The fundamental theorem of arithmetic inpractice:Prime numbers are the basic building blocks of numbersCryptographic protocols are based on Prime NumbersTHE APP:At left: two abacus (two numbers stacked).At right two circles with the prime factors. (two circles withprime numbers stacked)At right edge: all the prime numbers available to the app.To create a number: Tap on the cells at left. The app shows thenumberTo add: Drag the tokens from one abacus to the otherTo subtract: Tap the sign key and drag from one abacus to theotherTo multiply: (the numbers must be previously created with theearlier previous steps)Drag from one prime circle to the other prime circleTo Divide a number:Drag the prime numbers outside the prime circle:Release prime factors to the other prime circle (integer divisionand multiplication)Release prime factors between the prime circles (integerdivision)Release prime factors in the list of the right edge: (integerdivision and erase the prime factor)Scroll and pick a prime number from the list of the rightedge:And release it in the free zone, or in a prime circle(multiplication)With this you can add, subtract, multiply and divide (integerdivision) of any integer of any sign.(Practically, the app is operative up to 9 digits)(The biggest prime number available in this program is19.874.419)In General menu there are 3 options:Refresh all (erases all the tokens)Refresh upper chart (Erases all the upper tokens)Refresh lower chart (Erases all the lower tokens)And info:The upper current available prime number.(The app calculates new prime numbers each 20 seconds while the appis not used)Based in the fundamental theorem of arithmetic, also called theunique factorization theorem or the unique-prime-factorizationtheorem, states that every integer greater than 1 either is primeitself or is the product of prime numbers, and that this product isunique, up to the order of the factorsMore in the Nummolt blog: and Acknowledgements:http://nummolt.blogspot.com/2015/11/touch-integers.htmlIDEAS TO¨PLAY WITH: "TOUCH INTEGERS":YouTube Playlist:https://www.youtube.com/playlist?list=PLo4AMY8jDHYZ7SuX3UZpLn_m2v1709no4Open-ended explorations: Mersenne, Woodall, Wagstaff primegenerationDEVELOPER NOTES:Is easy add and subtract graphically. One can regroup the tokens ofeach order, regroup, carry or borrow tokens, and you can obtain theresultNot so easy to practice multiplication or division in this visualand interactive way:Look inside of the numbers:Inside the numbers there are The prime factorsMultiplication of two integers: regroup the prime components of thetwo numbersTo divide a integer, you must separate the prime components of acomposite numberThe program only works with integers. adds, subtract, multipliesand divides (but only exact division)/ / T E C H N I C A L N O T E / /The app starts with a greatest prime number stored equal to951.697When nobody fiddles on the screen, the app get more prime numberseach 20 secondsUntil the app gets the prime number 19.874.419Here stops the search, because is the store limit of manydevicesIf you work with numbers greatest than 19.000.000 the results maybe not be complete (then, the app is not able to show the primefactorization)/ / E N D N O T E / /ACKNOWLEDGEMENTS:Without them this program would not have been possible:Jacobo Bulaevsky (Arcytech)Brian Sutherland ( )Agustín Rayo (SciAm)Ulrich Kortenkamp (“Place Value Chart'.)Christian Urff ('Rechentablett')Wendy Petti (mathcats: 20 years of support)Jeff LeMieux (Builder, teacher and software developer)Joan Jareño (From: CREAMAT team) Author of Calaix +ie.Next step:If you have used this program, you have basis enough to play with"Touch fractions ℚ" (Same developer)Nummolt apps:"Mathematics is the toughest toy. However mischievous a child maybe, will never be able to break them".Maurici Carbó Jordiof: nummolt.com

Time Elapsed / Time Countdown. Live time calculator. Time betweentwo dates

Nine digits. Improve skills on 3 digits addition. Needs reflectionsabout MOD 9

Adding mixed fractions and multiplication of fractions

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Apples & Oranges - AlgebraAdding Apples and Oranges Version with 1 decimalThis new application is a basic tool to learn algebra.Trying solving a system of linear equations with two equationsandtwo unknown variables. (Two purchases)Based on the same problem seen at the free "Adding ApplesandOranges."(https://play.google.com/store/apps/details?id=com.appleorange.addingapplesandoranges)whereonly used integers.Now, this new program works externally with a decimal.It contains:. A button that generates new questions ("two new purchasesoffruits").. Two drop-downs to select a solution and a button to verify:Theverification button checks the solution, and adds it to the listofthe session.You can edit the statements. The program checks ifthedeterminant 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 purchasesoffruits.Contains tools to add one column to another, multiply, divideandchange the sign for to get to have one apple on a side and andanorange at the other.The result of the two additions are the values of appleandorange.* Tool 2: Graphic:Contains a graphic frame and 2 drop-downs to find thesolution,using the method essay / error.The problem posed is a linear system of equations, so theresultsmust 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 thevaluesof the orange.Above the diagonal, one enters the price of the orange.The meeting point of the two lines is represented by ayellowdot.* Tool 3: Two weighing scales:Shows two weighing balances. On the left, due to itsdrop-down,which determines the value proposed for apples: resultsgives theprice of oranges in terms of the two equations.The right hand scale gives the results from the proposed pricefororanges.When a scale is balanced, gives the results of both the price oftheapples and oranges.* Tool 4: Cramer's rule:This tool solves the problem at once.Contrary to what happens in other tools, here we have tomanuallyenter the data of the problem. The two equations (twopurchases)are represented in horizontal rows.If you have not entered data, the tool warns that you can notsolvethe problem.It can also warn when the determinant is zero:The determinant is zero when the two lines that we saw inthegraphical tool, are not crossing. This happens when theyareparallel. And the lines are parallel when a purchase (equation)islinear 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 automaticallyandin landscape format (each purchase is a row)The resolution tool there are the terms of the two equations ontheleft and the identity matrix at right.The objective is to calculate the inverse matrix.This is achieved by operating the rows, until the data fromtheequations (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 matrixgivesthe solution.This program shows rounded numbers.Internally works with all decimals needed.If you try to do these calculations with a calculator, you'llseethat this program displays the friendly face of algebra.Mathforum MathTools Reference:http://mathforum.org/mathtools/tool/219536/Math 7: Linear relationships, Find slope, Slope-interceptform,Equation of the line, Rect coordinate geometry, Firstquadrant,Geometry in the planeAlgebra II: Solving systems of equations, Cramer'srule,Matrices, Elimination, SubstitutionBuying this program will help develop new nummolt apps.Credits:Feature graphic by: http://photo-lgz.blogspot.com/

Calculation of bending of steel beams

Build proper fractions using 2, 3 or 4 different unit fractions.