# Denominator

Denominator[expr]

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.

# Examples

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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:

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: