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Irreducible Fractions

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)

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Irreducible Fractions -

Tag(s) : Arithmetics, Symbolic Computation, Mathematics

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Irreducible Fractions

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Simplify in Irreducible Fractions



Decimal to Fraction in Lowest Term Converter


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)

Answers to Questions

How to make a fraction in lowest term?

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

Consider the fraction \( 12/10 \), with \( 12 \) the numerator and \( 10 \) the denominator. You can 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 \( 6/5 \)

How to calculate and give the result under the lowest term form?

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

How to make a fraction from a decimal number?

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

Consider the number \( 0.14 = 0.14/1 \), you can multiplied by \( 10/10 \) until having no comma: \( 0.14/1 = 1.4/10 = 14/100 \) then you can 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.

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, you can multiply \( x \) by \( 10^n \) and then subtract \( x \).

\( x = 0.1666666 ... \), the smallest repeated portion is \( 6 \), which has a single digit so that \( n = 1 \). You 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 \( 1/6 = 0.1666666 ... \)

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