Maxima is a free computer algebra system. Download and install it from Sourceforge. When you type in a command, you need to press SHIFT + ENTER simultaneously. For example: divisors(24); returns all the divisors of 24, 3*7; (a simple calculation, 21), and 6**2; is six raised to the power of two, 36.
You can use Maxima as a fast and reliable calculator (5.23*4.25;). You can find the prime factorisation of a given number (factor(420);), get the irreducible fraction equivalent to a given fraction (12/56;), and do arithmetic with fractions (6/5+9/6;).
Once you have defined your polynomials (p: 4*x^2 -1, q: 6*x^2+x+1), you can operate with them (p+q, 2*p-q), and simplify them. ratsimp(%); asks Maxima to simplify the last expression.
Observe in the screenshot how Maxima can factor some polynomials (factor(p); expresses the polynomial -p- as the product of polynomial expressions (x-3)(x+2)) or expand them (in other words, it asks Maxima to carry out the operations to simplify the expression).
Maxima can solve algebraic equations, too. The polynomial p has two roots (solve(p,x); returns 3, -5), so it can be expressed (factor(p);) as (x-3)(x+5).
JFractionLab is a free (it is licensed by the GNU GPL license), multi-platform (it runs on Windows, macOS, and Linux), and easy to use program for practicing fractions at school or at home.
It gives you graphical feedback, so you can always see and understand what you are doing. It runs on Windows, GNU/Linux, and macOS, but it requires the installation of the Java Runtime Environment. If you use Ubuntu or other Debian-based distributions, type this command in your terminal: sudo apt install jfractionlab.
Launch it (JFractionLab), and select one category: Clicking the numerator, Defining or comparing fractions, or Extending fractions.
Observe that 3⁄6 is the fraction that is represented in the screenshot. The pie is divided into six parts and there are only three pieces which are colored yellow.
There are people who think that Internet is Google. This is not true, but Google has become synonymous with easy searching and fast results. Google offers a built-in calculator among its many services.
It allows you to do: basic mathematical operations (2.5*3.5); percentages (50% of 220); units (45 cm to inches, 38 Celsius to Fahrenheit), and currency conversions (21 dollars into Euros); conversions between different numerical systems (12 in binary, 12 in octal, 12 in roman), etc. You can now plot functions in Google’s search engine, too.
Wolfram Alpha is a computational search engine. Just go to Wolfram Alpha and type a fraction (9/6). It returns the equivalent irreducible fraction (3/2), a pie chart representing it, and its decimal form (1.5).
Wolfram Alpha can calculate just about anything. It can do arithmetic on fractions (1/2 * (3 + 3/5)), solve equations (solve x^2 − 7*x + 12=0), plot 2d and 3d functions or compute indefinite and definite integrals of one or more variables (integrate x^2 + sin^2 x dx).
For instance, given a decimal number (0.5) or an improper fraction (improper fractions are those whose numerator is greater than the denominator, 11⁄4), WolframAlpha returns its equivalent fractions (1⁄2, 2 3⁄4) and represents them in the Number Line.
Gnuplot is a free, open source, and graph plotting program. Follow these instructions to get it up and running:
Get the latest stable version for your operating system.
Define the function (f(x)=x**3 + 2*x**2 -5*x -6 where x**3 means raise x to the power of three, x3) and ask gnuplot to plot it (plot(f(x)). It is a little difficult, but it is incredibly powerful and available free of charge!
GeoGebra is a free mathematics software program especially created for teaching and learning. It is an open-source software available for multiple platforms (iOS, Android, Windows, Mac OS, and Linux) and it has been translated into many languages. It has an easy-to-use interface and yet many powerful features.
GeoGebra is both an online web application and an o ine downloadable application. You only need to use the appropriate tools in the Toolbar to create geometric constructions on the Graphics View with your mouse. For example, select Line, click twice on the Graphics View and you will get two points (A, B) and a line.
NumericalChameleon is free, open source, platform-independent and comprehensive software in order to convert units. An alternative is ConvertAll.
Octave is a high-level interpreted language, primarily intended for numerical computations. It is a free alternative (and is quite similar) to Matlab (proprietary and pricey software). It has extensive tools for solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations. Another option is FreeMat.
R is a free software environment for statistical computing and graphics.
Kids: Gcompris (arithmetic activities), Omnitux (counting activities), and The KDE Education Project (KBruch is a small program to practice calculating with fractions and percentages). Tux of Math Command is a fun arcade-style math game to practice addition, subtraction, multiplication, division, negatives, and more!
Kitsune is a version of the famous “Des chiffres et des lettres” television game show, literally Numbers and Letters. Here is an example to illustrate this point: How do you get 715 with the numbers 6, 4, 7, 8, 75, and 10, and the operations “+”, “-”, “x” and “:”? The solution is: 1. 75 - 10 = 65. 2. 7 + 4 = 11. 3. 65 x 11 = 715.
TuxMathScrabble is a maths version of the classic word game Scrabble. It challenges kids to construct compound equations and to consider multiple abstract possibilities.