Irreducible Fraction

An irreducible fraction is a fraction p/q for which GCD(p,q)=1, i.e., p and q are relatively prime. For example, in the complex plane, (4+7i)/(2+i)=3+2i is reducible, while (5+5i)/(7+i)=4/5+3i/5 is not.


The figure above shows the irreducible fractions plotted in the complex plane (Pickover 1997; Trott 2004, p. 29).

See also

Fraction, Reducible Fraction

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Pickover, C. A. "A Note on Geometric Representations of Gaussian Rational Numbers." Visual Comput. 13, 127-130, 1997.Trott, M. The Mathematica GuideBook for Graphics. New York: Springer-Verlag, 2004.

Referenced on Wolfram|Alpha

Irreducible Fraction

Cite this as:

Weisstein, Eric W. "Irreducible Fraction." From MathWorld--A Wolfram Web Resource.

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