings and ceiling), Park Güell (Roofing and continuous bench)

## Touch Pythagoras

The Pythagorean Theorem Interactive: a^2 + b^2 = c^2

App :

change the lengths of the legs (dragging).

change the length of the hypotenuse with two fingers.

zoom (pinch zoom) and rotate the figure (dragging).

There are 6 ways to view the Pythagorean theorem.

- Unit surfaces.

- Two equivalent square containing the same surface.

- The square for each leg in the square of the hypotenuse (Euclid)

- Pingi - Dudeney proof.

- Da Vinci.

- Bhaskara reasoning.

Change the precision of the lengths. (In the contextual menu)

This application is also a small laboratory to investigate about the Pythagorean Theorem:

For example, you can experiment easily, looking for the exact solutions of the Pythagorean Theorem:

3² + 4² = 5² is not the only exact solution:

Below 21, there are 3 primitive triples:

3² + 4² = 5²

5² + 12² = 13²

6² + 8² = 10² (Not a true primitive result: Multiple of 3,4,5)

8² + 15² = 17²

9² + 12² = 15² (Not a true primitive result: Multiple of 3,4,5)

12² + 16² = 20² (Not a true primitive result: Multiple of 3,4,5)

Likewise it is also possible to find the solutions below 31 (11 solutions in all: but only 5 primitives)

Or solutions below 101 (52 solutions in all: but only 16 primitives)

More about this: Pythagorean triples: http://en.wikipedia.org/wiki/Pythagorean_triples

Touch Math Apps:

http://www.nummolt.com

MathTools reference of this app:

Math 4 Triangles

Math 6 All previous and: Geometry in the plane, Pythagorean theorem

Math 7 All previous and: Quadrilateral properties

Geometry All previous Right Triangles, Pythagorean theorem, Trigonometry

Algebra Exponents

Algebra II General

Trigonometry

## Apples and oranges 1 decimal

Apples & Oranges - Algebra

Adding Apples and Oranges Version with 1 decimal

Adding Apples and Oranges Version with 1 decimal

This new application is a basic tool to learn algebra.

Trying solving a system of linear equations with two equations and two unknown variables. (Two purchases)

Based on the same problem seen at the free "Adding Apples and Oranges." (https://play.google.com/store/apps/details?id=com.appleorange.addingapplesandoranges) where only used integers.

Now, this new program works externally with a decimal.

It contains:

. A button that generates new questions ("two new purchases of fruits").

. Two drop-downs to select a solution and a button to verify: The verification button checks the solution, and adds it to the list of the session.

You can edit the statements. The program checks if the determinant of the proposed statement is nonzero.

. The 5 tools to help resolve the problem:

* Tool 1: Gauss-Jordan elimination:

The two equations are represented as two purchases of fruits.

Contains tools to add one column to another, multiply, divide and change the sign for to get to have one apple on a side and and an orange at the other.

The result of the two additions are the values of apple and orange.

* Tool 2: Graphic:

Contains a graphic frame and 2 drop-downs to find the solution, using the method essay / error.

The problem posed is a linear system of equations, so the results must be ever into two lines that intersect.

To get the answer, one should find this point.

You can also click directly on the chart.

The graph is divided by the diagonal.

Below the diagonal, apple values are entered, for to get the values of the orange.

Above the diagonal, one enters the price of the orange.

The meeting point of the two lines is represented by a yellow dot.

* Tool 3: Two weighing scales:

Shows two weighing balances. On the left, due to its drop-down, which determines the value proposed for apples: results gives the price of oranges in terms of the two equations.

The right hand scale gives the results from the proposed price for oranges.

When a scale is balanced, gives the results of both the price of the apples and oranges.

* Tool 4: Cramer's rule:

This tool solves the problem at once.

Contrary to what happens in other tools, here we have to manually enter the data of the problem. The two equations (two purchases) are represented in horizontal rows.

If you have not entered data, the tool warns that you can not solve the problem.

It can also warn when the determinant is zero:

The determinant is zero when the two lines that we saw in the graphical tool, are not crossing. This happens when they are parallel. And the lines are parallel when a purchase (equation) is linear function of the other. (eg 1 A + 2 O= n1 and 2 A + 4 O = n2)

The program automatically never generates such problems.

* Tool 5: Inverse matrix:

The tool represents the terms of the equation automatically and in landscape format (each purchase is a row)

The resolution tool there are the terms of the two equations on the left and the identity matrix at right.

The objective is to calculate the inverse matrix.

This is achieved by operating the rows, until the data from the equations (on the left) become the identity matrix.

At this time to the right we have the inverse matrix.

The multiplication of the results vector by the inverse matrix gives the solution.

This program shows rounded numbers.

Internally works with all decimals needed.

If you try to do these calculations with a calculator, you'll see that this program displays the friendly face of algebra.

Mathforum MathTools Reference:

http://mathforum.org/mathtools/tool/219536/

Math 7: Linear relationships, Find slope, Slope-intercept form, Equation of the line, Rect coordinate geometry, First quadrant, Geometry in the plane

Algebra II: Solving systems of equations, Cramer's rule, Matrices, Elimination, Substitution

Buying this program will help develop new nummolt apps.

Credits:

Feature graphic by: http://photo-lgz.blogspot.com/