Tool to reduce fractions 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

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

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

Tool to reduce fractions 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 calculated GCD.

Example: The fraction $ 12/10 $ has $ 12 $ for numerator and $ 10 $ for 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 offers tools to calculate the GCD via, for example, Euclid's algorithm.

Use the aboce calculator form: enter the expressions / fractions and the simplifier will use formal calculations in order to keep variables and find the irreducible form of the division (fraction in lowest term).

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: The number $ 0.14 $ is equivalent to $ 0.14/1 $, multiply by $ 10/10 (=1) $ 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: The number $ 0.166666666 ... $ where the $ 6 $ is repeated

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

dCode retains ownership of the source code of the script Irreducible Fractions online. 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, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Irreducible Fractions script for offline use on PC, iPhone or Android, ask for price quote on contact page !

fraction,irreducible,lowest,term,numerator,denominator,algorithm,euclide,simplify,simplification,division,calculator

Source : https://www.dcode.fr/irreducible-fraction

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲