gives the denominator of expr.

Details and Options

  • Denominator picks out terms which have superficially negative exponents. Numerator picks out all remaining terms.
  • An exponent is "superficially negative" if it has a negative number as a factor.
  • The standard representation of rational expressions as products of powers means that you cannot simply use Part to extract denominators.
  • Denominator can be used on rational numbers.


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Basic Examples  (3)

Extract denominator of a rational number:

Extract denominator of a rational expression:

Extract the denominator of a symbolic expression:

Scope  (9)

Rational numbers:

Gaussian rationals:

Rational expressions:

Select terms with syntactically negative exponents:

All exponents syntactically negative:

No syntactically negative exponents:

Denominator automatically threads over lists:

Compute the denominator with over the integers modulo 5:

Compute the denominator while incorporating common trigonometric identities:

Options  (2)

Modulus  (1)

Find denominators over integers modulo m:

Trig  (1)

Denominators of trigonometric functions:

Applications  (2)

Explore patterns in reduced rational numbers:

View the occurrences of integers as the denominator in reduced rational numbers:

Properties & Relations  (5)

Numerator gives the terms without negative exponents:

An expression is a quotient of its numerator and denominator:

Use Cancel to cancel common factors between the numerator and the denominator:

Together writes an expression as a fraction and cancels common terms:

Use ExpandDenominator to directly expand all denominators:

Neat Examples  (2)

Cyclic addition [more info]:

Wolfram Research (1988), Denominator, Wolfram Language function,


Wolfram Research (1988), Denominator, Wolfram Language function,


Wolfram Language. 1988. "Denominator." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (1988). Denominator. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_denominator, author="Wolfram Research", title="{Denominator}", year="1988", howpublished="\url{}", note=[Accessed: 13-July-2024 ]}


@online{reference.wolfram_2024_denominator, organization={Wolfram Research}, title={Denominator}, year={1988}, url={}, note=[Accessed: 13-July-2024 ]}