Tool to reduce a fraction in lowest term. A Fraction in Lowest Terms (Irreducible Fraction) is a reduced fraction in shich the numerator and the denominator are coprime (they do not share common factors)

Irreducible Fractions - dCode

Tag(s) : Arithmetics, Symbolic Computation, Mathematics

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

Sponsored ads

Tool to reduce a fraction in lowest term. A Fraction in Lowest Terms (Irreducible Fraction) is a reduced fraction in shich the numerator and the denominator are coprime (they do not share common factors)

To simplify a fraction \( a / b \) or \( frac{a}{b} \) composed of a numerator \( a \) and a denominator \( b \), find the greatest common divisor (GCD) of the numbers \( a \) and \( b \). The irreducible fraction is obtained by dividing the numerator and the denominator by the obtained PGCD.

Example: Fraction \( 12/10 \), with \( 12 \) the numerator and \( 10 \) the denominator. Calculate that \( GCD(12,10) = 2 \) and divide both the numerator \( 12/2 = 6 \) and the denominator \( 10/2 = 5 \), so the corresponding irreducible fraction is \( 6/5 \)

dCode uses formal calculations in order to keep variables and find the irreducible form.

If the number has a **limited decimal development** then it only needs to be multiplied by the right power of 10, then simplify the fraction and solve the equation.

Example: Consider the number \( 0.14 = 0.14/1 \), multiply by \( 10/10 \) until having no comma: \( 0.14/1 = 1.4/10 = 14/100 \) then simplify \( 14/100 = 7/50 \)

If the number has a **non finite decimal expansion**, then it is necessary to locate the repeating portion of the number after the repeating decimal point.

Example: Consider the number \( 0.166666666 ... \) where the \( 6 \) is repeated

We call \( x \) the number, and \( n \) the size (number of digits) of the smallest repeated portion. To obtain a fraction, multiply \( x \) by \( 10^n \) and then subtract \( x \).

Example: \( x = 0.1666666 ... \), the smallest repeated portion is \( 6 \), which has a single digit so that \( n = 1 \). Then compute \( 10^1 \ times x = 1.6666666 ... \) and \( 10x-x \).

$$ 10x-x = 9x = 1.666666 ... - 0.1666666 ... = 1.5 \\ \iff 9x = 1.5 \\ \Rightarrow x = 1.5 / 9 = 15/90 = 1/6 $$

Example: So \( 1/6 = 0.1666666 ... \)

dCode retains ownership of the source code of the script Irreducible Fractions. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Irreducible Fractions script for offline use, for you, your company or association, see you on contact page !

fraction,irreductible,numerator,denominator,algorithm,euclide,simplify,simplification,common,coprime,division

Source : http://www.dcode.fr/irreductible-fraction

© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode